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

Modern microscopic techniques following the stochastic motion of labelled tracer particles have uncovered significant deviations from the laws of Brownian motion in a variety of animate and inanimate systems. Such anomalous diffusion can have different physical origins, which can be identified from careful data analysis. In particular, single particle tracking provides the entire trajectory of the traced particle, which allows one to evaluate different observables to quantify the dynamics of the system under observation. We here provide an extensive overview over different popular anomalous diffusion models and their properties. We pay special attention to their ergodic properties, highlighting the fact that in several of these models the long time averaged mean squared displacement shows a distinct disparity to the regular, ensemble averaged mean squared displacement. In these cases, data obtained from time averages cannot be interpreted by the standard theoretical results for the ensemble averages. Here we therefore provide a comparison of the main properties of the time averaged mean squared displacement and its statistical behaviour in terms of the scatter of the amplitudes between the time averages obtained from different trajectories. We especially demonstrate how anomalous dynamics may be identified for systems, which, on first sight, appear to be Brownian. Moreover, we discuss the ergodicity breaking parameters for the different anomalous stochastic processes and showcase the physical origins for the various behaviours. This Perspective is intended as a guidebook for both experimentalists and theorists working on systems, which exhibit anomalous diffusion.

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Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking.

Chemical methods developed over the past two decades enable preparation of colloidal nanocrystals with uniform size and shape. These Brownian objects readily order into superlattices. Recently, the range of accessible inorganic cores and tunable surface chemistries dramatically increased, expanding the set of nanocrystal arrangements experimentally attainable. In this review, we discuss efforts to create next-generation materials via bottom-up organization of nanocrystals with preprogrammed functionality and self-assembly instructions. This process is often driven by both interparticle interactions and the influence of the assembly environment. The introduction provides the reader with a practical overview of nanocrystal synthesis, self-assembly, and superlattice characterization. We then summarize the theory of nanocrystal interactions and examine fundamental principles governing nanocrystal self-assembly from hard and soft particle perspectives borrowed from the comparatively established fields of micro...

Self-Assembly of Colloidal Nanocrystals: From Intricate Structures to Functional Materials

Journal of Physics Condensed Matter: Preface

The Theory of Stochastic Processes. By D. R. Cox and H. D. Miller. Pp. x, 398. 70s. (Methuen)

A statistical model has been developed describing the magnetostatic properties of dense ferrocolloids and the dielectric properties of polar fluids. The model is based on the relation between the magnetization and the pair correlation function of a spatially homogeneous system of dipole particles. This approach allows us to calculate the ferrofluid magnetization (polarization density of polar fluid) in a form of expansion over both the particle concentration and the potential of the interparticle dipole-dipole interaction U(d). The obtained expressions for the ferrocolloid initial magnetic susceptibility, the dielectric constant of polar fluid and the ferrofluid magnetization with the accuracy approximately U(2)(d) describe well the experimental data and the results of computer modeling. The model justifies the validity of the "modified mean-field approach," and the effective field is calculated as a function of the Langevin magnetization.

Magnetic properties of dense ferrofluids: an influence of interparticle correlations.

We consider a thermodynamic model of a stable macroscopically homogeneous ferrocolloid containing identical spherical particles with permanent moments suspended in a non-dissociated liquid on the basis of the hard sphere perturbation theory. Magnetostatic properties and the phase diagram of the ferrocolloid are shown to agree very well with experimental evidence. Dipole interparticle interactions result in an effective attraction between the particles which increase, as the strength of an externally applied magnetic field grows, favours the phase separation and cause a reduction in the coefficient of mutual Brownian diffusion of the particles.

Equilibrium properties of ferrocolloids

The theory of particle association in flexible chains in dilute ferrofluids is generalized to the case of an arbitrarily strengthened magnetic field. The chain distribution in dynamic equilibrium is obtained on the basis of free energy minimization method under the neglect of interchain interaction. The chain partition function is calculated analytically with the help of the rotation matrix technique under the condition when the interparticle dipole-dipole interaction between the nearest neighboring ferroparticles in each chain is taken into account. At weak fields, the chain distribution and the initial susceptibility are shown to be dependent on the value of the correlation coefficient describing the zero field mutual orientational correlations between the magnetic moments of two neighboring ferroparticles in a chain. The internal chain orientational correlations and the field dependent chain lengthening result in higher magnetization of the aggregated ferrofluid in comparison with the Langevin magnetization.

Ferrofluid aggregation in chains under the influence of a magnetic field.

Experimental magnetization curves for a polydisperse ferrofluid at various concentrations are examined using analytical theories and computer simulations with the aim of establishing a robust method for obtaining the magnetic-core diameter distribution function p(x). Theoretical expressions are fitted to the experimental data to yield the parameters of p(x). It is shown that the majority of available theories yield results that depend strongly on the ferrofluid concentration, even though the magnetic composition should be fixed. The sole exception is the second-order modified mean-field (MMF2) theory of Ivanov and Kuznetsova [Phys. Rev. E 64, 041405 (2001)] which yields consistent results over the full experimental range of ferrofluid concentration. To check for consistency, extensive molecular dynamics and Monte Carlo simulations are performed on systems with discretized versions of p(x) corresponding as closely as possible to that of the real ferrofluid. Essentially perfect agreement between experiment, theory, and computer simulation is demonstrated. In addition, the MMF2 theory provides excellent predictions for the initial susceptibility measured in simulations.

https://www.pure.ed.ac.uk/ws/files/8898269/Magnetic_properties_of_polydisperse_ferrofluids.pdf

Magnetic properties of polydisperse ferrofluids: a critical comparison between experiment, theory, and computer simulation.

The theory of particle association in chains in dilute ferrofluids and dipole fluids is generalized to the case of polydisperse systems. The chains could be formed by ferroparticles of different sizes, so various types of chain aggregates are considered. The probabilities of chain structure appearance are calculated, and the phase diagram, allowing to find the most probable structure with only the continuous particle size distribution known, is built. Our results demonstrate that in spite of a very weak dipole-dipole interaction between the small size fraction particles, their presence exerts a decisive influence on the ferrofluid microstructure. The chain shortening caused by the small particles sticking to the edges of chains formed by large particles is discovered theoretically. The latter effect is proved to exist by the recent computer simulations on bidisperse ferrofluid makeup. The application of the developed model to the description of magnetic birefringence phenomena in weak external magnetic fields shows a very good agreement with experimental data.

Alexey O. Ivanov

Papers

Magnetic properties of dense ferrofluids: an influence of interparticle correlations.

Equilibrium properties of ferrocolloids

Ferrofluid aggregation in chains under the influence of a magnetic field.

Magnetic properties of polydisperse ferrofluids: a critical comparison between experiment, theory, and computer simulation.

Chain aggregate structure and magnetic birefringence in polydisperse ferrofluids.