Spin diffusion and relaxation in three-dimensional isotropic Heisenberg antiferromagnets

A theory is proposed for kinetic effects in isotropic Heisenberg antiferromagnets at temperatures above the Neel point. A metod based on the analysis of a set of Feynman diagrams for the kinetic coefficients is developed for studying the critical dynamics. The scaling behavior of the generalized coefficient of spin diffusion and relaxation constant in the paramagnetic phase is studied in terms of the approximation of coupling modes. It is shown that the kinetic coefficients in an antiferromagnetic system are singular in the fluctuation region. The corresponding critical indices for diffusion and relaxation processes are calculated. The scaling dimensionality of the kinetic coefficients agrees with the predictions of dynamic scaling theory and a renormalization group analysis. The proposed theory can be used to study the momentum and frequency dependence of the kinetic parameters, and to determine the form of the scaling functions. The role of nonlocal correlations and spin-liquid effects in magnetic systems is briefly discussed.Comment: 10 pages, RevTeX, 3 EPS figures include

Kinetic Bandgap Analysis of Plasma Photonic Crystals

The dispersion relation of plasma and plasma-dielectric photonic multilayer structures is approached in terms of a one-dimensional Particle-in-Cell simulation. For several plasma-dielectric configurations, the system response is obtained using a pulsed excitation and a subsequent two-dimensional frequency analysis. It is first shown that the dispersion relation of a single, homogeneous plasma slab is well described by the cold-plasma model even at low pressures of 1 Pa. The study is extended to the simulation of plasma photonic crystals with a variety of configurations, based on the work of Hojo and Mase [J. Plasma Fusion Res. 80, 89 (2004)]. Considering a one-dimensional plasma photonic crystal made from alternating layers of dielectric and homogeneous plasma slabs, it is shown that the assumption of a cold-plasma description is well justified also in this case. Moreover, in this work the results are reformatted and analyzed in a band diagram representation, in particular based on the lattice constant $a$. Based on these considerations a scaling invariant representation is presented, utilizing a generalized set of parameters. The study is completed with an exemplary comparison of three plasma-dielectric photonic crystal configurations and their corresponding band diagrams

A note on the lattice Boltzmann method beyond the Chapman Enskog limits

A non-perturbative analysis of the Bhatnagar-Gross-Krook (BGK) model kinetic equation for finite values of the Knudsen number is presented. This analysis indicates why discrete kinetic versions of the BGK equation, and notably the Lattice Boltzmann method, can provide semi-quantitative results also in the non-hydrodynamic, finite-Knudsen regime, up to $Kn\sim {\cal O}(1)$. This may help the interpretation of recent Lattice Boltzmann simulations of microflows, which show satisfactory agreement with continuum kinetic theory in the moderate-Knudsen regime.Comment: 7 PAGES, 1 FIGUR

An operator splitting scheme for the fractional kinetic Fokker-Planck equation

In this paper, we develop an operator splitting scheme for the fractional kinetic Fokker-Planck equation (FKFPE). The scheme consists of two phases: a fractional diffusion phase and a kinetic transport phase. The first phase is solved exactly using the convolution operator while the second one is solved approximately using a variational scheme that minimizes an energy functional with respect to a certain Kantorovich optimal transport cost functional. We prove the convergence of the scheme to a weak solution to FKFPE. As a by-product of our analysis, we also establish a variational formulation for a kinetic transport equation that is relevant in the second phase. Finally, we discuss some extensions of our analysis to more complex systems

A Method to Study Complex Enzyme Kinetics Involving Numerical Analysis of Enzymatic Schemes. The Mannitol Permease of Escherichia coli as an Example

An analysis of complex kinetic mechanisms is proposed that consists of two steps, (i) building of an kinetic scheme from experimental data other than steady-state kinetics and (ii) numerical simulation and analysis of the kinetics of the proposed scheme in relation to the experimental kinetics. Procedures are introduced to deal with large numbers of enzymatic states and rate constants, and numerical tools are defined to support the analysis of the scheme. The approach is explored by taking the mannitol permease of Escherichia coli as an example. This enzyme catalyzes both the transport of mannitol across the cytoplasmic membrane and the phosphorylation of mannitol. The challenge is to deduce the transport properties of this dimeric enzyme from the phosphorylation kinetics. It is concluded that (i) the steady-state kinetic behavior is largely consistent with the proposed catalytic cycle of the monomeric subunit, (ii) the kinetics provide no direct support but also do not disprove a coupled translocation of the binding sites on the two monomeric subunits. The approach reveals the need for further experimentation where the implementation of experimental results in the scheme conflict with the experimental kinetics and where specific experimental characteristics do not show up in the simulations of the proposed kinetic scheme.

Hydrodynamic limit of a B.G.K. like model on domains with boundaries and analysis of kinetic boundary conditions for scalar multidimensional conservation laws

In this paper we study the hydrodynamic limit of a B.G.K. like kinetic model on domains with boundaries via $BV_{loc}$ theory. We obtain as a consequence existence results for scalar multidimensional conservation laws with kinetic boundary conditions. We require that the initial and boundary data satisfy the optimal assumptions that they all belong to $L^1\cap L^\infty$ with the additional regularity assumptions that the initial data are in $BV_{loc}$. We also extend our hydrodynamic analysis to the case of a generalized kinetic model to account for forces effects and we obtain as a consequence the existence theory for conservation laws with source terms and kinetic boundary conditions