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

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

Physical Review B

The nature of the lowest states in a quantum rod is studied as a function of aspect ratio using a four-band Burt-Foreman model. Contrary to earlier work, the aspect ratio at crossing is found to be shape but not size dependent, and it is shown that the nonseparability and multiband nature of the problem leads to a complex ground-state envelope function and also to the phenomenon of level crossing. The intrinsic difference between the valence states of a quantum rod and those of a quantum wire is demonstrated.

Influence of Aspect Ratio on the Lowest States of Quantum Rods

With a one-band envelope function theory, we investigate the dynamics of a finite nanowire superlattice driven by an ac electric field by solving numerically the time-dependent Schr\"odinger equation. We find that for an ac electric field resonant with two energy levels located in two different minibands, the coherent dynamics in nanowire superlattices is much more complex as compared to the standard two-level description. Depending on the energy levels involved in the transitions, the coherent oscillations exhibit different patterns. A signature of barrier-well inversion phenomenon in nanowire superlattices is also obtained.

Dynamics of a nanowire superlattice in an ac electric field

A multiband k⋅p theory was recently proposed [L. H. Peng and C. G. Fonstad, J. Appl. Phys. 77, 747 (1995)] in order to discuss the influence of band mixing on the selection rules for intersubband and interband optical transitions in quantum wells. We point out here that the analysis presented is incorrect.

Morten Willatzen

Papers

Influence of Aspect Ratio on the Lowest States of Quantum Rods

Dynamics of a nanowire superlattice in an ac electric field

Comment on ‘‘Multiband coupling effects on electron quantum well intersubband transitions’’ [J. Appl. Phys. 77, 747 (1995)]

High performance piezotronic devices based on non-uniform strain

Crystal orientation effects on the piezoelectric field of strained zinc-blende quantum-well structures