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Department of Mathematics University of Texas 1 University Station C1200 Austin, Texas 78712-0257 Office: 512 471 1138 ..... Fax: 512 471 9038 E-Mail: og@math.utexas.edu |
| Research Interests | My general interests are in computational and applied mathematics with an emphasis on classical continuum mechanics. My current efforts are focussed on modeling the mechanical properties of DNA at various length scales. Keywords: modeling, numerical analysis, differential equations, integral equations, geometry of curves and surfaces. |
| Education |
Doctor of Philosophy in Applied Mechanics Stanford University, June 1996 Advisors: Juan C. Simo and Andrew M. Stuart Thesis Title: Design and analysis of conserving integrators for nonlinear hamiltonian systems with symmetry Master of Science in Scientific Computing & Computational Mathematics Stanford University, June 1996 Master of Science in Applied Mechanics Stanford University, June 1992 Bachelor of Science in Mechanical Engineering University of Texas at Austin, May 1991 with Highest Honors |
| Grants & Awards |
NSF Grant DMS-0706951, (PI, $166,898) 2007-2010 NSF Grant DMS-0405955, (PI, $142,000) 2004-2007 University Summer Research Award, (PI, $15,778) 2004 NSF Grant DMS-0322962, (Co-PI) 2003-2004 College of Natural Sciences Teaching Excellence Award, 2003 NSF Grant DMS-0102476, (PI, $102,000) 2001-2004 NSF Mathematical Sciences Postdoctoral Fellowship, 1997-2000 NSF Graduate Fellowship, Stanford University, 1992-1995 Stanford Graduate Fellowship, Stanford University, 1991 All-American Scholar, 1991 National Collegiate Engineering Award, 1991 Engineering Scholar, University of Texas at Austin, 1988,89,90,91 Texas Achievement Award, University of Texas at Austin, 1986,87,88,89 Texas Valedictorian Tuition Award, University of Texas at Austin, 1986 |
| Academic Positions |
2006 - present Associate Professor, Department of Mathematics, University of Texas, Austin. 2000 - 2006 Assistant Professor, Department of Mathematics, University of Texas, Austin. June 1999 - August 1999 Lecturer, Scientific Computing and Computational Mathematics Program, Department of Computer Science, Stanford University. October 1997 - August 2000 NSF Postdoctoral Fellow, Department of Mathematics, Swiss Federal Institute of Technology, Lausanne. April 1996 - December 1997 Postdoctoral Research Associate, Institute for Physical Science and Technology, University of Maryland, College Park. |
| Teaching Experience |
Fall 2006, 2004, 2003 Numerical treatment of differential equations, a first-year graduate course on the approximation of differential equations by numerical methods. The main methods considered are one-step and multi-step methods for systems of ordinary differential equations, and finite difference and finite element methods for elliptic, parabolic and hyperbolic partial differential equations. An analysis of consistency, stability and convergence is given for various classic methods applied to standard model problems. Spring 2006, 2002 Topics in computational modeling, a graduate course on various topics in the theory of rigid bodies and elastic filaments with applications. The goal is to derive, analyze and interpret the fundamental equations in the theory of rigid bodies and elastic filaments, discuss applications of these equations in the mechanical modeling of DNA and other physical systems, and develop numerical methods for their approximation. Special topics include the modeling of an elastic filament in an incompressible Stokes fluid and various optimal packing problems for filaments. Spring 2009, 2008, 2007, 2005, 2003 Mathematical modeling in science and engineering, a course designed primarily for advanced undergraduate and first-year graduate students who are interested in mathematical modeling, analysis and computation. The main topics include dimensional analysis and scaling, regular and singular perturbation methods, boundary layers and matched asymptotic expansions, optimization and calculus of variations, and stability and bifurcation theory. Spring 2009, 2004 Scientific computation in numerical analysis, a course designed primarily for advanced undergraduates with an interest in the theory and application of numerical methods and computer programming. The main topics include nonlinear algebraic equations, polynomial interpolation, numerical differentiation and integration, initial-value problems for ordinary differential equations, and direct methods for systems of linear algebraic equations. Fall 2002 Applied linear algebra, a course designed primarily for advanced undergraduates with an interest in linear algebra and its applications to dynamical systems and data analysis. The main topics include vector spaces, linear operators, eigenvalues, diagonalization, normal mode expansions, inner products, orthogonality and Fourier series. Fall 2005 Linear algebra and matrix theory, an undergraduate course designed primarily for math majors which covers a variety of topics in the theory of vectors and matrices and provides an introduction to proofs and abstract mathematics. The main topics include vectors and matrices, systems of linear equations, determinants and eigenvalues, vector spaces, linear transformations and orthogonality. Spring 2001 Advanced calculus for applications I, an undergraduate course on the theory of ordinary differential equations. The main topics include initial value problems, exact and approximate solution techniques, basic existence and uniqueness theorems, fundamental sets of solutions and linear independence, series expansions, Laplace transforms, boundary value problems, Fourier series and an introduction to partial differential equations. Spring 2008, 2007, 2006, 2005, 2004, 2003 Differential and integral calculus II, a second course in calculus that focuses on the concepts of infinite series, vectors and multivariable functions. The main topics include L'Hospital's rules for limits, infinite sequences and sums, power and Taylor series, polar coordinates and parametric equations for plane curves, algebra and calculus of vectors, and partial derivatives, gradients, optimization and integration of multivariable functions. Fall 2008, 2007, 2006, 2005, 2004, 2003, 2002, 2001, 2000 Differential and integral calculus I, a first course in calculus that focuses on the elementary theory of functions of one variable. The main topics include limits, continuity, derivatives and their applications, integrals and their applications, the fundamental theorems of calculus, and trigonometric, exponential and logarithmic functions. Fall 1999, Spring 2000 (Assistant) Analysis III and IV, a year-long advanced undergraduate course on multivariable calculus and vector analysis, Fourier series and transforms, and complex analysis. Summer 1999 Introduction to scientific computing, an undergraduate course on the theory and application of numerical methods. The main topics include nonlinear algebraic equations, polynomial interpolation, numerical differentiation and integration, initial-value problems for ordinary differential equations, and methods for systems of linear algebraic equations. Fall 1998, Spring 1999 (Assistant) Mathematical modeling of DNA, an advanced undergraduate course in mathematical modeling. The main topics include the theory of elastic rods; calculus of variations; DNA structure and topology; link, twist and writhe of framed curves; polymer physics. Spring 1997 Multivariable and vector calculus, a third-semester calculus course. The main topics include the algebra and calculus of vectors; partial derivatives, gradients, optimization and integration of multivariable functions; line and surface integrals; classic theorems of vector calculus. Fall 1996 (Assistant) Methods and models in applied mathematics, a first-year graduate course in methods of applied mathematics. The main topics include dimensional analysis and scaling; regular and singular perturbation methods; boundary layers and matched asymptotic expansions; Floquet theory and parametric resonance; calculus of variations. Fall 1995 (Assistant) Introduction to continuum mechanics, a first-year graduate course in the basic principles of continuum mechanics. The main topics include tensor analysis in three-dimensional Euclidean space; continuum mass and force distributions; deformation and strain; balance laws of mass, momentum, energy and entropy; the principle of material frame-indifference; ideal, compressible and viscous fluids; linear and nonlinear elastic solids; thermo-mechanical theories of fluids and solids. |
| Invited Presentations |
Applied Math RTG Seminar,
University of Texas, April 2009, Austin, TX Blackwell-Tapia Conference, November 2008, Research Triangle Park, NC Workshop on Multiscale Modeling and Analysis, University of Texas, August 2008, Austin, TX Mathematical Modeling in Biology Session, AMS Sectional Meeting, March 2008, Baton Rouge, LA Introduction to Research Seminar, University of Texas, March 2007, Austin, TX Summer Math Institute, Cornell University, July 2006, Ithaca, NY Mathematics of Biomolecules Conference, University of Warwick, January 2006, Coventry, England Math Majors Seminar, Trinity University, October 2005, San Antonio, TX Keynote Address: MAA Sectional Meeting, March 2005, Lawrence, KS Bioscience Initiative Lecture, University of Kansas, March 2005, Lawrence, KS Theoretical Chemistry Seminar, University of Texas, February 2005, Austin, TX SIAM Conference on Analysis of PDEs, December 2004, Houston, TX SACNAS National Conference, October 2004, Austin, TX Math in Science Lecture, ``Optimal shapes of curves with finite thickness,'' February 2004, Department of Mathematics, University of Texas, Austin, TX Mathematical Physics Seminar, ``Sedimentation dynamics of rigid filaments,'' February 2004, Department of Mathematics, University of Texas, Austin, TX Joint AMS-MAA-SIAM Meeting, ``Sedimentation dynamics of rigid filaments,'' January 2004, Phoenix, AZ Introduction to Research Seminar, ``Mathematical problems in the modeling of filaments and DNA,'' September 2003, Institute for Computational Engineering and Sciences, University of Texas, Austin, TX Workshop on knots, random walks and biomolecules, ``Sedimentation dynamics of rigid filaments,'' July 2003, Les Diableretes, Switzerland SIAM Minisymposium on Mechanical models of DNA, ``Extracting parameters for basepair models of DNA from molecular dynamics simulations,'' May 2003, Snowbird, UT AMS Special Session on Numerical Methods, Calculations and Simulations in Knot Theory and Its Applications, ``Sedimentation dynamics of rigid filaments,'' May 2003, San Francisco, CA AMS Special Session on Optimal Geometry of Curves and Surfaces, ``Optimal shapes of curves with finite thickness,'' University of Wisconsin, October 2002, Madison, WI Workshop on topology in condensed matter physics, ``Sedimentation dynamics of rigid, knotted filaments,'' Max Planck Institute for the Physics of Complex Systems, July 2002, Dresden, Germany Introduction to Research Seminar, ``Mathematical problems in the modeling of filaments and DNA'', Department of Mathematics, University of Texas, April 2002, Austin, TX Applied Math Colloquium, ``Optimal shapes of curves with finite thickness,'' Department of Mathematics, University of Arizona, March 2002, Tucson, AZ GADGET Seminar, ``Tight knots and optimal packing of curves with finite thickness,'' Department of Mathematics, University of Texas, November 2001, Austin, TX TACG Seminar, ``Some geometric problems inspired by bacteriophage DNA,'' Department of Mathematics, University of Texas, October 2001, Austin, TX Workshop on long molecules and thin films, ``Base-pair and continuum mechanics models of DNA,'' Center Stefano Franscini, July 2001, Ascona, Switzerland Applied Analysis Seminar, ``Global curvature and existence of ideal knots,'' Department of Mathematics, Swiss Federal Institute of Technology, June 2001, Lausanne, Switzerland Workshop on computational SDEs, ``Continuum mechanics models of DNA: constitutive relations, stochastics and invariant measures,'' Mathematics Research Centre, University of Warwick, March 2001, Conventry, United Kingdom. TACG Seminar, ``A straight interpretation of Benham's model for strand separation in duplex DNA,'' Department of Mathematics, University of Texas, December 2000, Austin, TX Geometry Seminar, ``Optimal shapes of elastic filaments with applications to biology,'' Department of Mathematics, University of Texas, November 2000, Austin, TX Mathematical Physics Seminar, ``Optimal shapes of elastic filaments with applications to biology,'' Department of Mathematics, University of Texas, September 2000, Austin, TX Applied Mathematics/Special Seminar, ``Global Curvature, Ideal Knots and Models of DNA Self-Contact,'' Numerical Analysis/Special Seminar, ``Energy and Momentum Conserving Algorithms in Continuum Mechanics,'' Department of Mathematics, University of Michigan, January 2000, Ann Arbor, MI Numerical Analysis Seminar, ``Formulations for the Numerical Treatment of Lagrangian DAEs and PDAEs,'' Department of Mathematics, University of Geneva, February 1999, Geneva, Switzerland Applied Analysis Seminar, ``Curves, Tubes and the Ideal Shapes of Knots,'' Department of Mathematics, Swiss Federal Institute of Technology, May 1998, Lausanne, Switzerland Applied Analysis Seminar, ``Mathematical Modeling of an Elastic Rod in a Viscous Solvent,'' Department of Mathematics, Swiss Federal Institute of Technology, December 1997, Lausanne, Switzerland Meeting on Numerical Dynamics and Elasticity, ``Time Integration Schemes for Constrained Elastic Continua,'' July 1996, Lawrence, KS SIAM Annual Meeting, ``Conserving Algorithms for General Models in Nonlinear Elasticity,'' July 1996, Kansas City, MO Computational Mechanics Seminar, ``Conserving Time Integration Schemes for Constrained Mechanical Systems,'' Division of Structural Engineering, Mechanics and Materials, Department of Civil Engineering, University of California, February 1996, Berkeley, CA Numerical Analysis Seminar, ``Conserving Time Integration Schemes for Constrained Mechanical Systems,'' Department of Mathematics, University of Kansas, February 1996, Lawrence, KS Numerical Analysis Seminar, ``Conserving Time Integration Schemes for Holonomically Constrained Mechanical Systems,'' Department of Mathematics, University of Maryland, February 1996, College Park, MD SciCADE Conference, ``Conserving Integrators for Nonlinear Hamiltonian Systems with Symmetry,'' March 1995, Stanford, CA Third SIAM Conference on Applications of Dynamical Systems, ``On the Stability of Symplectic and Conserving Schemes for Hamiltonian Systems,'' May 1995, Snowbird, UT Conference in honor of Robert L. Taylor, ``Recent Results on the Numerical Integration of Infinite-Dimensional Hamiltonian Systems,'' September 1994, Palo Alto, CA Meeting on Geometric Mechanics and Nonholonomic Systems, August 1994, Berkeley, CA |
| Publications |
Books O. Gonzalez & A. Stuart, A First Course in Continuum Mechanics, Cambridge Texts in Applied Mathematics, Cambridge University Press (2008). ISBN 978-0-521-88680-2 hardback, ISBN 978-0-521-71424-2 paperback, www.cambridge.org/9780521714242 (Complete solutions manual available to instructors) Articles Convergence of the Nystrom method for weakly singular integral equations, (with J. Li), in preparation. J. Walter, O. Gonzalez & J.H. Maddocks, On the stochastic modeling of rigid body systems with application to polymer dynamics, submitted. O. Gonzalez & J. Li, On the hydrodynamic diffusion of rigid particles of arbitrary shape with application to DNA, submitted. F. Lankas, O. Gonzalez, L.M. Heffler, G. Stoll, M. Moakher and J.H. Maddocks, On the parameterization of rigid base and basepair models of DNA from molecular dynamics simulations, Physical Chemistry Chemical Physics, 11 (2009) 10565-10588. DOI:10.1039/b919565n. O. Gonzalez & J. Li, On the Nystrom approximation of a new boundary integral formulation of exterior Stokes flow, preprint. O. Gonzalez, On stable, complete and singularity-free boundary integral formulations of exterior Stokes flow, SIAM Journal of Applied Mathematics 69 (2009) 933-958. O. Gonzalez & J. Li, Modeling the sequence-dependent diffusion coefficients of short DNA sequences, Journal of Chemical Physics 129 (2008) 165105. O. Gonzalez & J. Li, An analysis of the regularized stokeslet method, preprint. O. Gonzalez, A.B.A. Graf & J.H. Maddocks, Dynamics of a rigid body in a Stokes fluid, Journal of Fluid Mechanics 519 (2004) 133-160. O. Gonzalez & R. de la Llave, Existence of ideal knots, Journal of Knot Theory and Its Ramifications 12 (2003) 123-133. J.R. Banavar, O. Gonzalez, J.H. Maddocks & A. Maritan, Self-interactions of strands and sheets, Journal of Statistical Physics 110 (2003) 35-50. O. Gonzalez, J.H. Maddocks & J. Smutny, Curves, circles and spheres, Contemporary Mathematics 304 (2002) 195-215. O. Gonzalez, J.H. Maddocks, F. Schuricht & H. von der Mosel, Global curvature and self-contact of nonlinearly elastic curves and rods, Calculus of Variations and Partial Differential Equations 14 (2002) 29-68. O. Gonzalez & J.H. Maddocks, Extracting parameters for base-pair level models of DNA from molecular dynamics simulations, Theoretical Chemistry Accounts 106 (2001) 76-82. O. Gonzalez, J.H. Maddocks & R.L. Pego, Multi-multiplier ambient space formulations of constrained dynamical systems, with an application to elastodynamics, Archive for Rational Mechanics and Analysis 157 (2001) 285-323. O. Gonzalez, Exact energy-momentum conserving algorithms for general models in nonlinear elasticity, Computer Methods in Applied Mechanics and Engineering 190 (2000) 1763-1783. O. Gonzalez & J.H. Maddocks, Global curvature, thickness and the ideal shapes of knots, The Proceedings of the National Academy of Sciences, USA 96 (1999) 4769-4773. O. Gonzalez, Mechanical systems subject to holonomic constraints: differential-algebraic formulations and conservative integration, Physica D 132 (1999) 165-174. O. Gonzalez, D.J. Higham & A.M. Stuart, Qualitative properties of modified equations, IMA Journal of Numerical Analysis 19 (1999) 169-190. A. Stasiak, J. Dubochet, P. Furrer, O. Gonzalez & J. Maddocks, DNA: uncooked, al dente, or scotti?, Science 283 (1999) 1641. O. Gonzalez & A.M. Stuart, On the qualitative properties of modified equations, in Foundations of Computational Mathematics, edited by F. Cucker & M. Shub, Springer Verlag, Berlin (1997) 169-179. O. Gonzalez, Time integration and discrete hamiltonian systems, Journal of Nonlinear Science 6 (1996) 449-467. O. Gonzalez & J.C. Simo, On the stability of symplectic and energy-momentum algorithms for nonlinear hamiltonian systems with symmetry, Computer Methods in Applied Mechanics and Engineering 134 (1996) 197-222. J.C. Simo & O. Gonzalez, Recent results on the numerical integration of infinite-dimensional hamiltonian systems, in Recent Developments in Finite Element Analysis, edited by T.J.R. Hughes, E. Onate, and O.C. Zienkiewicz, International Center for Numerical Methods in Engineering, Barcelona, Spain (1994) 255-271. J.C. Simo & O. Gonzalez, Assessment of energy-momentum and symplectic schemes for stiff dynamical systems, American Society of Mechanical Engineers, proceedings of the ASME Winter Annual Meeting, New Orleans, Louisiana (1993) 1-12. |
| Students |
Jun Li (PhD, Computational and Applied Mathematics, UT-Austin, expected 2010) Joshua Fisher (MS, Mathematics, UT-Austin, May 2006) Mathias Carlen (Diplome, Physics, EPFL, Switzerland, Feb 2005) Changsub Lee (MS, Mathematics, UT-Austin, May 2004) Shubing Wang (MS, Mathematics, UT-Austin, Dec 2003) Michele Renehan (MS, Mathematics, UT-Austin, Aug 2003) Monica Shaw (MS, Computational and Applied Mathematics, UT-Austin, Aug 2003) Cecilia Diniz (MS, Mathematics, UT-Austin, May 2002) |
| Service |
NSF Review Panel, member (2008, 2003) Mathematics Graduate Studies Sub-Committee (GSSC) (2006-2007) University Admissions and Registration Committee (2006-2007) University Recruitment and Retention Committee (2005-2007) University Faculty Council, elected member (2005-2007) University Parking and Traffic Appeals Committee (2001-2005) CAM Graduate Studies Sub-Committee (GSSC) (2003) CAM Admissions Committee (2002, 2003) Peer reviewer for : |