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

Measuring the Strangeness of Strange Attractors

http://experimentationlab.berkeley.edu/sites/default/files/AFMImages/butt_AFM.pdf

Force measurements with the atomic force microscope: Technique, interpretation and applications

We present an extensive molecular‐dynamics simulation for a bead spring model of a melt of linear polymers. The number of monomers N covers the range from N=5 to N=400. Since the entanglement length Ne is found to be approximately 35, our chains cover the crossover from the nonentangled to the entangled regime. The Rouse model provides an excellent description for short chains N<Ne, while the dynamics of the long chains can be described by the reptation model. By mapping the model chains onto chemical species we give estimates of the times and distances of onset of the slowing down in motion due to reptation. Comparison to neutron spin‐echo data confirm our mapping procedure, resolving a discrepancy between various experiments. By considering the primitive chain we are able to directly visualize the confinement to a tube. Analyzing the Rouse mode relaxation allows us to exclude the generalized Rouse models, while the original reptation prediction gives a good description of the data.

Dynamics of entangled linear polymer melts: A molecular‐dynamics simulation

Cellular automata are used as simple mathematical models to investigate self-organization in statistical mechanics. A detailed analysis is given of "elementary" cellular automata consisting of a sequence of sites with values 0 or 1 on a line, with each site evolving deterministically in discrete time steps according to definite rules involving the values of its nearest neighbors. With simple initial configurations, the cellular automata either tend to homogeneous states, or generate self-similar patterns with fractal dimensions \ensuremath{\simeq} 1.59 or \ensuremath{\simeq} 1.69. With "random" initial configurations, the irreversible character of the cellular automaton evolution leads to several self-organization phenomena. Statistical properties of the structures generated are found to lie in two universality classes, independent of the details of the initial state or the cellular automaton rules. More complicated cellular automata are briefly considered, and connections with dynamical systems theory and the formal theory of computation are discussed.

Statistical mechanics of cellular automata

When a spilled drop of coffee dries on a solid surface, it leaves a dense, ring-like deposit along the perimeter (Fig 1a) The coffee—initially dispersed over the entire drop—becomes concentrated into a tiny fraction of it Such ring deposits are common wherever drops containing dispersed solids evaporate on a surface, and they influence processes such as printing, washing and coating1,2,3,4,5 Ring deposits also provide a potential means to write or deposit a fine pattern onto a surface Here we ascribe the characteristic pattern of the deposition to a form of capillary flow in which pinning of the contact line of the drying drop ensures that liquid evaporating from the edge is replenished by liquid from the interior The resulting outward flow can carry virtually all the dispersed material to the edge This mechanism predicts a distinctive power-law growth of the ring mass with time—a law independent of the particular substrate, carrier fluid or deposited solids We have verified this law by microscopic observations of colloidal fluids

/pdf/capillary-flow-as-the-cause-of-ring-stains-from-dried-liquid-5dw0ckou95.pdf

Capillary flow as the cause of ring stains from dried liquid drops

A model for random aggregates is studied by computer simulation The model is applicable to a metal-particle aggregation process whose correlations have been measured previously Density correlations within the model aggregates fall off with distance with a fractional power law, like those of the metal aggregates The radius of gyration of the model aggregates has power-law behavior The model is a limit of a model of dendritic growth

/pdf/diffusion-limited-aggregation-a-kinetic-critical-phenomenon-5g3g9ojzf6.pdf

Diffusion-limited aggregation, a kinetic critical phenomenon

Solids dispersed in a drying drop will migrate to the edge of the drop and form a solid ring. This phenomenon produces ringlike stains and occurs for a wide range of surfaces, solvents, and solutes. Here we show that the migration is caused by an outward flow within the drop that is driven by the loss of solvent by evaporation and geometrical constraint that the drop maintain an equilibrium droplet shape with a fixed boundary. We describe a theory that predicts the flow velocity, the rate of growth of the ring, and the distribution of solute within the drop. These predictions are compared with our experimental results.

/pdf/contact-line-deposits-in-an-evaporating-drop-45ym6o6aeo.pdf

Contact line deposits in an evaporating drop

Models of a wide range of ethylene-butene copolymers have been made by the saturation of polybutadienes with a range of vinyl content. The viscoelastic of these polymers have been measured very precisely and their chain dimensions have been determined by SANS. To a high degree of correlation, it is found that the mean square unperturbed end-to-end distance 0 , the density ρ and molecular weight M are related to the plabteau modulus, G 0 , G N 0 ∞ { 0 ρ/M} 3 , a finding in accord with that of Ronca

Connection between polymer molecular weight, density, chain dimensions, and melt viscoelastic properties

Diffusion-limited aggregation (DLA) is an idealization of the process by which matter irreversibly combines to form dust, soot, dendrites, and other random objects in the case where the rate-limiting step is diffusion of matter to the aggregate. We study the process from several points of view stressing the fact that it apparently gives rise to scale-invariant objects whose Hausdorff dimension is independent of short-range details. We show that DLA has no upper critical dimension. We apply scale invariance to study growth, gelation, and the structure factor of aggregates.

Thomas A. Witten

Papers

Capillary flow as the cause of ring stains from dried liquid drops

Diffusion-limited aggregation, a kinetic critical phenomenon

Contact line deposits in an evaporating drop

Connection between polymer molecular weight, density, chain dimensions, and melt viscoelastic properties

Diffusion-limited aggregation