Bernard Shizgal

Faculty Directory Header Image

Bernard Shizgal

Profile

Research and Teaching Interests

The research work involves basic investigations in statistical mechanics with applications to atmospheric and space scie nce, ion and electron transport, chemical kinetics including hot atom reactions, stochastic processes, and rarefied gas dynamics.

The basis for most of the work is the Boltzmann equation or Fokker-Planck equation for the distribution function or probability density function. An important aspect of the work is the development of new methods of solution of the transport equations. A combination of analytical and numerical techniques is employed. In recent years, a Quadrature Discretization Method (QDM) has been used with considerable success in the solution of kinetic theory as well as quantum mechanical problems.

Shizgal Group

The QDM of solution of the Boltzmann equation is employed to determine the distribution functions in a variety of physical situations. These include the velocity distribution of ions in suitable moderators; the relaxation of electrons in atomic and molecular systems; the reaction and relaxation of hot atoms; diffusion in bistable potentia ls and the escape of atomic and molecular species from the atmospheres of the planets.

Work is in progress towards an accurate solution of the Boltzmann equation for a planetary atmosphere including the escape of lighter constituents. The nonthermal escape of atomic and molecular species from the atmospheres of Earth, Mars and Venus is also considered. This research involves the theoretical modeling of the terrestrial exosphere and the coupling with the ionosphere-magnetosphere systems. A major objective will be the modeling of the exosphere-ionosphere system from the collision dominated region at low altitudes to the collisionless region at high altitudes. This includes the kinetic theory of energetic species, notably atomic oxygen and O+, and in particular the energization mechanisms that lead to escape. The project is one of several research projects in preparation for the launch of the Enhanced Polar Outflow Probe (ePOP) in 2011, and is carried out in collaboration with Professor Andrew Yau of the Institute of Space Imaging Science at the University of Calgary. A description of the satellite mission, science objectives and the science team can be found at http://epop.phys.ucalgary.ca/index.html. The theoretical modeling results will be compared with data from ePOP.

A number of physical situations such as reaction rates in solution, optical bistability in lasers, reaction diffusion equations in modelling cardiac arrhythmias and other diffusive-type processes are studied with the Kramers and/or Fokker-Planck equations. Efficient methods of solution of these equations have been developed.

Recent work includes the development of the Inverse Polynomial Reconstruction Method (IPRM) in the resolution of Gibbs phenomenon. This new method for the removal of spurious oscillations in Fourier representations will provide a new method for the reconstruction of images in tomography.

Contact

Real name: 
Email: 
Office Room Number(s): 
Chemistry D326
Office Phone Number: 
604-822-3997
Fax Number: 
604-822-2847

Curriculum Vitae

B.Sc., McGill (1964); Ph.D., Columbia (M. Karplus, 1968); Postdoctoral, Leiden (P. Mazur, 1968-69) and British Columbia (R.F. Snider, 1969-70). Killam Research Fellowship (1987). Fellow of the Japanese Society for the Promotion of Science (1984, 1987, 1994, 1995, 1997, 2004). Visiting Professor, Univ. Aix-Marseille, Univ. de Nice Sophia-Antipolis, Institute for Space and Astronautical Scence (Japan), Univ. Catholique de Louvain-la-Neuve, Univ. Libre de Bruxelles, Univ. of Hokkaido (Japan), Communications Research Laboratory (Japan).

Publications

2010

Shizgal, B. D. ; Dridi, R. Maple Code For The Calculation Of The Matrix Elements Of The Boltzmann Collision Operators For Mixtures. Computer Physics Communications 2010, 181, 1633 - 1640.

2009

Shizgal, B. D. Comment On "approach To Thermal Equilibrium In Atomic Collisions". Physical Review Letters 2009, 103, 1.
Olmos, D. ; Shizgal, B. D. Pseudospectral Method Of Solution Of The Fitzhugh-Nagumo Equation. Mathematics and Computers in Simulation 2009, 79, 2258-2278.
Chang, Y. B. ; Shizgal, B. D. Compact Collision Kernels For Hard Sphere And Coulomb Cross Sections; Fokker-Planck Coefficients. In Rarefied Gas Dynamics; Abe, T. ; Rarefied Gas Dynamics; Amer Inst Physics: Melville, 2009; Vol. 1084, pp. 140-145.
Chang, Y. B. ; Shizgal, B. D. Pseudospectral Solution Of The Boltzmann Equation: Quantum Cross Sections. In Rarefied Gas Dynamics; Abe, T. ; Rarefied Gas Dynamics; Amer Inst Physics: Melville, 2009; Vol. 1084, pp. 421-426.
Shizgal, B. D. Relaxation Behavior For The Lorentz Fokker Planck Equation: Model Cross Sections And Nonextensive Entropy. In Rarefied Gas Dynamics; Abe, T. ; Rarefied Gas Dynamics; Amer Inst Physics: Melville, 2009; Vol. 1084, pp. 39-44.

2008

Lo, J. Q. W. ; Shizgal, B. D. An Efficient Mapped Pseudospectral Method For Weakly Bound States: Vibrational States Of He-2, Ne-2, Ar-2 And Cs-2. Journal of Physics B-Atomic Molecular and Optical Physics 2008, 41, 13.
Napier, D. G. ; Shizgal, B. D. Sound Dispersion In Single-Component Systems. Physica a-Statistical Mechanics and Its Applications 2008, 387, 4099-4118.

2007

Jung, J. H. ; Shizgal, B. D. On The Numerical Convergence With The Inverse Polynomial Reconstruction Method For The Resolution Of The Gibbs Phenomenon. Journal of Computational Physics 2007, 224, 477-488.
Shizgal, B. D. Suprathermal Particle Distributions In Space Physics: Kappa Distributions And Entropy. Astrophysics and Space Science 2007, 312, 227-237.

2006

Shizgal, B. D. ; Chikhaoui, A. On The Use Temperature Parameterized Rate Coefficients In The Estimation Of Non-Equilibrium Reaction Rates. Physica a-Statistical Mechanics and Its Applications 2006, 365, 317-332.
Gibelli, L. ; Shizgal, B. D. Spectral Convergence Of The Hermite Basis Function Solution Of The Vlasov Equation: The Free-Streaming Term. Journal of Computational Physics 2006, 219, 477-488.
Olmos, D. ; Shizgal, B. D. A Pseudospectral Method Of Solution Of Fisher’S Equation. Journal of Computational and Applied Mathematics 2006, 193, 219-242.

2005

Jung, J. H. ; Shizgal, B. D. Inverse Polynomial Reconstruction Of Two Dimensional Fourier Images. Journal of Scientific Computing 2005, 25, 367-399.

2004

Jung, J. H. ; Shizgal, B. D. Generalization Of The Inverse Polynomial Reconstruction Method In The Resolution Of The Gibbs Phenomenon. Journal of Computational and Applied Mathematics 2004, 172, 131-151.
Shizgal, B. D. Neutral Particle Collisional Relaxation Of Suprathermal Distributions In Aeronomy. Planetary and Space Science 2004, 52, 915-922.

2003

Shizgal, B. D. ; Jung, J. H. Towards The Resolution Of The Gibbs Phenomena. Journal of Computational and Applied Mathematics 2003, 161, 41-65.
Kabin, K. ; Shizgal, B. D. Exact Evaluation Of Collision Integrals For The Nonlinear Boltzmann Equation. In Rarefied Gas Dynamics; Ketsdever, A. D. ; Muntz, E. P. ; Rarefied Gas Dynamics; Amer Inst Physics: Melville, 2003; Vol. 663, pp. 35-42.

2002

Kabin, K. ; Shizgal, B. D. Velocity Distributions Of Energetic Atoms In Planetary Exospheres From Dissociative Recombination. Journal of Geophysical Research-Planets 2002, 107, 9.
Vasenkov, A. V. ; Shizgal, B. D. Numerical Study Of A Direct Current Plasma Sheath Based On Kinetic Theory. Physics of Plasmas 2002, 9, 691-700.
Vasenkov, A. V. ; Shizgal, B. D. Self-Consistent Kinetic Theory Of A Plasma Sheath. Physical Review E 2002, 65, 9.

2001

Chen, H. ; Shizgal, B. D. A Spectral Solution Of The Sturm-Liouville Equation: Comparison Of Classical And Nonclassical Basis Sets. Journal of Computational and Applied Mathematics 2001, 136, 17-35.
Vasenkov, A. V. ; Shizgal, B. D. Nonhydrodynamic Aspects Of Electron Transport Near A Boundary: The Milne Problem. Physical Review E 2001, 63, 11.
Shizgal, B. D. Hot Oxygen In The Exosphere Of Venus. In Rarefied Gas Dynamics; Bartel, T. J. ; Gallis, M. A. ; Rarefied Gas Dynamics; Amer Inst Physics: Melville, 2001; Vol. 585, pp. 119-126.

2000

Chen, H. L. ; Su, Y. H. ; Shizgal, B. D. A Direct Spectral Collocation Poisson Solver In Polar And Cylindrical Coordinates. Journal of Computational Physics 2000, 160, 453-469.

1999

Shizgal, B. D. Escape Of H And D From Mars And Venus By Energization With Hot Oxygen. Journal of Geophysical Research-Space Physics 1999, 104, 14833-14846.

1998

Chen, H. L. ; Shizgal, B. D. The Quadrature Discretization Method (Qdm) In The Solution Of The Schrodinger Equation. Journal of Mathematical Chemistry 1998, 24, 321-343.
Kowari, K. ; Leung, K. ; Shizgal, B. D. The Coupling Of Electron Thermalization And Electron Attachment In Ccl4/ar And Ccl4/ne Mixtures. Journal of Chemical Physics 1998, 108, 1587-1600.

1997

Shizgal, B. D. ; Chen, H. L. The Quadrature Discretization Method In The Solution Of The Fokker-Planck Equation With Nonclassical Basis Functions. Journal of Chemical Physics 1997, 107, 8051-8063.

1996

Shizgal, B. D. ; Arkos, G. G. Nonthermal Escape Of The Atmospheres Of Venus, Earth, And Mars. Reviews of Geophysics 1996, 34, 483-505.
Shizgal, B. D. ; Lordet, F. Vibrational Nonequilibrium In A Supersonic Expansion With Reaction: Application To O-2-O. Journal of Chemical Physics 1996, 104, 3579-3597.
Shizgal, B. D. ; Napier, D. G. Nonequilibrium Effects In Reactive Systems; The Effect Of Reaction Products And The Validity Of The Chapman-Enskog Method. Physica a-Statistical Mechanics and Its Applications 1996, 223, 50-86.

1995

Napier, D. G. ; Shizgal, B. D. Nonequilibrium Effects In Model Reactive Systems - The Role Of Species Temperatures. Physical Review E 1995, 52, 3797-3811.

1994

Merryfield, W. J. ; Shizgal, B. D. Discrete Velocity Model For An Escaping Single-Component Atmosphere. Planetary and Space Science 1994, 42, 409-419.
Kowari, K. ; Shizgal, B. D. Electron Degradation And Thermalization In Sih4 Gas. Chemical Physics 1994, 185, 1-11.
Demeio, L. ; Shizgal, B. D. Wentzel-Kramers-Brillouin Approach To Time-Dependent Nucleation. In Rarefied Gas Dynamics: Theory and Simulations; Shizgal, B. D. ; Weaver, D. P. ; Rarefied Gas Dynamics: Theory and Simulations; Amer Inst Aeronautics & Astronautics: Washington, 1994; Vol. 159, pp. 682-690.
Yang, H. H. ; Shizgal, B. Chebyshev Pseudospectral Multidomain Technique For Viscous-Flow Calculation. Computer Methods in Applied Mechanics and Engineering 1994, 118, 47-61.
Clarke, A. S. ; Shizgal, B. Relaxation Dynamics Of Hot Protons In A Thermal Bath Of Atomic-Hydrogen. Physical Review E 1994, 49, 347-358.

1993

Mansell, G. ; Merryfield, W. ; Shizgal, B. ; Weinert, U. A Comparison Of Differential Quadrature Methods For The Solution Of Partial-Differential Equations. Computer Methods in Applied Mechanics and Engineering 1993, 104, 295-316.
Merryfield, W. J. ; Shizgal, B. Properties Of Collocation 3Rd-Derivative Operators. Journal of Computational Physics 1993, 105, 182-185.
Clarke, A. S. ; Shizgal, B. On The Generation Of Orthogonal Polynomials Using Asymptotic Methods For Recurrence Coefficients. Journal of Computational Physics 1993, 104, 140-149.
Demeio, L. ; Shizgal, B. Time-Dependent Nucleation .2. A Semiclassical Approach. Journal of Chemical Physics 1993, 98, 5713-5719.
Demeio, L. ; Shizgal, B. A Uniform Wentzel-Kramers-Brillouin Approach To Electron-Transport In Molecular Gases. Journal of Chemical Physics 1993, 99, 7638-7651.

1992

Shizgal, B. ; Clarke, A. S. The Dynamics Of Hot-F Atoms In Low-Pressure Plasma-Etching Reactors. Chemical Physics 1992, 166, 317-328.
Barrett, J. ; Demeio, L. ; Shizgal, B. Coulomb Milne Problem. Physical Review A 1992, 45, 3687-3699.
Kowari, K. ; Demeio, L. ; Shizgal, B. Electron Degradation And Thermalization In Ch4 Gas. Journal of Chemical Physics 1992, 97, 2061-2074.

1991

Shizgal, B. A Uniform Wkb Analysis Of The Coupling Of Electron-Attachment And Thermalization In Gases. Journal of Physics B-Atomic Molecular and Optical Physics 1991, 24, 2909-2923.
Kowari, K. ; Shizgal, B. The Partial Continuous Slowing Down Approximation (Pcsda) In The Solution Of The Spencer-Fano Equation. Chemical Physics Letters 1991, 176, 575-580.
Kim, C. S. ; Shizgal, B. Relaxation Of Hot-Electron Distributions In Gaas. Physical Review B 1991, 44, 2969-2978.

1990

Leung, K. ; Barrett, J. C. ; Shizgal, B. Thermal Mobilities Of Electrons In Binary Rare-Gas Mixtures. Chemical Physics 1990, 147, 257-270.
Shizgal, B. ; Nishigori, T. A Uniform Wkb Approach To Electron Thermalization In Gases. Chemical Physics Letters 1990, 171, 493-498.

1989

Shizgal, B. ; Barrett, J. C. Time-Dependent Nucleation. Journal of Chemical Physics 1989, 91, 6505-6518.
Shizgal, B. ; McMahon, D. R. A. ; Viehland, L. A. Thermalization Of Electrons In Gases. Radiation Physics and Chemistry 1989, 34, 35-50.

1988

Nishigori, T. ; Shizgal, B. Short-Time Behavior Of Electron Thermalization In Gases. Journal of Chemical Physics 1988, 89, 3275-3278.
Shizgal, B. The Coupling Of Electron Thermalization And Electron-Attachment - Sf6 And Ccl4 In Rare-Gas Moderators. Journal of Physics B-Atomic Molecular and Optical Physics 1988, 21, 1699-1715.
Shizgal, B. ; Hatano, Y. Electron Thermalization Times For Helium-Krypton Mixtures. Journal of Chemical Physics 1988, 88, 5980-5981.
Viehland, L. A. ; Ranganathan, S. ; Shizgal, B. Transient Microwave Conductivity Of Electrons In Helium And Argon. Journal of Chemical Physics 1988, 88, 362-370.

1987

Ness, K. F. ; Shizgal, B. Transient Nonequilibrium Effects In The Attachment Of Electrons To Chlorofluoroethanes. Journal of Chemical Physics 1987, 86, 7065-7078.
Shizgal, B. Electron-Distribution Functions For Electron-Attachment To Sf6 And Model Systems. Chemical Physics Letters 1987, 138, 65-70.
Weinert, U. ; Shizgal, B. Radial Dependence Of The Density In A Planetary Exosphere. Planetary and Space Science 1987, 35, 199-207.
Shizgal, B. ; Ness, K. Thermalization And Annihilation Of Positrons In Helium And Neon. Journal of Physics B-Atomic Molecular and Optical Physics 1987, 20, 847-865.
Ranganathan, S. ; Shizgal, B. Transient Microwave Conductivity Of Electrons In Helium. Chemical Physics Letters 1987, 134, 220-224.

1986

McMahon, D. R. A. ; Ness, K. ; Shizgal, B. Electric-Field Dependence Of Transient Electron Longitudinal And Tranverse Diffusion-Coefficients In Rare-Gas Moderators. Journal of Physics B-Atomic Molecular and Optical Physics 1986, 19, 2759-2777.
Shizgal, B. ; Blackmore, R. A Collisional Kinetic-Theory Of A Plane Parallel Evaporating Planetary Atmosphere. Planetary and Space Science 1986, 34, 279-291.
Shizgal, B. Transient Electron Mobilities In Ethene And Cyclopropane. Chemical Physics 1986, 105, 325-332.

1985

McMahon, D. R. A. ; Shizgal, B. Hot-Electron Zero-Field Mobility And Diffusion In Rare-Gas Moderators. Physical Review A 1985, 31, 1894-1905.
Blackmore, R. ; Shizgal, B. A Solution Of Kramers Equation For The Isomerization Of Normal-Butane In Ccl4. Journal of Chemical Physics 1985, 83, 2934-2941.
Blackmore, R. ; Shizgal, B. Discrete-Ordinate Method Of Solution Of Fokker-Planck Equations With Nonlinear Coefficients. Physical Review A 1985, 31, 1855-1868.
Shizgal, B. ; McMahon, D. R. A. Electric-Field Dependence Of Transient Electron-Transport Properties In Rare-Gas Moderators. Physical Review A 1985, 32, 3669-3680.

1984

Shizgal, B. ; Blackmore, R. Discrete Ordinate Method Of Solution Of A Fokker-Planck Equation With A Bistable Potential. Chemical Physics Letters 1984, 109, 242-245.
Shizgal, B. ; Blackmore, R. A Discrete Ordinate Method Of Solution Of Linear Boundary-Value And Eigenvalue Problems. Journal of Computational Physics 1984, 55, 313-327.
Shizgal, B. Discrete Versus Continuum Relaxation Modes Of A Hard-Sphere Gas. Canadian Journal of Physics 1984, 62, 97-103.
Shizgal, B. ; McMahon, D. R. A. Electron-Distribution Functions And Thermalization Times In Inert-Gas Moderators. Journal of Physical Chemistry 1984, 88, 4854-4862.

1983

Shizgal, B. Electron Thermalization In Gases. Journal of Chemical Physics 1983, 78, 5741-5744.
Shizgal, B. Energy Relaxation Of Electrons In Helium. Chemical Physics Letters 1983, 100, 41-44.
Lindenfeld, M. J. ; Shizgal, B. The Milne Problem - A Study Of The Mass Dependence. Physical Review A 1983, 27, 1657-1670.
Fahr, H. J. ; Shizgal, B. Modern Exospheric Theories And Their Observational Relevance. Reviews of Geophysics 1983, 21, 75-124.

1982

Shizgal, B. ; Lindenfeld, M. J. A Simple Kinetic-Theory Calculation Of Terrestrial Atomic-Hydrogen Escape Fluxes Induced By Charge-Exchange Collisions. Journal of Geophysical Research-Space Physics 1982, 87, 853-858.

1981

Shizgal, B. ; Lindenfeld, M. J. ; Reeves, R. Eigenvalues Of The Boltzmann Collision Operator For Binary Gases - Mass Dependence. Chemical Physics 1981, 56, 249-260.

1980

Shizgal, B. ; Fitzpatrick, J. M. Non-Equilibrium Time-Dependent Theory Of Hot Atom Reactions .1. Model-Calculations. Journal of Chemical Physics 1980, 72, 3143-3155.
Berlinsky, A. J. ; Shizgal, B. Spin-Exchange Scattering Cross-Sections For Hydrogen-Atoms At Low-Temperatures. Canadian Journal of Physics 1980, 58, 881-885.
Shizgal, B. ; Lindenfeld, M. J. Further-Studies Of Non-Maxwellian Effects Associated With The Thermal Escape Of A Planetary Atmosphere. Planetary and Space Science 1980, 28, 159-163.

1979

Shizgal, B. Comparison Of Mu-H And H-H Electron-Spin Exchange Cross-Sections. Journal of Physics B-Atomic Molecular and Optical Physics 1979, 12, 3611-3617.
Shizgal, B. Eigenvalues Of The Lorentz Fokker-Planck Equation. Journal of Chemical Physics 1979, 70, 1948-1951.
Shizgal, B. ; Lindenfeld, M. J. Energy-Distribution Function Of Translationally Hot O(P-3) Atoms In The Atmosphere Of Earth. Planetary and Space Science 1979, 27, 1321-1332.
Fitzpatrick, J. M. ; Shizgal, B. Explicit Demonstration Of Epochal Relaxation In A Binary Gas-Mixture. Physics of Fluids 1979, 22, 436-438.
Lindenfeld, M. J. ; Shizgal, B. Matrix-Elements Of The Boltzmann Collision Operator For Gas-Mixtures. Chemical Physics 1979, 41, 81-95.
Lindenfeld, M. J. ; Shizgal, B. Non-Maxwellian Effects Associated With The Thermal Escape Of A Planetary Atmosphere. Planetary and Space Science 1979, 27, 739-751.
Shizgal, B. ; Fitzpatrick, J. M. Statistical Mechanical Interpretation Of The Translational Energy-Dependence Of Rate Processes. Canadian Journal of Physics 1979, 57, 486-489.

1978

Shizgal, B. ; Fitzpatrick, J. M. Possible Failure Of Relaxation-Time Comparison In Justification Of Local Thermodynamic-Equilibrium. Physical Review A 1978, 18, 267-276.
Shizgal, B. Steady States In Hot Atom Chemistry. Journal of Chemical Physics 1978, 69, 5354-5360.

1977

Shizgal, B. Departure From Translational Equilibrium For Interstellar Molecular-Hydrogen. Astrophysical Journal 1977, 217, 78-82.

1976

1975

Shizgal, B. ; Fitzpatrick, J. M. Temperature Relaxation In A Binary Gas .2. Time-Dependent Solution. Journal of Chemical Physics 1975, 63, 138-142.
Dickinson, A. S. ; Shizgal, B. Comparison Of Classical And Quantum Continuum Expectation Values. Molecular Physics 1975, 30, 1221-1228.
Fitzpatrick, J. M. ; Shizgal, B. Temperature Relaxation In A Binary Gas .1. Steady-State Solution. Journal of Chemical Physics 1975, 63, 131-137.

1974

Shizgal, B. Calculation Of Nmr Relaxation-Time Of Dilute Xe-129 Gas. Chemical Physics 1974, 5, 464-470.

1973

Shizgal, B. Kinetic-Theory Calculation Of Nmr Relaxation-Time Of Dilute He-3 Gas. Journal of Chemical Physics 1973, 58, 3424-3431.
Shizgal, B. Method For Obtaining Potential Parameters For Helium From T1 Measurements. Chemical Physics Letters 1973, 20, 265-268.