Content-Type: multipart/mixed; boundary="-------------0808051657112" This is a multi-part message in MIME format. ---------------0808051657112 Content-Type: text/plain; name="08-146.comments" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="08-146.comments" Later versions of this preprint may be obtained at http://www.ma.texas.edu/users/radin/papers.html ---------------0808051657112 Content-Type: text/plain; name="08-146.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="08-146.keywords" random loose packing, granular, Monte Carlo, hard squares ---------------0808051657112 Content-Type: application/postscript; name="text45.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="text45.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %%Title: text45.dvi %%Pages: 25 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: CMBX10 CMR10 CMMI10 CMSY10 CMTI10 CMMI7 CMR7 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TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N /vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N /rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N /@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ /hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B /@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ /urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known {userdict/md get type/dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup length 20 add dict copy def}if end md begin /letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{ itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack} if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{ noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr 2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{ Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale }if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedState save N userdict maxlength dict begin/magscale true def normalscale currentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts /psf$y psfts/psf$x psfts currentpoint/psf$cy X/psf$cx X/psf$sx psf$x psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub TR/showpage{}N/erasepage{}N/setpagedevice{pop}N/copypage{}N/p 3 def @MacSetUp}N/doclip{psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath moveto}N/endTexFig{end psf$SavedState restore}N /@beginspecial{SDict begin/SpecialSave save N gsave normalscale currentpoint TR @SpecialDefaults count/ocount X/dcount countdictstack N} N/@setspecial{CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR}{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury lineto closepath clip}if/showpage{}N/erasepage{}N /setpagedevice{pop}N/copypage{}N newpath}N/@endspecial{count ocount sub{ pop}repeat countdictstack dcount sub{end}repeat grestore SpecialSave restore end}N/@defspecial{SDict begin}N/@fedspecial{end}B/li{lineto}B /rl{rlineto}B/rc{rcurveto}B/np{/SaveX currentpoint/SaveY X N 1 setlinecap newpath}N/st{stroke SaveX SaveY moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X/yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc savematrix setmatrix}N end %%EndProcSet %%BeginFont: CMSY9 %!PS-AdobeFont-1.1: CMSY9 1.0 %%CreationDate: 1991 Aug 15 07:22:27 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-30 -958 1146 777}readonly def /UniqueID 5000819 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI9 %!PS-AdobeFont-1.1: CMMI9 1.100 %%CreationDate: 1996 Jul 23 07:53:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-29 -250 1075 750}readonly def /UniqueID 5087384 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR9 %!PS-AdobeFont-1.1: CMR9 1.0 %%CreationDate: 1991 Aug 20 16:39:59 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueID 5000792 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1F3352E22A1452E73FECA8A4 87100FB1FFC4C8AF409B2067537220E605DA0852CA49839E1386AF9D7A1A455F 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI5 %!PS-AdobeFont-1.1: CMMI5 1.100 %%CreationDate: 1996 Aug 02 08:21:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{37 -250 1349 750}readonly def /UniqueID 5087380 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueID 5000817 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 16 /parenleftBig put dup 17 /parenrightBig put dup 80 /summationtext put dup 88 /summationdisplay put dup 104 /bracketleftBig put dup 105 /bracketrightBig put dup 113 /radicalBig put dup 115 /radicalBigg put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF5B8CABB9FFC6CC3F1E9AE32F234EB60FE7D E34995B1ACFF52428EA20C8ED4FD73E3935CEBD40E0EAD70C0887A451E1B1AC8 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{0 -250 1171 750}readonly def /UniqueID 5087382 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D77639DF1232A4D6233A9CAF69B151DFD33F C0962EAC6E3EBFB8AD256A3C654EAAF9A50C51BC6FA90B61B60401C235AFAB7B 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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(relativ)m(ely)f(quic)m(kly)-8 b(,)32 b(in)m(to)i(the)g(range)h(0)p Fm(:)p Fn(76)21 b Fl(\006)j Fn(0)p Fm(:)p Fn(01;)33 b(see)h(Figs.)138 2849 y(1)i(and)h(2.)54 b(The)37 b(equilibrium)f(v)-6 b(alue)37 b(is)f(found)i(to)e(dep)s(end)j(on)d(the)h(n)m(um)m(b)s(er)h (of)f(squares)g(in)g(the)138 2969 y(system.)42 b(The)26 b(main)f(goal)f(of)i(our)g(w)m(ork)f(is)g(an)h(analysis)f(of)g(the)h (distribution)g(of)f(v)m(olume)h(fraction)138 3088 y({)36 b(b)s(oth)g(the)g(mean)h(and)f(standard)h(deviation)e({)h(as)g(the)g(n) m(um)m(b)s(er)i(of)e(particles)g(increases.)54 b(W)-8 b(e)138 3208 y(conclude)41 b(that)e(the)h(limiting)e(standard)i (deviation)f(as)h(particle)f(n)m(um)m(b)s(er)i(go)s(es)f(to)f (in\014nit)m(y)g(is)138 3328 y(zero,)31 b(so)f(the)h(mo)s(del)f (exhibits)g(a)g(sharp)h(v)-6 b(alue)30 b(for)g(the)h(random)f(lo)s(ose) g(pac)m(king)h(densit)m(y)-8 b(,)30 b(whic)m(h)138 3447 y(w)m(e)k(estimate)f(to)f(b)s(e)i(appro)m(ximately)e(0)p Fm(:)p Fn(754.)337 3567 y(The)41 b(heart)g(of)g(our)f(argumen)m(t)h(is) g(the)f(degree)i(to)e(whic)m(h)h(w)m(e)g(can)g(demonstrate)g(that)f(in) 138 3686 y(this)h(mo)s(del)g(there)h(is)f(a)g(sharp)g(v)-6 b(alue,)43 b(appro)m(ximately)d(0)p Fm(:)p Fn(754,)i(for)f(the)g (equilibrium)g(v)m(olume)138 3806 y(fraction)27 b(of)h(large)f (systems,)h(and)g(w)m(e)f(p)s(ostp)s(one)h(analysis)f(of)g(error)h (bars)f(to)g(later)g(sections.)42 b(But)138 3925 y(to)e(understand)i (the)e(v)-6 b(alue)40 b(0)p Fm(:)p Fn(754,)h(consider)g(the)f(follo)m (wing)g(crude)h(estimate)f(of)h(the)f(v)m(olume)138 4045 y(in)34 b(phase)i(space)f(of)g(all)e(allo)m(w)m(able)h(pac)m(kings)h (at)f(\014xed)g(v)m(olume)h(fraction)f Fm(\036)p Fn(.)48 b(First)34 b(notice)g(that)138 4164 y(the)g(conditions)h(of)f(the)g(mo) s(del)g(prev)m(en)m(t)h(the)f(p)s(ossibilit)m(y)f(of)h(an)m(y)g (\\holes")g(in)g(a)g(con\014guration.)138 4284 y(F)-8 b(urthermore,)32 b(if)f(w)m(e)h(consider)g(an)m(y)f(rectangle)h(in)f (the)g(in)m(terior)g(of)h(a)f(con\014guration,)g(eac)m(h)i(hor-)138 4403 y(izon)m(tal)g(ro)m(w)g(in)h(the)g(rectangle)f(con)m(tains)h(the)g (same)g(n)m(um)m(b)s(er)h(of)e(squares.)46 b(\(One)34 b(consequence)138 4523 y(is)42 b(that)g(in)g(the)h(in\014nite)g(v)m (olume)f(limit)f(eac)m(h)i(con\014guration)g(m)m(ust)g(ha)m(v)m(e)g(a)f (sharply)g(de\014ned)138 4643 y(densit)m(y)-8 b(.\))70 b(No)m(w)41 b(consider)i(a)f(v)m(ery)f(symmetrical)h(con\014guration)g (of)g(squares)h(at)e(an)m(y)h(desired)138 4762 y(v)m(olume)35 b(fraction)g Fm(\036)p Fn(,)h(with)f(the)h(squares)g(in)f(eac)m(h)h (horizon)m(tal)f(ro)m(w)g(equally)f(spaced,)j(and)f(gaps)138 4882 y(b)s(et)m(w)m(een)28 b(squares)f(eac)m(h)h(of)e(size)h(\(1)9 b Fl(\000)g Fm(\036)p Fn(\))p Fm(=\036)27 b Fn(cen)m(tered)h(o)m(v)m (er)f(squares)g(in)f(the)h(next)g(lo)m(w)m(er)f(horizon-)138 5001 y(tal)34 b(ro)m(w;)h(see)h(Fig.)e(3.)49 b(Consider)35 b(these)h(squares)f(to)g(represen)m(t)h(a)m(v)m(erage)f(p)s(ositions,)g (\014x)g(all)f(but)138 5121 y(one)e(square)g(in)g(suc)m(h)h(a)f(p)s (osition,)f(and)h(consider)h(the)f(\(horizon)m(tal\))f(degree)i(of)f (motion)f(allo)m(w)m(ed)138 5240 y(to)40 b(the)i(remaining)e(square.)67 b(There)42 b(are)f(t)m(w)m(o)g(constrain)m(ts)g(on)g(its)g(mo)m(v)m (emen)m(t:)60 b(the)41 b(gap)f(size)1958 5519 y(2)p eop end %%Page: 3 4 TeXDict begin 3 3 bop 138 100 a Fn(separating)31 b(it)g(from)h(its)f(t) m(w)m(o)g(neigh)m(b)s(ors)h(in)g(its)f(horizon)m(tal)g(ro)m(w,)g(and)h (the)g(length)f(to)g(whic)m(h)h(its)138 219 y(top)e(edge)g(and)g(b)s (ottom)f(edge)h(in)m(tersects)h(the)f(squares)g(in)g(the)g(horizon)m (tal)g(ro)m(ws)g(ab)s(o)m(v)m(e)f(and)h(b)s(e-)138 339 y(lo)m(w)i(it.)43 b(These)33 b(t)m(w)m(o)f(constrain)m(ts)h(are)f(to)g (opp)s(osite)g(e\013ect:)44 b(increasing)33 b(the)f(gap)g(size)h (decreases)138 458 y(the)h(necessary)g(supp)s(ort)g(in)g(the)f(ro)m(ws) h(ab)s(o)m(v)m(e)f(and)h(b)s(elo)m(w.)45 b(A)33 b(simple)g(calculation) g(sho)m(ws)h(that)138 578 y(the)k(square)h(has)f(optim)m(um)g(allo)m(w) m(ed)h(motion)e(when)i(the)f(gap)g(size)h(is)f(1)p Fm(=)p Fn(3,)g(corresp)s(onding)h(to)138 697 y(a)k(densit)m(y)h(of)f(0)p Fm(:)p Fn(75,)i(roughly)e(as)g(found)i(in)e(the)g(sim)m(ulations.)74 b(In)44 b(other)f(w)m(ords,)j(this)e(crude)138 817 y(estimate)36 b(suggests)g(that)f(the)h(v)m(olume)g(in)g(phase)g(space)h(\(whic)m(h)f (w)m(e)h(e\013ectiv)m(ely)e(estimate,)h(for)138 936 y Fm(N)i Fn(squares,)29 b(to)f(b)s(e)g Fm(L)947 900 y Fj(N)1049 936 y Fn(where)h Fm(L)e Fn(is)h(the)g(allo)m(w)m(ed)f(degree)i(of)f (motion)f(of)g(one)h(square)g(considered)138 1056 y(ab)s(o)m(v)m(e\))g (is)g(maximized)g(among)g(allo)m(w)m(ed)h(pac)m(kings)f(of)h(\014xed)g (v)m(olume)f(fraction)g(b)m(y)h(the)g(pac)m(kings)138 1176 y(of)k(v)m(olume)h(fraction)f(ab)s(out)g(0)p Fm(:)p Fn(75.)337 1295 y(T)-8 b(o)36 b(obtain)f(accurate)i(ph)m(ysical)f (measuremen)m(ts)i(a)e(metho)s(d)h(of)f(sedimen)m(tation)g(has)h(b)s (een)138 1415 y(dev)m(elop)s(ed)28 b(to)f(prepare)h(samples)f(of)h (millions)e(of)h(grains)g(in)g(a)g(con)m(trolled)g(manner;)j(see)e ([JS])e(and)138 1534 y(references)k(therein)d(for)h(the)f(curren)m(t)h (state)f(of)h(the)f(exp)s(erimen)m(tal)g(data.)42 b(In)27 b(these)h(exp)s(erimen)m(ts)138 1654 y(mono)s(disp)s(erse)k(grains)f (sedimen)m(t)h(in)f(a)g(\015uid.)44 b(The)31 b(sedimen)m(t)i(is)d(of)i (uniform)f(v)m(olume)g(fraction,)138 1773 y(at)k(or)h(ab)s(o)m(v)m(e)f (0.55)g(dep)s(ending)i(on)f(v)-6 b(arious)36 b(exp)s(erimen)m(tal)g (parameters.)52 b(T)-8 b(o)35 b(ac)m(hiev)m(e)h(the)g(lo)m(w)138 1893 y(v)-6 b(alue)39 b(\(0)p Fm(:)p Fn(55)24 b Fl(\006)i Fn(0)p Fm(:)p Fn(001)38 b([JS]\),)g(the)h(grains)f(need)i(to)e(ha)m(v)m (e)h(a)f(high)h(friction)f(co)s(e\016cien)m(t)i(and)f(the)138 2012 y(\015uid)c(needs)g(to)f(ha)m(v)m(e)g(mass)h(densit)m(y)f(only)g (sligh)m(tly)f(lo)m(w)m(er)h(than)g(the)g(grains,)g(to)g(minimize)g (the)138 2132 y(destabilizing)43 b(e\013ect)g(of)h(gra)m(vit)m(y)-8 b(.)71 b(\(In)43 b(the)g(absence)i(of)e(gra)m(vit)m(y)e(one)j(could)f (still)f(pro)s(duce)i(a)138 2252 y(gran)m(ular)38 b(b)s(ed)g(b)m(y)f (pressure;)42 b(w)m(e)37 b(do)h(not)f(kno)m(w)h(of)g(exp)s(erimen)m(ts) g(rep)s(orting)f(a)h(random)f(lo)s(ose)138 2371 y(pac)m(king)c(v)-6 b(alue)34 b(for)f(suc)m(h)i(an)e(en)m(vironmen)m(t.\))337 2491 y(Our)42 b(results)f(suggest)g(that)f(whatev)m(er)h(the)g(initial) e(lo)s(cal)g(densit)m(y)i(of)g(the)g(b)s(ed,)i(on)d(sedi-)138 2610 y(men)m(tation)d(\(in)h(lo)m(w)f(e\013ectiv)m(e)h(gra)m(vit)m(y\)) d(most)j(samples)g(w)m(ould)g(ha)m(v)m(e)f(a)h(w)m(ell-de\014ned)h(v)m (olume)138 2730 y(fraction,)25 b(the)f(random)f(lo)s(ose)g(pac)m(king)g (densit)m(y)h(of)f(ab)s(out)g(0.55,)h(with)f Fk(no)j(intrinsic)f(lower) i(b)-5 b(ound)138 2849 y Fn(on)31 b(the)h(sharpness)h(of)e(the)h(v)-6 b(alue.)43 b(This)31 b(should)h(b)s(e)g(v)m(eri\014able)f(b)m(y)g(a)g (sequence)i(of)e(exp)s(erimen)m(ts)138 2969 y(of)i(increasing)h (dimensions.)337 3088 y(There)d(ha)m(v)m(e)f(b)s(een)h(previous)g (probabilistic)e(in)m(terpretations)h(of)g(the)h(random)f(lo)s(ose)g (pac)m(k-)138 3208 y(ing)24 b(densit)m(y)-8 b(,)25 b(for)f(instance)h ([MP)-8 b(,PC].)21 b(A)j(distinguishing)g(feature)h(of)f(our)g(results) g(is)g(our)f(analysis)138 3328 y(of)35 b(the)h(degree)g(of)g(sharpness) h(of)e(the)h(basic)g(notion,)f(whic)m(h,)h(as)f(w)m(e)h(shall)f(see)h (b)s(elo)m(w,)f(requires)138 3447 y(un)m(usual)g(care)e(in)g(the)h (treatmen)m(t)f(of)h(error)f(analysis.)138 3687 y Fo(2.)51 b(Results)337 3866 y Fn(W)-8 b(e)45 b(p)s(erformed)g(Mark)m(o)m(v)f(c)m (hain)h(Mon)m(te)f(Carlo)g(sim)m(ulations)g(on)g(our)g(gran)m(ular)g (mo)s(del,)138 3986 y(whic)m(h)d(w)m(e)f(no)m(w)g(describ)s(e)h(more)f (precisely)-8 b(.)65 b(W)-8 b(e)40 b(b)s(egin)g(with)g(a)f(\014xed)i(n) m(um)m(b)s(er)g(of)f(unit)g(edge)138 4105 y(squares)c(con)m(tained)h (in)e(a)h(large)f(rectangular)g(b)s(o)m(x)h Fm(B)5 b Fn(.)50 b(A)36 b(collection)f(of)h(squares)g(is)f(\\allo)m(w)m(ed")138 4225 y(if)g(they)f(do)h(not)g(o)m(v)m(erlap)f(with)h(p)s(ositiv)m(e)f (area,)g(their)h(edges)g(are)g(parallel)f(to)g(those)h(of)g(the)g(b)s (o)m(x)138 4344 y Fm(B)5 b Fn(,)37 b(and)h(the)g(lo)m(w)m(er)f(edge)h (of)g(eac)m(h)g(square)f(in)m(tersects)i(either)e(the)h(\015o)s(or)f (of)g(the)h(b)s(o)m(x)f Fm(B)42 b Fn(or)37 b(the)138 4464 y(upp)s(er)g(edge)g(of)f(eac)m(h)h(of)f(t)m(w)m(o)g(other)g (squares;)i(see)f(Fig.)e(3.)52 b(Note)36 b(that)f(although)h(the)g (squares)138 4583 y(ha)m(v)m(e)41 b(con)m(tin)m(uous)g(translational)e (degrees)i(of)g(freedom)g(in)f(the)g(horizon)m(tal)g(direction,)i(this) e(is)138 4703 y(not)27 b(in)h(evidence)h(in)e(the)h(v)m(ertical)f (direction)g(b)s(ecause)i(of)f(the)g(stabilit)m(y)e(condition:)41 b(the)28 b(squares)138 4823 y(inevitably)k(app)s(ear)i(at)e(discrete)i (horizon)m(tal)f(\\lev)m(els".)337 4942 y(Mark)m(o)m(v)25 b(c)m(hain)g(sim)m(ulations)g(w)m(ere)h(p)s(erformed)g(as)f(follo)m (ws.)41 b(In)25 b(the)g(rectangular)g(con)m(tainer)138 5062 y Fm(B)44 b Fn(a)39 b(\014xed)g(n)m(um)m(b)s(er)i(of)f(squares)f (are)h(in)m(tro)s(duced)g(in)f(a)g(simple)h(\\crystalline")e (con\014guration:)138 5181 y(squares)k(are)g(arranged)g(equally)f (spaced)i(in)f(horizon)m(tal)f(ro)m(ws,)j(the)e(spacing)h(determined)g (b)m(y)1958 5519 y(3)p eop end %%Page: 4 5 TeXDict begin 4 4 bop 138 100 a Fn(a)35 b(preassigned)j(v)m(olume)d (fraction)h Fm(\036)p Fn(,)g(and)g(with)f(squares)i(cen)m(tered)g(ab)s (o)m(v)m(e)f(the)g(cen)m(ters)h(of)f(the)138 219 y(gaps)31 b(in)g(the)g(ro)m(w)g(b)s(elo)m(w)g(it;)g(see)h(Fig.)e(4.)43 b(The)31 b(basic)h(step)f(in)g(the)g(sim)m(ulation)g(is)g(the)g(follo)m (wing.)138 339 y(A)26 b(square)h(is)f(c)m(hosen)j(at)d(random)g(from)h (the)g(curren)m(t)h(con\014guration)f(and)g(all)e(p)s(ossible)i(p)s (ositions)138 458 y(are)38 b(determined)h(to)e(whic)m(h)h(it)f(ma)m(y)g (b)s(e)h(relo)s(cated)g(and)g(pro)s(duce)h(an)e(allo)m(w)m(ed)h (con\014guration.)138 578 y(Note)31 b(that)f(if)i(the)f(c)m(hosen)i (square)e(supp)s(orts)i(a)e(square)g(ab)s(o)m(v)m(e)g(it)g(then)h(it)e (can)i(only)e(b)s(e)i(allo)m(w)m(ed)138 697 y(a)41 b(relativ)m(ely)f (small)h(horizon)m(tal)h(motion;)i(otherwise)e(it)f(ma)m(y)g(b)s(e)h (placed)g(atop)f(some)h(pair)g(of)138 817 y(squares,)k(or)d(the)h (\015o)s(or.)74 b(So)43 b(the)h(b)s(oundary)f(of)h(the)g (con\014guration)f(pla)m(ys)g(a)h(crucial)f(role)g(in)138 936 y(the)c(abilit)m(y)e(of)h(the)h(c)m(hain)f(to)g(c)m(hange)i(the)e (v)m(olume)g(fraction.)59 b(In)39 b(an)m(y)f(case)h(the)f(p)s(ositions) g(to)138 1056 y(whic)m(h)k(the)g(c)m(hosen)g(square)g(ma)m(y)f(b)s(e)g (mo)m(v)m(ed)h(constitute)f(a)g(union)h(of)g(in)m(terv)-6 b(als.)68 b(A)41 b(random)138 1176 y(p)s(oin)m(t)d(is)f(selected)i (from)f(this)g(union)g(of)g(in)m(terv)-6 b(als)38 b(and)g(the)g(square) g(is)g(mo)m(v)m(ed.)57 b(The)39 b(random)138 1295 y(mo)m(v)m(emen)m(t)h (of)g(a)f(random)h(square)g(is)f(the)h(basic)g(elemen)m(t)g(of)f(the)h (Mark)m(o)m(v)f(c)m(hain.)64 b(It)39 b(is)g(easy)138 1415 y(to)c(see)i(that)e(this)h(proto)s(col)f(is)h(transitiv)m(e)f(and) i(satis\014es)f(detailed)g(balance,)h(so)f(the)g(c)m(hain)h(has)138 1534 y(the)g(desired)h(uniform)g(probabilit)m(y)e(distribution)h(as)g (its)f(asymptotic)g(state)h([NB].)e(See)j(Fig.)e(5)138 1654 y(for)j(a)g(con\014guration)h(of)f(399)g(squares)h(after)f(10)2003 1618 y Fi(6)2087 1654 y Fn(mo)m(v)m(es.)62 b(Our)40 b(in)m(terest)g(is) f(in)g(random)g(lo)s(ose)138 1773 y(pac)m(king,)d(whic)m(h)h(o)s(ccurs) g(in)f(the)h(top)f(\(bulk\))f(la)m(y)m(er)h(of)g(a)g(gran)m(ular)g (pile.)53 b(W)-8 b(e)36 b(emphasize)h(that)138 1893 y(our)f(proto)s (col)e(is)i(not)f(particularly)f(appropriate)i(for)f(studying)h(other)f (questions)h(suc)m(h)h(as)f(the)138 2012 y(statistical)27 b(shap)s(e)h(of)h(the)f(b)s(oundary)g(of)g(a)g(gran)m(ular)g(pile,)h (or)f(prop)s(erties)g(asso)s(ciated)g(with)g(high)138 2132 y(densit)m(y)-8 b(,)33 b(suc)m(h)i(as)e(random)h(close)f(pac)m (king.)337 2252 y(After)j(a)g(prescrib)s(ed)h(n)m(um)m(b)s(er)h(of)e 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Fm(j)49 b Fn(=)43 b(0,)h(for)e(whic)m(h)h Fm(n)1695 2984 y Fj(j)1779 2969 y Fn(is)g(at)e(least)h(0)p Fm(:)p Fn(75)p Fm(p)g Fn(times)g(the)h (length)f(of)h(the)f(b)s(o)m(x's)138 3088 y(\015o)s(or.)56 b(Supp)s(ose)39 b Fm(L)882 3106 y Fj(J)7 b Fi(\()p Fj(p)p Fi(\))1079 3088 y Fn(is)37 b(the)h(highest)g(lev)m(el)f(suc)m(h)i(that) e(it,)h(and)g(all)e(lev)m(els)i(b)s(elo)m(w)g(it,)f(satisfy)138 3208 y(the)d(condition.)44 b(W)-8 b(e)33 b(then)h(assign)g(the)f(v)m (olume)g(fraction)1620 3512 y Fm(\036)p Fn(\()p Fm(p)p Fn(\))28 b(=)1952 3355 y Fh(P)2057 3380 y Fj(J)7 b Fi(\()p Fj(p)p Fi(\))2057 3460 y Fj(j)t Fi(=0)2232 3430 y Fm(n)2292 3445 y Fj(j)p 1952 3489 383 4 v 1959 3529 a Fh(P)2063 3554 y Fj(J)g Fi(\()p Fj(p)p Fi(\))2063 3634 y Fj(j)t Fi(=0)2239 3604 y Fm(s)2286 3619 y Fj(j)3701 3512 y Fn(\(1\))138 3771 y(to)29 b(the)h(assem)m(bly)h(of)f(squares.)43 b(\(The)30 b(v)-6 b(ariable)29 b Fm(p)h Fn(allo)m(ws)f(us)i(to)e(c)m(hec)m(k)i (the)f(homogeneit)m(y)g(of)g(the)138 3891 y(v)m(olume)37 b(fraction.)55 b(Note)36 b(ho)m(w)m(ev)m(er)i(that)f(an)m(y)g(t)m(w)m (o)g(suc)m(h)h(calculations)f(of)g(v)m(olume)g(fraction)g(of)138 4010 y(the)j(same)g(con\014guration)g(ma)m(y)f(only)h(di\013er)g(b)m(y) f(a)h(term)g(prop)s(ortional)f(to)g(the)h(length)g(of)g(the)138 4130 y(b)s(oundary)c(of)g(the)g(con\014guration,)h(so)f(an)m(y)g (inhomogeneit)m(y)f(is)h(limited)f(to)h(this)g(size.\))52 b(Suc)m(h)37 b(a)138 4250 y(calculation)22 b(of)h(v)m(olume)f(fraction) h(w)m(as)g(p)s(erformed)g(regularly)-8 b(,)24 b(after)f(appro)m (ximately)e(10)3470 4213 y Fi(6)3537 4250 y Fn(mo)m(v)m(es,)138 4369 y(pro)s(ducing)35 b(a)g(time)f(series)i(of)f(v)m(olume)g (fractions)g Fm(\036)2117 4384 y Fj(t)2187 4369 y Fn(for)g(the)g(giv)m (en)g(n)m(um)m(b)s(er)h(of)f(squares.)49 b(\(W)-8 b(e)138 4489 y(suppress)41 b(reference)h(to)d(the)g(v)-6 b(ariable)39 b Fm(p)g Fn(for)h(ease)g(of)f(reading.\))62 b(V)-8 b(ariables)39 b Fm(\036)3186 4504 y Fj(t)3261 4489 y Fn(and)g Fm(\036)3519 4504 y Fj(t)p Fi(+1)3695 4489 y Fn(are)138 4608 y(highly)29 b(dep)s(enden)m(t,)k(but)d(w)m(e)g(can)g(b)s(e)g(guaran)m(teed)h(that)f (if)g(the)g(series)g(is)g(long)f(enough)i(then)g(the)138 4728 y(sample)j(mean:)1822 4962 y(1)p 1802 5007 91 4 v 1802 5098 a Fm(N)1958 4905 y Fj(N)1921 4935 y Fh(X)1928 5146 y Fj(t)p Fi(=1)2082 5029 y Fm(\036)2141 5044 y Fj(t)3701 5029 y Fn(\(2\))138 5280 y(will)40 b(b)s(e)h(a)g(go)s(o)s(d)f(appro)m (ximation)g(to)g(the)i(true)f(mean)g(of)g(the)g(target)g(\(uniform\))g (probabilit)m(y)1958 5519 y(4)p eop end %%Page: 5 6 TeXDict begin 5 5 bop 138 100 a Fn(distribution)33 b(for)h(the)f(giv)m (en)g(n)m(um)m(b)s(er)i(of)f(squares)g([KV].)337 219 y(W)-8 b(e)28 b(created)g(suc)m(h)h(time)d(series)j Fm(\036)1606 234 y Fj(t)1641 219 y Fn(,)f(eac)m(h)g(of)g(ab)s(out)f(10)2402 183 y Fi(4)2473 219 y Fn(terms)h(\(roughly)e(10)3240 183 y Fi(10)3352 219 y Fn(elemen)m(tary)138 339 y(mo)m(v)m(es\),)46 b(using)f(v)-6 b(alues)44 b Fm(p)i Fn(=)g(0)p Fm(:)p Fn(2)p Fm(;)17 b Fn(0)p Fm(:)p Fn(4)p Fm(;)g Fn(0)p Fm(:)p Fn(6)p Fm(;)g Fn(0)p Fm(:)p Fn(8,)41 b(on)k(systems)f(for)g(the)h (follo)m(wing)e(n)m(um)m(b)s(ers)j(of)138 458 y(squares:)e(100)p Fm(m)p Fn(,)33 b(and)g(1000)p Fm(m)p Fn(,)f(for)h Fm(m)28 b Fn(=)h(1)p Fm(;)17 b Fn(2)p Fm(;)g(:)g(:)g(:)c(;)k Fn(9,)31 b(with)i(v)-6 b(arying)32 b(initial)f(v)m(olume)i(fractions.) 138 578 y(F)-8 b(or)43 b(eac)m(h)h(system)f(w)m(e)h(needed)h(to)e (determine)h(the)g(initialization)d(p)s(erio)s(d)i({)g(the)h(n)m(um)m (b)s(er)h(of)138 697 y(mo)m(v)m(es)e(necessary)g(to)f(reac)m(h)i (equilibrium)d({)i(and)f(then)i(the)e(total)f(n)m(um)m(b)s(er)j(of)f (mo)m(v)m(es)g(to)f(b)s(e)138 817 y(p)s(erformed.)h(Both)26 b(of)h(these)h(determinations)f(w)m(ere)g(made)h(based)f(on)g(v)-6 b(arian)m(ts)27 b(of)g(the)g(\(sample\))138 936 y(auto)s(correlation)32 b(function)i Fm(f)11 b Fn(\()p Fm(k)s Fn(\))32 b(of)h(the)g(time)g (series)h Fl(f)p Fm(\036)2335 951 y Fj(t)2403 936 y Fl(j)f Fn(1)27 b Fl(\024)h Fm(t)g Fl(\024)g Fm(T)14 b Fl(g)33 b 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2459 y Fl(\000)2658 2433 y Fn(\026)2645 2459 y Fm(\036)p Fn(\))p Fm(;)930 b Fn(\(4\))138 2743 y(whic)m(h)40 b(reduces)h(the)f(v)-6 b(alue)39 b(of)h Fm(f)11 b Fn(\()p Fm(k)s Fn(\))38 b(for)h(large)g Fm(k)s Fn(.)62 b(\(See)40 b(pages)g(321-324)e(of)i(Priestley)e([P])h(for)138 2863 y(a)34 b(discussion)i(of)e(this)h(biased)g(v)-6 b(arian)m(t.\))46 b(W)-8 b(e)35 b(consider)g(b)s(oth)f(v)-6 b(arian)m(ts)34 b(of)h(auto)s(correlation;)e(to)138 2983 y(refer)h(to)f(either)h(w)m(e)f(use)h(the)g(term)f Fm(f)1550 2998 y Fj(j)1592 2983 y Fn(.)337 3102 y(With)27 b(these)h(auto)s (correlations)d(w)m(e)j(determined)g(the)f(smallest)f Fm(k)31 b Fn(=)d Fm(k)3000 3117 y Fj(z)3072 3102 y Fn(suc)m(h)g(that)f Fm(f)3549 3117 y Fj(j)3590 3102 y Fn(\()p Fm(k)s Fn(\))g(=)138 3222 y(0.)69 b(W)-8 b(e)42 b(then)h(computed)f(the)g(sample)h(standard) f(deviation)f Fm(\033)2614 3237 y Fj(f)2653 3247 y Ff(j)2737 3222 y Fn(a)m(w)m(a)m(y)g(from)h(zero)g(of)g Fm(f)3628 3237 y Fj(j)3711 3222 y Fn(re-)138 3341 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y(closeness)c(of)e(the)g(slop)s(es)h(in)f(Figs.)g(8)g(and)g (10)g(to)g Fl(\000)p Fn(1)p Fm(=)p Fn(2.)43 b(A)31 b(slop)s(e)g(of)g Fl(\000)p Fn(1)p Fm(=)p Fn(2)g(w)m(ould)h(b)s(e)f(exp)s(ected)138 2012 y(if)41 b(it)f(w)m(ere)i(true)f(that)f(an)h(equilibrium)g (con\014guration)g(of)g Fm(N)51 b Fn(squares)42 b(could)f(b)s(e)g (partitioned)138 2132 y(in)m(to)h(similar)f(subblo)s(c)m(ks)i(whic)m(h) g(are)f(roughly)g(indep)s(enden)m(t)i({)e(a)g(prop)s(osition)g(whic)m (h)h(w)m(ould)138 2252 y(not)37 b(b)s(e)h(surprising)g(giv)m(en)g(a)f (phase)i(in)m(terpretation)e(of)h(gran)m(ular)f(media)h([R].)f(V)-8 b(erifying)36 b(suc)m(h)138 2371 y(indep)s(endence)43 b(migh)m(t)d(b)s(e)h(of)f(some)h(indep)s(enden)m(t)h(in)m(terest)f(but) f(w)m(ould)h(require)f(m)m(uc)m(h)i(more)138 2491 y(data)33 b(and)h(m)m(uc)m(h)g(longer)f(running)i(times.)337 2610 y(This)43 b(is)g(our)g(main)f(result,)k(since)d(it)f(sho)m(ws)i(ho)m(w) f(to)f(mak)m(e)h(sense)h(of)f(a)g(p)s(erfectly)g(w)m(ell-)138 2730 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Fm(J)43 b Fl(j)33 b Fm(\026)2710 3194 y Fj(g)2784 3179 y Fl(2)28 b Fm(I)8 b Fn(\))785 3348 y(=)29 b(Prob)o(\()p Fm(\026)1201 3363 y Fj(g)1275 3348 y Fl(2)f Fm(I)8 b Fn(\))1477 3254 y Fh(X)1534 3466 y Fj(i)1637 3348 y Fn(Prob\()p Fm(\033)1945 3363 y Fj(g)2019 3348 y Fl(2)28 b Fm(J)43 b Fl(j)33 b Fm(\026)2332 3363 y Fj(g)2406 3348 y Fl(2)28 b Fm(I)2544 3363 y Fj(i)2577 3348 y Fn(\)Prob)o(\()p Fm(\026)2926 3363 y Fj(g)3000 3348 y Fl(2)g Fm(I)3138 3363 y Fj(i)3204 3348 y Fl(j)33 b Fm(\026)3325 3363 y Fj(g)3399 3348 y Fl(2)28 b Fm(I)8 b Fn(\))p Fm(;)3701 3310 y Fn(\(6\))138 3674 y(where)36 b Fl(f)p Fm(I)522 3689 y Fj(i)555 3674 y Fl(g)f Fn(is)g(a)g(partition)f (of)h Fm(I)8 b Fn(.)49 b(W)-8 b(e)36 b(ha)m(v)m(e)g(discussed)h(ho)m(w) e(to)g(obtain)g Fm(I)42 b Fn(so)36 b(that)e(the)i(factor)138 3793 y(Prob\()p Fm(\026)449 3808 y Fj(g)523 3793 y Fl(2)28 b Fm(I)8 b Fn(\))32 b(is)g(at)g(least)g(0)p Fm(:)p Fn(95.)43 b(W)-8 b(e)33 b(no)m(w)f(w)m(an)m(t)h(to)f(obtain)g Fm(J)42 b Fn(so)33 b(that)f(the)g(factor)h(Prob\()p Fm(\033)3688 3808 y Fj(g)3762 3793 y Fl(2)138 3913 y Fm(J)49 b Fl(j)38 b Fm(\026)368 3928 y Fj(g)452 3913 y Fl(2)g Fm(I)8 b Fn(\))38 b(is)h(also)f(at)h(least)g(0)p Fm(:)p Fn(95,)g(and)g (therefore)i(Prob)o(\()p Fm(\026)2542 3928 y Fj(g)2626 3913 y Fl(2)d Fm(I)i Fn(and)34 b Fm(\033)3065 3928 y Fj(g)3149 3913 y Fl(2)j Fm(J)10 b Fn(\))39 b(is)g(at)f(least)138 4033 y(\(0)p Fm(:)p Fn(95\)\(0)p Fm(:)p Fn(95\))25 b Fm(>)j Fn(0)p Fm(:)p Fn(90.)337 4152 y(Consider,)34 b(for)f(eac)m(h)h (constan)m(t)g Fm(K)7 b Fn(,)33 b(the)h(random)f(v)-6 b(ariable)1270 4439 y(\006)1342 4454 y Fj(K)1447 4439 y Fn(=)1552 4303 y Fh(s)p 1652 4303 1017 4 v 136 x Fn(\(1)p Fm(=w)s Fn(\))1921 4345 y Fh(X)1973 4557 y Fj(j)2063 4439 y Fn([)p Fl(h)p Fm(g)t Fn(\()p Fm(c)p Fn(\))p Fl(i)2342 4454 y Fj(j)2404 4439 y Fl(\000)23 b Fm(K)7 b Fn(])2624 4410 y Fi(2)2668 4439 y Fm(:)1005 b Fn(\(7\))138 4802 y(Using)35 b(\(5\))g(with)g(\()p Fm(g)t Fn(\()p Fm(c)p Fn(\))22 b Fl(\000)i Fm(K)7 b 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Fj(g)2555 5280 y Fn(.)55 b(So)36 b(if)h(w)m(e)g(let)g Fm(J)43 b Fn(=)34 b Fl([)3447 5295 y Fj(i)3481 5280 y Fm(J)3536 5295 y Fj(i)3569 5280 y Fn(,)j(then)1958 5519 y(7)p eop end %%Page: 8 9 TeXDict begin 8 8 bop 138 100 a Fn(Prob\()p Fm(\033)446 115 y Fj(g)524 100 y Fl(2)32 b Fm(J)46 b Fl(j)36 b Fm(\026)847 115 y Fj(g)925 100 y Fl(2)d Fm(I)1068 115 y Fj(i)1100 100 y Fn(\))f Fm(>)h Fn(0)p Fm(:)p Fn(95)i(for)h(all)f Fm(i)p Fn(,)h(and)h(therefore)g(Prob\()p Fm(\033)2814 115 y Fj(g)2892 100 y Fl(2)32 b Fm(J)46 b Fl(j)35 b Fm(\026)3214 115 y Fj(g)3293 100 y Fl(2)d Fm(I)8 b Fn(\))32 b Fm(>)g Fn(0)p Fm(:)p Fn(95.)138 219 y(In)i(practice)f(the)h(union)f Fm(J)38 b Fn(=)28 b Fl([)1351 234 y Fj(i)1385 219 y Fm(J)1440 234 y Fj(i)1506 219 y Fn(is)34 b(easy)f(to)f(compute.)337 339 y(In)45 b(the)g(ab)s(o)m(v)m(e)g(argumen)m(ts)g(w)m(e)g(ha)m(v)m(e) g(assumed)h(t)m(w)m(o)e(prop)s(erties)i(of)e(the)h(batc)m(h)h(means,) 138 458 y(normalit)m(y)32 b(and)h(indep)s(endence,)j(whic)m(h)d(do)g 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Fn(1.)74 b(Note)43 b(that)g(v)-6 b(ariables)43 b Fm(X)3120 2023 y Fj(t)3198 2008 y Fn(and)h Fm(X)3485 2023 y Fj(t)p Fi(+)p Fj(m)3695 2008 y Fn(are)138 2128 y(indep)s(enden)m(t)36 b(for)d Fm(m)28 b Fl(\025)g Fn(2)p Fm(M)33 b Fl(\000)22 b Fn(1.)337 2247 y(A)33 b(simple)h(calculation)e(sho)m(ws)i(that:)870 2439 y Fj(M)7 b Fg(\000)p Fi(1)890 2468 y Fh(X)877 2679 y Fj(m)p Fi(=0)1072 2563 y Fm(X)1155 2578 y Fj(tM)g Fi(+)p Fj(m)1432 2563 y Fn(=)1538 2452 y Fh(\020)1609 2496 y Fm(M)33 b Fn(+)22 b(1)p 1609 2540 280 4 v 1724 2631 a(2)1900 2452 y Fh(\021)1960 2563 y Fm(X)2043 2578 y Fj(tM)2183 2563 y Fn(+)2282 2452 y Fh(\020)2354 2496 y Fm(M)32 b Fl(\000)23 b Fn(1)p 2354 2540 V 2468 2631 a(2)2645 2452 y Fh(\021)2704 2563 y Fm(X)2787 2581 y Fi(\()p Fj(t)p Fi(+1\))p Fj(M)3069 2563 y Fm(:)604 b Fn(\(9\))138 2842 y(Then)34 b(another)g(simple)f(calculation)g(sho)m(ws)h(that:)270 3277 y Fm(S)331 3292 y Fj(T)422 3277 y Fl(\021)604 3210 y Fn(1)p 539 3254 180 4 v 539 3346 a Fm(T)14 b(M)747 3153 y Fj(T)d(M)c Fg(\000)p Fi(1)797 3183 y Fh(X)783 3394 y Fj(m)p Fi(=0)1007 3277 y Fm(X)1090 3292 y Fj(m)1193 3277 y Fn(=)1321 3210 y(1)p 1310 3254 73 4 v 1310 3346 a Fm(T)1394 3167 y Fh(h)1457 3153 y Fj(T)k Fg(\000)p Fi(1)1465 3183 y Fh(X)1472 3394 y Fj(t)p Fi(=1)1634 3277 y Fm(X)1717 3292 y Fj(tM)1857 3277 y Fn(+)1969 3210 y(1)p 1969 3254 50 4 v 1969 3346 a(2)2030 3277 y(\()p Fm(X)2152 3292 y Fi(0)2219 3277 y Fn(+)22 b Fm(X)2401 3292 y Fj(T)11 b(M)2547 3277 y Fn(\))22 b(+)2773 3210 y(1)p 2719 3254 158 4 v 2719 3346 a(2)p Fm(M)2889 3277 y Fn(\()p Fm(X)3011 3292 y Fi(0)3077 3277 y Fl(\000)g Fm(X)3259 3292 y Fj(T)11 b(M)3405 3277 y Fn(\))3444 3167 y Fh(i)3491 3277 y Fm(:)132 b Fn(\(10\))138 3606 y(In)34 b(other)f(w)m(ords)h Fm(S)870 3621 y Fj(T)966 3606 y Fn(is)f(the)h(mean)f(of)h(roughly)f Fm(K)40 b Fk(indep)-5 b(endent)32 b Fn(v)-6 b(ariables.)337 3726 y(Returning)27 b(to)e(the)g(question)h(of)g(the)g(assumptions)g (in)g(the)f(t-test,)i(the)f(to)m(y)f(mo)s(del)g(suggests)138 3845 y(that)42 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@lly 840 @urx 736 @ury 3321 @rwi @setspecial %%BeginDocument: lowdensity-edit.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: MATLAB, The Mathworks, Inc. Version 7.6.0.324 (R2008a). Operating System: Linux 2.6.20-16-386 #2 Wed May 23 01:42:57 UTC 2007 i686. %%Title: /home/daristoff/lowdensity-edit.eps %%CreationDate: 08/02/2008 19:16:31 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%LanguageLevel: 2 %%Pages: 1 %%BoundingBox: -228 54 840 736 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s {show newpath} bdef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinewidth 2 div 0 360 arc fill PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup 3 mul string currentfile 3 index 0 eq {/ASCIIHexDecode filter} {/ASCII85Decode filter 3 index 2 eq {/RunLengthDecode filter} if } ifelse exch readstring pop dup 0 3 index getinterval /rbmap xdef dup 2 index dup getinterval /gbmap xdef 1 index dup 2 mul exch getinterval /bbmap xdef pop pop}bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform rbmap gbmap bbmap true 3 colorimage gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: -228 54 840 736 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode -2736 8832 csm 0 0 12816 8173 rc 85 dict begin %Colortable dictionary /c0 { 0.000000 0.000000 0.000000 sr} bdef /c1 { 1.000000 1.000000 1.000000 sr} bdef /c2 { 0.900000 0.000000 0.000000 sr} bdef /c3 { 0.000000 0.820000 0.000000 sr} bdef /c4 { 0.000000 0.000000 0.800000 sr} bdef /c5 { 0.910000 0.820000 0.320000 sr} bdef /c6 { 1.000000 0.260000 0.820000 sr} bdef /c7 { 0.000000 0.820000 0.820000 sr} bdef c0 1 j 1 sg 0 0 12817 8174 rf 6 w 0 7049 10049 0 0 -7049 1627 7478 4 MP PP -10049 0 0 7049 10049 0 0 -7049 1627 7478 5 MP stroke 4 w DO SO 6 w 0 sg 1627 7478 mt 11676 7478 L 1627 429 mt 11676 429 L 1627 7478 mt 1627 429 L 11676 7478 mt 11676 429 L 1627 7478 mt 11676 7478 L 1627 7478 mt 1627 429 L 1632 7478 mt 1632 7377 L 1632 430 mt 1632 530 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 288 FMSR 1552 7780 mt (0) s 2636 7478 mt 2636 7377 L 2636 430 mt 2636 530 L 2396 7780 mt (200) s 3641 7478 mt 3641 7377 L 3641 430 mt 3641 530 L 3401 7780 mt (400) s 4646 7478 mt 4646 7377 L 4646 430 mt 4646 530 L 4406 7780 mt (600) s 5651 7478 mt 5651 7377 L 5651 430 mt 5651 530 L 5411 7780 mt (800) s 6656 7478 mt 6656 7377 L 6656 430 mt 6656 530 L 6336 7780 mt (1000) s 7661 7478 mt 7661 7377 L 7661 430 mt 7661 530 L 7341 7780 mt (1200) s 8666 7478 mt 8666 7377 L 8666 430 mt 8666 530 L 8346 7780 mt (1400) s 9671 7478 mt 9671 7377 L 9671 430 mt 9671 530 L 9351 7780 mt (1600) s 10676 7478 mt 10676 7377 L 10676 430 mt 10676 530 L 10356 7780 mt (1800) s 1627 7478 mt 1727 7478 L 11676 7478 mt 11575 7478 L 1192 7585 mt (0.5) s 1627 6303 mt 1727 6303 L 11676 6303 mt 11575 6303 L 1032 6410 mt (0.55) s 1627 5128 mt 1727 5128 L 11676 5128 mt 11575 5128 L 1192 5235 mt (0.6) s 1627 3954 mt 1727 3954 L 11676 3954 mt 11575 3954 L 1032 4061 mt (0.65) s 1627 2779 mt 1727 2779 L 11676 2779 mt 11575 2779 L 1192 2886 mt (0.7) s 1627 1604 mt 1727 1604 L 11676 1604 mt 11575 1604 L 1032 1711 mt (0.75) s 1627 430 mt 1727 430 L 11676 430 mt 11575 430 L 1192 537 mt (0.8) s 1627 7478 mt 11676 7478 L 1627 429 mt 11676 429 L 1627 7478 mt 1627 429 L 11676 7478 mt 11676 429 L gs 1627 430 10050 7049 rc gr /c8 { 0.000000 0.000000 1.000000 sr} bdef c8 36 36 1637 6838 FO 36 36 1642 6787 FO 36 36 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36 36 1913 4806 FO 36 36 1918 4791 FO 36 36 1923 4715 FO 36 36 1928 4781 FO 36 36 1933 4718 FO 36 36 1938 4718 FO 36 36 1943 4693 FO 36 36 1948 4661 FO 36 36 1953 4629 FO 36 36 1958 4582 FO 36 36 1963 4521 FO 36 36 1968 4539 FO 36 36 1973 4497 FO 36 36 1978 4499 FO 36 36 1983 4380 FO 36 36 1988 4357 FO 36 36 1993 4326 FO 36 36 1998 4325 FO 36 36 2003 4290 FO 36 36 2008 4230 FO 36 36 2013 4071 FO 36 36 2018 4023 FO 36 36 2023 4024 FO 36 36 2028 4011 FO 36 36 2033 4058 FO 36 36 2039 4024 FO 36 36 2044 3979 FO 36 36 2049 4016 FO 36 36 2054 3963 FO 36 36 2059 3861 FO 36 36 2064 3882 FO 36 36 2069 3932 FO 36 36 2074 3889 FO 36 36 2079 3852 FO 36 36 2084 3826 FO 36 36 2089 3800 FO 36 36 2094 3740 FO 36 36 2099 3706 FO 36 36 2104 3748 FO 36 36 2109 3782 FO 36 36 2114 3785 FO 36 36 2119 3751 FO 36 36 2124 3699 FO 36 36 2129 3724 FO 36 36 2134 3736 FO 36 36 2139 3713 FO 36 36 2144 3707 FO 36 36 2149 3612 FO 36 36 2154 3575 FO 36 36 2159 3637 FO 36 36 2164 3596 FO 36 36 2169 3595 FO 36 36 2174 3622 FO 36 36 2179 3623 FO 36 36 2184 3540 FO 36 36 2189 3477 FO 36 36 2194 3439 FO 36 36 2199 3420 FO 36 36 2204 3387 FO 36 36 2209 3335 FO 36 36 2214 3315 FO 36 36 2219 3321 FO 36 36 2224 3163 FO 36 36 2229 3145 FO 36 36 2234 3145 FO 36 36 2239 3145 FO 36 36 2245 3106 FO 36 36 2250 3028 FO 36 36 2255 2973 FO 36 36 2260 3047 FO 36 36 2265 3085 FO 36 36 2270 3086 FO 36 36 2275 3137 FO 36 36 2280 3013 FO 36 36 2285 3032 FO 36 36 2290 3041 FO 36 36 2295 2955 FO 36 36 2300 2932 FO 36 36 2305 2946 FO 36 36 2310 2920 FO 36 36 2315 2880 FO 36 36 2320 2977 FO 36 36 2325 2948 FO 36 36 2330 2940 FO 36 36 2335 2950 FO 36 36 2340 2833 FO 36 36 2345 2781 FO 36 36 2350 2819 FO 36 36 2355 2767 FO 36 36 2360 2677 FO 36 36 2365 2591 FO 36 36 2370 2595 FO 36 36 2375 2636 FO 36 36 2380 2549 FO 36 36 2385 2573 FO 36 36 2390 2578 FO 36 36 2395 2574 FO 36 36 2400 2593 FO 36 36 2405 2521 FO 36 36 2410 2479 FO 36 36 2415 2497 FO 36 36 2420 2537 FO 36 36 2425 2447 FO 36 36 2430 2514 FO 36 36 2435 2504 FO 36 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4289 1604 FO 36 36 4295 1559 FO 36 36 4300 1526 FO 36 36 4305 1554 FO 36 36 4310 1542 FO 36 36 4315 1602 FO 36 36 4320 1561 FO 36 36 4325 1495 FO 36 36 4330 1600 FO 36 36 4335 1539 FO 36 36 4340 1552 FO 36 36 4345 1583 FO 36 36 4350 1570 FO 36 36 4355 1556 FO 36 36 4360 1531 FO 36 36 4365 1499 FO 36 36 4370 1484 FO 36 36 4375 1455 FO 36 36 4380 1467 FO 36 36 4385 1511 FO 36 36 4390 1493 FO 36 36 4395 1511 FO 36 36 4400 1554 FO 36 36 4405 1421 FO 36 36 4410 1461 FO 36 36 4415 1478 FO 36 36 4420 1460 FO 36 36 4425 1494 FO 36 36 4430 1464 FO 36 36 4435 1496 FO 36 36 4440 1491 FO 36 36 4445 1512 FO 36 36 4450 1504 FO 36 36 4455 1435 FO 36 36 4460 1471 FO 36 36 4465 1500 FO 36 36 4470 1525 FO 36 36 4475 1470 FO 36 36 4480 1390 FO 36 36 4485 1467 FO 36 36 4490 1478 FO 36 36 4495 1465 FO 36 36 4501 1453 FO 36 36 4506 1432 FO 36 36 4511 1391 FO 36 36 4516 1459 FO 36 36 4521 1404 FO 36 36 4526 1436 FO 36 36 4531 1456 FO 36 36 4536 1432 FO 36 36 4541 1444 FO 36 36 4546 1406 FO 36 36 4551 1463 FO 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1423 FO 36 36 4822 1394 FO 36 36 4827 1440 FO 36 36 4832 1347 FO 36 36 4837 1361 FO 36 36 4842 1343 FO 36 36 4847 1388 FO 36 36 4852 1274 FO 36 36 4857 1362 FO 36 36 4862 1329 FO 36 36 4867 1330 FO 36 36 4872 1378 FO 36 36 4877 1309 FO 36 36 4882 1324 FO 36 36 4887 1282 FO 36 36 4892 1313 FO 36 36 4897 1297 FO 36 36 4902 1353 FO 36 36 4907 1338 FO 36 36 4913 1374 FO 36 36 4918 1359 FO 36 36 4923 1385 FO 36 36 4928 1342 FO 36 36 4933 1368 FO 36 36 4938 1391 FO 36 36 4943 1377 FO 36 36 4948 1387 FO 36 36 4953 1365 FO 36 36 4958 1366 FO 36 36 4963 1370 FO 36 36 4968 1383 FO 36 36 4973 1357 FO 36 36 4978 1295 FO 36 36 4983 1287 FO 36 36 4988 1294 FO 36 36 4993 1341 FO 36 36 4998 1294 FO 36 36 5003 1394 FO 36 36 5008 1398 FO 36 36 5013 1362 FO 36 36 5018 1331 FO 36 36 5023 1337 FO 36 36 5028 1379 FO 36 36 5033 1417 FO 36 36 5038 1376 FO 36 36 5043 1406 FO 36 36 5048 1378 FO 36 36 5053 1346 FO 36 36 5058 1313 FO 36 36 5063 1291 FO 36 36 5068 1365 FO 36 36 5073 1365 FO 36 36 5078 1369 FO 36 36 5083 1368 FO 36 36 5088 1445 FO 36 36 5093 1343 FO 36 36 5098 1469 FO 36 36 5103 1416 FO 36 36 5108 1402 FO 36 36 5114 1399 FO 36 36 5119 1371 FO 36 36 5124 1292 FO 36 36 5129 1337 FO 36 36 5134 1389 FO 36 36 5139 1413 FO 36 36 5144 1419 FO 36 36 5149 1437 FO 36 36 5154 1435 FO 36 36 5159 1354 FO 36 36 5164 1388 FO 36 36 5169 1390 FO 36 36 5174 1414 FO 36 36 5179 1469 FO 36 36 5184 1439 FO 36 36 5189 1417 FO 36 36 5194 1397 FO 36 36 5199 1487 FO 36 36 5204 1478 FO 36 36 5209 1446 FO 36 36 5214 1477 FO 36 36 5219 1493 FO 36 36 5224 1470 FO 36 36 5229 1505 FO 36 36 5234 1493 FO 36 36 5239 1519 FO 36 36 5244 1444 FO 36 36 5249 1492 FO 36 36 5254 1446 FO 36 36 5259 1447 FO 36 36 5264 1507 FO 36 36 5269 1497 FO 36 36 5274 1491 FO 36 36 5279 1516 FO 36 36 5284 1579 FO 36 36 5289 1616 FO 36 36 5294 1551 FO 36 36 5299 1465 FO 36 36 5304 1481 FO 36 36 5309 1571 FO 36 36 5314 1562 FO 36 36 5320 1571 FO 36 36 5325 1597 FO 36 36 5330 1535 FO 36 36 5335 1553 FO 36 36 5340 1484 FO 36 36 5345 1551 FO 36 36 5350 1512 FO 36 36 5355 1622 FO 36 36 5360 1566 FO 36 36 5365 1528 FO 36 36 5370 1559 FO 36 36 5375 1586 FO 36 36 5380 1531 FO 36 36 5385 1511 FO 36 36 5390 1510 FO 36 36 5395 1467 FO 36 36 5400 1461 FO 36 36 5405 1494 FO 36 36 5410 1481 FO 36 36 5415 1481 FO 36 36 5420 1409 FO 36 36 5425 1426 FO 36 36 5430 1475 FO 36 36 5435 1428 FO 36 36 5440 1440 FO 36 36 5445 1466 FO 36 36 5450 1409 FO 36 36 5455 1490 FO 36 36 5460 1445 FO 36 36 5465 1442 FO 36 36 5470 1446 FO 36 36 5475 1423 FO 36 36 5480 1459 FO 36 36 5485 1399 FO 36 36 5490 1400 FO 36 36 5495 1330 FO 36 36 5500 1392 FO 36 36 5505 1344 FO 36 36 5510 1375 FO 36 36 5515 1350 FO 36 36 5520 1375 FO 36 36 5526 1373 FO 36 36 5531 1435 FO 36 36 5536 1356 FO 36 36 5541 1329 FO 36 36 5546 1371 FO 36 36 5551 1377 FO 36 36 5556 1333 FO 36 36 5561 1365 FO 36 36 5566 1306 FO 36 36 5571 1305 FO 36 36 5576 1311 FO 36 36 5581 1279 FO 36 36 5586 1307 FO 36 36 5591 1313 FO 36 36 5596 1373 FO 36 36 5601 1347 FO 36 36 5606 1343 FO 36 36 5611 1351 FO 36 36 5616 1296 FO 36 36 5621 1384 FO 36 36 5626 1417 FO 36 36 5631 1346 FO 36 36 5636 1331 FO 36 36 5641 1346 FO 36 36 5646 1353 FO 36 36 5651 1392 FO 36 36 5656 1302 FO 36 36 5661 1364 FO 36 36 5666 1357 FO 36 36 5671 1359 FO 36 36 5676 1373 FO 36 36 5681 1416 FO 36 36 5686 1374 FO 36 36 5691 1344 FO 36 36 5696 1423 FO 36 36 5701 1329 FO 36 36 5706 1297 FO 36 36 5711 1317 FO 36 36 5716 1298 FO 36 36 5721 1291 FO 36 36 5726 1357 FO 36 36 5732 1366 FO 36 36 5737 1337 FO 36 36 5742 1316 FO 36 36 5747 1242 FO 36 36 5752 1260 FO 36 36 5757 1303 FO 36 36 5762 1295 FO 36 36 5767 1289 FO 36 36 5772 1269 FO 36 36 5777 1349 FO 36 36 5782 1261 FO 36 36 5787 1302 FO 36 36 5792 1255 FO 36 36 5797 1286 FO 36 36 5802 1288 FO 36 36 5807 1277 FO 36 36 5812 1299 FO 36 36 5817 1261 FO 36 36 5822 1224 FO 36 36 5827 1282 FO 36 36 5832 1325 FO 36 36 5837 1313 FO 36 36 5842 1324 FO 36 36 5847 1342 FO 36 36 5852 1320 FO 36 36 5857 1321 FO 36 36 5862 1326 FO 36 36 5867 1342 FO 36 36 5872 1315 FO 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Operating System: Linux 2.6.20-16-386 #2 Wed May 23 01:42:57 UTC 2007 i686. %%Title: /home/daristoff/initialization1.eps %%CreationDate: 08/01/2008 15:51:52 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%LanguageLevel: 2 %%Pages: 1 %%BoundingBox: -24 203 637 587 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s {show newpath} bdef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinewidth 2 div 0 360 arc fill PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup 3 mul string currentfile 3 index 0 eq {/ASCIIHexDecode filter} {/ASCII85Decode filter 3 index 2 eq {/RunLengthDecode filter} if } ifelse exch readstring pop dup 0 3 index getinterval /rbmap xdef dup 2 index dup getinterval /gbmap xdef 1 index dup 2 mul exch getinterval /bbmap xdef pop pop}bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform rbmap gbmap bbmap true 3 colorimage gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: -24 203 637 587 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode -0288 7044 csm 0 0 7943 4605 rc 85 dict begin %Colortable dictionary /c0 { 0.000000 0.000000 0.000000 sr} bdef /c1 { 1.000000 1.000000 1.000000 sr} bdef /c2 { 0.900000 0.000000 0.000000 sr} bdef /c3 { 0.000000 0.820000 0.000000 sr} bdef /c4 { 0.000000 0.000000 0.800000 sr} bdef /c5 { 0.910000 0.820000 0.320000 sr} bdef /c6 { 1.000000 0.260000 0.820000 sr} bdef /c7 { 0.000000 0.820000 0.820000 sr} bdef c0 1 j 1 sg 0 0 7944 4606 rf 6 w 0 3938 5465 0 0 -3938 1429 4096 4 MP PP -5465 0 0 3938 5465 0 0 -3938 1429 4096 5 MP stroke 4 w DO SO 6 w 0 sg 1429 4096 mt 6894 4096 L 1429 158 mt 6894 158 L 1429 4096 mt 1429 158 L 6894 4096 mt 6894 158 L 1429 4096 mt 6894 4096 L 1429 4096 mt 1429 158 L 1429 4096 mt 1429 4041 L 1429 158 mt 1429 213 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 144 FMSR 1389 4264 mt (0) s 2340 4096 mt 2340 4041 L 2340 158 mt 2340 213 L 2180 4264 mt (2000) s 3251 4096 mt 3251 4041 L 3251 158 mt 3251 213 L 3091 4264 mt (4000) s 4162 4096 mt 4162 4041 L 4162 158 mt 4162 213 L 4002 4264 mt (6000) s 5073 4096 mt 5073 4041 L 5073 158 mt 5073 213 L 4913 4264 mt (8000) s 5984 4096 mt 5984 4041 L 5984 158 mt 5984 213 L 5784 4264 mt (10000) s 6895 4096 mt 6895 4041 L 6895 158 mt 6895 213 L 6695 4264 mt (12000) s 1429 4096 mt 1483 4096 L 6895 4096 mt 6840 4096 L 1110 4149 mt (-0.2) s 1429 3439 mt 1483 3439 L 6895 3439 mt 6840 3439 L 1314 3492 mt (0) s 1429 2783 mt 1483 2783 L 6895 2783 mt 6840 2783 L 1194 2836 mt (0.2) s 1429 2127 mt 1483 2127 L 6895 2127 mt 6840 2127 L 1194 2180 mt (0.4) s 1429 1471 mt 1483 1471 L 6895 1471 mt 6840 1471 L 1194 1524 mt (0.6) s 1429 815 mt 1483 815 L 6895 815 mt 6840 815 L 1194 868 mt (0.8) s 1429 158 mt 1483 158 L 6895 158 mt 6840 158 L 1314 211 mt (1) s 1429 4096 mt 6894 4096 L 1429 158 mt 6894 158 L 1429 4096 mt 1429 158 L 6894 4096 mt 6894 158 L gs 1429 159 5467 3938 rc gr /c8 { 0.000000 0.000000 1.000000 sr} bdef c8 36 36 1429 299 FO 36 36 1429 379 FO 36 36 1430 448 FO 36 36 1430 510 FO 36 36 1431 570 FO 36 36 1431 628 FO 36 36 1432 686 FO 36 36 1432 741 FO 36 36 1433 796 FO 36 36 1433 851 FO 36 36 1434 904 FO 36 36 1434 957 FO 36 36 1434 1008 FO 36 36 1435 1059 FO 36 36 1435 1104 FO 36 36 1436 1150 FO 36 36 1436 1196 FO 36 36 1437 1241 FO 36 36 1437 1287 FO 36 36 1438 1331 FO 36 36 1438 1374 FO 36 36 1439 1414 FO 36 36 1439 1457 FO 36 36 1439 1496 FO 36 36 1440 1535 FO 36 36 1440 1574 FO 36 36 1441 1611 FO 36 36 1441 1647 FO 36 36 1442 1683 FO 36 36 1442 1720 FO 36 36 1443 1752 FO 36 36 1443 1786 FO 36 36 1444 1816 FO 36 36 1444 1846 FO 36 36 1444 1876 FO 36 36 1445 1908 FO 36 36 1445 1936 FO 36 36 1446 1963 FO 36 36 1446 1990 FO 36 36 1447 2018 FO 36 36 1447 2045 FO 36 36 1448 2074 FO 36 36 1448 2101 FO 36 36 1449 2127 FO 36 36 1449 2157 FO 36 36 1449 2182 FO 36 36 1450 2206 FO 36 36 1450 2233 FO 36 36 1451 2258 FO 36 36 1451 2285 FO 36 36 1452 2311 FO 36 36 1452 2337 FO 36 36 1453 2360 FO 36 36 1453 2380 FO 36 36 1454 2403 FO 36 36 1454 2427 FO 36 36 1454 2448 FO 36 36 1455 2468 FO 36 36 1455 2489 FO 36 36 1456 2507 FO 36 36 1456 2525 FO 36 36 1457 2545 FO 36 36 1457 2563 FO 36 36 1458 2579 FO 36 36 1458 2596 FO 36 36 1459 2613 FO 36 36 1459 2628 FO 36 36 1459 2643 FO 36 36 1460 2659 FO 36 36 1460 2673 FO 36 36 1461 2687 FO 36 36 1461 2702 FO 36 36 1462 2720 FO 36 36 1462 2735 FO 36 36 1463 2751 FO 36 36 1463 2768 FO 36 36 1464 2781 FO 36 36 1464 2796 FO 36 36 1464 2807 FO 36 36 1465 2819 FO 36 36 1465 2830 FO 36 36 1466 2845 FO 36 36 1466 2860 FO 36 36 1467 2872 FO 36 36 1467 2887 FO 36 36 1468 2898 FO 36 36 1468 2910 FO 36 36 1469 2923 FO 36 36 1469 2932 FO 36 36 1469 2948 FO 36 36 1470 2960 FO 36 36 1470 2972 FO 36 36 1471 2981 FO 36 36 1471 2993 FO 36 36 1472 3007 FO 36 36 1472 3017 FO 36 36 1473 3027 FO 36 36 1473 3036 FO 36 36 1474 3045 FO 36 36 1474 3055 FO 36 36 1475 3068 FO 36 36 1475 3080 FO 36 36 1475 3092 FO 36 36 1476 3101 FO 36 36 1476 3106 FO 36 36 1477 3114 FO 36 36 1477 3128 FO 36 36 1478 3139 FO 36 36 1478 3151 FO 36 36 1479 3160 FO 36 36 1479 3169 FO 36 36 1480 3181 FO 36 36 1480 3190 FO 36 36 1480 3198 FO 36 36 1481 3209 FO 36 36 1481 3221 FO 36 36 1482 3233 FO 36 36 1482 3241 FO 36 36 1483 3255 FO 36 36 1483 3265 FO 36 36 1484 3275 FO 36 36 1484 3286 FO 36 36 1485 3294 FO 36 36 1485 3304 FO 36 36 1485 3313 FO 36 36 1486 3323 FO 36 36 1486 3330 FO 36 36 1487 3337 FO 36 36 1487 3345 FO 36 36 1488 3351 FO 36 36 1488 3361 FO 36 36 1489 3369 FO 36 36 1489 3376 FO 36 36 1490 3381 FO 36 36 1490 3386 FO 36 36 1490 3389 FO 36 36 1491 3392 FO 36 36 1491 3398 FO 36 36 1492 3404 FO 36 36 1492 3410 FO 36 36 1493 3416 FO 36 36 1493 3421 FO 36 36 1494 3426 FO 36 36 1494 3431 FO 36 36 1495 3435 FO 36 36 1495 3439 FO 36 36 1495 3441 FO 36 36 1496 3448 FO 36 36 1496 3454 FO 36 36 1497 3458 FO 36 36 1497 3463 FO 36 36 1498 3468 FO 36 36 1498 3472 FO 36 36 1499 3475 FO 36 36 1499 3478 FO 36 36 1500 3477 FO 36 36 1501 3478 FO 36 36 1501 3482 FO 36 36 1502 3483 FO 36 36 1502 3484 FO 36 36 1503 3485 FO 36 36 1503 3489 FO 36 36 1504 3488 FO 36 36 1505 3482 FO 36 36 1505 3476 FO 36 36 1505 3474 FO 36 36 1506 3472 FO 36 36 1506 3473 FO 36 36 1507 3473 FO 36 36 1508 3476 FO 36 36 1508 3480 FO 36 36 1509 3484 FO 36 36 1509 3488 FO 36 36 1510 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1718 3540 FO 36 36 1719 3543 FO 36 36 1719 3546 FO 36 36 1720 3551 FO 36 36 1720 3552 FO 36 36 1720 3554 FO 36 36 1721 3557 FO 36 36 1721 3561 FO 36 36 1722 3563 FO 36 36 1722 3566 FO 36 36 1723 3567 FO 36 36 1723 3568 FO 36 36 1724 3569 FO 36 36 1725 3569 FO 36 36 1726 3570 FO 36 36 1726 3571 FO 36 36 1727 3571 FO 36 36 1728 3573 FO 36 36 1728 3574 FO 36 36 1729 3577 FO 36 36 1729 3580 FO 36 36 1730 3588 FO 36 36 1730 3593 FO 36 36 1730 3596 FO 36 36 1731 3599 FO 36 36 1731 3601 FO 36 36 1732 3604 FO 36 36 1732 3607 FO 36 36 1733 3611 FO 36 36 1733 3612 FO 36 36 1734 3611 FO 36 36 1735 3614 FO 36 36 1735 3613 FO 36 36 1736 3612 FO 36 36 1736 3613 FO 36 36 1736 3617 FO 36 36 1737 3619 FO 36 36 1737 3621 FO 36 36 1738 3624 FO 36 36 1738 3627 FO 36 36 1739 3626 FO 36 36 1739 3625 FO 36 36 1740 3627 FO 36 36 1740 3624 FO 36 36 1741 3623 FO 36 36 1741 3620 FO 36 36 1741 3622 FO 36 36 1742 3620 FO 36 36 1742 3617 FO 36 36 1743 3615 FO 36 36 1743 3616 FO 36 36 1744 3613 FO 36 36 1744 3612 FO 36 36 1745 3612 FO 36 36 1745 3610 FO 36 36 1746 3607 FO 36 36 1746 3606 FO 36 36 1747 3605 FO 36 36 1748 3603 FO 36 36 1749 3604 FO 36 36 1749 3605 FO 36 36 1750 3606 FO 36 36 1750 3604 FO 36 36 1751 3601 FO 36 36 1751 3600 FO 36 36 1752 3599 FO 36 36 1752 3597 FO 36 36 1753 3594 FO 36 36 1753 3592 FO 36 36 1754 3593 FO 36 36 1754 3595 FO 36 36 1755 3595 FO 36 36 1755 3593 FO 36 36 1756 3590 FO 36 36 1756 3589 FO 36 36 1756 3588 FO 36 36 1757 3585 FO 36 36 1757 3587 FO 36 36 1758 3587 FO 36 36 1758 3583 FO 36 36 1759 3579 FO 36 36 1759 3576 FO 36 36 1760 3575 FO 36 36 1761 3573 FO 36 36 1761 3571 FO 36 36 1761 3567 FO 36 36 1762 3567 FO 36 36 1762 3565 FO 36 36 1763 3563 FO 36 36 1763 3556 FO 36 36 1764 3549 FO 36 36 1764 3544 FO 36 36 1765 3537 FO 36 36 1765 3532 FO 36 36 1766 3530 FO 36 36 1766 3527 FO 36 36 1766 3525 FO 36 36 1767 3523 FO 36 36 1767 3518 FO 36 36 1768 3515 FO 36 36 1768 3510 FO 36 36 1769 3505 FO 36 36 1769 3501 FO 36 36 1770 3499 FO 36 36 1770 3494 FO 36 36 1771 3492 FO 36 36 1771 3489 FO 36 36 1771 3487 FO 36 36 1772 3485 FO 36 36 1772 3483 FO 36 36 1773 3482 FO 36 36 1773 3480 FO 36 36 1774 3478 FO 36 36 1774 3476 FO 36 36 1775 3472 FO 36 36 1775 3466 FO 36 36 1776 3464 FO 36 36 1777 3460 FO 36 36 1777 3456 FO 36 36 1777 3452 FO 36 36 1778 3450 FO 36 36 1778 3449 FO 36 36 1779 3449 FO 36 36 1779 3446 FO 36 36 1780 3448 FO 36 36 1780 3447 FO 36 36 1781 3446 FO 36 36 1781 3444 FO 36 36 1782 3443 FO 36 36 1783 3440 FO 36 36 1783 3438 FO 36 36 1784 3439 FO 36 36 1784 3437 FO 36 36 1785 3437 FO 36 36 1785 3436 FO 36 36 1786 3436 FO 36 36 1786 3439 FO 36 36 1787 3439 FO 36 36 1787 3438 FO 36 36 1787 3437 FO 36 36 1788 3440 FO 36 36 1789 3439 FO 36 36 1789 3438 FO 36 36 1790 3439 FO 36 36 1790 3437 FO 36 36 1791 3437 FO 36 36 1791 3436 FO 36 36 1792 3439 FO 36 36 1792 3438 FO 36 36 1793 3435 FO 36 36 1793 3433 FO 36 36 1794 3430 FO 36 36 1795 3427 FO 36 36 1795 3425 FO 36 36 1796 3423 FO 36 36 1796 3419 FO 36 36 1797 3418 FO 36 36 1797 3417 FO 36 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3392 FO 36 36 6877 3391 FO 36 36 6878 3388 FO 36 36 6878 3387 FO 36 36 6879 3385 FO 36 36 6879 3383 FO 36 36 6879 3382 FO 36 36 6880 3380 FO 36 36 6880 3379 FO 36 36 6881 3378 FO 36 36 6881 3379 FO 36 36 6882 3379 FO 36 36 6882 3380 FO 36 36 6883 3380 FO 36 36 6883 3379 FO 36 36 6884 3381 FO 36 36 6884 3384 FO 36 36 6884 3387 FO 36 36 6885 3389 FO 36 36 6885 3391 FO 36 36 6886 3392 FO 36 36 6886 3394 FO 36 36 6887 3395 FO 36 36 6888 3395 FO 36 36 6888 3396 FO 36 36 6889 3398 FO 36 36 6889 3400 FO 36 36 6890 3400 FO 36 36 6890 3401 FO 36 36 6891 3404 FO 36 36 6891 3407 FO 36 36 6892 3411 FO 36 36 6892 3415 FO 36 36 6893 3417 FO 36 36 6893 3420 FO 36 36 6894 3423 FO 36 36 6894 3427 FO 36 36 6894 3431 FO 36 36 6895 3434 FO 36 36 6895 3435 FO gs 1429 159 5467 3938 rc 5467 0 1429 3341 2 MP stroke 5467 0 1429 3537 2 MP stroke gr 0 sg 3149 4462 mt (number of moves in units of 10) s %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 108 FMSR 5110 4390 mt (6) s %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 144 FMSR 1023 3956 mt -90 rotate (autocorrelation of volume fraction, and standard deviation) s 90 rotate end %%Color Dict eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument @endspecial 179 x Fn(Figure)28 b(6a.)42 b(Plot)28 b(of)g(biased)h (auto)s(correlation)e(\(for)i(8000)e(particles\))h(v)m(ersus)i(n)m(um)m (b)s(er)f(of)g(mo)m(v)m(es,)138 2661 y(with)k(horizon)m(tal)g(lines)g (denoting)h(one)g(standard)g(deviation)e(a)m(w)m(a)m(y)h(from)h(zero.) 138 5064 y @beginspecial -24 @llx 203 @lly 637 @urx 587 @ury 3690 @rwi @setspecial %%BeginDocument: initialization2.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: MATLAB, The Mathworks, Inc. Version 7.6.0.324 (R2008a). Operating System: Linux 2.6.20-16-386 #2 Wed May 23 01:42:57 UTC 2007 i686. %%Title: /home/daristoff/initialization2.eps %%CreationDate: 08/01/2008 15:53:00 %%DocumentNeededFonts: Helvetica %%+ Courier %%DocumentProcessColors: Cyan Magenta Yellow Black %%LanguageLevel: 2 %%Pages: 1 %%BoundingBox: -24 203 637 587 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s {show newpath} bdef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinewidth 2 div 0 360 arc fill PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup 3 mul string currentfile 3 index 0 eq {/ASCIIHexDecode filter} {/ASCII85Decode filter 3 index 2 eq {/RunLengthDecode filter} if } ifelse exch readstring pop dup 0 3 index getinterval /rbmap xdef dup 2 index dup getinterval /gbmap xdef 1 index dup 2 mul exch getinterval /bbmap xdef pop pop}bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform rbmap gbmap bbmap true 3 colorimage gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: -24 203 637 587 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode -0288 7044 csm 0 0 7943 4605 rc 85 dict begin %Colortable dictionary /c0 { 0.000000 0.000000 0.000000 sr} bdef /c1 { 1.000000 1.000000 1.000000 sr} bdef /c2 { 0.900000 0.000000 0.000000 sr} bdef /c3 { 0.000000 0.820000 0.000000 sr} bdef /c4 { 0.000000 0.000000 0.800000 sr} bdef /c5 { 0.910000 0.820000 0.320000 sr} bdef /c6 { 1.000000 0.260000 0.820000 sr} bdef /c7 { 0.000000 0.820000 0.820000 sr} bdef c0 1 j 1 sg 0 0 7944 4606 rf 6 w 0 3938 5466 0 0 -3938 1429 4096 4 MP PP -5466 0 0 3938 5466 0 0 -3938 1429 4096 5 MP stroke 4 w DO SO 6 w 0 sg 1429 4096 mt 6895 4096 L 1429 158 mt 6895 158 L 1429 4096 mt 1429 158 L 6895 4096 mt 6895 158 L 1429 4096 mt 6895 4096 L 1429 4096 mt 1429 158 L 1429 4096 mt 1429 4041 L 1429 158 mt 1429 213 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 144 FMSR 1389 4264 mt (0) s 1975 4096 mt 1975 4041 L 1975 158 mt 1975 213 L 1855 4264 mt (100) s 2522 4096 mt 2522 4041 L 2522 158 mt 2522 213 L 2402 4264 mt (200) s 3068 4096 mt 3068 4041 L 3068 158 mt 3068 213 L 2948 4264 mt (300) s 3615 4096 mt 3615 4041 L 3615 158 mt 3615 213 L 3495 4264 mt (400) s 4162 4096 mt 4162 4041 L 4162 158 mt 4162 213 L 4042 4264 mt (500) s 4708 4096 mt 4708 4041 L 4708 158 mt 4708 213 L 4588 4264 mt (600) s 5255 4096 mt 5255 4041 L 5255 158 mt 5255 213 L 5135 4264 mt (700) s 5801 4096 mt 5801 4041 L 5801 158 mt 5801 213 L 5681 4264 mt (800) s 6348 4096 mt 6348 4041 L 6348 158 mt 6348 213 L 6228 4264 mt (900) s 6895 4096 mt 6895 4041 L 6895 158 mt 6895 213 L 6735 4264 mt (1000) s 1429 4096 mt 1483 4096 L 6895 4096 mt 6840 4096 L 1110 4149 mt (-0.2) s 1429 3439 mt 1483 3439 L 6895 3439 mt 6840 3439 L 1314 3492 mt (0) s 1429 2783 mt 1483 2783 L 6895 2783 mt 6840 2783 L 1194 2836 mt (0.2) s 1429 2127 mt 1483 2127 L 6895 2127 mt 6840 2127 L 1194 2180 mt (0.4) s 1429 1471 mt 1483 1471 L 6895 1471 mt 6840 1471 L 1194 1524 mt (0.6) s 1429 815 mt 1483 815 L 6895 815 mt 6840 815 L 1194 868 mt (0.8) s 1429 158 mt 1483 158 L 6895 158 mt 6840 158 L 1314 211 mt (1) s 1429 4096 mt 6895 4096 L 1429 158 mt 6895 158 L 1429 4096 mt 1429 158 L 6895 4096 mt 6895 158 L gs 1429 159 5467 3938 rc gr /c8 { 0.000000 0.000000 1.000000 sr} bdef c8 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3448 FO 36 36 3741 3449 FO 36 36 3746 3454 FO 36 36 3752 3456 FO 36 36 3757 3458 FO 36 36 3762 3463 FO 36 36 3768 3466 FO 36 36 3773 3469 FO 36 36 3779 3472 FO 36 36 3784 3473 FO 36 36 3790 3473 FO 36 36 3795 3474 FO 36 36 3801 3475 FO 36 36 3806 3473 FO 36 36 3812 3477 FO 36 36 3817 3475 FO 36 36 3823 3471 FO 36 36 3828 3470 FO 36 36 3834 3470 FO 36 36 3839 3470 FO 36 36 3844 3469 FO 36 36 3850 3468 FO 36 36 3855 3466 FO 36 36 3861 3464 FO 36 36 3866 3461 FO 36 36 3872 3461 FO 36 36 3877 3459 FO 36 36 3883 3457 FO 36 36 3888 3455 FO 36 36 3894 3453 FO 36 36 3899 3454 FO 36 36 3905 3447 FO 36 36 3910 3442 FO 36 36 3916 3438 FO 36 36 3921 3434 FO 36 36 3926 3430 FO 36 36 3932 3431 FO 36 36 3937 3429 FO 36 36 3943 3426 FO 36 36 3948 3423 FO 36 36 3954 3419 FO 36 36 3959 3417 FO 36 36 3965 3415 FO 36 36 3970 3413 FO 36 36 3976 3413 FO 36 36 3981 3412 FO 36 36 3987 3413 FO 36 36 3992 3416 FO 36 36 3998 3418 FO 36 36 4003 3419 FO 36 36 4008 3422 FO 36 36 4014 3421 FO 36 36 4019 3419 FO 36 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eop end %%Page: 13 14 TeXDict begin 13 13 bop -416 4486 a @beginspecial -24 @llx 102 @lly 637 @urx 690 @ury 4797 @rwi @setspecial %%BeginDocument: sigma_biased-edit.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: MATLAB, The Mathworks, Inc. Version 7.6.0.324 (R2008a). Operating System: Linux 2.6.20-16-386 #2 Wed May 23 01:42:57 UTC 2007 i686. %%Title: /home/daristoff/sigma_biased-edit.eps %%CreationDate: 08/01/2008 15:20:24 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%LanguageLevel: 2 %%Pages: 1 %%BoundingBox: -24 102 637 690 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s {show newpath} bdef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinewidth 2 div 0 360 arc fill PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup 3 mul string currentfile 3 index 0 eq {/ASCIIHexDecode filter} {/ASCII85Decode filter 3 index 2 eq {/RunLengthDecode filter} if } ifelse exch readstring pop dup 0 3 index getinterval /rbmap xdef dup 2 index dup getinterval /gbmap xdef 1 index dup 2 mul exch getinterval /bbmap xdef pop pop}bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform rbmap gbmap bbmap true 3 colorimage gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: -24 102 637 690 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode -0288 8280 csm 0 0 7943 7055 rc 85 dict begin %Colortable dictionary /c0 { 0.000000 0.000000 0.000000 sr} bdef /c1 { 1.000000 1.000000 1.000000 sr} bdef /c2 { 0.900000 0.000000 0.000000 sr} bdef /c3 { 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32 1 34 0 34 1 34 1 36 0 36 1 36 0 38 1 38 0 39 1 40 0 41 1 41 0 42 1 44 1 44 0 45 1 47 0 47 1 49 0 49 1 46 1467 299 214 MP stroke gr 0 sg 3732 6889 mt (particle number) s 985 5286 mt -90 rotate (standard deviation of volume fraction, 90% confidence inter\ vals) s 90 rotate end %%Color Dict eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument @endspecial 138 4726 a Fn(Figure)44 b(7.)76 b(Plot)43 b(of)h(the)h(standard)f(deviation)g(of)g(the)g(v)m(olume)g(fraction)g (v)m(ersus)h(n)m(um)m(b)s(er)h(of)138 4845 y(squares,)34 b(using)f Fm(f)828 4860 y Fi(2)906 4845 y Fn(for)g(con\014dence)j(in)m (terv)-6 b(als.)1933 5519 y(13)p eop end %%Page: 14 15 TeXDict begin 14 14 bop -416 4486 a @beginspecial -24 @llx 102 @lly 637 @urx 690 @ury 4797 @rwi @setspecial %%BeginDocument: sigma_biased_log-edit.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: MATLAB, The Mathworks, Inc. 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Operating System: Linux 2.6.20-16-386 #2 Wed May 23 01:42:57 UTC 2007 i686. %%Title: /home/daristoff/sigma_biased_log-edit.eps %%CreationDate: 08/01/2008 15:20:18 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%LanguageLevel: 2 %%Pages: 1 %%BoundingBox: -24 102 637 690 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s {show newpath} bdef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinewidth 2 div 0 360 arc fill PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef 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restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 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Operating System: Linux 2.6.20-16-386 #2 Wed May 23 01:42:57 UTC 2007 i686. %%Title: /home/daristoff/sigma_unbiased_log-edit.eps %%CreationDate: 08/01/2008 15:20:40 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%LanguageLevel: 2 %%Pages: 1 %%BoundingBox: -24 102 637 690 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s {show newpath} bdef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point 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/FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef 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add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds 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1 2 0 3 1 2 0 3 1 2 0 3 1 2 0 3 1 3 1 2 0 3 1 2 0 3 1 3 0 2 1 3 0 3 1 3 0 2 1 3 1 3 0 2 1 3 0 3 1 3 0 3 1 3 0 2 1 3 0 3 1 3 0 3 1 3 1 3 0 3 1 3 0 3 1 3 0 3 1 3 0 3 1 3 0 3 1 3 0 3 1 3 1 3 0 3 1 4 0 3 1 3 0 3 1 3 0 4 1 3 0 3 1 3 1 4 0 3 1 3 0 4 1 3 0 4 1 3 0 3 1 4 0 3 1 4 0 3 1 4 1 4 0 3 1 4 0 3 1 4 0 4 1 3 0 4 1 4 0 4 1 3 1 4 0 4 1 4 0 4 1 4 0 3 1 4 0 4 1 4 0 4 1 4 0 4 1 4 1 5 0 4 1 4 0 4 1 4 0 4 1 5 0 4 1 4 0 5 1 4 1 4 0 5 1 4 0 5 1 4 0 5 1 4 0 5 1 5 0 4 1 5 0 5 1 5 1 4 0 5 1 5 0 5 1 5 0 5 1 5 0 5 1 5 0 5 1 5 0 5 1 6 1 5 0 5 1 6 0 5 1 5 0 6 1 5 0 6 1 5 0 6 1 6 1 5 0 6 1 6 0 6 1 6 0 6 1 6 0 6 1 6 0 6 1 6 0 6 1 7 1 6 0 6 1 7 0 6 1 7 0 6 1 7 0 7 1 7 0 6 1 7 1 7 0 7 1 7 0 8 1 7 0 7 1 7 0 8 1 7 0 8 1 8 0 7 1 8 1 8 0 8 1 8 0 8 1 8 0 8 1 8 0 9 1 8 0 9 1 9 0 8 1 9 1 9 0 9 1 9 0 9 1 10 0 9 1 10 0 9 1 10 0 10 1 10 1 10 0 10 1 10 0 11 1 10 0 11 1 11 0 10 1 11 0 12 1 11 0 11 1 12 1 12 0 11 1 12 0 13 1 12 0 12 1 13 0 13 1 13 0 13 1 13 1 14 0 14 1 14 0 14 1 14 0 14 1 15 0 15 1 15 0 16 1 15 0 16 1 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TeXDict begin 18 18 bop -416 4486 a @beginspecial -24 @llx 102 @lly 637 @urx 690 @ury 4797 @rwi @setspecial %%BeginDocument: mu_unbiased-edit.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: MATLAB, The Mathworks, Inc. 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Operating System: Linux 2.6.20-16-386 #2 Wed May 23 01:42:57 UTC 2007 i686. %%Title: /home/daristoff/mu_unbiased-edit.eps %%CreationDate: 08/01/2008 15:20:54 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%LanguageLevel: 2 %%Pages: 1 %%BoundingBox: -24 102 637 690 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s {show newpath} bdef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinewidth 2 div 0 360 arc fill PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 get sub exch } bdef /tri_to_matrix { 2 0 asub 3 1 asub 4 0 asub 5 1 asub dup 0 get exch 1 get 7 -1 roll astore } bdef /compute_transform { dmat dtri tri_to_matrix tmat1 invertmatrix smat stri tri_to_matrix tmat2 concatmatrix } bdef /ds {stri astore pop} bdef /dt {dtri astore pop} bdef /db {2 copy /cols xdef /rows xdef mul dup 3 mul string currentfile 3 index 0 eq {/ASCIIHexDecode filter} {/ASCII85Decode filter 3 index 2 eq {/RunLengthDecode filter} if } ifelse exch readstring pop dup 0 3 index getinterval /rbmap xdef dup 2 index dup getinterval /gbmap xdef 1 index dup 2 mul exch getinterval /bbmap xdef pop pop}bdef /it {gs np dtri aload pop moveto lineto lineto cp c cols rows 8 compute_transform rbmap gbmap bbmap true 3 colorimage gr}bdef /il {newpath moveto lineto stroke}bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: -24 102 637 690 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode -0288 8280 csm 0 0 7943 7055 rc 85 dict begin %Colortable dictionary /c0 { 0.000000 0.000000 0.000000 sr} bdef /c1 { 1.000000 1.000000 1.000000 sr} bdef /c2 { 0.900000 0.000000 0.000000 sr} bdef /c3 { 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1547 925 L 6936 925 mt 6873 925 L 1120 973 mt (0.768) s 1485 305 mt 1547 305 L 6936 305 mt 6873 305 L 1194 353 mt (0.77) s 1485 6506 mt 6936 6506 L 1485 305 mt 6936 305 L 1485 6506 mt 1485 305 L 6936 6506 mt 6936 305 L gs 1485 305 5452 6202 rc /c8 { 0.000000 0.000000 1.000000 sr} bdef c8 0 445 1538 2041 2 MP stroke 97 0 1490 2041 2 MP stroke 97 0 1490 2486 2 MP stroke 0 301 1591 2714 2 MP stroke 97 0 1542 2714 2 MP stroke 97 0 1542 3015 2 MP stroke 0 205 1645 3143 2 MP stroke 97 0 1596 3143 2 MP stroke 97 0 1596 3348 2 MP stroke 0 111 1710 3552 2 MP stroke 97 0 1661 3552 2 MP stroke 97 0 1661 3663 2 MP stroke 0 111 1755 3669 2 MP stroke 97 0 1707 3669 2 MP stroke 97 0 1707 3780 2 MP stroke 0 132 1812 3862 2 MP stroke 97 0 1763 3862 2 MP stroke 97 0 1763 3994 2 MP stroke 0 134 1861 3927 2 MP stroke 97 0 1812 3927 2 MP stroke 97 0 1812 4061 2 MP stroke 0 177 1915 3994 2 MP stroke 97 0 1867 3994 2 MP stroke 97 0 1867 4171 2 MP stroke 0 144 1982 4093 2 MP stroke 97 0 1934 4093 2 MP stroke 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b(38)512 b(262)555 3496 y(913)470 b(2)445 b(0.2)385 b(77)536 b(75)512 b(132)555 3606 y(996)447 b(12)c(1)436 b(18)536 b(18)512 b(687)547 3715 y(1001)409 b(12)443 b(1)436 b(16)536 b(16)512 b(755)547 3825 y(1955)409 b(12)443 b(1)436 b(38)536 b(38)512 b(318)547 3934 y(2980)409 b(12)443 b(1)436 b(56)536 b(56)512 b(218)547 4044 y(3003)409 b(12)443 b(1)436 b(51)536 b(54)512 b(230)547 4153 y(3933)409 b(12)443 b(1)436 b(76)536 b(78)512 b(156)547 4263 y(4008)409 b(12)443 b(1)428 b(101)498 b(88)512 b(135)547 4373 y(4995)409 b(12)443 b(1)428 b(191)491 b(177)496 b(67)547 4482 y(5908)409 b(12)443 b(1)428 b(179)491 b(100)473 b(120)547 4592 y(6030)409 b(12)443 b(1)428 b(139)491 b(151)496 b(80)547 4701 y(7037)409 b(12)443 b(1)428 b(220)491 b(290)496 b(41)547 4811 y(7161)409 b(12)443 b(1)428 b(199)491 b(186)496 b(47)547 4921 y(8015)409 b(12)443 b(1)428 b(131)491 b(126)496 b(95)547 5030 y(8991)409 b(12)443 b(1)428 b(282)491 b(355)496 b(33)547 5140 y(8995)409 b(12)443 b(1)428 b(565)491 b(609)496 b(19)1933 5519 y Fn(20)p eop end %%Page: 21 22 TeXDict begin 21 21 bop 1821 219 a Fn(T)-8 b(able)33 b(3)1622 459 y(V)-8 b(olume)33 b(F)-8 b(raction)791 771 y Fe(n)m(um)m(b)s(er)31 b(of)123 b(sample)31 b(v)-5 b(alue)167 b(end)31 b(p)s(oin)m(ts)g(of)212 b(end)31 b(p)s(oin)m(ts)g(of)848 881 y(squares)818 b(95\045)31 b(con\014dence)124 b(95\045)30 b(con\014dence)804 990 y(in)g(pac)m(king)829 b(in)m(terv)-5 b(al)30 b(for)294 b(in)m(terv)-5 b(al)30 b(for)2055 1100 y(true)g(v)-5 b(alue,)309 b(true)31 b(v)-5 b(alue,)2105 1209 y(using)31 b Fd(f)2391 1219 y Fb(1)2842 1209 y Fe(using)g Fd(f)3128 1219 y Fb(2)950 1428 y Fe(99)426 b(0.7637)268 b(0.7637)p Fa(\006)p Fe(0.0007)153 b(0.7637)p Fa(\006)p Fe(0.0007)926 1538 y(100)404 b(0.7631)268 b(0.7631)p Fa(\006)p Fe(0.0007)153 b(0.7631)p Fa(\006)p Fe(0.0007)926 1648 y(195)404 b(0.7617)268 b(0.7617)p Fa(\006)p Fe(0.0005)153 b(0.7617)p Fa(\006)p Fe(0.0005)926 1757 y(205)404 b(0.7608)268 b(0.7608)p Fa(\006)p Fe(0.0005)153 b(0.7608)p Fa(\006)p Fe(0.0005)926 1867 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b(0.7558)p Fa(\006)p Fe(0.0003)153 b(0.7558)p Fa(\006)p Fe(0.0003)919 4168 y(4995)365 b(0.7555)268 b(0.7555)p Fa(\006)p Fe(0.0004)153 b(0.7555)p Fa(\006)p Fe(0.0005)919 4278 y(5908)365 b(0.7549)268 b(0.7549)p Fa(\006)p Fe(0.0003)153 b(0.7549)p Fa(\006)p Fe(0.0003)919 4387 y(6030)365 b(0.7551)268 b(0.7551)p Fa(\006)p Fe(0.0004)153 b(0.7551)p Fa(\006)p Fe(0.0003)919 4497 y(7037)365 b(0.7545)268 b(0.7545)p Fa(\006)p Fe(0.0005)153 b(0.7545)p Fa(\006)p Fe(0.0004)919 4607 y(7161)365 b(0.7550)268 b(0.7550)p Fa(\006)p Fe(0.0005)153 b(0.7550)p Fa(\006)p Fe(0.0007)919 4716 y(8015)365 b(0.7551)268 b(0.7551)p Fa(\006)p Fe(0.0004)153 b(0.7551)p Fa(\006)p Fe(0.0004)919 4826 y(8991)365 b(0.7551)268 b(0.7551)p Fa(\006)p Fe(0.0004)153 b(0.7551)p Fa(\006)p Fe(0.0012)919 4935 y(8995)365 b(0.7550)450 b(none)564 b(none)1933 5519 y Fn(21)p eop end %%Page: 22 23 TeXDict begin 22 22 bop 1821 219 a Fn(T)-8 b(able)33 b(4)1154 459 y(Standard)h(deviation)e(of)i(v)m(olume)f(fraction)791 771 y Fe(n)m(um)m(b)s(er)e(of)123 b(sample)31 b(v)-5 b(alue)167 b(end)31 b(p)s(oin)m(ts)g(of)212 b(end)31 b(p)s(oin)m(ts)g(of)848 881 y(squares)818 b(90\045)31 b(con\014dence)124 b(90\045)30 b(con\014dence)804 990 y(in)g(pac)m(king)829 b(in)m(terv)-5 b(al)30 b(for)294 b(in)m(terv)-5 b(al)30 b(for)2055 1100 y(true)g(v)-5 b(alue,)309 b(true)31 b(v)-5 b(alue,)2105 1209 y(using)31 b Fd(f)2391 1219 y Fb(1)2842 1209 y Fe(using)g Fd(f)3128 1219 y Fb(2)950 1428 y Fe(99)426 b(0.0160)268 b(0.0160)p Fa(\006)p Fe(0.0005)153 b(0.0160)p Fa(\006)p Fe(0.0005)926 1538 y(100)404 b(0.0157)268 b(0.0157)p Fa(\006)p Fe(0.0006)153 b(0.0157)p Fa(\006)p Fe(0.0006)926 1648 y(195)404 b(0.0110)268 b(0.0110)p Fa(\006)p Fe(0.0004)153 b(0.0110)p Fa(\006)p Fe(0.0004)926 1757 y(205)404 b(0.0108)268 b(0.0108)p Fa(\006)p Fe(0.0004)153 b(0.0108)p Fa(\006)p Fe(0.0004)926 1867 y(294)404 b(0.0090)268 b(0.0090)p Fa(\006)p Fe(0.0003)153 b(0.0090)p Fa(\006)p Fe(0.0003)926 1976 y(294)404 b(0.0090)268 b(0.0090)p Fa(\006)p 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Fa(\006)p Fe(0.0002)919 4278 y(5908)365 b(0.0021)268 b(0.0021)p Fa(\006)p Fe(0.0002)153 b(0.0021)p Fa(\006)p Fe(0.0002)919 4387 y(6030)365 b(0.0020)268 b(0.0020)p Fa(\006)p Fe(0.0002)153 b(0.0020)p Fa(\006)p Fe(0.0002)919 4497 y(7037)365 b(0.0018)268 b(0.0019)p Fa(\006)p Fe(0.0002)153 b(0.0019)p Fa(\006)p Fe(0.0002)919 4607 y(7161)365 b(0.0019)268 b(0.0020)p Fa(\006)p Fe(0.0003)153 b(0.0021)p Fa(\006)p Fe(0.0004)919 4716 y(8015)365 b(0.0016)268 b(0.0017)p Fa(\006)p Fe(0.0002)153 b(0.0017)p Fa(\006)p Fe(0.0002)919 4826 y(8991)365 b(0.0017)268 b(0.0017)p Fa(\006)p Fe(0.0003)153 b(0.0021)p Fa(\006)p Fe(0.0008)919 4935 y(8995)365 b(0.0016)450 b(none)548 b(none)1933 5519 y Fn(22)p eop end %%Page: 23 24 TeXDict begin 23 23 bop 1821 219 a Fn(T)-8 b(able)33 b(5)303 459 y(F)-8 b(raction)32 b(of)i(times)f(the)h(giv)m(en)f(batc)m (h)h(size)f(giv)m(es)g(acceptable)i(con\014dence)g(in)m(terv)-6 b(al)33 b(for)350 578 y(giv)m(en)h(segmen)m(t)g(of)f(total)f(data)h(of) h(long)e(runs,)i(using)g(un)m(biased)h(auto)s(correlation)d Fm(f)3571 593 y Fi(1)1161 987 y Fe(20-100)207 b(100-200)185 b(200-300)f(300-400)h(400-500)f(500-600)1154 1097 y(mixing)217 b(mixing)f(mixing)h(mixing)f(mixing)h(mixing)1131 1206 y(times)30 b(of)171 b(times)31 b(of)171 b(times)30 b(of)171 b(times)31 b(of)171 b(times)30 b(of)171 b(times)31 b(of)1092 1316 y(total)f(data)92 b(total)30 b(data)92 b(total)31 b(data)92 b(total)30 b(data)92 b(total)31 b(data)92 b(total)30 b(data)p 1045 1426 2903 4 v 1041 1535 4 110 v 826 1615 a(1-5)p 1041 1645 V 214 w(0.0849)236 b(0.0867)f(0.1119)h(0.1191)f (0.1938)h(0.2082)186 1725 y(n)m(um)m(b)s(er)32 b(of)207 b(6-10)p 1041 1754 V 191 w(0.9410)236 b(0.9394)f(0.9830)h(1.0000)f (1.0000)h(1.0000)186 1834 y(mixing)319 b(11-15)p 1041 1864 V 168 w(0.9648)236 b(0.9231)f(0.9656)h(1.0000)f(1.0000)h(1.0000) 186 1944 y(times)378 b(16-20)p 1041 1974 V 168 w(0.9524)236 b(0.9095)f(0.9777)h(0.9879)f(1.0000)h(1.0000)186 2053 y(p)s(er)31 b(batc)m(h)210 b(21-31)p 1041 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4 110 v 826 4388 a(1-5)p 1041 4418 V 214 w(0.0833)236 b(0.0924)f(0.1182)h(0.1259)f (0.2006)h(0.2326)186 4497 y(n)m(um)m(b)s(er)32 b(of)207 b(6-10)p 1041 4527 V 191 w(0.9245)236 b(0.9784)f(0.9805)h(0.9552)f (0.9762)h(1.0000)186 4607 y(mixing)319 b(11-15)p 1041 4637 V 168 w(0.9107)236 b(0.9451)f(0.9607)h(0.9524)f(0.9707)h(1.0000) 186 4717 y(times)378 b(16-20)p 1041 4746 V 168 w(0.9728)236 b(0.9212)f(0.9745)h(0.9493)f(0.9655)h(1.0000)186 4826 y(p)s(er)31 b(batc)m(h)210 b(21-31)p 1041 4856 V 168 w(0.9486)236 b(0.9059)f(0.9592)h(0.9547)f(0.9744)h(1.0000)780 4936 y(31-40)p 1041 4966 V 168 w(0.9780)g(0.9190)f(0.9592)h(0.9704)f (0.9852)h(1.0000)780 5045 y(41-51)p 1041 5075 V 168 w(0.9000)g(0.8639)f (0.9441)h(0.9565)f(0.9814)h(1.0000)1933 5519 y Fn(23)p eop end %%Page: 24 25 TeXDict begin 24 24 bop 138 219 a Fo(Ac)m(kno)m(wledgemen)m(ts)p Fn(.)38 b(W)-8 b(e)25 b(gratefully)f(ac)m(kno)m(wledge)i(useful)g (discussions)g(with)e(P)-8 b(.)24 b(Diaconis,)138 339 y(W.D.)33 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y(567-573.)177 4046 y([S])49 b(G.D.)33 b(Scott,)g(P)m(ac)m(king)g(of)g(spheres,)i (Nature)e(\(London\))h(188)f(\(1960\))e(908-909.)99 4165 y([SK])50 b(G.D.)38 b(Scott)g(and)h(D.M.)f(Kilgour,)h(The)g(densit)m(y) f(of)h(random)f(close)h(pac)m(king)f(of)g(spheres,)337 4285 y(Brit.)43 b(J.)33 b(Appl.)44 b(Ph)m(ys.)h(\(J.)32 b(Ph)m(ys.)45 b(D\))33 b(2)g(\(1969\))f(863-866.)102 4404 y([SN])49 b(M.)37 b(Sc)m(hr\177)-50 b(oter,)38 b(S.)f(N\177)-50 b(agle,)36 b(C.)g(Radin)i(and)f(H.L.)f(Swinney)-8 b(,)37 b(Phase)g(transition)f(in)h(a)f(static)337 4524 y(gran)m(ular)e (system,)f(Europh)m(ys.)44 b(Lett.)g(78)33 b(\(2007\))f(44004.)88 4643 y([TT])49 b(S.)42 b(T)-8 b(orquato,)42 b(T.M.)f(T)-8 b(rusk)m(ett)41 b(and)h(P)-8 b(.G.)41 b(Deb)s(enedetti,)j(Is)e(random)f (close)h(pac)m(king)g(of)337 4763 y(spheres)35 b(w)m(ell)e(de\014ned?,) i(Ph)m(ys.)44 b(Rev.)h(Lett.)f(84)32 b(\(2000\))g(2064-2067.)1933 5519 y(24)p eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF 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