Statistical coarse-graining of molecular dynamics into peridynamics.

This paper describes an elegant statistical coarse-graining of molecular dynamics at finite temperature into peridynamics, a continuum theory. Peridynamics is an efficient alternative to molecular dynamics enabling dynamics at larger length and time scales. In direct analogy with molecular dynamics, peridynamics uses a nonlocal model of force and does not employ stress/strain relationships germane to classical continuum mechanics. In contrast with classical continuum mechanics, the peridynamic representation of a system of linear springs and masses is shown to have the same dispersion relation as the original spring-mass system

Krylov subspace iterations for the calculation of K-Eigenvalues with sn transport codes

We apply the Implicitly Restarted Arnoldi Method (IRAM), a Krylov subspace iterative method, to the calculation of k-eigenvalues for criticality problems. We show that the method can be implemented with only modest changes to existing power iteration schemes in an SN transport code. Numerical results on three dimensional unstructured tetrahedral meshes are shown. Although we only compare the IRAM to unaccelerated power iteration, the results indicate that the IRAM is a potentially efficient and powerful technique, especially for problems with dominance ratios approaching unity. Key Words: criticality eigenvalues, Implicitly Restarted Arnoldi Method (IRAM), deterministic transport method

Substructured multibody molecular dynamics.

We have enhanced our parallel molecular dynamics (MD) simulation software LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator, lammps.sandia.gov) to include many new features for accelerated simulation including articulated rigid body dynamics via coupling to the Rensselaer Polytechnic Institute code POEMS (Parallelizable Open-source Efficient Multibody Software). We use new features of the LAMMPS software package to investigate rhodopsin photoisomerization, and water model surface tension and capillary waves at the vapor-liquid interface. Finally, we motivate the recipes of MD for practitioners and researchers in numerical analysis and computational mechanics

A mathematical framework for multiscale science and engineering : the variational multiscale method and interscale transfer operators.

This report is a collection of documents written as part of the Laboratory Directed Research and Development (LDRD) project A Mathematical Framework for Multiscale Science and Engineering: The Variational Multiscale Method and Interscale Transfer Operators. We present developments in two categories of multiscale mathematics and analysis. The first, continuum-to-continuum (CtC) multiscale, includes problems that allow application of the same continuum model at all scales with the primary barrier to simulation being computing resources. The second, atomistic-to-continuum (AtC) multiscale, represents applications where detailed physics at the atomistic or molecular level must be simulated to resolve the small scales, but the effect on and coupling to the continuum level is frequently unclear

Topology and the Cosmic Microwave Background

Nature abhors an infinity. The limits of general relativity are often signaled by infinities: infinite curvature as in the center of a black hole, the infinite energy of the singular big bang. We might be inclined to add an infinite universe to the list of intolerable infinities. Theories that move beyond general relativity naturally treat space as finite. In this review we discuss the mathematics of finite spaces and our aspirations to observe the finite extent of the universe in the cosmic background radiation.Comment: Hilarioulsy forgot to remove comments to myself in previous version. Reference added. Submitted to Physics Report

SANDIA REPORT Statistical Coarse-Graining of Molecular Dynamics into Peridynamics NOTICE: Statistical Coarse-Graining of Molecular Dynamics into Peridynamics

Abstract This paper describes an elegant statistical coarse-graining of molecular dynamics at finite temperature into peridynamics, a continuum theory. Peridynamics is an efficient alternative to molecular dynamics enabling dynamics at larger length and time scales. In direct analogy with molecular dynamics, peridynamics uses a nonlocal model of force and does not employ stress/strain relationships germane to classical continuum mechanics. In contrast with classical continuum mechanics, the peridynamic representation of a system of linear springs and masses is shown to have the same dispersion relation as the original spring-mass system. 3

Compiler Blockability of Dense Matrix Factorizations

Recent architectural advances have made memory accesses a significant bottleneck for computational problems. Even though cache memory helps in some cases, it fails to alleviate the bottleneck for problems with large working sets. As a result, scientists are forced to restructure their codes by hand to reduce the working-set size to fit a particular machine. Unfortunately, these hand optimizations create machine-specific code that is not portable across multiple architectures without a significant loss in performance or a significant effort to re-optimize the code. It is the thesis of this paper that most of the hand optimizations performed on matrix factorization codes are unnecessary because they can and should be performed by the compiler. It is better for the programmer to express algorithms in a machine-independent form and allow the compiler to handle the machine-dependent details. This gives the algorithms portability across architectures and removes the error-prone, expensive an..