Self-consistent Kinetic Equations Research Articles

Relaxation in a Fuzzy Dark Matter Halo. II. Self-consistent Kinetic Equations

Abstract Fuzzy dark matter (FDM) is composed of ultra-light bosons having a de Broglie wavelength that is comparable to the size of the stellar component of galaxies at typical galactic velocities. FDM behaves like cold dark matter on large scales. However, on the scale of the de Broglie wavelength, an FDM halo exhibits density fluctuations that lead to relaxation, a process similar to the two-body relaxation that occurs in classical gravitational N-body systems and is described by the Fokker–Planck equation. We derive the FDM analog of that kinetic equation, which describes the evolution of the velocity distribution in a spatially homogeneous FDM halo. We show that the evolution of the velocity distribution predicted by our kinetic equation matches numerical solutions of the coupled Schrödinger–Poisson equations. We also determine the dielectric function and the dispersion relation for linear waves in an FDM halo.

Математическая модель радиационно-индуцированной проводимости в кварце при воздействии мощного рентгеновского излучения

A model of generation and dynamics of radiation conductivity in quartz under the action of powerful soft X-ray radiation is constructed. The charge carrier dynamics model is based on the joint solution of self-consistent kinetic equations and Maxwell's equations. The model was verified by comparing the current calculations on the quartz surface with experiments on the Angara-5-1 thermonuclear installation. The current over the surface of the quartz sensor generated by a powerful pulse of soft X-ray radiation from the Angara-5-1 setup was taken as experimental data.

Multicomponent Conduction and Selectivity of Biological Channels

We consider multispecies conduction and selectivity of narrow biological filters such as KcsA [1] and NaChBac [2]. We use equilibrium statistical theory to find filter occupation and conductivities when coupled to the bath solutions with mixed types of conducting ions. The analysis of the filter conduction and selectivity conduction and selectivity is thus reduced to the analysis of the effective grand canonical distribution of ions within the filter [3], energy spectra, and density of the states within the filter [4]. The effects of energy quantization due to discrete number of ions and due to dehydration are taken into account. To account for the interaction between fluxes of different species within the channel we introduce Maxwell-Stefan theory [5] of the ion channel conduction. The fluxes of various species through the filter are obtained analytically in the limit of weak coupling. The theory is applied to derive Eisenman relations of the filter selectivity from the condition of nearly diffusion limited conduction in KscA channel. The model predictions are compared with experimental results using self-consistent kinetic equations. The transition rates in kinetic model are derived using effective grand canonical ensemble. A good agreement with the experiment is demonstrated. An application of the theory to analysis of the channel mutation experiments are discussed.

An Oceanic Ultra-Violet Catastrophe, Wave-Particle Duality and a Strongly Nonlinear Concept for Geophysical Turbulence

There is no theoretical underpinning that successfully explains how turbulent mixing is fed by wave breaking associated with nonlinear wave-wave interactions in the background oceanic internal wavefield. We address this conundrum using one-dimensional ray tracing simulations to investigate interactions between high frequency internal waves and inertial oscillations in the extreme scale separated limit known as “Induced Diffusion”. Here, estimates of phase locking are used to define a resonant process (a resonant well) and a non-resonant process that results in stochastic jumps. The small amplitude limit consists of jumps that are small compared to the scale of the resonant well. The ray tracing simulations are used to estimate the first and second moments of a wave packet’s vertical wavenumber as it evolves from an initial condition. These moments are compared with predictions obtained from the diffusive approximation to a self-consistent kinetic equation derived in the ‘Direct Interaction Approximation’. Results indicate that the first and second moments of the two systems evolve in a nearly identical manner when the inertial field has amplitudes an order of magnitude smaller than oceanic values. At realistic (oceanic) amplitudes, though, the second moment estimated from the ray tracing simulations is inhibited. The transition is explained by the stochastic jumps obtaining the characteristic size of the resonant well. We interpret this transition as an adiabatic ‘saturation’ process which changes the nominal background wavefield from supporting no mixing to the point where that background wavefield defines the normalization for oceanic mixing models.

Diffusion-induced growth of nanowires: Generalized boundary conditions and self-consistent kinetic equation

In this work, we present a theoretical analysis of the diffusion-induced growth of “vapor–liquid–solid” nanowires, based on the stationary equations with generalized boundary conditions. We discuss why and how the earlier results are modified when the adatom chemical potential is discontinuous at the nanowire base. Several simplified models for the adatom diffusion flux are discussed, yielding the 1/Rp radius dependence of the length, with p ranging from 0.5 to 2. The self-consistent approach is used to couple the diffusion transport with the kinetics of 2D nucleation under the droplet. This leads to a new growth equation that contains only two dimensional parameters and the power exponents p and q, where q=1 or 2 depends on the nucleus position. We show that this equation describes the size-dependent depression of the growth rate of narrow nanowires much better than the Gibbs–Thomson correction in several important cases. Overall, our equation fits very well the experimental data on the length–radius correlations of III–V and group IV nanowires obtained by different epitaxy techniques.

Nonergodic activated kinetics in polar media

A theoretical formulation is developed for the activated kinetics when some subset of nuclear modes of the thermal bath is slower than the reaction and ergodicity of the thermal bath is not maintained. Nonergodic free energy profiles along the reaction coordinate are constructed by using restricted canonical ensembles with the phase space available to the system found by solving a self-consistent kinetic equation. The resulting activation barrier incorporates not only thermodynamic parameters but also dynamical information from the time autocorrelation function of the solute-solvent interaction energy. The theory is applied to the reactions of solvolysis and charge transfer in polar media.

A self-consistent mean field theory for diffusion in alloys

Starting from a microscopic model of the atomic transport via vacancies and interstitials in alloys, a self-consistent mean field (SCMF) kinetic theory yields the phenomenological coefficients Lij. In this theory, kinetic correlations are accounted for through a set of effective interactions within a non-equilibrium distribution function of the system. The introduction of a master equation describing the evolution with time of the distribution function and its moments leads to general self-consistent kinetic equations. The Lij of a face centered cubic alloy are calculated using the kinetic equations of Nastar (M. Nastar, Philos. Mag., 2005, 85, 3767, ref. 1) derived from a microscopic broken bond model of the vacancy jump frequency. A first approximation leads to an analytical expression of the Lij and a second approximation to a better agreement with the Monte Carlo simulations. A change of sign of the Lij is studied as a function of the microscopic parameters of the jump frequency. The Lij of a cubic centered alloy obtained for the complex diffusion mechanism of the dumbbell configuration of the interstitial (V. Barbe and M. Nastar, Philos. Mag., 2006, in press, ref. 2) are used to study the effect of an on-site rotation of the dumbbell on the transport.

Nonstationary acceleration in a planar diode

The electron dynamics in a planar gap with a variable accelerating potential across it is studied with a model solution to a self-consistent kinetic equation.

Phase diagram of a Gaussian random copolymer

We study the stationary limit of the self-consistent kinetic equations derived earlier by us for a model of a Gaussian random copolymer. The phase diagram of the model contains five different states separated by the collapse, glass, and folding 'transitions.' We perform a finite-size chain analysis and find that the kinetic accessibility of the folded state is strongly impeded for sufficiently long chains. For the high-density globule we propose a simplified treatment in terms of the three main order parameters. This approximation yields a qualitatively correct phase diagram and allows us to demonstrate the thermodynamic stability of the folded state.

Theory of ion motion in normal liquid 3He

We present the solution of the problem of heavy particle dynamics in a Fermi liquid environment which is asymptotically exact in a strong coupling limit. It is based on a path integral method and transforms into the self-consistent kinetic equation of Josephson and Lekner only in the case of weak scattering potential (small scattering phase shifts). In the general case the mobility can not be obtained by iterations of the kinetic equation. The theory explains the puzzling difference between the positive and negative ion mobility experiments and predicts rather unusual thermodynamic properties of ions in normal 3 He. An enormous renormalization of the electron bubble effective mass, M Bubble≥10 4m 3 , is predicted below the superfluid transition temperature.

Microscopic description of dissipative fragmentation

A method to calculate intermediate mass fragment production in intermediate energy heavy ion collisions with a self-consistent kinetic equation approach is presented. Inclusive mass distributions, energy spectra and mass correlations are compared to experimental data.

On one method for solving self-consistent kinetic equations

A method of solving self-consistent kinetic equations is described which is based on an implicit calculation of the distribution functions from the characteristics.

Locally coupled evolution of wave and particle distribution in general magnetoplasma geometry

Self-consistent kinetic equations are obtained for the evolution of plasma-wave action density in ray phase space and oscillation-center density in guiding-center phase space. Both resonant and nonresonant interactions are included, in a strong, weakly nonuniform magnetic field. Energy conservation and entropy production are the hallmarks of self-consistency.

Self-consistent kinetic equations and the evolution of a relativistic plasma in an ambient magnetic field

A kinetic theory is developed for a relativistic, spatially- homogeneous multispecies plasma embedded in a uniform ambient magnetic field. The theory treats individual particle effects and collective effects on equal footing, and thereby describes both stable and weakly unstable plasma. The three-particle correlation, and nonlinear mode-mode coupling terms are neglected and a 'quasi- longitudinal, weak-field' approximation is employed in calculating the electric and magnetic field fluctuations. The final equations for the long time evolution of the particle distribution functions and the plasma wave intensities emphasize that the evolution of particles and their 'self-excited' waves is coupled in a non-linear manner. Specialized equations for a plasma consisting of cold electrons and protons and a relativistic proton 'tail' are given. These are particularly suited to a discussion of cosmic ray propagation through the interstellar medium no matter whether the cosmic ray distribution is stable or unstable.

Proton dynamics in H-bonded ferroelectrics: I. Kinetic equations for correlation functions above T c

Using a spin-like description of the tunnelling model for the H-bonded ferroelectrics, we derive a set of self-consistent kinetic equations for the correlation functions in the region T ≥ T c . Our main approximation is the Weiss limit, where the number of interacting neighbours tends to infinity. To dominant order, these correlation functions, are determined by the well-known protonic mode; we also obtain an approximate description of the damping of this mode. The drone fermion operator technique is employed in the course of the derivation.