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

Statistics for Spatial Data.

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

비만아 부모의 돌봄 경험: q 방법론

A POINT PROCESS APPROACH FOR SPATIAL STOCHASTIC MODELING OF THUNDERSTORM CELLSIn this paper we consider two different approaches for spatial stochastic modeling of thunderstorms. Thunderstorm cells are represented using germ-grain models from stochastic geometry, which are based on Coxor doubly-stochastic cluster processes. We present methods for the operationa lfitting of model parameters based on available point probabilities and thunderstorm records of past periods. Furthermore, we derive formulas forthe computation of point and area probabilities according to the proposed germ-grain models. We also introduce a conditional simulation algorithm in order to increase the model’s ability to precisely predict thunderstorm events. A systematic comparison of area probabilities, which are estimated from the proposed models, and thunderstorm records conclude the paper.

/pdf/a-point-process-approach-for-spatial-stochastic-modeling-of-2knr0zfekq.pdf

A point process approach for spatial stochastic modeling of thunderstorm cells

The aim of this paper is to evaluate an ambitious imaging experiment and to contribute to the methodology of statistical inference of the three-dimensional microstructure of polycrystalline materials. The microstructure of the considered Al-3Mg-0.2Sc alloy was investigated by three-dimensional electron backscattered diffraction (3D-EBSD), i.e., tomographic imaging with xenon plasma focused ion beam (Xe-FIB) alongside EBSD. The samples were subjected to severe plastic deformations by equal channel angular pressing (ECAP) and annealed subsequently prior to the mapping. First we compared the misorientation level needed for a reliable segmentation of grains distinguishing between conventional evaluation of two-dimensional cuts and the 3D data set. Then, using methods of descriptive spatial statistics, various morphological characteristics of a large number of grains were analyzed, as well as the crystallographic texture and the spatial distribution of grain boundaries. According to the results stated so far in the literature, an even microstructure was expected, nevertheless local inhomogeneities in grains and grain boundaries with regard to their size, texture and spatial distribution were observed and justified.

/pdf/analysis-of-polycrystalline-microstructure-of-almgsc-alloy-1r5hmmwp2k.pdf

Analysis of Polycrystalline Microstructure of AlMgSc Alloy Observed by 3D EBSD

Solar power generation at solar plants is a strongly fluctuating non-deterministic variable depending on many influencing factors. In general, it is not clear which and how certain variables influence solar power supply at feed-in points in a distribution network. Therefore, analyzing the dependence structure of measured solar power supply and other variables is very informative and can be helpful in designing probabilistic prediction models. In this paper multivariate D-vine copulas are fitted to investigate the relationship between solar power supply and certain meteorological variables in the current time period of one hour length as well as solar power supply in previous time periods. The meteorological variables considered in this analysis are global horizontal irradiation, temperature, wind speed, humidity, precipitation and pressure. By applying parametric D-vine copulas useful insight is gained into the dependence structure of solar power supply and the considered meteorological variables. The main goal lies in determining suitable explanatory variables for the design of probabilistic prediction models for solar power supply at single feed-in points and analyzing their impact on the validation of conditional level-crossing probabilities.

Probabilistic Analysis of Solar Power Supply Using D-Vine Copulas Based on Meteorological Variables

We are going to introduce the concept of stochastic 3D modeling of geometrically complex (disordered) microstructures as a tool for virtual materials testing, including applications to battery electrodes as well as to electrodes of fuel cells, and solar cells. Using stochastic 3D models, one can generate a large variety of stochastically simulated micrsotructures with little computational effort. These virtual microstructures can be used as data basis to elucidate microstructure-property relationships. In this way, for example, effective conductivity can be expressed by microstructural characteristics such as volume fraction, tortuosity (windedness of transport paths) and costrictivity (bottleneck criterion) of the considered material phase. In another recent simulation study, we analysed more than 8000 virtual microstructures for various microstructural scenarios. Using data mining techniques like artificial neural networks and random forests, we were able to accurately predict effective conductivities given microstructure properties like volume fraction, tortuosity and constrictivity.

Stochastic 3d modeling of amorphous microstructures - a powerful tool for virtual materials testing

The notion of stationary Apollonian packings in the d-dimensional Euclidean space is introduced as a mathematical formalization of so-called random Apollonian packings and rotational random Apollonian packings, which constitute popular grain packing models in physics. Apart from dealing with issues of existence and uniqueness in the entire Euclidean space, asymptotic results are provided for the growth durations and it is shown that the packing is space-filling with probability 1, in the sense that the Lebesgue measure of its complement is zero. Finally, the phenomenon is studied that grains arrange in clusters and properties related to percolation are investigated.

/pdf/stationary-apollonian-packings-58g7tkz14y.pdf

Volker Schmidt

Papers

A point process approach for spatial stochastic modeling of thunderstorm cells

Analysis of Polycrystalline Microstructure of AlMgSc Alloy Observed by 3D EBSD

Probabilistic Analysis of Solar Power Supply Using D-Vine Copulas Based on Meteorological Variables

Stochastic 3d modeling of amorphous microstructures - a powerful tool for virtual materials testing

Stationary Apollonian Packings