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

It is shown that the phenomenon of inversion recently discovered in a one-band model [L. C. Lew Yan Voon and M. Willatzen, J. Appl. Phys. 93, 9997 (2003)] is much more general and is present in both multiband theories and in the excited states. Predictions of the one-band and of a four-band model are in good agreement for the ground state. A critical radius of around 15A(7A) is obtained for holes in InGaAs∕InP(GaAs∕AlAs) modulated nanowires. This phenomenon should be readily observable in both optical spectroscopy and transport.

Prediction of barrier localization in modulated nanowires

Tight-binding calculation of spin splittings in semiconductor superlattices.

Contact electrification (CE) involves a complex interplay of physical interactions in realistic material systems. For this reason, scientific consensus on the qualitative and quantitative importance of different physical mechanisms on CE remains a formidable task. The CE mechanism at a water/polymer interface is a crucial challenge owing to the poor understanding of charge transfer at the atomic level. First-principle density functional theory (DFT), used in the present work, proposes a new paradigm to address CE. Our results indicate that CE follows the same trend as the gap between the highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO) of polymers. Electron transfer occurs at the outmost atomic layer of the water/polymer interface and is closely linked to the functional groups and atom locations. When the polymer chains are parallel to the water layer, most electrons are transferred; conversely, if they are perpendicular to each other, the transfer of charges can be ignored. We demonstrate that a decrease in the interface distance between water and the polymer chains leads to CE in quantitative agreement with the electron cloud overlap model. We finally use DFT calculations to predict the properties of CE materials and their potential for triboelectric nanogenerator energy harvesting devices.

/pdf/understanding-contact-electrification-at-water-polymer-7bamrsj5.pdf

Understanding Contact Electrification at Water/Polymer Interface

A simple computationally effective method is developed for solving the Ben Daniel - Duke equations for nanowire semiconductor heterostructures. The method allows eigenstates and associated energy levels of nanowires with varying cross- sectional shape and/ or varying composition to be obtained, and is based on expanding the envelope function eigenstates on local eigenstates of the corresponding cross- sectional problem. In this way, the original partial differential equation problem is reduced to a set of coupled ordinary differential equations ( this set can to a good approximation be limited to a small number of coupled equations). In the first part of the paper, the model equation framework is derived; it can be easily modified to account for a more general set of partial differential equations. In the second part of the paper, three different cases of axisymmetrical nanowire problems are analysed in terms of eigenstates and energy eigenvalues. The cases considered are ( a) conical nanowires, ( b) a nanowire with a step in radius, and ( c) a conical GaAs/ GaAlAs nanowire. Comparison with computationally more expensive finite- element results on a two- dimensional domain is made, and good agreement is found. (Less)

https://iopscience.iop.org/article/10.1088/0953-8984/19/13/136217/pdf

The Ben Daniel-Duke model in general nanowire structures

We study the impact of using the fully coupled electromechanical equations including piezoelectric effect and spontaneous polarization as compared to the semi-coupled approach, where the strain is solved first without piezoelectric coupling and then inserted into the equation for the electric potential. We show that for circular GaN/AlN quantum dots the fully coupled approach is needed for dots with a radius comparable to or larger than the height, however, when the radius is smaller than the height the semi-coupled approach is sufficient. We highlight this by studying the effect on the electronic structure using an effective mass approximation.

Morten Willatzen

Papers

Prediction of barrier localization in modulated nanowires

Tight-binding calculation of spin splittings in semiconductor superlattices.

Understanding Contact Electrification at Water/Polymer Interface

The Ben Daniel-Duke model in general nanowire structures

Electromechanical effects in electron structure for GaN/AlN quantum dots