My research primarily concerns itself with computing the structure and dynamics of atomic and molecular liquid systems. Both dynamic N-body computer simulations and solutions to the integrodifferential equations of many-body physics are demanding computational challenges. This laboratory's mathematical and computational interests are broad and range from the basic mathematical physics governing polar molecules in the liquid state to work which is aimed at elucidating the fundamental aspects of biomolecular conformational structure and dynamics in solution.

We are involved in a number of efforts related to algorithm development on massively parallel machines. With several such machine on campus of varied architecture we are well positioned to test different programming models on a variety of algorithms. Scaling with respect to both processor number/bandwidth and intrinsic physical problem size are of current significance. We are interested in developing techniques for shared memory architectures as well as distributed systems. Much of our work concerns when to use the extremes of domain decomposition versus replicated data or to use the more flexible semireplicated strategies which are practical on shared memory machines. Specifically, dynamically load balancing can lead to irreproducible trajectories. We are currently using genetic optimization techniques to pre-explore the load on a a given system over time and choose the best load balance for a long production run in advance.

A number of the computational grand challenges facing our society involve biological molecules atomic-level behavior. Basic advances in theory and understanding of the liquid systems have provided new insights into the microscopic mechanisms of conformational changes in small biologically interesting molecules. This is an exciting area of science for which new approaches are being developed in this laboratory. We have analyzed the conformations of neurotransmitters and antiviral drug molecules in saline solution. New methods are being developed in the group to examine the free energy consequences of changing both functional sidechains and conformations near a substrate to study the elementary physical processes involved in binding and recognition. This work in molecular design provides several collaborating experimental groups with several new candidates for synthesis.

We are alos interested in the fusion of informatics and physics. How one gets from Biophysics to bioinformatics is a powerful challenge at present requiring considerable Computer Science. New tools and concepts in complexity theory as well as effcient algorithms are required. We have discovered a number of features of whole genomes which allow us to use the tools of statistical distribution functions to understand the information (and randomness) of genomes.

"Molecular Dynamics on a Distributed-Memory Multiprocessor", J. Comp. Chem., 13, 1022-1035 (1992); S. L. Lin, J. Mellor-Crummey, B.M. Pettitt, and G.N. Phillips.

"Ordinary Differential Equations of Molecular Dynamics, Comp. Math. Applic., 28 319-326 (1994); J. Andrew McCammon, Ridgway Scott and B. M. Pettitt.

"The Scaling of Molecular Dynamics On the KSR-1", I.E.E.E. Proceedings, Vol 5, 142-152 (1995); R. Haacke and B.M. Pettitt.

"Non-isotropic Solutions of an OZ equation: Matrix Methods for Integral Equations", Comp. Phys. Comm. 85 239-250 (1995); Z.-M. Chen and B.M. Pettitt.

"Efficient Ewald Electrostatic Calculations for Large Systems", Comp. Phys. Comm. 91 339-344 (1995); P.E. Smith and B.M. Pettitt.

"Ewald Artifacts in Liquid State Molecular Dynamics Simulations," by J. Chem. Phys. 105 4289-4293 (1996); Paul E. Smith and B. M. Pettitt.

"Numerical considerations in the computation of the electrostatic free energy of interaction within the Poisson-Boltzmann theory," J. Comp. Physics 136 263-271 (1997); A. M. Micu, B. Bagheri, A. V. Ilin, L. R. Scott and B. M. Pettitt.

"On the Presence of Rotational Ewald Artifacts in the Equilibrium and Dynamical Properties of a Zwitterionic Tetrapeptide in Solution," J. Phys. Chem. 101 3886-3890 (1997); Paul Smith, Herb Blatt and B. M. Pettitt.

"Computationally useful bridge diagram series for the structure and thermodynamics of Lennard-Jones fluids," Theo. Chem. Accounts 96 61-70 (1997); John Perkyns, and B. M. Pettitt.

"A Reexamination of the Virial Coefficients of the Lennard-Jones Fluid," T. Chem. Acc. 105 244-251 (2001); Kippi Dyer, J.S. Perkyns and B. M. Pettitt.

"Large Scale Distributed Data Repository: Design of a Molecular Dynamics Trajectory Database" Future Generation Computer Systems, 16 101-110 (1999); Michael Feig, Matin Abdullah, Lennart Johnsson, and B. M. Pettitt.

"SimDB: A Problem Solving Environment for Molecular Dynamics Simulation and Analysis" 1st EGRID Forum (2000) L. Johnsson, Michael Feig and B.M. Pettitt.

"Numerical Simulation of the Sedimentation of a Tripole-like body in an incompressible Viscous Fluid" Applied Math. Lett. (2002); L. H. Juarez, R. Glowinski, B. M. Pettitt.

"Reconstruction of the genetic regulatory dynamics of the Rat spinal cord develop- ment: Local Invariants Approach" J. Biomed. Informatics (submitted); Y. Fofanov and B.M. Pettitt.

"Short subsequences in genomes: How random are they?" Genomic Research (submit- ted); Yi Luo, Charles Katili, Jim Wang, Yuri Y. Belosludtsev, Thomas F. Powdrill, Viacheslav Fofanov, Sergey Chumakov, Yuriy Fofanov, and B. M. Pettitt.

"How correlated (independent) are appearances of n-mers in different genomes?" Genomic Research (submitted); Yi Luo, Charles Katili, Jim Wang, Yuri Y. Belosludtsev, Thomas F. Powdrill, Viacheslav Fofanov, Sergey Chumakov, Yuriy Fofanov, and B. M. Pettitt.

"A fast solver for the Ornstein-Zernike Equations", J. Comp. Phys. 197/2 491-501 (2004); C.T. Kelly and B.M. Pettitt.

"How correlated (independent) are appearances of n-mers in different genomes?" Bioinformatics (in press); Yi Luo, Charles Katili, Jim Wang, Yuri Y. Belosludtsev, Thomas F. Powdrill, Viacheslav Fofanov, Sergey Chumakov, Yuriy Fofanov, and B. M. Pettitt.

"Communications Overlapping in Fast Multipole Particle Dynamics Methods", J. Comp. Phys. (in press); Jakub Kurzak, B. M. Pettitt.

"Short subsequences in genomes: How random are they?" Technical Report, Comp. Sci. U of H (2004); Yi Luo, Charles Katili, Jim Wang, Yuri Y. Belosludtsev, Thomas F. Powdrill, Viacheslav Fofanov, Sergey Chumakov, Yuriy Fofanov, and B. M. Pettitt.

"Using Statistical Properties of Short Subsequences in Microbial Identification", Proc. Int. Con. Math. Eng. Tech. Med. Bio. Sci. S. Chumakov, Catherine Putonti, B. M. Pettitt, George E. Fox, Richard C. Willson, Yuriy Fofanov, (Las Vegas, Nevada), 2004: 363-367.

"Massively Parallel Implementation of a Fast Multipole Method for Distributed Mem- ory Machines" Journal of Parallel and Distributed Computing 65 870-881 (2005); Jakub Kurzak, B.M. Pettitt.

"The theoretical basis of universal identification systems for bacteria and viruses", The Journal of Biological Physics and Chemistry 5, 121-11128 (2005); S. Chumakov, C. Belapurkar, C. Putonti, T.-B. Li, B.M. Pettitt, G. E. Fox, R. C. Willson and Y. Fofanov.

"Fast Multipole Methods for Particle Dynamics" Molecular Simulations 32 1-17 (2006); Jakub Kurzak, B.M. Pettitt.

"Using Mutual Information to Discover Temporal Patterns in Gene Expression Data", Medical Physics: Ninth Mexican Symposium on Medical Physics, 854 25-30 (2006); Chumakov S., Ballesteros E., Snchez Rodrguez, J.E., Chvez, A., Zhang, M., Pettitt, B.M. and Fofanov, Y.

" A Systematic Investigation of Theories of Transport in the Lennard-Jones Fluid", "PIDA: A new algorithm for pattern identification", O. J. Bioinf. (in press) Catherine Putonti, B. M. Pettitt, Jeffrey Reid and Yuriy Fofanov.

"Generation of FFT's for Translations of Multipole Expansions in Spherical Harmonics" J. High Perf. Comp., (in press); Jakub Kurzak, Dragan Mirkovic, B.M. Pettitt and S. Lennart Johnsson.

"Message-Passing Implementation of the Data Diffusion Communication Model in Fast Multipole Methods: Large Scale Biomolecular Simulations" J. Algor. Comp. Tech., (in press); Jakub Kurzak, B.M. Pettitt