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

This paper presents a theoretical investigation of phonon dispersion in piezoelectric slabs of hexagonal crystal symmetry (wurtzite). Specifically we solve the fully coupled dispersion relations in a GaN free standing quantum well by varying the crystal growth direction from the [001] axis to the [010] axis. Accounting for the Drude model in solving the fully-coupled dispersion relations, phonon modes will generate an additional phonon band, with a high local density of phonon states, close to the plasma frequency. As opposed to cubic crystals with isotropic permittivity, the location of this band varies with crystal orientation. We also find that the phonon mode dependence on the crystal orientation is more pronounced for small in-plane wavenumbers.

https://robots.iopscience.iop.org/article/10.1088/1361-6641/aa69f6/pdf

Acousto-optical phonon excitation in piezoelectric wurtzite slabs and crystal growth orientation effects

In this contribution, we implement a self-consistent procedure for the solution of the Poisson-Schrmodel applied here for the analysis of coupled effects in wide bandgap wurtzite heterostructures. Such effects are demonstrated on ex- amples for three-layer systems, in particular AlN/GaN quantum well heterojunctions, which are promising components in a number of optoelectronic device applications. A major emphasis is given to the effects of boundary conditions, piezoelectricity and spontaneous polarization. I. INTRODUCTION Electronic properties of wide bandgap wurtzite heterostruc- tures can pronouncedly be influenced by a range of additional effects such as strain, piezoelectric effect, and spontaneous polarization. In designing new optoelectronic devices these effects should be taken into account. In (1), we have recently reported an illustrative study of lattice misfit induced strain and piezoelectric effect on the resonant frequency in AlN/GaN nanostructures. In such three-layer structures, a GaN well con- fined by AlN barriers. In the present contribution we continue the study of coupled effects in such nanostructures. First, we analyze the effect of boundary conditions in these structures, focusing on their influence on the strain and the electric potential distribution. The analysis is based on the Poisson- Schrodinger model. Then, in the same modeling framework we discuss the effect of piezoelectricity and spontaneous polarization, as well as the coupling between the Poisson and Schrodinger equations via the electron density.

odinger Model in the Analysis of Coupled Effects in Quantum Well Nanostructures

https://briefs.techconnect.org/wp-content/volumes/Nanotech2004v3/pdf/B3-14.pdf

Valence-band Energies of GaAs/AlGaAs and InGaAs/InP V-groove [1-10] Quantum Wires

Spatial emission characteristics of waveguiding organic nanofibers

The dynamics of reciprocal transducer systems is modelled accounting for a nonlinear con- stitutive relation between the electric displacement and the electric field as reported in Refs. (1, 2, 3) us- ing an ecient nonlinear numerical scheme. The two transducers are assumed connected in series with a general electrical impedance. Particular emphasis is given to transmitter and receiver temporal responses in the cases with and without nonlinearities and dif- ferences between the two model cases are highlighted.

http://www.iaeng.org/publication/WCE2007/WCE2007_pp1242-1246.pdf

Morten Willatzen

Papers

Acousto-optical phonon excitation in piezoelectric wurtzite slabs and crystal growth orientation effects

odinger Model in the Analysis of Coupled Effects in Quantum Well Nanostructures

Valence-band Energies of GaAs/AlGaAs and InGaAs/InP V-groove [1-10] Quantum Wires

Spatial emission characteristics of waveguiding organic nanofibers

Modelling of reciprocal transducer system accounting for nonlinear constitutive relations