Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented, together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover, the role and the complexity of escape in driven systems exhibiting possibly multiple, metastable stationary nonequilibrium states is identified. At lower temperatures, quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed, thereby providing a description of dissipative escape events at all temperatures. In addition, an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.

Reaction-rate theory: fifty years after Kramers

http://wwwcourses.sens.buffalo.edu/ce435/Riess03.pdf

Micellization of block copolymers

Jets, ie collimated streams of matter, occur from the microscale up to the large-scale structure of the universe Our focus will be mostly on surface tension effects, which result from the cohesive properties of liquids Paradoxically, cohesive forces promote the breakup of jets, widely encountered in nature, technology and basic science, for example in nuclear fission, DNA sampling, medical diagnostics, sprays, agricultural irrigation and jet engine technology Liquid jets thus serve as a paradigm for free-surface motion, hydrodynamic instability and singularity formation leading to drop breakup In addition to their practical usefulness, jets are an ideal probe for liquid properties, such as surface tension, viscosity or non-Newtonian rheology They also arise from the last but one topology change of liquid masses bursting into sprays Jet dynamics are sensitive to the turbulent or thermal excitation of the fluid, as well as to the surrounding gas or fluid medium The aim of this review is to provide a unified description of the fundamental and the technological aspects of these subjects

Physics of liquid jets

Vesicles consisting of a bilayer membrane of amphiphilic lipid molecules are remarkably flexible surfaces that show an amazing variety of shapes of different symmetry and topology. Owing to the fluidity of the membrane, shape transitions such as budding can be induced by temperature changes or the action of optical tweezers. Thermally excited shape fluctuations are both strong and slow enough to be visible by video microscopy. Depending on the physical conditions, vesicles adhere to and unbind from each other or a substrate. This article describes the systematic physical theory developed to understand the static and dynamic aspects of membrane and vesicle configurations. The preferred shapes arise from a competition between curvature energy, which derives from the bending elasticity of the membrane, geometrical constraints such as fixed surface area and fixed enclosed volume, and a signature of the bilayer aspect. These shapes of lowest energy are arranged into phase diagrams, which separate regi...

Configurations of fluid membranes and vesicles

The field theoretical approach developed in an earlier work (Kawasaki, K.; et al. Macromolecules 1988, 21, 2972) was recast in such a way as to avoid power series expansion in the concentration variable. The general scaling behavior was found, which naturally gives rise to the well-known two-thirds power law of the domain size. The theory is related to other approaches by Helfand and co-workers and by Semenov. Numerical consequences of the theory are aslo presented that clearly demonstrate approach to the correct asymptotic behavior

Equilibrium morphology of block copolymer melts

We describe a morphological image analysis method to characterize images in terms of geometry and topology. We present a method to compute the morphological properties of the objects building up the image and apply the method to triply periodic minimal surfaces and to images taken from polymer chemistry.

Morphological image analysis

We show that a strong segregation of a two-component surfactant system coupled to the local membrane curvature has a pronounced effect on the shape of unilamellae or closed vesicles. For an average flat lamella, the preferred periodicity in the local composition as well as the lamellar shape is calculated and depends on the ratio between surface tension and bending modulus. In the case of a closed visicle with a fixed total area, there is no selected periodicity in contrast to the unilamellar case. For vesicles subjected to positive or negative inner pressure, we calculate their shape numerically, whereas when there is no added inner pressure, the shape is found analytically to be composed of circular sections.

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Equilibrium shape of two-component unilamellar membranes and vesicles

We propose a theoretical scheme for a hybrid simulation technique where self-consistent field theory and molecular dynamics simulation are combined (MD-SCF). We describe the detail of the main implementation issues on the evaluation of a smooth three-dimensional spatial density distribution and its special gradient based on the positions of particles. The treatments of our multiscale model system on an atomic scale or on a specific coarse-grained scale are carefully discussed. We perform a series of test simulations on this hybrid model system and compare the structural correlations on the atomic scale with those of classical MD simulations. The results are very encouraging and open a way to an efficient strategy that possess the main advantages common to the SCF and the atomistic approaches, while avoiding the disadvantages of each of the treatments.

Hybrid particle-field molecular dynamics simulations for dense polymer systems

We investigate unilamellar membranes and vesicles composed of an A/B mixture of partially miscible amphiphiles. Assuming a simple bilinear coupling between relative composition and local curvature, and in the strong segregation limit of the A/B mixture, we show for unilamellar open-shape membranes that the competition between surface tension and curvature results in a phase with a selected periodiaty (modulated phase) both in the shape and in the A/B composition. The limits of large and small surface tension are discussed separately. These findings extend previous results obtained close to the A/B critical point (shallow quench). For the same limit of strong segregation, we also investigate the coupling between the separation of the system into A and B domains, and the overall shape of closed-shape vesicles. For cylindrical vesicles of fixed overall area (or equivalently vesicles embedded in a two-dimensional space), equilibrium shapes and phase diagrams are obtained. We also consider the effect of an added pressure difference (osmotic pressure) across the vesicle. The results are extended to axial symmetric vesicles embedded in a three-dimensional space

Toshihiro Kawakatsu

Papers

Equilibrium morphology of block copolymer melts

Morphological image analysis

Equilibrium shape of two-component unilamellar membranes and vesicles

Hybrid particle-field molecular dynamics simulations for dense polymer systems

Phase transitions and shapes of two component membranes and vesicles II : weak segregation limit