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

Characterization of hierarchically structured electrodes with different thicknesses by means of experiments and image analysis

Optimization of functional materials is a challenging task. Thereby, stochastic morphology models can provide helpful methods. Three classes of stochastic models are presented describing different micro-structures of functional materials by means of methods from stochastic geometry, graph theory and time series analysis. The structures of these materials strongly differ from each other, where we consider organic solar cells being an anisotropic composite of two materials, nonwoven gas-diffusion layers in proton exchange membrane fuel cells consisting of a system of curved carbon fibers, and graphite electrodes in Li-ion batteries which are built up by an isotropic two-phase system (i.e., consisting of a pore and a solid phase). The goal is to give an overview how the stochastic modeling of functional materials can be organized and to provide an outlook how these models can be used for material optimization with respect to functionality.

https://link.springer.com/content/pdf/10.1007%2F978-3-319-10064-7_4.pdf

Stochastic 3D Models for the Micro-structure of Advanced Functional Materials

Three different electrode morphologies are generated from three different starting powders, spheres representing non aggregated powders, agglomerates of spheres and high aspect ratio cylinders modelling splats formed in plasma sprays. Electrodes from each morphology are analysed using finite volumes to predict the effective transport coefficients, the triple phase boundary length and the performance of the electrode. The same structures are also analysed using morphological characterization which can be much more efficient. It was found that high aspect ratio base particles are favourable, and that constrictivity correlates best with the finite volume transport calculations.

/pdf/the-effect-of-electrode-morphology-on-solid-oxide-fuel-cell-2blldg9aak.pdf

The Effect of Electrode Morphology on Solid Oxide Fuel Cell Performance

From simulating galaxy formation to viral transmission in a pandemic, scientific models play a pivotal role in developing scientific theories and supporting government policy decisions that affect us all. Given these critical applications, a poor modelling assumption or bug could have far-reaching consequences. However, scientific models possess several properties that make them notoriously difficult to test, including a complex input space, long execution times, and non-determinism, rendering existing testing techniques impractical. In fields such as epidemiology, where researchers seek answers to challenging causal questions, a statistical methodology known as Causal Inference has addressed similar problems, enabling the inference of causal conclusions from noisy, biased, and sparse data instead of costly experiments. This paper introduces the Causal Testing Framework: a framework that uses Causal Inference techniques to establish causal effects from existing data, enabling users to conduct software testing activities concerning the effect of a change, such as Metamorphic Testing, a posteriori. We present three case studies covering real-world scientific models, demonstrating how the Causal Testing Framework can infer metamorphic test outcomes from reused, confounded test data to provide an efficient solution for testing scientific modelling software.

Volker Schmidt

Papers

Characterization of hierarchically structured electrodes with different thicknesses by means of experiments and image analysis

Stochastic 3D Models for the Micro-structure of Advanced Functional Materials

The Effect of Electrode Morphology on Solid Oxide Fuel Cell Performance

Testing Causality in Scientific Modelling Software

Stochastic Modeling of Fuel‐Cell Components