[blubar]

RESEARCH AND PUBLICATIONS

RESEARCH

The general areas of my research are Scientific Computing, Mathematical Modeling and Dynamical Systems, as they relate to problems in physics and engineering. Problems that interest me can be broadly classified as fluids. These include plasmas, free surface problems with external forces, flow in micro/nano tubes, etc. As a class of problems, these types of fluids have a very rich and complex range of behaviors which require both analysis and simulation to understand.

Current active areas of research include the development of fully Lagrangian methods for problems in plasma physics, transport theory for coarse grained kinetic models, computational gas dynamics and the evolution of free surfaces in conducting fluids. In addition, I am interested in the study of convergence and stability of fast summation algorithms for the inversion of dense matrices.

PUBLICATIONS

Thesis

  • `Computational Methods for Long Mean Free Path Problems', Christlieb A.J, Ph. D. thesis, University of Wisconsin-Madison, 2001.

Journal Articles

  • `Grid-Free Monte Carlo Methods for Gas and Plasma Dynamics Simulations', Christlieb A.J. and S. Olson, Submitted SEP 2006
  • `Grid-Free Plasma Simulation Techniques', Christlieb A.J., R. Krasny, J.P. Verboncoeur, J. Emhoff and I.D. Boyd, IEEE Transactions on Plasma Science, Volume 34, Num. 2, pg. 149, 2006
  • `The Broadwell Model in a Thin Channel', Christlieb, A.J., J.A. Rossmanith and P. Smereka, Communications in the Mathematical Sciences, Volume 2, pg. 443, 2004
  • `A Treecode Algorithm for Simulating Electron Dynamics in a Penning-Malmberg Trap', Christlieb A.J., R. Krasny and J.P. Verboncoeur, Computer Physics Communications, Volume 164, pg. 306, 2004
  • `Efficient Particle Simulation of a Virtual Cathode using a Grid-Free Treecode Poisson Solver', Christlieb A.J., R. Krasny and J.P. Verboncoeur, IEEE Transactions on Plasma Science-Special Issue, Volume 32, Num. 2, pg. 384, 2004.
  • `Kinetic Description of Flow Past a Micro-Plate', Christlieb A.J., W.N.G. Hitchon, I.D. Boyd and Q. Sun, Journal of Computational Physics, Volume 195, pg 508, 2004.
  • `Three-Dimensional Solutions of the Boltzmann Equation: Heat Transport at Long Mean Free Paths', Christlieb A.J. and W.N.G. Hitchon, Physical Review E, Volume 65, Issue 5, Articles 056708, May 2002.
  • `A computational investigation of the effects of varying discharge geometry for inductively coupled plasmas', Christlieb A.J., W.N.G. Hitchon and E. Keiter, IEEE Transactions on Plasma Science, 28:2214, 2000.

Conference Papers

  • 'Simulations of Charged Droplets Using Level Sets and the Boundary Integral Formulation of Electric Fields', VanderWyst A., A. Christlieb, M. Sussman, and I.D. Boyd, 2nd Colloid Thruster/Nano Electrojet Workshop at MIT, Cambridge, MA, April 2005
  • 'Boundary Integral Formulation of Electric Fields in Level Set Simulation of Charged Droplets', VanderWyst A., A. Christlieb, M. Sussman, and I.D. Boyd, 36th AIAA Plasmadynamics and Lasers Conference, Toronto, Canada, June 2005
  • 'Level Set Simulations of Charged Droplets Using a Boundary Integral Method', VanderWyst A., A. Christlieb, M. Sussman, and I.D. Boyd, 29th International Electric Propulsion Conference (IEPC), Princeton, NJ, November 2005
  • `The Limiting Behavior of the Broadwell Model (Flow in a Thin Channel) ',Christlieb, A.J., J. Rossmanith and P. Smereka, 24rd Symposium on Rarefied Gas Dynamic, Bari, Italy, July 10-15, 2004.
  • `Grid-free Plasma Simulations Based on Hierarchical Treecode Field Solvers ', Christlieb A.J., R. Krasny, J.W. Emhoff and I.D. Boyd, 24rd Symposium on Rarefied Gas Dynamic, Bari, Italy, July 10-15, 2004.
  • `An Accurate Kinetic Scheme for 3D Solution of the Boltzmann Equation', Christlieb A.J. and W.N.G. Hitchon, 23rd Symposium on Rarefied Gas Dynamic, Whistler, British Columbia, Canada, July 20-25, 2002.
  • `Application of the Transition Probability Matrix Method to High Knudsen Number Flow Past a Micro-Plate', Christlieb A.J., W.N.G. Hitchon, Q. Sun and I.D. Boyd, 23rd Symposium on Rarefied Gas Dynamic, Whistler, British Columbia, Canada, July 20-25, 2002.
  • 52nd Gaseous Electronics Conference, Norfolk, VA, USA, October 5-8, 1999. Poster Session on Transport Phenomenon, 'A self consistent kinetic scheme for ions in complex geometry', Christlieb A.J. and W.N.G. Hitchon.

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christlieb@math.msu.edu