Search

A statistical description for the processes of catalytic hydrogen oxidation is proposed taking into account the reaction--diffusion processes for magnetoactive ions and atoms adsorbed on the metal surface. The basic non-Markov transfer equations are obtained for the abbreviated description parameters of reaction-diffusion processes for magnetoactive ions and atoms adsorbed on the metal surface in the method of nonequilibrium statistical Zubarev operator. Weakly nonequilibrium reaction-diffusion processes are also considered.

Mathematical model of the subdiffusion impedance in multilayer nanostructures is considered on the basis of the Cattaneo-type diffusion equation in fractional derivatives. The Nyquist diagrams are calculated for different values of subdiffusion coefficient and time parameter (time for which the flow delays concerning the gradient of charge carriers concentration). A qualitative agreement is obtained for the GaSe system with encapsulated β-cyclodextrin.

A statistical approach to description of the charge carrier transfer processes in hybrid nanostructures taking into account electromagnetic fields is proposed using the method of the nonequilibrium statistical operator Zubarev. Generalized transfer equations are obtained, which describe non-Markov processes of charge transfer in the system taking into account magnetic and polarization processes under the influence of external and induced internal electromagnetic fields. Weakly nonequilibrium charge transfer processes in nanostructures are considered, and a nonequilibrium statistical operator is obtained, by means of which the magneto-diffusion transfer equations for electrons in layered nanostructures are obtained. A generalized Cattaneo-type diffusion equation in time fractional derivatives is obtained for electrons with a characteristic relaxation time and a generalized model is proposed that takes into account the complexity of relaxation electro-magnetic diffusion processes for electrons in layered nanostructures.

Отримано нове немарковське рівняння дифузії частинок у просторово неоднорідному середовищі з фрактальною структурою та узагальнене рівняння дифузії Кеттано–Максвелла з урахуванням просторово-часової нелокальності. Знайдено дисперсійні співвідношення для рівняння дифузії типу Кеттано–Максвелла з урахуванням просторово-часової нелокальності у дробових похідних. Розраховано частотний спектр, фазову та групову швидкості й показано його хвильову поведінку зі стрибкоподібними розривами, які проявляються також у зміні фазової швидкості. The new non-Markovian diffusion equations of ions in spatially heterogeneous environment with fractal structure and generalized Cattaneo–Maxwell diffusion equation with taking into account the space-time nonlocality are obtained. Dispersion relations for the Cattaneo–Maxwell-type diffusion equation with taking into account the space-time nonlocality in fractional derivatives are found. The frequency spectrum, phase and group velocities are calculated. It is shown that it has a wave behavior with discontinuities, which are also manifested in behavior of the phase velocity.

Based on the non-Markov diffusion equation taking into account the spatial fractality and modeling for the generalized coefficient of particle diffusion $D^{\alpha\alpha'}(\mathbf{r},\mathbf{r}';t,t')=W(t,t')\bar{D}^{\alpha\alpha'}(\mathbf{r},\mathbf{r}')$ using fractional calculus the generalized Cattaneo--Maxwell--type diffusion equation in fractional time and space derivatives has been obtained. In the case of a constant diffusion coefficient, analytical and numerical studies of the frequency spectrum for the Cattaneo--Maxwell diffusion equation in fractional time and space derivatives have been performed. Numerical calculations of the phase and group velocities with change of values of characteristic relaxation time, diffusion coefficient and indexes of temporal $\xi$ and spatial $\alpha$ fractality have been carried out., Comment: 23 pages, 4 figures

We presented a general approach for obtaining the generalized transport equations with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and Zubarev’s nonequilibrium statistical operator (NSO) method within Renyi statistics. New non-Markovian diffusion equations for particles in spatially heterogeneous environment with fractal structure and a generalized Cattaneo-type diffusion equation with taking into account nonlocality of space–time are obtained. Different models of frequency-dependent memory functions, which lead to known diffusion equations with nonlocality of space–time and their generalizations are studied.

A formulation of nonequilibrium thermo-field dynamics has been performed using the nonequilibrium statistical operator method by D.N. Zubarev. Generalized transfer equations for a consistent description of the kinetics and hydrodynamics of the dense quantum field system with strongly-bound states are derived.

In the present paper we used ion-polarization model to study collective excitations in ionic melts. Based on the extended model for collective dynamics in ionic melts (which takes into account fluctuations of charge density, charge current, and its time derivative) we obtained the set of collective excitations in the system, containing relaxation mode related to electric conductivity, two propagating optic-like modes and relaxation mode due to polarization processes. The received analytical expressions for the collective modes take into account corrections caused by ion polarizability comparing to rigid-ion model. The obtained results correctly describe a reduction of frequency of optic-like modes and an increase of damping due to polarization processes. The results are consistent with other theoretical works and results of computer simulations.

Physical and technological principles of formation of clathrate structures for supramolecular electronics are given in this paper. It has been established that supramolecular nature of the “host–guest” conjunction, in general, and hierarchical architecture of the corresponding clathrates, in particular, provide realization of such an extraordinary effect as an optically or a magnetically controlled phenomenon of colossal “negative capacity” with a predicted frequency interval of manifestation, magnitude, and multiplicity. For the first time, the experimental confirmation of the behavior of the electretized fractal clathrate GaSe⟨β-CD⟨FeSO4⟩⟩ as a dissipative element, which accumulates inductive energy, is demonstrated. A general approach for obtaining the generalized transport equations with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and the Zubarev nonequilibrium statistical operator method within Renyi statistics is presented. N...

We present a generalization of Zubarev’s nonequilibrium statistical operator method based on the principle of maximum Renyi entropy. In the framework of this approach, we obtain transport equations for the basic set of parameters of the reduced description of nonequilibrium processes in a classical system of interacting particles using Liouville equations with fractional derivatives. For a classical systems of particles in a medium with a fractal structure, we obtain a non-Markovian diffusion equation with fractional spatial derivatives. For a concrete model of the frequency dependence of a memory function, we obtain generalized Kettano-type diffusion equation with the spatial and temporal fractality taken into account. We present a generalization of nonequilibrium thermofield dynamics in Zubarev’s nonequilibrium statistical operator method in the framework of Renyi statistics.

The new non-Markovian electrodiffusion equations of ions in spatially heterogeneous environment with fractal structure and generalized Cattaneo-type diffusion equation with taking into account fractality of space-time are obtained. Different models of the frequency dependence of memory functions, which lead to known diffusion equations with fractality of space-time and their generalizations are considered. Отримано новi немарковськi рiвняння електродифузiї iонiв у просторово неоднорiдному середовищi з фрактальною структурою та узагальненi рiвняння дифузiї типу Кеттано з врахуванням просторово-часової фрактальностi. Розглянуто рiзнi моделi частотної залежностi для функцiй пам’ятi, якi приводять до вiдомих рiвнянь дифузiї з просторово-часовою фрактальнiстю, а також їх узагальнень.

The model of impedance subdiffusion based on the Cattaneo equation in fractional derivatives in applications to multilayer nanostructures is considered. Nyquist diagrams with changes of the parameter (time for which the flow is delayed with respect to the concentration gradient) and the subdiffusion coefficient D are calculated. Розглянуто модель субдифузiйного iмпедансу на основi рiвняння Кеттано у дробових похiдних у застосуваннi до мультишарових наноструктур. Розраховано дiаграми Найквiста iз змiною параметрiв (час, на який потiк затримується вiдносно градiєнта концентрацiї) та субдифузiйного коефiцiєнта D.

To describe kinetic processes in gases and liquids far from equilibrium, we obtain the nonequilibrium statistical operator (NSO) and the generalized kinetic equations for the nonequilibrium one- and two-particle distribution functions based on the Zubarev NSO method and the maximum entropy principle for the Renyi entropy. We consider a q-generalization of the Liouville equation and obtain its general solution using the NSO method.

In a theoretical study of gas adsorption on carbon nanotubes (CNTs), we conduct a series of ab initio simulations for a “gas–single-wall carbon nanotube” system for gases of particular practical interest: He and NO. The obtained values of adsorption energy reveal preferable localization sites of absorbed He atoms as well as their dependency on the adsorption distances. A significant effect of NO adsorption on CNT electronic properties is demonstrated. The effect of the presence of a vacancy on the adsorption nature is analyzed. It is shown that under the influence of vacancy formation the CNT structure undergoes reconstruction that enables chemisorption of NO molecules.

By using the Zubarev nonequilibrium statistical operator method, and the Liouville equation with fractional derivatives, a generalized diffusion equation with fractional derivatives is obtained within the Renyi statistics. Averaging in generalized diffusion coefficient is performed with a power distribution with the Renyi parameter $q$., 12 pages

A systematic approach to derivation of hydrodynamic-like balance equations for systems with a smooth continuous potential as well as hard sphere repulsion is represented. Cases of many-particle local and two-particle nonlocal hydrodynamic densities are considered. The results are applied for construction of balance equations for fluxes of momentum and energy, which form the first extension of conventional hydrodynamics. Explicit balance equations for the stress tensor and the heat flux in the local frame of reference are obtained.

We discuss the important role of the Zubarev nonequilibrium statistical operator method in the generalized molecular hydrodynamics of fluids. Using this method allows developing a consistent approach of generalized collective excitations for simple, ion, polar, magnetic, and some other fluids. We construct a nonequilibrium statistical operator and derive the corresponding transport equations for a system that relaxes and passes into the state of molecular hydrodynamics.

Chain of kinetic equations for non-equilibrium single, double and s-particle distribution functions of particles is obtained taking into account nonlin- ear hydrodynamic fluctuations. Non-equilibrium distribution function of non-linear hydrodynamic fluctuations satisfies a generalized Fokker-Planck equation. The method of non-equilibrium statistical operator by Zubarev is applied. A way of calculating of the structural distribution function of hydrodynamic collective variables and their hydrodynamic velocities (above Gaussian approximation) contained in the generalized Fokker-Planck equa- tion for the non-equilibrium distribution function of hydrodynamic collective variables is proposed., 31 pages

Generalized transport equations for description of diffusion-reaction processes in chemically active mixtures are obtained. The nonequilibrium statistical operator method by Zubarev is used and both strong and weak nonequilibrium processes are analyzed. In the approximation of the second order in fluctuations we get generalized equations of chemical kinetics for bimolecular reactions with generalized rate constants. In the case of spatial uniformity the integro-differential equation for the matrix of partial scattering functions is received, which are related to partial dynamic structure factors of chemically reactive system by the time Fourier transformation.

A new technological approach to the synthesis of multi-layer nanostructures is suggested; it enables us to ensure them unique properties and extraordinary possibilities of their practical application. In particular, it is shown that the synthesis of nanostructures of GaSe⟨β-cyclodextrin⟨FeSO4⟩⟩ hierarchy architecture in superposed electric and light-wave fields causes especially strong changes in their magnetic impedance response. In this case, the impedance response of the synthesized clathrate takes inductive character in the frequency range of 10−3–105 Hz. The relationship between the impedance behaviour of such hierarchical structures and frequency fractionality is investigated on the basis of Cettano equations. The prospect of application of the synthesized nanohybrids for active elements of gyrator-free nanolines of delay, for super-sensitive capacitance sensors of magnetic field and of light-wave field, and for quantum batteries at room temperature is shown.

Dynamic properties of multicomponent mixtures of magnetic and non-magnetic particles were considered. We start from the general case of a multicomponent mixture, some components of which possess a magnetic momentum, being described by m + 2 parameters of abbreviated description. The equations of generalized hydrodynamics and those for time correlation functions are derived. Then we calculate eigenvalues of the hydrodynamic equations for small wave-number k , which yielded sound velocity and sound damping coefficients for two propagating modes, and damping coefficients for the rest modes which are purely diffusive. The scheme, which allows us to obtain weight coefficients for time correlation functions is proposed. Expressions for time correlation functions are analyzed for the paramagnetic case, when the coupling between the spin and fluid degrees of freedom can be neglected.

The collective excitation spectrum of semiquantum 4 He at temperatures T = 4 K and 8 K is investigated on the basis of a thermoviscous model of a fluid. Partial contributions of every collective mode to the symmetrized dynamic structure factor are evaluated. The problem is considered in relation with neutron scattering experimental data and theoretical results previously known.

The reinforced concrete structure built over the destroyed reactor of Chernobyl Nuclear Power Plant is known as the object “Shelter”. It contains a lot of radioactive materials. The aqueous medium increases their mobility so that dangerous elements persistently penetrate into the environment with ground water. This situation and recent measurements are discussed. The egress is supposed to have a diffusion nature. A model for the diffusion treatment of the active elements migrating with ground and subterranean water is proposed. The necessary diffusion coefficients are derived from nonequilibrium statistical mechanics. These coefficients are expressed by singlet and pair equilibrium distribution functions to be evaluated for radioactive particles near a dielectric wall modeling the ground at various concentrations.

A more general formulation of the collective-mode approach is proposed to describe the processes of dynamical polarization in liquids. It is based on a consistent inclusion of non-Markovian terms into the kinetic memory kernels. This has allowed us to reproduce quantitatively the entire frequency dependence of the dielectric functions and identify the primary polarization modes for an interaction site model of water over the whole wavelength range.

The dynamic properties of semiquantum 4He are analyzed at two temperatures above the point of superfluid phase transition. Investigations are carried out in the framework of the dynamic thermal viscous model for low and intermediate values of the wave vector. The “momentum–momentum” and “enthalpy–enthalpy” time correlation functions are evaluated and the partial contributions of the collective excitations to these functions are separated. The recurrent relations for memory kernels are used to calculate the time–space dispersion of the generalized transport coefficients.

An Enskog-Landau kinetic equation for a many-component system of charged hard spheres is proposed. It has been obtained from the Liouville equation with modified boundary conditions by the method of nonequilibrium statistical operator. On the basis of this equation the normal solutions and transport coefficients such as bulk kappa and shear eta viscosities, thermal conductivity lambda, mutual diffusion D^{\alpha\beta} and thermal diffusion D_T^\alpha have been obtained for a binary mixture in the first approximation using the Chapman-Enskog method. Numerical calculations of all transport coefficients for mixtures Ar-Kr, Ar-Xe, Kr-Xe with different concentrations of compounds have been evaluated for the cases of absence and presence of long-range Coulomb interactions. The results are compared with those obtained from other theories and experiment., Comment: 24 LaTeX209 pages, 3 EPS figures (4 files). To be published in Physica A

A general theoretical approach is developed for describing the dynamic properties of semiquantum fluids on the basis of the nonequilibrium statistical operator technique. A set of equations of generalized hydrodynamics is derived and the particular case of thermo-viscoelastic model of a fluid is analyzed in details in the hydrodynamic limit. The case of intermediate and large values of the wave vector is also discussed. The Markov approximation for transport kernels is used to obtain a closed set of equations for dynamic correlation functions. The problem is considered in the context of relation with the experimental data on neutron scattering and the theoretical results known previously in the literature.

The Zubarev nonequilibrium statistical operator is used to describe the generalized hydrodynamic state of a magnetic fluid in an external magnetic field. The magnetic fluid is modeled with “liquid-state” and “magnetic” subsystems described using the classical and quantum statistics methods respectively. Equations of the generalized statistical hydrodynamics for a magnetic fluid in a nonhomogeneous external magnetic field with the Heisenberg spin interaction are derived for “liquid-state” and “magnetic” subsystems characterized by different nonequilibrium temperatures. These equations can be used to describe both the weakly and strongly nonequilibrium states. Some limiting cases are analyzed in which the variables of one of the subsystems can be formally neglected.

A solution to the BBGKY hierarchy for nonequilibrium distribution functions is obtained within modified boundary conditions. The boundary conditions take into account explicitly both the nonequilibrium one-particle distribution function as well as local conservation laws. As a result, modified group expansions are proposed. On the basis of these expansions, a generalized kinetic equation for hard spheres and a generalized Bogolubov-Lenard-Balescu kinetic equation for a dense electron gas are derived within the polarization approximation.

The generalized transport equations for a consistent description of kinetic and hydrodynamic processes in dense gases and liquids are considered. The inner structure of the generalized transport kernels for these equations is established. It is shown how in this approach to obtain the transport equation of molecular hydrodynamics. For the model potential of interaction presented as a sum of the hard spheres potential and certain long-range potential a spectrum of collective modes in the system is investigated., 28 pages

A new kinetic equation for dense gases and liquids with the interparticle potential of interaction in a form of the multistep function is proposed. The equation is consistently derived on the basis of Zubarev's nonequilibrium statistical operator method using a modification for weakening correlations principle which takes into account local conservation laws. In particular cases this equation coincides with the well known kinetic equations for hard-sphere and square-well potentials. Application of the obtained kinetic equation to real systems is discussed. A proof of a global H-theorem is given.

Using Zubarev's method of nonequilibrium statistical operator, the generalized hydrodynamic equations are obtained for a model of magnetic liquid in an inhomogeneous external field. In this model the “liquid” subsystem is treated as a classical one and the “magnetic” subsystem is described by quantum mechanical methods. The properties of the transport equations are analysed in the case of a weak nonequilibrium. The equations for time correlation functions and collective mode spectrum are also found in the same manner. It is shown that the generalized hydrodynamic equations reduce to the well-known results in the limiting cases when the dynamic variables of one subsystem are formally neglected. As an illustration, a simple model of spin relaxation is considered, and the frequency matrix and the matrix of memory functions are calculated. A comparison with previous works is made.

The generalized collective mode approach proposed by de Schepper, Cohen and co-workers (Kamgar-Parsi, B., Cohen, E. G. D., and de Schepper, I. M., 1987, Phys. Rev. A, 35, 4781; de Schepper, I. M., Cohen, E. G. D., Bruin, C., van Rijs, J. C., Montfrooij, W., and de Graaf, L. A., 1988, Phys. Rev. A, 38, 271) for the investigation of time correlation functions of dense fluids is developed in a computer-adapted form which is free of any adjustable parameters. The generalized collective mode spectra of a Lennard-Jones fluid at reduced density n* = nσ3 LJ = 0·845 and reduced temperature T* = k B T/eLJ = 1·706 have been calculated using molecular dynamics for the seven-mode description of the longitudinal fluctuations and also for the three-mode description of the transverse fluctuations. The results are presented as functions of wavevector k for reduced wavenumbers 0 < kσLJ < 24. For longitudinal fluctuations two new kinetic modes are found in addition to the five modes known previously. It is shown that mode-c...

Statistical description of hydrodynamic processes for ionic melts is proposed with taking into account polarization effects caused by the deformation of external ionic shells. This description is carried out by means of the Zubarev nonequilibrium statistical operator method, appropriate for investigations of both strong and weak nonequilibrium processes. The nonequilibrium statistical operator and the generalized hydrodynamic equations that take into account polarization processes are received for ionic-polarization model of ionic molten salts when the nonequilibrium averaged values of densities of ions number, their momentum, dipole momentum and total energy are chosen for the reduced description parameters. A spectrum of collective excitations is investigated within the viscoelastic approximation for ion-polarization model of ionic melts., Comment: 24 pages, RevTex4.1-format, no figures

Zubarev's nonequilibrium statistical operator method is used to give a statistical description of a nonequilibrium plasma in its electromagnetic self-field. Generalized transport equations are obtained for the charged particles and the oscillators of the electromagnetic field with allowance made for the local conservation laws. The case of a nonequilibrium plasma is considered.

The paper discusses one of the approaches to the kinetics and hydrodynamics of dense gases and liquids based on modification of Bogolyubov's conditions of correlation weakening for the Liouville equation for the nonequilibrium distribution function. An entropy of a nonequilibrium state that depends on both the kinetic and the hydrodynamic parameters is defined. Generalized transport equations are obtained for the hydrodynamic variables, and these equations are consistent with the kinetic equation for the single-particle distribution function.

The problem of relaxation of a nonequilibrium state to the state of molecular hydrodynamics is considered for a classical system of interacting particles using the Zubarev nonequilibrium statistical operator method. The wave-vector and frequency dependencies of the dynamical structure factor and momentum-momentum transverse correlation function are investigated on the basis of the appropriate generalized transport equations. Comparison with the results of molecular hydrodynamics and molecular-dynamics simulations is given and the characteristic time intervals of the studied relaxation processes are determined.

The generalization of the Zubarev nonequilibrium statistical operator method for the case of Renyi statistics is proposed when the relevant statistical operator (or distribution function) is obtained based on the principle of maximum for the Renyi entropy. The nonequilibrium statistical operator and corresponding generalized transport equations for the reduced-description parameters are obtained. A consistent description of kinetic and hydrodynamic processes in the system of interacting particles is considered as an example., 13 pages, RevTeX4-format

The development of methods of construction of the theory of nonequilibrium processes for finite-temperature quantum-field systems is one of the important directions of modern theoretical physics. The modern methods of quantum field theory [1-8], on the one hand, and nonequilibrium statistical mechanics [9-16] on the other, are powerful tools in investigations of interacting quantum fields and particles. The unification of these methods can be helpful and have significant influence on the solution of many problems in the study of nonequilibrium states of finite-temperature quantum-field systems. In earlier years, the methods of quantum field theory (Green's function method, renormalization-group method) were helpful in statistical mechanics [17-20] (for example, in the theory of magnetism [21], in the theory of phase transitions [22,23]).

A simplified model for a collective dynamics in ionic melts is proposed for the description of optic-like excitations. Within a polarization model of ionic melt the analytical expressions for optic and relaxation dipole modes are obtained. The considered model allows one to describe a softening of frequency and an increase of damping of optic modes caused by polarization processes in comparison with the rigid-ion model. The contributions related with ion polarization to time correlation functions are calculated., 19 pages, 2 figures