Abstract

Statistical Mechanics is used to determine how a particle system behaves when it resides at thermal equilibrium - the concept that any flow of heat (thermal conduction, thermal radiation) is in balance. When a particle system is at thermal equilibrium (e.g., typical behavior of ideal gases), the particles are distributed in a specific way: There are many particles with small velocities and few with large velocities. It is possible to write a mathematical equation describing the number of particles found at each velocity (or kinetic energy); this mathematical expression is called a Maxwell-Boltzmann distribution. Classical Statistical Mechanics and Maxwell-Boltzmann distribution have stood the test of time for describing particle systems residing at thermal equilibrium. However, this formalism cannot adequately describe complex systems, residing in stationary states out of the classical thermal equilibrium.

These systems are distributed such that there are more high velocity/energy particles than there should be if the system was in equilibrium. The mathematical equation that is used to describe them is called a “kappa distribution”. The underlying statistical mechanics is based on a generalization of the classical Boltzmann-Gibbs entropy which is consistent with thermodynamics, and offers a theoretical basis for describing and analyzing complex systems out of equilibrium. Applications can be found in a wide variety of topics and disciplines; among others: nonlinear dynamics; condensed-matter; earthquakes; turbulent fluids; atomic and nuclear energy statistics; astrophysical and space plasmas; sociology–sociometry; internet; citation networks; urban agglomeration; linguistics; economy; biochemistry; population dynamics.

The seminar will review theoretical aspects and applications of this modern adaptation of statistical mechanics.

About the Speaker

Dr. Livadiotis completed all his degree work through the University of Athens, Greece. His 1999 B.Sc. thesis title was “Applications in general relativity. Extension to Finsler geometry” (9.3/10 grade).
His 2001 M.Sc. thesis title was “Order and chaos in 1-dimensional nonlinear maps” (10/10 grade). His 2008 B.Sc. thesis title was “Nonextensive Thermostatistics. Applications in non-Arrhenius kinetics” (9/10 grade). His 2007 Ph.D. in Physics’ thesis title was on the topics of nonlinear dynamics and statistical mechanics applied in solar physics: “Sunspot Evolution: The photometric-magnetic dynamical model - General optimization methods” (10/10 grade).

While studying for his B.Sc. Chemistry degree, Dr. Livadiotis was employed as a research associate at the University of Athens, Greece. His research was on the theoretical modeling of sunspots evolution. In 2008, Dr. Livadiotis began work at SwRI as a researcher scholar, focusing on theoretical modeling and data analysis of space plasmas, using observations from ACE, IBEX, and numerous other missions. In 2012, he was promoted to research scientist, focusing on theoretical research in statistical mechanics, thermodynamics, plasma, and space physics, with applications in space plasmas. In 2015, he was promoted to senior research scientist.

Contact: This email address is being protected from spambots. You need JavaScript enabled to view it.

View all CyI events.