** PLEASE DESCRIBE THIS IMAGE **
Contact Info:
Office: Sandridge 233 (Science Center)
Office Phone: (276) 328-0179
Fax: (276) 376-4603
Email: jf3zc@uvawise.edu
Mail: Department of Natural Sciences
The University of Virginia's College at Wise
One College Avenue
Wise,VA 24293
Current courses:

College Physics:

PHY 1010 section 01, 02
PHY 1011 section 01, 02, 03

Research Interests: My research interests are mainly in the application of the methods of statistical physics. There are two general directions in my research, one more mathematical and one more directly related to physical systems. One general problem is the study of the connections between spectral analysis and phase transitions. A good example of such a connection is provided by a one-dimensional model defined on Farey fractions (see publications below). These models are of interest to both physicists and number theorists. The interactions between the "spins" are long-range, which leads to an unusual phase transition. Here we can find an associated transfer operator and analyze its spectrum to understand the character of the phase transition. The phase transition is continuous, but there are logarithmic corrections due to the presence of a marginal field when analyzed by renormalization group methods. The study of these models leads to connections with the Riemann Zeta function, modular theory, Maas cusp forms, the Lewis three term equation, and classical and quantum motion on the hyperbolic upper half plane. Further research on extensions of these models by including an external field may lead to more rigorous results.

The second direction is the study of the dynamics of first-order phase transitions, including phenomena such as nucleation, spinodal decomposition, and late stage growth and coarsening. In a typical situation, a system is rapidly quenched from a one-phase, thermal equilibrium state to a metastable or unstable state. Such a quenched system then gradually evolves to an equilibrium state.

Here is example of my simulations of the Ising model with a long range interaction. I study the early time morphology of the ordering with nonconserved order parameter (i.e. continuous ordering - model A) and with conserved order parameter (i.e.spinodal decomposition).

 

"Science is built upon facts, as a house is built of stones; but an accumulation of facts is no more a science that a heap of stones is a house."

"Mathematics is the art of giving the same name to different things. [As opposed to the quotation: Poetry is the art of giving different names to the same thing]."

"It is through science that we prove, but through intuition that we discover."                                   Henri Poincaré

Dissertation (pdf file)

Publications:
-Asymptotics of the Farey Fraction Spin Chain Free Energy at the Critical Point, O. F. Bandtlow, J. Fiala, P. Kleban, and T. Prellberg, J.Stat.Phys. 138, 447-464 (2010). (pdf)
-Intervals between Farey fractions in the limit of infinite level, J. Fiala, and P. Kleban, Ann. Sci. Math. Québec 34, no 1, 63–71 (2010). (pdf)
- Cluster Approximation for the Farey Fraction Spin Chain, T. Prellberg, P. Kleban, J. Fiala, J. Stat. Phys., 123, 455-471 (2006) (pdf)
- Generalized Number Theoretic Spin Chain-Connections to Dynamical Systems and Expectation Values, J. Fiala, P. Kleban, J. Stat. Phys., 121, 553-577 (2005) (pdf)
- Thermodynamics of the Farey Fraction Spin Chain, J. Fiala, P. Kleban, J. Stat. Phys., 116, 1471-1490 (2004) (pdf)
- The Phase Transition in Statistical Models Defined on Farey Fractions, J. Fiala, P. Kleban, and A. Ozluk, J. Stat. Phys., 110, 73-86 (2003) (pdf)

My Photogallery: Landscape; Animals - birds:1, 2 ; insects; Plants; others


More web sites: Science, Physics Today, Nature, Scientific American (Czech Rep.), National Geographic;
Preprints, PROLA, J. Stat. Phys., J. Math. Phys., J. Chem. Phys., J. Phys.: Condens Matter (more),
Am. J. Phys. (Resource Letters), Phys. Educ., Physica A: Statistical Mechanics and its Applications;

Last updated 08/19/2014