Dates

Spekers

Title and Abstract

04/15/2015

Wednesday
11:00-12:00PM
POB 4.304

Gil Ariel,
(Mathematics,
Bar Ilan University)

Multiscale dynamics of marching locust swarms.

A key question in the study of collective animal motion is how the details of animal locomotion and interaction between individuals affect the macroscopic dynamics of the hoard, flock or swarm. Motivated by lab experiments with marching locust nymphs we suggest a generic principle, in which intermittent animal motion can be considered as a sequence of individual decisions, in which animals repeatedly reassess their situation and decide whether or not to swarm. This interpretation implies some generic characteristics regarding the build-up and emergence of collective order in swarms: in particular, that order and disorder are generic meta-stable states of the system, suggesting that the emergence of order is kinetic and does not necessarily require external environmental changes. Joint work with Yotam Ophir, Sagi Levi, Eshel Ben-Jacob and Amir Ayali.

04/17/2015

Friday
3:00-4:00 PM
POB 6.304

Sebastian Acosta
(Baylor College of Medicine)

Thermoacoustic imaging in an enclosure with variable wave speed

Unlike the free-space setting, we consider thermoacoustic imaging in a region enclosed by a surface where an impedance boundary condition is imposed. This condition models physical boundaries such as acoustic mirrors or detectors. By recognizing that the inverse problem is equivalent to boundary observability, we use control operators to derive a solvable equation for the unknown initial condition. If well-known geometrical conditions are satisfied, this approach is naturally suited for variable wave speed and for measurements on a subset of the boundary. We will also discuss some preliminary results and challenges concerning the numerical solution of the proposed reconstruction equation

04/24/2015

Friday
3:00-4:00PM
POB 6.304

David Aristoff
(Mathematics, Colorado State University)

The parallel replica method for Markov Chains

Markov chains have widespread applications in computational math, chemistry, physics and statistics. For instance, in Markov chain Monte Carlo, Markov chains are used to estimate deterministic quantities for which closed-form expressions are unknown. Another example is in computational chemistry, where Markov chains are used to model molecular dynamics. Of course, it is essential that the Markov chains can be simulated efficiently. We present a very general algorithm for improving the real-time efficiency of Markov chain simulations. In many cases of practical interest, the chains tend to get "stuck" in certain subsets of configuration space. Our algorithm uses many replicas of the chain, simulated in parallel, to help it get "unstuck". The algorithm can be seen as a generalization of A.F. Voter's parallel replica method for simulating Langevin dynamics.

05/05/2015

Tuesday

11:00AM-12:00

POB 6.304

Jianliang Qian

(Mathematics, Michigan State University)

Fast Huygens sweeping methods for Helmholtz equations in inhomogeneous media in the high frequency regime

In some applications, it is reasonable to assume that geodesics (rays) have a consistent orientation so that the Helmholtz equation may be viewed as an evolution equation in one of the spatial directions. With such applications in mind, we propose a new Eulerian computational geometrical-optics method, dubbed the fast Huygens sweeping method, for computing Green’s functions of the Helmholtz equations in inhomogeneous media in the high-frequency regime and in the presence of caustics. The first novelty of the new method is that the Huygens-Kirchhoff secondary source principle is used to integrate many locally valid asymptotic solutions to yield a globally valid asymptotic solution so that caustics associated with the usual geometrical optics ansatz can be treated automatically. The second novelty is that a butterfly algorithm is adapted to carry out the matrix-vector products induced by the Huygens-Kirchhoff integration in O(N log N ) operations, where N is the total number of mesh points, and the proportionality constant depends on the desired accuracy and is independent of the frequency parameter. The new method enjoys the following desired features: (1) it precomputes a set of local traveltime and amplitude tables; (2) it automatically takes care of caustics; (3) it constructs Green’s functions of the Helmholtz equation for arbitrary frequencies and for many point sources; (4) for a specified number of points per wavelength it constructs each Green’s function in nearly optimal complexity in terms of the total number of mesh points, where the prefactor of the complexity only depends on the specified accuracy and is independent of the frequency parameter. Both two-dimensional (2-D) and three-dimensional (3-D) numerical experiments are presented to demonstrate the performance and accuracy of the new method. This is a joint work with Songting Luo and Robert Burridge.

05/07/2015

Thursday

11:00AM-12:00

POB 6.304

Gustaf Soderlind

(Center for Mathematical Sciences, Lund University)

Digital Filters in Multigrid

Multigrid methods are based on a separate iterative treatment of high
frequency (HF) and low frequency (LF) errors. HF is suppressed by a
smoother, and LF is taken care of by “coarse grid correction”. Mapping
fine grid residuals to the coarse grid is fraught with aliasing, and in
this talk we examine special restriction operators based on
anti-aliasing digital filters used in down-sampling in signal and image
processing. Without anti-aliasing, the coarse grid correction is not
sufficiently accurate, but with dedicated high order anti-aliasing
filters, in combination with corresponding reconstruction filters, there
is a possibility to use “aggressive” coarsening, bypassing intermediate
grids. We demonstrate proof of concept for two-point boundary value
problems and outline a two-grid (two-scale) method, with broadband
smoothing and up to 16:1 coarsening with fast convergence.