Peter S. Lomdahl

The discrete self-trapping equation

Abstract A simple system of ordinary differential equations is introduced which has applications to the dynamics of small molecules, molecular crystals, self-trapping in amorphous semiconductors, and globular proteins. Analytical, numerical and perturbation methods are used to study the properties of stationary solutions. General solution trajectories can be either sinusoidal, periodic, quasiperiodic or chaotic.

Message-passing multi-cell molecular dynamics on the Connection Machine 5

Abstract We present a new scalable algorithm for short-range molecular dynamics simulations on distributed memory MIMD multicomputers based on a message-passing multi-cell approach. We have implemented the algorithm on the Connection Machine 5 (CM-5) and demonstrate that meso-scale molecular dynamics with more than 108 particles is now possible on massively parallel MIMD computers. Typical runs show single particle update-times of 0.15 μs in 2 dimentions (2D) and approximately 1 μs in 3 dimensions (3D) on a 1024 node CM-5 without vector units, corresponding to more than 1.8 Gflops overall performance. We also present a scaling equation which agrees well with actually observed timings.

MOLECULAR DYNAMICS COMES OF AGE: 320 BILLION ATOM SIMULATION ON BlueGene/L

As computational power is increasing, molecular dynamics simulations are becoming more important in materials science, chemistry, physics, and other fields of science. We demonstrate weak and strong scaling of our classical molecular dynamics code SPaSM on Livermores BlueGene/L architecture containing 131 072 IBM PowerPC440 processors. A maximum of 320 billion atoms have been simulated in double precision, corresponding to a cubic piece of solid copper with an edge length of 1.56 μm.

Benjamin-Feir turbulence in convective binary fluid mixtures

Abstract Binary mixtures of water and alcohol or 3 He and 4 He provide an excellent vehicle for studying the onset of a rich variety of dynamical behavior. For different values of the separation ratio, these systems exhibit both steady and oscillatory convection, competition between the two, and in another parameter range, a weakly turbulent state. In this paper we develop a general theory which is valid near onset and which can account for each of these features. A universal equation of Ginzburg-Landau type with complex coefficients obtains and is investigated numerically and analytically in one and two spatial dimensions. The most novel prediction is that some of the a periodic behavior seen in experiment is due to the universal Benjamin-Feir instability and we call this phenomenon Benjamin-Feir turbulence. Although the possibility of this effect has been discussed theoretically in the literature for over ten years, binary mixture convection provides the first vehicle in which the prediction can be quantitatively tested. We also discuss mean drift effects and the consequences of fixed lateral boundaries.

Between the local-mode and normal-mode limits

Abstract A simple model system is introduced for the vibrational analysis of polyatomic molecules. This classical system is based on complex mode amplitudes and reduces to either the normal-mode (NM) or the local-mode (LM) description in appropriate limits. Upon analysis without perturbative assumptions, the system exhibits sinusoidal, periodic, quasi-periodic and chaotic behaviors between the NM and the LM limits.

Influence of solitons in the initial state on chaos in the driven damped sine-Gordon system

Abstract The appearance of chaos in the a.c. driven, damped sine-Gordon equation is studied numerically. Several transitions from periodic to chaotic behaviour are investigated in detail for flat initial conditions. Spatial structures (breather, kink) in the initial conditions smooth out many of these transitions and give rise to an interesting symbiosis of time and spatial intermittency. This symbiosis appears to be due to the competition between the background tendency towards chaos and the systems preference to maintain a spatial pattern. The way that this competition is relieved is also found to depend very strongly on symmetry in the initial conditions.

Lightweight Computational Steering of Very Large Scale Molecular Dynamics Simulations

We present a computational steering approach for controlling, analyzing, and visualizing very large scale molecular dynamics simulations involving tens to hundreds of millions of atoms. Our approach relies on extensible scripting languages and an easy to use tool for building extensions and modules. The system is easy to modify, works with existing C code, is memory efficient, and can be used from inexpensive workstations over standard Internet connections. We demonstrate how we have been able to explore data from production MD simulations involving as many as 104 million atoms running on the CM-5 and Cray T3D. We also show how this approach can be used to integrate common scripting languages (including Python, Tcl/Tk, and Perl), simulation code, user extensions, and commercial data analysis packages.

50 GFlops molecular dynamics on the Connection Machine-5

The authors present timings and performances numbers for a new short range three dimensional (3-D) molecular dynamics (MD) code, SPaSM, on the Connection Machine-5 (CM-5). They demonstrate that runs with more than 10/sup 8/ particles are now possible on massively parallel MIMD computers. To the best of their knowledge this is at least an order of magnitude more particles than what was previously been reported. Typical production runs show sustained performance (including communication) in the range of 47-50 GFlops on a 1024 node CM-5 with vector units (VUs). The speed of the code scales linearly with the number of processors and with the number of particles and shows 95% parallel efficiency in the speedup.

LARGE-SCALE MOLECULAR-DYNAMICS SIMULATION OF 19 BILLION PARTICLES

We have performed parallel large-scale molecular-dynamics simulations on the QSC-machine at Los Alamos. The good scalability of the SPaSM code is demonstrated together with its capability of efficient data analysis for enormous system sizes up to 19 000 416 964 particles. Furthermore, we introduce a newly-developed graphics package that renders in a very efficient parallel way a huge number of spheres necessary for the visualization of atomistic simulations. These abilities pave the way for future atomistic large-scale simulations of physical problems with system sizes on the μ-scale.

Evolution of the order parameter in situations with broken rotational symmetry

Abstract We describe the evolution of the envelope of a wavetrain which, at a critical value of the stress parameter, breaks the rotational symmetry of the governing equations. The new envelope equation is a generalization to wavelike disturbances of the Newell-Whitehead-Segel equation and the one-dimensional complex Ginzburg-Landau equation. The most novel prediction of the new theory is that spatially uniform envelopes are rarely stable and that the dynamics is dominated by terms which c...onserve phase space volume. In particular, it turns out that the strongest spatial modulation takes place along the wave crests, perpendicular to the direction of the propagation. We also discuss mean drift effects and in particular their consequences near lateral boundaries.