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

Nanostructure shape effects have become a topic of increasing interest due to advancements in fabrication technology. In order to pursue novel physics and better devices by tailoring the shape and size of nanostructures, effective analytical and computational tools are indispensable. In this chapter, we present analytical and computational differential geometry methods to examine particle quantum eigenstates and eigenenergies in curved and strained nanostructures. Example studies are carried out for a set of ring structures with different radii and it is shown that eigenstate and eigenenergy changes due to curvature are most significant for the groundstate eventually leading to qualitative and quantitative changes in physical properties. In particular, the groundstate in-plane symmetry characteristics are broken by curvature effects, however, curvature contributions can be discarded at bending radii above 50 nm. In the second part of the chapter, a more complicated topological structure, the Mobius nanostructure, is analyzed and geometry effects for eigenstate properties are discussed including dependencies on the Mobius nanostructure width, length, thickness, and strain.

Differential Geometry Applied to Rings and Möbius Nanostructures

In the present work we calculate the electronic band structure of single-wall helical carbon nanotubes following an effective-mass approach. We include curvature effects and strain due to bending in the band structure. The curvature energy ΔE, and the change in the electronic energy ΔEs due to strain, depend upon the coil pitch and coil diameter of the tube. We find 0.003 ≤|ΔE|≤ 1.3 eV and 0 ≤ΔEs ≤ 4.0 eV for the single-wall helical carbon nanotubes considered here.

Electronic Structure of Helically Coiled Carbon Nanotubes

We present results of the computational stability and efficiency in simulating two-phase flow and heat transfer in a horizontal tube. Two structurally different models of the process are presented and compared for two dynamic computational scenarios; dynamic response for a constant and changing number of flow-zones, respectively. The first model is a simple generic lumped model of the moving boundary type and the second is a fully distributed model in one dimension. The moving boundary model is solved as a set of conventional ordinary differential equations whereas the distributed model is solved using a highly-efficient numerical scheme following Kurganov & Tadmor (2000). The governing equations are formulated in terms of mass flow, enthalpy, pressure, and tube wall temperature based on the continuity-, momentum- and energy equations for the fluid. A wall heat-exchange equation accounts for convective heat exchange between the fluid and the ambient air. The comparison demonstrates a significant difference in the results obtained using the two models, especially in the case where the number of fluid zones is changing. This emphasizes the importance of using either more advanced moving boundary models or fully distributed models in the simulation of systems comprising two-phase flows. In contrast to conventional belief we find that the finite difference model is indeed both stable to discontinuities in boundary conditions; changing number of fluid zones; high frequency perturbations and also at the same time numerically fast enough for real-time simulation and control.

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Efficient Numerical Solution of One-Dimensional Governing Equations for Evaporating Flow in a Tube

In this paper we theoretically investigate the allowed energies and associate wave-functions for Mo¨bius strips with varying thicknesses. We show that the induced strain in fabricating these Mo¨bius strips will have an pronounced impact on the energies and wave-functions for thick strips, while for thin strips the impact of strain is negligible. We furthermore, show that a simpler strain free approximate theory base on differential geometry is in excellent agreement with detailed finite element calculations.

Effects of hydrostatic strain on eigenstates of Möbius strips

It is well known that the origin of one type of spurious solutions in multiband k(.)p theory is the failure to restrict the Fourier coefficients of the envelope functions to the first Brillouin zone. Often, the set of differential equations obtained is supplemented with interfacial boundary conditions derived by integrating the differential equations across the interface; however, this leads to a mathematically ill-posed problem as the envelope functions cannot simultaneously fulfill these boundary conditions and the requirement that the Fourier coefficients be restricted to the first Brillouin zone. We show, by way of an example, the origin of these spurious solutions and how to remove them.

Morten Willatzen

Papers

Differential Geometry Applied to Rings and Möbius Nanostructures

Electronic Structure of Helically Coiled Carbon Nanotubes

Efficient Numerical Solution of One-Dimensional Governing Equations for Evaporating Flow in a Tube

Effects of hydrostatic strain on eigenstates of Möbius strips

Spurious solutions and boundary conditions in k · p theory