Modeling and Computation Seminar

The Modeling & Computation Seminar is held on Thursdays at 12:30 PM, in Mathematics 402.

Spring 2008

January

01/03
Jean-Guy Caputo
Laboratoire de Mathematiques
INSA de Rouen, France

Electromagnetically induced switching of ferroelectric thin films

We analyze the interaction of an electromagnetic spike (one cycle) with a thin layer of ferroelectric medium with two equilibrium states. The model is the set of Maxwell equations coupled to the undamped Landau-Khalatnikov equation, where we do not assume slowly varying envelopes. From linear scattering theory, we show that low amplitude pulses can be completely reflected by the medium. Large amplitude pulses can switch the ferroelectric. Using numerical simulations and analysis, we study this switching for long and short pulses, estimate the switching times and provide useful information for experiments.

01/24

Organizational meeting

01/31
Alexander O. Korotkevich
L.D. Landau Institute for Theoretical Physics, RAS

Simultaneous Observation of Direct and Inverse Cascade in Surface Gravity Waves Turbulence

By direct numerical simulation direct and inverse cascades in surface gravity waves turbulence were observed. Formation of condensate in the low frequency waves region leads to the distortion of the exponents in Kolmogorov-like spectra predicted by the theory of weak turbulence. Also the influence of the wavenumbers grid discreteness was observed. The parameters of the simulation are typical for the laboratory water tanks experiments.

February

02/21
Eran Sharon
The Racah Institute of Physics, The Hebrew University of Jerusalem

Experiments in Non-Euclidean Plates and Leaves

I will present results from experiments on shaping of thin sheets via lateral growth. Scaling of lengths scales and energies will be suggested and a possible geometrical origin of the appearance of small scale structure will be discussed. I will present first results from a study of growing leaves and will describe ongoing experiments.

02/28
Catalin Turc
Department Mathematics and Statistics
University of North Carolina at Charlotte

Fast, high-order, well-conditioned algorithms for the solution of three-dimensional acoustic and electromagnetic scattering problems

We present a novel computational methodology aimed at overcoming the aforementioned difficulties. At the heart of our approach are integral equation formulations that exhibit excellent spectral properties. In the case of scattering from perfectly conducting structures, and just as the classical Combined Field Integral Equation (CFIE), our equations result from representations of the scattered fields as a combination of magnetic- and electric-dipole distributions on the surface of the scatterer. In contrast with the classical equations, however, our electric-dipole operators involve use of certain types of regularizing operators whose design is based on the pseudodifferential calculus on manifolds. We call the resulting equations Regularized Combined Field Integral Equations (CFIE-R). Unlike the CFIE, the CFIE-R are well-conditioned equations; careful selection of coupling parameters, further, yields CFIE-R operators with excellent spectral distributions--with closely clustered eigenvalues--so that small numbers of iterations suffice to solve the corresponding equations by means of Krylov subspace iterative solvers such as GMRES. We present a high-order Nystrom approach based on use of partitions of unity and high-order integration schemes that produces high-order algorithms for acoustic and electromagnetic scattering problems. A variety of numerical results demonstrate that, for a given accuracy, the new equations can give rise to order-of-magnitude reductions in computational costs over those resulting from previous approaches.

March

03/06
Laurent Boue
Laboratoire de Physique Statistique de l'Ecole Normale Superieure, Paris

A Statistical Physics Approach to Packing Problems

Tightly packed elastic structures can be found in a wide variety of physical and biological systems. Traditionally mechanical and geometrical aspects are treated separately due to the complex nature of the observed patterns (e.g., a piece of crumpled paper). We present a statistical field theory to study the packing of an elastic rod (1D) confined in 2D space. An advantage of this approach is that it puts geometry and mechanics on an equal footing. We show that a self-reorganization of the rod becomes favorable at a critical density. This configurational phase transition (isotropic-nematic) leads to a more efficient packing. For even higher confinements we predict the existence of a jamming transition hinting at the glassy character of this system.

03/13
Samy Missoum
Aerospace and Mechanical Engineering
The University of Arizona

Probabilistic Optimal Design for Highly Nonlinear Problems

The simulation-based design of nonlinear systems is hampered by several hurdles such as high CPU times, the difficulty to evaluate gradients, and the acute sensitivity of responses to loading and design uncertainties. In addition, the system's responses might be discontinuous due to the presence of numerous limit and bifurcation points. This considerably limits the blind use of traditional optimization and probabilistic methods. Typical examples of problems with discontinuous behaviors are structural impacts and nonlinear aeroelasticity with limit cycle oscillations (LCO).

This seminar will describe a methodology which facilitates the probabilistic (optimal) simulation-based design of nonlinear problems. The approach, referred to as explicit design space decomposition, is based on data mining and machine learning techniques. The main feature of this approach lies in the explicit definition of limit state functions (or constraints) constructed from a design of experiments (DOE). A method to adaptatively update the limit state function and refine the DOE will be presented.

Several test examples will demonstrate the efficiency of the approach in the case of the reliability-based optimization of nonlinear structures and LCO problems.

03/27
Andrew Hausrath
Department of Biochemistry and Molecular Biophysics
The University of Arizona

Applications of Geometry in Protein Structure Analysis

The remarkable functional versatility of proteins is made possible by the diverse array of three-dimensional folds that they adopt. The conventional representation of protein structure is a discrete coordinate model listing the positions of all atoms in the structure. While this representation is very useful for understanding intricate chemical details, it is not well suited to addressing more general questions about the nature of protein folds, their variability, and the relationships between them. To investigate such questions, we have developed a continuous representation of proteins based on the geometry of space curves. The description of a protein fold in terms of its underlying geometry has proved to be much more efficient than the coordinate representation, suggesting that sparse experimental data may be sufficient to restrain a curve model where a conventional coordinate model would be underdetermined. Many proteins are not amenable to high-resolution structural analysis, and for these challenging cases it is important to make the best use of the limited experimental information available. The talk will describe the application of the curve representation to diffraction techniques focusing in particular on low-resolution X-ray crystallography.

April

04/03
Young-Jun Son
Systems and Industrial Engineering Department
The University of Arizona

Distributed Federation of Multi-paradigm Simulations and Decision Models for Planning and Control: From Shop Floor to Top Floor

In this talk, we first discuss simulation-based shop floor planning and control, where 1) on-line simulation is used to evaluate decision alternatives at the planning stage, 2) the same simulation model (executing in the fast mode) used at the planning stage is used as a real-time task generator (real-time simulation) during the control stage, and 3) the real-time simulation drives the manufacturing system by sending and receiving messages to an executor (Finite State Automata). We then discuss how simulation-based shop floor planning and control can be extended to enterprise level activities (top floor). To this end, we discuss the analogies between the shop floor and top floor in terms of the components required to construct simulation-based planning and control systems such as resource models, coordination models, physical entities, and simulation models. Differences between them are also discussed in order to identify new challenges that we face for top floor planning and control. A major difference is the way a simulation model is constructed so that it can be used for planning, depending on whether time synchronization among member simulations becomes an issue or not. We also discuss the distributed computing platform using web services and grid computing technologies, which allow us to integrate simulation and decision models, and software and hardware components. Finally, we discuss other emerging applications for the proposed simulation-based planning and control, such as emergency evacuation and blood supply network.

04/10
Jared Barber
Program in Applied Mathematics
The University of Arizona

Two-Dimensional Model of Red Blood Cell Motion in Microvessels

Red blood cell movement, deformation, and partitioning in small diverging microvessel bifurcations are simulated using a two-dimensional, flexible-particle model. For isolate red blood cell movement, while simulated red blood cell trajectories tend to follow background fluid streamlines, significant deviations from these streamlines can occur because of red blood cell migration towards vessel centerlines and red blood cell obstruction of downstream vessels. The net effect of these behaviors is explored in symmetric and asymmetric vessels to produce results comparable with experiment. In addition, preliminary results and insights are presented for multiple red blood cell motion in straight vessels and in bifurcations.

04/17
Paul Krause
Department of Mathematics
The University of Arizona

The Diffusion Kernel Filter

Particle Filters are sample-based numerical methods for the discrete-time Filtering Problem. These methods suffer from large operations count and troubles defining prediction. This work introduces a particle filter method for the discrete-time Filtering Problem with SODEs, along with a suitable definition of prediction. The method, to be called Diffusion Kernel Filter, applies when the dynamics of the SODE develops few moments (i.e., is weakly nonlinear) on branches of prediction'' between the filtering times (which is expected to be the case in several applications in the geosciences) and is arrived at by a parametrization of small fluctuations of Wiener-driven paths about deterministic paths and a local use of this parametrization in the referential Bootstrap Filter. The parametrization is derived by reformulation of the SODE problem into a Liouville SPDE problem, application of Duhamel's principle to this problem, restriction of the resulting to nonlinear SODE open problems for the flows of branches of prediction, closure of these. This was inspired by Chorin's ``Optimal prediction with memory, where a similar technique is used to tackle the dimension reduction problem for the dynamics of a nonlinear ODE. Results obtained with the early Lorenz equations and a set of equations of point-vortex interactions are presented.

04/24
Christopher Bergevin
Department of Mathematics
The University of Arizona

Modeling Otoacoustic Emission Group Delays in the Lizard Auditory Periphery

Otoacoustic emissions (OAEs) are sounds generated and subsequently emitted by a healthy ear (detectable using a sensitive microphone) which appear in a wide range of vertebrate species. While the exact generation mechanisms remain unclear, OAEs evoked using an external stimulus exhibit significant group delays across a wide frequency range, on the order of 1-2 ms or greater. In mammals such as humans, these delays are generally thought to arise due to the presence of cochlear traveling waves. However, in classes such as lizards, such waves are noticeably absent. The present study hypothesizes that these delays are in fact associated with the sharp tuning manifested in the auditory periphery and represent the build-up time of highly tuned coupled oscillators. Preliminary model results for the gecko ear show remarkable agreement with empirical data and predict that emission group delays increase with increasing sharpness of tuning (as typically measured via auditory nerve fiber responses).

May

05/01
Jorge Ramirez
Department of Mathematics
The University of Arizona

Large-Scale Stochastic Modeling of Oceanic Wave-Breaking

We propose a simple spatio-temporal marked Poisson point process to describe the large structure of breaking waves in the ocean. The breaking events are "marked" with the associated local energy drop. This model is suitable for estimating dissipation at large scales (ocean currents) induced by small-scale events (waves breaking). Finally I will use a Gaussian model for the sea surface to calculate some notions of the probability of wave-breaking and the distribution of the associated energy drop. This is joint work with Juan Restrepo.