Professor of Mathematics
![Jan Vrbik (IMG_9481-RS square for website) Headshot of Jan Vrbik, Brock University Professor of Mathematics](https://brocku.ca/mathematics-science/mathematics/wp-content/uploads/sites/107/Jan-Vrbik-IMG_9481-RS-square-for-website-560x560.jpg?x22860)
PhD, MSc (Calgary), MSc, BSc (Charles’ University Prague)
Office: Mackenzie Chown J410
905 688 5550 x3298
jvrbik@brocku.ca
- Celestial Mechanics – perturbed Kepler problem.
- Probability and Statistics – sampling distributions, Normal approximation, parameter estimation, autoregressive models.
- Monte Carlo techniques – applied to Quantum Chemistry
- Numerical solution of integral equations – applied to Mechanical Engineering problems
Representative Publications
- J. Vrbik,
“Solving Lunar problem via perturbed K-S equation”
New Astronomy 11 #5(2006), 366-373 - J. Vrbik,
“Population moments of sampling distributions”
Computational Statistics 20 #4(2005), 611-621 - J. Vrbik,
“Finite-n corrections to Normal approximation”
Communications in Statistics (Simulation and Computation) 34 #4(2005), 827-837 - J. Vrbik,
“Moments of AR(1)-model estimators”
Communications in Statistics (Simulation and Computation) 34 #3(2005), 595-600 - J. Vrbik,
“Zonal-harmonics perturbations”
Celestial Mechanics & Dynamical Astronomy91 (2005), 217-237 - Rokne J, Singh B M, Dhaliwal R S and J. Vrbik,
“The axisymmetric Boussinesq-type problem for half-space under optimal heating of arbitrary profile”
Int. J. of Math. and Math. Sciences 40 (2004), 2123-2131 - Vrbik J, Singh BM, Rokne J, et al.,
“On the expansion of a penny-shaped crack by a rigid circular disc inclusion in a thick plate”
ZAMM 84 #8(2004), 538-550 - Rokne J, Singh BM, Dhaliwal RS and Vrbik J,
“The Reissner-Sagoci type problem for a nonhomogeneous elastic cylinder embedded in and elastic non-homogeneous half-space”
IMA J. Appl. Math.69 #2(2004), 159-173 - Rokne J, Singh B M, Dhaliwal RS and Vrbik J,
“Mixed boundary value problem in a nonhomogeneous medium under steady distribution of temperature”
Meccanica39 #2(2004), 113-123 - J. Vrbik,
“A novel solution to Kepler’s problem”
European J. of Phys.24 #6 (2003), 575-583 - Singh BM, Danyluk HT, Vrbik J, et al.,
“The Reisner-Sagoci problem for a non-homogeneous half-space with a surface constraint”
Meccanica38 #4 (2003), 453-465 - Singh B M, Rokne, J, Dhaliwal R S and J. Vrbik,
“Contact problem for bonded nonhomogeneous materials under shear loading”
Int. J. of Math. and Math. Sci.2003 #29 (2003), 1821-1832 - Vrbik J, Singh B M, Rokne J, at al.,
“The breaking of a non-homogeneous fiber embedded in an infinite non-homogeneous medium”
Z. Angew Math. Phys.54 #2 (2003), 212-223 - Vrbik J, Singh B M, Rokne J, et al.,
“The problem of a penny-shaped crack in a nonhomogeneous medium under shear”
Eur. J. Mech. A-Solid21 #5 (2002), 773-777 - Vrbik J,
“Erratum: oblateness perturbations to forth order”
Monthly Notices of the Royal Astronomical Society331 #4 (2002), 1072 - Vrbik J, Singh B M, Rokne J and Dhaliwal R S,
“Plastic deformation at the tip of an edge crack”
ZAMM81 #9 (2001), 642-647 - Singh B M, Danyluk H T, Selvadurai A P S, Dhaliwal R S, Rokne J and Vrbik J, et al.,
“Effects of inclusion in ductile cracks”
ZAMP52 (2001), 680-695 - J. Vrbik, Singh B M, Rokne J, Dhaliwal R S,
“External crack in torsion in an infinite nonhomogeneous medium with a non-homogeneous cylindrical inclusion”
ZAMM81 #7 (2001), 489-497 - J. Vrbik,
“Quaternionic processo”
Celestial Mechanics and Dynamical Astronomy80 #2 (2001), 111-118 - J. Vrbik,
“Perturbative solution of an asteroid’s motion in resonance with Jupiter”
Monthly Notices of the Royal Astronomical Society (2000) - J. Vrbik,
“Simple simulation of solar system”
Astrophysics and Space Science 266 #4 (1999), 557-567. - J. Vrbik,
“Iterative solution to perturbed Kepler problem via Kustaanheimo-Stiefel equation”
Celestial Mechanics and Dynamical Astronomy 71 (1999), 273-287. - J. Vrbik,
“Novel analysis of tadpole and horseshoe orbits”
Celestial Mechanics and Dynamical Astronomy 69 (1998), 283-291. - P. Langfelder, S.M. Rothstein, and J. Vrbik,
“Diffusion quantum Monte Carlo calculations of nondifferential properties for atomic ground states”
J. Chem. Phys. 107 (1997), 8525-35. - J. Vrbik,
“Oblateness perturbations to fourth order”
Mon. Not. R. Astron. Soc. 291 (1997), 65-70. - J. Vrbik,
“Resonance formation of Kirkwood gaps and asteroid clusters”
J. Phys. A 29 #12 (1996), 3311-16. - H.T. Danyluk, B.M. Singh, and J. Vrbik,
“A Dugdale-type estimation of the plastic zone for a penny-shaped crack in a thick transversely isotropic layer due to radial shear”
Engineering Fracture Mechanics 51 (1995), 735-740. - J. Vrbik,
“Perturbed Kepler problem in quaternionic form”
J. Phys. A 28 (1995), 193-198. - J. Vrbik,
“Dirac equation and Clifford algebra”
J. Math. Phys. 35 #5 (May 1994), 2309-14. - J. Vrbik,
“Celestial mechanics via quaternions”
Can. J. Phys. 72 (1994), 141-146. - P. Belohorec, S.M. Rothstein, and J. Vrbik,
“Infinitesimal diffusion quantum Monte Carlo study of CuH spectroscopic constants”
J. Chem. Phys. 98 #8 (1993), 6401-05. - J. Vrbik,
“A chain sliding off a table”
Am. J. Phys. 61 #3 (March 1993), 258-261. - H.T. Danyluk, B.M. Singh, and J. Vrbik,
“Ductile penny-shaped crack in a transversely isotropic cylinder”
Int. J. Fract. 51 #4 (1991), 331-342. - J. Vrbik,
“A simple approximation to the pseudoskin factor resulting from restricted entry”
SPE Formation Evaluation (Dec 1991), 444-446. - A.L.L. East, S.M. Rothstein, and J. Vrbik,
“Reply to comment on: ‘Sampling the exact electron distribution by diffusion quantum Monte Carlo”
J. Chem. Phys. 92 #3 (1990), 2120. - D.A. Lagare, S.M. Rothstein, and J. Vrbik,
“Infinitesimal differential diffusion quantum Monte Carlo: Diatomic molecular properties”
J. Chem. Phys. 92 (Jan 1990), 1221-27. - M.C. Au, A. Cardou, B.M. Singh, A.P.S. Selvadurai, and J. Vrbik,
“Closed from solution for two finite-length cracks moving in an orthotropic layer under anti-plane loading”
Theor. Appl. Fract. Mech. 10 #3 (Dec 1988), 197-212. - S.M. Rothstein and J. Vrbik,
“A Green’s function used in diffusion Monte Carlo”
J. of Compt. Phys. 87 (1987), 1902-03. - J. Vrbik,
“Monte Carlo simulation of general elliptic operator”
J. of Phys. A. 20 (1987), 2693-98. - J. Vrbik,
“Calculating the pseudo-skin factor due to the partial well completion”
J. of Canadian Petroleum Technology 25 #5 (1986), 57-61. - J. Vrbik,
“Monte Carlo technique for finding the lowest eigenvalue of a modified Shroedinger equation”
J. of Phys. A. 18 (1985), 1327-35. - J. Vrbik,
“Asymptotic distribution of the coefficient of cross-association based on a simple Markov-chain model”
J. of Appl. Prob. 22 (1985), 946-950. - J. Vrbik,
“Statistical properties of the number of runs of matches between two random stratigraphic sections”
Math. Geol. 17 #1 (1985), 29-40. - R.S. Dhaliwal, B.M. Singh, and J. Vrbik,
“Diffraction of torsional waves by a flat annular crack at the interface of two bonded dissimilar elastic solids”
Eng. Fract. Mech. 19 #4 (1984), 771-776. - R.S. Dhaliwal, B.M. Singh, and J. Vrbik,
“Torsional impact of a layer or a cylinder bonded to an elastic half-space”
Int. J. of Eng. Sci. 21 #11 (1983), 1397-1408. - J. Vrbik,
“Test of independence by repeated matching of stratigraphic sections”
Math. Geol. J. 15 #3 (1983), 427-444. - M. Nosal and J. Vrbik,
“Stratigraphic analysis and the asymptotic distribution of the coefficient of cross-association”
Math. Geol. 14 #1 (1982), 11-36. - R.S. Dhaliwal, B.M. Singh, and J. Vrbik,
“Semi-infinite medium with a cylindrical inclusion twisted by an annular die”
J. of Elasticity 10 #2 (1980), 121-134.
Past Teaching Assignments
- MATH 1P12 Introductory Linear Algebra
- MATH 1P40 Mathematics Integrated with Computers and Applications I
- MATH 1P97 Differential and Integral Methods
- MATH 1P98 Basic Statistical Methods
- MATH 2P12 Linear Algebra II
- MATH 2P95 Mathematics and Music
- MATH 4/5P96 Technology and Mathematics Education