Detailed Research Work History

Abbreviations used: P = Paper, C = Conference proceedings, R = Report. Numbers that follow refer to the list of my publications.


May 2002 - present: Principal Scientist
LS Computing Ltd

Modeling of reaction-diffusion and electrochemical processes.


April 1993 - April 2002: Mathematical Modeler
Atomic Energy of Canada Limited, Whiteshell Laboratories, Fuel Waste Technology Branch, Pinawa, Manitoba, Canada R0E 1L0

Modeling gas pipeline corrosion.
Participation in studies related to the concept of the permanent underground disposal of nuclear waste (R6):
- Corrosion modeling (C13-16,18,20,21,23,24,26, R7,8,11,12,16,20-25,27-29, P43) - reaction-diffusion, electrochemistry; finite differences.
- Modeling other reaction-diffusion and diffusion-convection processes using finite elements (C10, R3,9,10,17), and other methods (C9,12, R2).
- Analysing oxidation and dissolution experiments (P41, C19,22,25, R2).
- Surface, island-like oxidation (P40, P42).
- Helping with processing experimental data (P41, C11,17, R4), mathematical consulting.
- Other studies (R15,18,19).

Highlights: In the corrosion modeling: treatment of very complex electrochemical boundary conditions and of precipitate or moisture layers of variable thickness; Method of moments applied to a moving-boundary diffusion-reaction problem (R2); Island formation on solid surfaces (P43).


1995 - present: Personal projects
- C package (TRANSIENT) of finite-difference code for numerical solution of systems of reaction-diffusion equations (or rather general partial differential equations of the parabolic type) in one spatial variable that uses some novel elements (a new adaptable time-step algorithm, improved treatment of internal interfaces and boundary conditions).
- Internet programming (CGI scripts, Tower of Hanoi).

Highlights: Some features of the TRANSIENT; Fast nonrecursive algorithms for the Tower of Hanoi puzzle.


Sept. 1991 - April 1993: Research Associate
Department of Chemistry, University of Lethbridge, Lethbridge, Alberta, Canada T1K 3M4

- Quantum path-integral Monte-Carlo simulations: application to a 1-dimensional (1D) model of surface adsorption; formulation of an efficient high-temperature approximation of the method (P39).
- Quasirandom number generation: found new fast algorithm for the generation of the Halton numbers (P34).
- Study of 1D aperiodic deterministic systems (superlattices) - continuation of the work started in Marseilles (P37,38, C8), Thue-Morse system (P35).
- Investigation of dynamical systems - periodic windows in the Lorenz model (C7), classical interacting electrons in magnetic fields (P32).

Highlights: More extensive mapping of the Lorenz parameter space than ever before (C7); Testing random number generators by running my quantum MC code for the harmonic oscillator case (P39); Halton numbers (P33).


July 1992: Visiting Professor
Centre de Physique Theorique, CNRS, Luminy Case 907, F-13288 Marseille Cedex 9, France

- Forefront study of the structure factor (diffraction spectra) of 1D aperiodic substitutional systems (superlattices), identification of new types of such diffraction spectra. From the mathematical point of view: study of a rather involved Fourier transform (of the density of scatterers of the probe radiation) (P36,37).

Highlight: Finding a new class of 1D quasicrystals (P36).


Sept. 1989 - July 1991: Japanese Science and Technology Agency International Fellow
Laboratory of Information Science, RIKEN, Wako-shi, Saitama, 351-01 Japan

- Manipulation of multivariate polynomials - proof of a theorem on the minimum number of terms of two exactly divisible multivariate polynomials that is sufficient for their recursive power series division (P33, C6).
- Participation in the testing and debugging of the new Japanese computer algebra system GAL.
- Symbolic-numeric calculation of a class of definite integrals (C4).
- Investigation of classical chaos: study of the dynamics of a waterwheel which led to finding the structure of the periodic windows for the Lorenz model and mapping the Lorenz parameter space (P29); application of the dynamical systems theory to the study of a spin model (P31, C5).
- Study of n-letter substitutions as applied to the investigation of 1D nonperiodic substitutional chains (classification, spectral and structural properties) (P26,27,29).

Highlights: Finding trace maps for arbitrary n-letter substitution rules (P27); Malkus waterwheel theory (P29).


Sept. 1987 - Aug. 1989: Research Associate
Department of Physics, University of Lethbridge, Lethbridge, Alberta, Canada T1K 3M4

- Nonperiodic ordered 1D structures (quasicrystals): Generalized Fibonacci superlattices, calculation of the magnetic excitations in such structures using periodic and real boundary conditions, investigation of the properties of the dynamical trace maps associated with the generalized Fibonacci sequences (pseudo-invariants, attractors), phase transition in generalized Fibonacci quantum Ising models, properties of the generalized Thue-Morse chains (P19-25).
- Semiclassical wave packet dynamics (scattering): Investigation of the ways of minimizing the global error of the propagation methods in which the wave-functions are approximated with Gaussian wave packets (P18, R1).
- Quantum chaos.

Highlights: Finding attractors of some of the Fibonacci trace maps (P21); Gaussian wave packet propagation (P18).


Jan. 1986 - Aug. 1987: Research Associate
Department of Chemistry, University of British Columbia, Vancouver, B.C., Canada V6T 1Y6

- Investigation of various mathematical and computational problems of the modeling of the evolution of biochemical systems, particularly the growth of giant single-celled algae: Types of area growth; discretized growth algorithms; formulation and "self-consistent" numerical solution (for the 1D and 2D cases) of coupled non-linear partial differential reaction-diffusion equations (e.g. of the Brusselator type) in a condensed medium that continuously expands everywhere in such a way that the local growth rate is proportional to one of the dependent variables (morphogen concentration) (P16).

Highlight: First self-consistent coupling of the growth with the reaction-diffusion equations for the 1D case (P16).


July 1984 - Dec. 1985: Post-Doctoral Fellow
Department of Physics, Simon Fraser University, Burnaby, B.C., Canada V5A 1S6

- Computation of electronic properties of liquid and amorphous metal clusters: clarification of the correct application of the recursion method in the case of non-orthogonal basis (overlapping atomic orbitals) - development of the recursion method for a general basis and a general GF element; testing of the approximations in the LCAO-type model used for these calculations (approximate Anderson pseudopotential, finite basis, exchange potential correction) (P14).

Highlight: Correct formulation of the recursion method for a non-orthogonal basis (P14).


Dec. 1983 - July 1984: Post-Doctoral Fellow
Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2G 3G1

- Field emission from the region of band gaps (P11,12,17).


Oct. 1983 - Dec. 1983: Visiting Scientist
Chair for Theoretical Chemistry, University of Naples, Naples, Italy

- "Quantum-chemical" approach to transition metals (P13).


July 1983 - Dec. 1983: Refugee
Refugee camps in Latina and Capua Vecchia Santa Lucia, Italy

- Translating between various languages.


Sept. 1976 - June 1983: Research Scientist
Institute of Physics, Czechoslovak Academy of Sciences, Prague, Czechoslovakia

- Surface states. Magnetic surface anisotropy of nickel. Integral characteristics of solid surfaces (P3-6,9,10).
- Local-density-functional atomic calculations (P8, C2).
- Calculation of electron structure of extended systems: construction of ab-initio atomic pseudopotentials; computer program for the self-consistent ab-initio pseudopotential calculation of electronic structure of semiconductors with zinc-blende lattice (intended for the investigation of deep-level impurities) (P7, C3).

Highlights: Integral surface characteristics in the tight-binding formalism (P4); Construction of the atomic pseudopotentials (C3); Code for the calculation of the pseudopotential matrix elements (P7).


Sept. 1972 - Aug. 1975: Graduate Student
Institute of Physics, Czechoslovak Academy of Sciences, Prague, Czechoslovakia

- Surface states and the magnetic surface anisotropy of nickel (P2, C1).


Spring 1972: Diploma work
Faculty of Mathematics and Physics, Charles' University, Prague, Czechoslovakia

- Electron surface diffraction (P1).