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

Inclusion of Nonlinear Strain Effects in the Hamiltonian for Nanoscale Semiconductor Structures

Theoretical study of the electromechanical efficiency of a loaded tubular dielectric elastomer actuator

A general theoretical analysis of a 3D generic TENG structure is presented. Using a dimensionless formulation, it is demonstrated that the optimal TENG geometry does not depend on the frequency of the moving dielectric but the external ohmic impedance for maximum power output is inversely proportional to the frequency. It is also found that the energy is proportional to the cube of the size of the TENG, the square of the triboelectric charge density σT, and the angular frequency ω of the moving dielectric. In the case of a spherical TENG where the moving dielectric is a sphere and the electrodes are spherical caps on a larger sphere three dimensionless parameters that determine the harvested energy are identified: the ratio between the radii of the two spheres r^ = r/R, the polar angle θ of the two spherical caps formed by the electrodes, and Z^ = ZεRω, where Z is the external impedance, R is the radius of the large sphere, ε is the permittivity of the system, and ω is the angular frequency of the moving sphere. Under the crude assumption of constant charge density on the electrodes, the optimal parameters can be easily calculated. It is found that θ = 1.1 rad, r^ = 0.67, and Z^ = 0.18.

/pdf/energy-optimization-of-a-mirror-symmetric-spherical-1aamc8jf.pdf

Energy Optimization of a Mirror‐Symmetric Spherical Triboelectric Nanogenerator

We argue that the two-dimensional elliptic quantum dot problem with finite barrier cannot be exactly solved, contrary to a recent assertion (van den Broek and Peeters, Physica E 11 (2001) 345 We also prove it explicitly by numerically calculating the correct energy spectrum

Comment on: “Confined states in two-dimensional flat elliptic quantum dots and elliptic quantum wires” [Physica E 11 (2001) 345] ☆

A static and dynamic analysis of the combined and self-consistent influence of spontaneous polarization, piezoelectric effects, lattice mismatch, and strain effects is presented for a three-layer one-dimensional AlN/GaN wurtzite quantum-well structure with GaN as the central quantum-well layer . It is shown that, contrary to the assumption of Fonoberov and Balandin J. Appl. Phys. 94, 7178 2003 ; J. Vac. Sci. Technol. B 22, 219

/pdf/dynamic-coupling-of-piezoelectric-effects-spontaneous-4w34vq1k3k.pdf

Morten Willatzen

Papers

Inclusion of Nonlinear Strain Effects in the Hamiltonian for Nanoscale Semiconductor Structures

Theoretical study of the electromechanical efficiency of a loaded tubular dielectric elastomer actuator

Energy Optimization of a Mirror‐Symmetric Spherical Triboelectric Nanogenerator

Comment on: “Confined states in two-dimensional flat elliptic quantum dots and elliptic quantum wires” [Physica E 11 (2001) 345] ☆

Dynamic coupling of piezoelectric effects, spontaneous polarization and strain in lattice-mismatched semiconducter quantum-well heterostructures