Showing papers on "Statistical weight published in 2002"

Generalized statistical mechanics and fully developed turbulence

Abstract: The statistical properties of fully developed hydrodynamic turbulence can be successfully described using methods from nonextensive statistical mechanics. The predicted probability densities and scaling exponents precisely coincide with what is measured in various turbulence experiments. As a dynamical basis for nonextensive behaviour we consider nonlinear Langevin equations with fluctuating friction forces, where Tsallis statistics can be proved rigorously.

The Unimolecular Isomerization of Methyl-d3 Isocyanide. Statistical-Weight Inverse Secondary Intermolecular Kinetic Isotope Effects in Nonequilibrium Thermal Systems

Abstract: The thermal isomerization of CD/sub 3/NC was studied at 230.4 deg over a range of pressures from 10/sup -2/ to 10/sup 4/ mm. The fall-off corresponds to an enhanced value of the effective number of oscillators relative to CR/sub 3/ NC. The difference in observed activation energy for the two species is very small ( approximates 0). The data were treated on an RRKM quantum statistical model. Calculations were made for various combinations of detailed assumptions in which vibrations were treated both on a harmonic basis and also with varying assumed degrees of anharmonicity and in which a figure axis rotation was treated both as active and as adiabatic.

New applications of non-hermitian random matrices

Abstract: We discuss recently discovered links of the statistical models of normal random matrices to some important physical problems of pattern formation and to the quantum Hall effect. Specifically, the large $N$ limit of the normal matrix model with a general statistical weight describes dynamics of the interface between two incompressible fluids with different viscousities in a thin plane cell (the Saffman-Taylor problem). The latter appears to be mathematically equivalent to the growth of semiclassical 2D electronic droplets in a strong uniform magnetic field with localized magnetic impurities (fluxes), as the number of electrons increases. The equivalence is most easily seen by relating the both problems to the matrix model.

Combinatorial interpretation of Haldane-Wu fractional exclusion statistics.

Abstract: Assuming that the maximal allowed number of identical particles in a state is an integer parameter, q, we derive the statistical weight and analyze the associated equation that defines the statistical distribution. The derived distribution covers Fermi-Dirac and Bose-Einstein ones in the particular cases q=1 and q--> infinity (n(i)/q-->1), respectively. We show that the derived statistical weight provides a natural combinatorial interpretation of Haldane-Wu fractional exclusion statistics, and present exact solutions of the distribution equation.

The Most Probable Distribution of the Thermal Energy

Abstract: In a previous work the probability of finding the energy of a particle in the vicinity of a given energy has been determined, taking into account the conservation of the energy during the exchanges of energy. The solution is a Dirac function which has the main properties of the Boltzmann, Fermi‐Dirac and Bose Einstein statistics. It avoids the use of the Boltzmann hypothesis between the differential of the entropy and the logarithm of the statistical weight dS = kdlnW. It is then possible to discuss the limit of validity of this hypothesis. Several new applications are proposed. The perturbations need to observe the most probable distribution suggest new considerations on the velocity distribution of Maxwell, and a possible origin of the paradox concerning the second law.