Session K10: Computational Physics

Fluid Phase Equilibria for SSSW Potentials Predicted Using Monte Carlo Simulations in the Gibbs Ensemble

Monte Carlo free energy calculations have been undertaken using the Gibbs ensemble method\footnote{See A. Z. Panagiotopoulos, Mol. Sim. 9:1-23, 1992, and Ch. 8 in D. Frenkel and B. Smit. Understanding Molecular Simulation From Algorithms to Applications. Academic Press, Elsevier, London, 2002.} for a fluid of hard spheres with repulsive square shoulders next to attractive square wells in order to predict properties of the fluid both above and below the gas-liquid critical point. In addition, for some choices of square-shoulder height and width and square-well depth and width there is at a lower temperature a transition to two-phase high density and low density liquid. Results will be presented and compared with published results of some molecular dynamics simulations and discussed in relation to the conjectured liquid- liquid phase transition in water.   

Simulation of X-ray Diffraction Patterns from Arbitrary Targets

I describe recent advances in simulation methods for the generation of X-ray diffraction patterns from an arbitrary sample. The sample consists of a set of $N$ atomic positions, which in practice is most often generated via molecular dynamics simulation. Unlike some commercially-available diffraction software, the sample need not be crystalline: Any set of atomic coordinates may be considered. The methods used include fast Fourier transform techniques which yield $\mathrm{O}\left(N \log N\right)$ scaling, as opposed to the $\mathrm{O}\left(N^2\right)$ scaling of a brute-force approach. This allows, for example, the simulation of in-situ experiments on the dynamically-changing diffraction pattern due to a shock front passing through a crystal, along with the attendant phase transitions. I will discuss several mathematical solutions and outstanding challenges to the problem of fast generation of such patterns from very large atomic coordinate data sets, and I will present various results in the form of diffraction patterns from some moderately-sized and large systems.   

Fast Solvers for Models of Thermosolutal Convection

Numerical simulation provides insight into the effect physical parameters have on fluid flows under conditions that often make physical experiments and theory intractable. However, these simulations are computationally demanding and in order to extend their applicability, highly scalable and efficient numerical methods are being developed. We discuss a novel block preconditioner based on domain decomposition and fast diagonalization that can be used to accelerate iterative solution methods. We then demonstrate how this technique provides an efficient means of simulating steady fluid flows, and discuss how this can be used in solving models for thermosolutal convection.   

Mathematical Methods for Fast Track Recognition

Integral mathematical model of track pattern based on logical OR in likelihood function provides recognition with number of operations proportional total number of hits in power one. This likelihood function comprises (observes simultaneously) all the measured hits and is a multi-extreme function of trajectory parameters. The recognition is based on the recent progress in mathematical analysis of multi-extreme functions. A demo version of 2D helix arcs reconstruction is presented. This method can be used for tracking and triggering.   

A Course in Computational Physics

The purpose of this undergraduate course, is 1) to familiarize the student with a tool like MATLAB for solving homework problems in other courses, or qualify for a job later on. And 2. to understand accuracy and suitability properties of the algorithms used. Rather than emphasizing numerical techniques, the focus is on physics problems, such as: the decent of a parachute, the oscillation of a pendulum for large angles, the vibrational modes of a clamped inhomogenous string, and least square fitting. These are coupled with a discussion of numerical algorithms such as the comparison of various types of quadratures, properties of basis functions for expansions, including Chebyshev polynomials and Sturm-Liouville functions, matrices, their eigenvalues and singular value decompositions. Examples will be presented in this talk, a manual is in preparation.   

Inferring Near-Surface Tornado Wind Fields from Simulated Surface Marks

In 1967, T. T. Fujita proposed estimating tornado wind speeds from various classes of surface marks left behind by translating, debris-laden tornadoes. Here we revisit this approach by merits of Fujita's idea in the context of simulated surface marks, after decades of inactivity by the scientific community. We employ large eddy simulations of tornadoes with fully-coupled, sand-like debris that may be lofted from and redeposited to the surface. The resulting patterns of debris removal and deposition are convolutions of events in space and time that contain information about the wind fields that created them. The most prominent marks are insensitive to modest changes in the parameterizations employed. We extend Fujita's original treatment of surface marks to encompass more general families of marks, inferring near-surface flow velocities and spatial scales in different types of simulated tornadoes. Finally, we show how our methods and results could be applied to improve interpretations of observational data.   

Physics of Lipofuscin Formation and Growth in Age Related Macular Degeneration

Age-related macular degeneration (AMD) is the leading cause of blindness beyond the age of 50 years. The most common pathogenic mechanism that leads to AMD is choroidal neovascularization (CNV). CNV is produced by accumulation of residual material caused by aging of retinal pigment epithelium cells (RPE). With time, incompletely degraded membrane material builds up in the RPE in the form of lipofuscin. Lipofuscin is made of free-radical-damaged protein and fat, which forms not only in AMD, but also Alzheimer disease, and Parkinson disease. We will present the results of a study of the kinetics of lipofuscin growth in RPE cells using Kinetic Monte Carlo simulations and scaling theory on a cluster aggregation model. The model captures the essential physics of lipofuscin growth in the cells. A remarkable feature is that small particles may be removed from the cells while the larger ones become fixed and grow by aggregation. We compare our results to the number of lipofuscin granules in eyes with early age-related degeneration.