Session B3: Computational Physics

Computer Simulations of Protein Interactions with Lipid Domains

Protein interactions with multi-component lipid bilayers are major molecular events in cell membranes. Using coarse-grained (CG) molecular dynamics simulations, we have studied the binding behavior and membrane disruption mechanics of a protein dimer on phase separated lipid rafts consisting of cholesterol, saturated and unsaturated lipids. Large size (50,000 CG-atoms) and long (3000 ns) simulations have been performed. We observed that the protein prefers to bind at the interface of liquid-ordered (Lo) and liquid-disordered (Ld) coexisting phases. When the polarity of cholesterol is increased, this interface becomes more distinct, and binding occurs sooner than normal; conversely, reducing the polarity of the cholesterol within the lipid raft leads to an unorganized Lo/Ld interface, and no binding occurs. We quantified our data by analyzing: 1) the extent to which dimer-lipid interaction affects the domains' sizes, 2) the minimum distance between the protein and various lipids during the binding event, and 3) the average transverse density profile of the dimer-lipid system.   

Continuing Studies of Hydrogenic Quantum Systems Using the Feynman-Kac Path Integral Method

The Feynman-Kac path integral method is applied to the atomic hydrogen quantum system for the purpose of evaluating eigenvalues. These are computed by random walk simulations on a discrete grid. The study provides the latest simulation analysis and includes the use of symmetry that allows higher order eigenstates to be computed. The method provides exact values in the limit of infinitesimal step size and infinite time for the lowest eigenstates.   

Dynamics of a Piecewise Linear Bouncer

The dynamical properties of a particle in a gravitational field colliding with a rigid wall moving with piecewise constant velocity are studied. We consider three distinct approaches to modeling the collision; elastic, inelastic with constant restitution coefficient and inelastic with a velocity-dependent restitution function. We confirm the existence of Fermi acceleration in the elastic model, and find periodic, quasi-periodic, and chaotic behavior in both inelastic models. We also examine the phenomenon of inelastic collapse. We address the related ``sticking solutions'' and their connection to both the overall dynamics and the phenomenon of self-reanimating chaos. Additionally we investigate the long-term behavior of the system as a function of both initial conditions and parameter values. The analytical and numerical investigations reveal that our model captures the essential features of the well-studied sinusoidally driven version and also exhibits behavior unique to the discontinuous dynamics.   

Charged Particle Motion in the Vicinity of a Magnetic Null Curve

A magnetic null curve is a 1D region of 3D space where the magnetic field is zero and is otherwise non-zero. Two geometries that produce null curves have been studied with classical trajectory Monte Carlo simulations to understand the properties of charged particle motion near the null curve. One system consists of two infinite, straight, parallel wires carrying identical current. In another system the null curve is generated by coaxial coils carrying identical current and separated axially by a small distance. The null curve is directly between the wires or coils, respectively. The motion of charged particles near the null curve and the conditions that produce charged particle confinement are discussed. Possible applications of systems containing magnetic null curves are given and specific experimental challenges are outlined.   

Asynchrony-tolerant finite difference method for partial differential equations at extreme scales

Computer simulations have been an important tool in understanding a wide variety of multiscale problems in physics: from molecular to geophysical to astrophysical phenomena. Many of these phenomena are modeled with partial differential equations that are often complex and nonlinear in nature, and thus demand massive computations. With increasing degree of parallelism in today's supercomputers, simulations are routinely performed on hundreds of thousands of processing elements (PEs) on Petascale machines. At this scale, communication between PEs take substantial amount of time during which PEs remain idle, leading to unused compute cycles and poor scalability. In this work, we propose a novel asynchronous method based on commonly used finite-difference schemes, where computations are carried out independent of the status of communication between PEs. We show that, while current schemes are stable and consistent under asynchrony, their accuracy is significantly affected. We derive new schemes that are tolerant to asynchrony due to slow communications relative to computations and maintain accuracy. We will also show results from numerical experiments to demonstrate the scalability of the method. These numerical schemes may provide a viable path towards true Exascale simulations.   

Calculating Relativistic Transition Matrix Elements for Hydrogenic Atoms Using Monte Carlo Methods

The nonrelativistic transition matrix elements for hydrogen atoms can be computed exactly and these expressions are given in a number of classic textbooks. The relativistic counterparts of these equations can also be computed exactly but these expressions have been described in only a few places in the literature. In part, this is because the relativistic equations lack the elegant simplicity of the nonrelativistic equations. In this talk I will describe how variational Monte Carlo methods can be used to calculate the energy and properties of relativistic hydrogen atoms and how the wavefunctions for these systems can be used to calculate transition matrix elements.   

Experimental Study of Short Time Scale Brownian Motion

We report our progress on the study of short-time Brownian motion of optically-trapped microspheres. In earlier work, we observed the instantaneous velocity of microspheres in gas and in liquid, verifying a prediction by Albert Einstein from 1907. We now report a more accurate test of the energy equipartition theorem for a particle in liquid. We also observe boundary effects on Brownian motion in liquid by setting a wall near the trapped particle, which changes the dynamics of the motion. We find that the velocity autocorrelation of the particle decreases faster as the particle gets closer to the wall.