There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

https://www.tau.ac.il/%7Eklafter1/258.pdf

The random walk's guide to anomalous diffusion: a fractional dynamics approach

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

General Theory: The Entropy Production for a Homogeneous Phase The Excess Entropy Production for the Surface Flux Equations and Onsager Relations Transport of Heat and Mass Transport of Mass and Charge Applications: Evaporation and Condensation A Non-Isothermal Concentration Cell Adiabatic Electrode Reactions The Formation Cell Modeling the Polymer Electrolyte Fuel Cell The Impedance of an Electrode Surface The Non-Equilibrium Two-Phase van der Waals Model and other chapters.

Non-Equilibrium Thermodynamics of Heterogeneous Systems

The theory of non-equilibrium thermodynamics is applied to a system of two immiscible fluids and their interface. A singular energy density at the interface, which is related to the phenomenon of surface tension, is taken into account. Furthermore the momentum and the heat currents are allowed to be singular at the interface. Using the conservation laws and the Gibbs' relation for the surface, an expression for the singular entropy production density at the interface is obtained. The linear phenomenological laws between fluxes and thermodynamic forces occurring in this singular entropy production density are given. Some of these linear laws are boundary conditions for the solution of the differential equations governing the evolution of the state variables in the bulk.

Boundary conditions and non-equilibrium thermodynamics

The Kirkwood-Buff formula for surface tension is used to derive an expression for the tail correction to the surface tension. This expression reduces to the expression for the tail correction, given by Chapela, G. A., Saville, G., Thompson, G., and Rowlinson, J. S. (1977, J. chem. Soc. Faraday Trans II, 8, 1133), when the interface is sharp but differs from it near the critical point. The difference appears to be the result of a mistake in the algebra by Chapela et al. In an example we show that, for a comparison with the surface tension of real fluids, both the tail correction to the surface tension, and the influence of the cut-off radius on the phase diagram are important.

Tail corrections to the surface tension of a Lennard-Jones liquid-vapour interface

Exact expressions for finite-volume Kirkwood−Buff (KB) integrals are derived for hyperspheres in one, two, and three dimensions. These integrals scale linearly with inverse system size. From this, accurate estimates of KB integrals for infinite systems are obtained, and it is shown that they converge much better than the traditional expressions. We show that this approach is very suitable for the computation of KB integrals from molecular dynamics simulations, as we obtain KB integrals for open systems by simulating closed systems.

/pdf/kirkwood-buff-integrals-for-finite-volumes-3i8xq3yi9u.pdf

Dick Bedeaux

Papers

Non-Equilibrium Thermodynamics of Heterogeneous Systems

Boundary conditions and non-equilibrium thermodynamics

Tail corrections to the surface tension of a Lennard-Jones liquid-vapour interface

Kirkwood–Buff Integrals for Finite Volumes

Brownian motion and fluctuating hydrodynamics