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

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Estimation of Small Failure Probabilities in High Dimensions by Subset Simulation

Dynamics of structures

Staff members at Los Alamos National Laboratory (LANL) produced a summary of the structural health monitoring literature in 1995. This presentation will summarize the outcome of an updated review covering the years 1996 2001. The updated review follows the LANL statistical pattern recognition paradigm for SHM, which addresses four topics: 1. Operational Evaluation; 2. Data Acquisition and Cleansing; 3. Feature Extraction; and 4. Statistical Modeling for Feature Discrimination. The literature has been reviewed based on how a particular study addresses these four topics. A significant observation from this review is that although there are many more SHM studies being reported, the investigators, in general, have not yet fully embraced the well-developed tools from statistical pattern recognition. As such, the discrimination procedures employed are often lacking the appropriate rigor necessary for this technology to evolve beyond demonstration problems carried out in laboratory setting.

A review of structural health monitoring literature 1996-2001

A general framework is presented for deriving the differential equations governing the evolution of the response cumulants of linear and nonlinear dynamical systems subjected to external and multiplicative non-Gaussian delta-correlated processes. Significant simplifications of these equations are given based on using appropriate recursive relationships for joint cumulants involving products of one or more variables. A compact form of the equations for the response cumulants is presented which provides insight into the structure of the cumulant equations for specific types of dynamical systems. The procedure developed can easily be implemented in computer software to derive symbolic cumulant equations and to estimate numerically the response cumulants of systems with power-law nonlinearities using approximate cumulant-neglect closure schemes. Comparison between the equations for cumulants and the equations for moments are also presented, with particular emphasis on the advantages and disadvantages of each formulation. Suggestions are given regarding the choice to use cumulant or moment equations for analysing the stochastic response of dynamical systems. The preferred formulation is shown to depend on the type of system analysed (linear or nonlinear), the type of system nonlinearity (polynomial or non-polynomial), and the type of excitation (external or multiplicative, delta-correlated or filtered).

Response cumulants of nonlinear systems subject to external and multiplicative excitations

This chapter presents a model reduction technique based on substructure coupling for dynamic analysis. The dynamic behavior of the substructures is described by a set of dominant fixed-interface normal modes along with a set of interface constraint modes that account for the coupling at each interface where the substructures are connected. Based on these modes, the corresponding reduced-order matrices are derived. The internal dynamic behavior of the substructures is then enhanced by consideration of the contribution of residual fixed-interface normal modes. Next, the interface degrees of freedom are reduced by consideration of a small number of characteristic constraint modes. Pseudo-codes are provided in order to illustrate how the reduced-order matrices are constructed, by including dominant and residual fixed-interface normal modes as well as interface reduction. Finally, the dynamic response of reduced-order models is discussed.

Model Reduction Techniques for Structural Dynamic Analyses

The main objective of the present work was to accurately predict the dynamic response of a gear transmission system. First, a nonlinear mathematical model is introduced. In this model, the housing of the gearbox is modeled by using finite elements, while the essential effects of the gear-pair, the bearings and the shafts are taken into account via a lumped nonlinear mathematical model. This model possesses strongly nonlinear characteristics, accounting for gear backlash, meshing stiffness, transmission error properties and bearing stiffness nonlinearities. Then, a Bayesian uncertainty quantification and propagation (UQ&P) framework is adopted in order to estimate the optimal values of the gearbox, gear-pair and bearing model parameters. In order to identify the values of the parameters, accelerations time histories are used, obtained during various operating conditions of the gearbox. These measurements are recorded from a special experimental device, which was designed and set up for this purpose. The effect of correlation in the prediction error models postulated in the Bayesian model selection and parameter estimation technique is investigated. Finally the experimental results was compared to those from the numerical model for verification of the numerical procedure and improvement of the numerical modeling of the gear transmission components.

Nonlinear Gear Transmission System Numerical Dynamic Analysis and Experimental Validation

A relatively straightforward formulation is presented for deriving the differential equations governing the evolution of the response cumulants and moments of a dynamical system. This is a very general framework which applies to linear and nonlinear systems subjected to external and multiplicative non-Gaussian, delta-correlated processes. This formulation provides an alternative to both the partial differential Fokker Planck equation that has sometimes been used in deriving moment or cumulant equations, and the differential (as opposed to derivative) relationships of the It8 calculus. It is believed that many analysts may find the technique used here to be more obvious than the alternatives, since the derivative relationships for the stochastic process are of the same form as in the more familiar ordinary differential equations.

Costas Papadimitriou

Papers

Response cumulants of nonlinear systems subject to external and multiplicative excitations

Model Reduction Techniques for Structural Dynamic Analyses

Nonlinear Gear Transmission System Numerical Dynamic Analysis and Experimental Validation

Finding Response Cumulants for Nonlinear Systems With Multiplicative Excitations

Fatigue reliability predictions in vibrating structures under uncertainty