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Award Abstract #1301537

DYNAMICAL MODELS FOR SUPERDIFFUSION AND SUPERCONDUCTIVITY

NSF Org: DMS
Division Of Mathematical Sciences
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Initial Amendment Date: April 3, 2013
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Latest Amendment Date: September 8, 2014
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Award Number: 1301537
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Award Instrument: Continuing grant
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Program Manager: Edward Taylor
DMS Division Of Mathematical Sciences
MPS Direct For Mathematical & Physical Scien
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Start Date: June 1, 2013
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End Date: May 31, 2016 (Estimated)
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Awarded Amount to Date: $108,089.00
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Investigator(s): Nandor Simanyi simanyi@uab.edu (Principal Investigator)
Nikolai Chernov (Former Principal Investigator)
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Sponsor: University of Alabama at Birmingham
AB 1170
Birmingham, AL 35294-0001 (205)934-5266
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NSF Program(s): ANALYSIS PROGRAM
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Program Reference Code(s): 9150
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Program Element Code(s): 1281

ABSTRACT

The proposal is devoted to mathematical models of statistical mechanics. Some of the most intriguing issues in modern research are the non-classical phenomena of superdiffusion and superconductivity and the newly discovered doubling effect for the second moment (representing the superdiffusion coefficient). The PI will investigate these phenomena by employing various chaotic dynamical systems -- periodic Lorentz gases, the Galton board, Bunimovich stadia, diamonds with cusps, etc. He will also study the classical gas of hard balls whose ergodicity remains to be proved in full generality. The proposal also includes multiparticle gases with a common thermostat and the fluid dynamics governed by Navier-Stokes equations and quasi-geostrophic equations.

The proposal has a potentially broader impact on physics and other sciences. All its problems come from physics and the proposed research activities will have direct relevance to statistical mechanics, hydrodynamics, studies of electricity and superconductivity. The PI closely collaborates with physicists, other scientists, statisticians, and engineers. The PI publishes books and survey articles, maintains a web page with all his publications (including numerical data from computer experiments and the code), and uploads computer programs to MATLAB exchange public forums.


PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH

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N. Chernov, Q. Huang, and H. Ma. "Fitting quadratic curves to data points," British Journal of Mathematics & Computer Science, v.4, 2014, p. 33.

N. Chernov and A. Korepanov. "Spatial structure of Sinai-Ruelle-Bowen measures," Physica D, 2014.

H. Abdul-Rahman and N. Chernov. "Fast and numerically stable circle fit," Journal of Mathematical Imaging and Vision, 2013. 

N. Chernov, H.-K. Zhang, and P. Zhang. "Electrical current in Sinai billiards under general small forces," Journal of Statistical Physics, v.153, 2013, p. 1065.

F. Bonetto, N. Chernov, A. Korepanov, J. Lebowitz. "Nonequilibrium Stationary State of a Current Carrying Thermostated System," A Letters Journal Exploring the Frontiers of Physics (EPL), v.102, 2013, p. 15001.

 

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