Theory of gas porosity produced as a result of diffusive decomposition of multicomponent systems

A complete set of equations, which describe the kinetics of formation of gas porosity, is derived. The large and small pores are defined and analyzed. The methods of solution for an arbitrary number of impurity atoms are given for the limiting cases of large and small pores. The filling of pores with a molecular gas containing matrix atoms is analyzed in detail. The obtained results are compared with the experimental data.     

Theory of diffusive decomposition of supersaturated solid solution under the condition of simultaneous operation of several mass-transfer mechanisms

The kinetics of diffusive decomposition of a supersaturated solid solution under the condition of simultaneous operation of several mass-transfer mechanisms are developed. It is shown that the expressions for the growth rate of the precipitate and for the size distribution function have one peak. The location of these peaks, which slowly changes with time, can be considered a slowly changing parameter.     

Formation of the universal distribution function in the dimension space for new-phase particles in the diffusive decomposition of the supersaturated solid solution

The method of time-asymptotic solution of nonlinear equations describing the decomposition of supersaturated solid solutions is developed. The distribution curve is plotted for any dimension at the given moment of time. The results are generalized for the case of volume sources of the solute, for the multicomponent multiphase solid solutions and for the different mass-transfer mechanisms.     

Phase competition in late stages of diffusive decomposition

The late stages of diffusive decomposition of a supersaturated solid solution into phases consisting of multicomponent stoichiometric compounds with a common element are investigated. It is shown that a competition is possible between phases for the common component, as a result of which only one of these phases survives. Fiz. Tverd. Tela (St. Petersburg) 40, 655–657 (April 1998)     

Change in primary extinction during decomposition of supersaturated solid solution

The integrated intensity of the matrix reflection (200) was measured during the precipitation of the, and phases. The observed effects were explained as the consequence of lattice defects formed in the neighbourhood of precipitate particles.

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(200) , . .

     

Driven diffusive systems with disorder

We discuss recent work on the static and dynamical properties of the asymmetric exclusion process, generalized to include the effect of disorder. We study in turn, random disorder in the properties of particles; disorder in the spatial distribution of transition rates, both with a single easy direction and with random reversals of the easy direction; dynamical disorder, where particles move in a disordered landscape which itself evolves in time. In every case, the system exhibits phase separation; in some cases, it is of an unusual sort. The time-dependent properties of density fluctuations are in accord with the kinematic wave criterion that the dynamical universality class is unaffected by disorder if the kinematic wave velocity is nonzero.     

Diffusion in multicomponent systems

Some consequences of the thermodynamics of irreversible processes on the diffusion coefficients are discussed. The corresponding inequalities for the diffusion coefficients are derived.Dedicated to Professor Miroslav Trlifaj on the occasion of his sixtieth birthday.     

Contrast in multicomponent systems

The forward scattering of radiation by multicomponent systems is expressed in terms of the chemical potentials and of the collision lengths associated with the components.Contrast lengths can be defined in various unequivalent ways. The formula giving the scattering cross section in terms of such contrasts is derived geometrically. This approach allows a discussion concerning the best definition of the contrast lengths.     

States of a supersaturated solution in limited-size systems

The features of phase transformations in limited-size systems have been described. The main specificity of small-size systems is the multivariance of equilibrium and metastable states whose stability and region of existence depend on the dimensions of the system, concentration, and temperature. A decrease in the dimensions of the system makes it possible to increase the solubility and to prevent the decay of the supersaturated solution. The properties described by the thermodynamic model are reproduced experimentally using the ensemble of evaporated drops of the solution.     

Nonequilibrium thermodynamics of multicomponent systems

A general formalism of nonequilibrium thermodynamics of multicomponent fluids is given. Reversible parts of balance equations for the extensive variables are constructed in such a way that the growth rate of the extensive variables are related to their conjugate intensive parameters in an antisymmetric manner. This enables us to give the balance equation for the diffusional flow which plays an important role in the study of superfluidity and complex fluids.     

Phase segregation in driven diffusive systems

Driven diffusive models describe an array of atoms in an external periodic potential, when the motion is damped due to energy exchange with the substrate. The systems of this class have wide application in modeling of charge and mass transport in solids. Recently, the driven diffusive models have been used in tribology, where the driving force emerges due to motion of one of two substrates, which are separated by a thin atomic layer. When a dc force is applied to the atoms, the system exhibits the locked-to-sliding transition. During the transition the system may split in domains of two kinds, the running domains where the atoms move with almost maximum velocity, and the immobile domains (“traffic jams”). We discuss a new model for a 1D chain, where the particles have a complex structure treated in a mean-field fashion: particle collisions are inelastic and also each particle is considered as having its own thermostat. This model exhibits a hysteresis and the “traffic jams” state even at high temperatures due to the clustering of atoms with the same velocity.     

Mode-coupling theory for purely diffusive systems

A mode-coupling formalism is developed for multicomponent systems of particles performing diffusive motion in a uniform host medium. The mode-coupling equations are derived from a set of nonlinear fluctuating diffusion equations by expanding the concentration-dependent diffusion constants about their equilibrium values. From the mode-coupling equations the dominant long time behavior of current-current and super-Burnett correlation functions is derived. As specific applications I consider the long time behaviors of these correlation functions for collective and tracer diffusion in a one-component lattice gas with particle-conserving stochastic dynamics. The results agree with those from exactly solvable models and computer simulations.     

Thermal response in driven diffusive systems

Evaluating the linear response of a driven system to a change in environment temperature(s) is essential for understanding thermal properties of nonequilibrium systems. The system is kept in weak contact with possibly different fast relaxing mechanical, chemical or thermal equilibrium reservoirs. Modifying one of the temperatures creates both entropy fluxes and changes in dynamical activity. That is not unlike mechanical response of nonequilibrium systems but the extra difficulty for perturbation theory via path-integration is that for a Langevin dynamics temperature also affects the noise amplitude and not only the drift part. Using a discrete-time mesh adapted to the numerical integration one avoids that ultraviolet problem and we arrive at a fluctuation expression for its thermal susceptibility. The algorithm appears stable under taking even finer resolution.     

Thermodynamics of diffusive DM/DE systems

We discuss the energy density, temperature and entropy of dark matter (DM) and dark energy (DE) as functions of the scale factor a in an expanding universe. In a model of non-interacting dark components we repeat a derivation from thermodynamics of the well-known relations between the energy density, entropy and temperature. In particular, the entropy is constant as a consequence of the energy conservation. We consider a model of a DM/DE interaction where the DM energy density increase is proportional to the particle density. In such a model the dependence of the energy density and the temperature on the scale factor a is substantially modified. We discuss (as a realization of the model) DM which consists of relativistic particles diffusing in an environment of DE. The energy gained by the dark matter comes from a cosmological fluid with a negative pressure. We define the entropy and free energy of such a non-equilibrium system. We show that during the universe evolution the entropy of DM is increasing whereas the entropy of DE is decreasing. The total entropy can increase (in spite of the energy conservation) as the DM and DE temperatures are different. We discuss non-equilibrium thermodynamics on the basis of the notion of the relative entropy.     

Anti-parity-time symmetric phase transition in diffusive systems

Parity-time (PT) symmetry/anti-parity-time (APT) symmetry in non-Hermitian systems reveal profound physics andspawn intriguing effects. Recently, it has been introduced into diffusive systems together with the concept of exceptionalpoints (EPs) from quantum mechanics and the wave systems. With the aid of convection, we can generate complex thermalconductivity and imitate various wavelike dynamics in heat transfer, where heat flow can be “stopped” or moving against thebackground motion. Non-Hermitian diffusive systems offer us a new platform to investigate the heat wave manipulation.In this review, we first introduce the construction of APT symmetry in a simple double-channel toy model. Then we showthe phase transition around the EP. Finally, we extend the double-channel model to the four-channel one for showing thehigh-order EP and the associated phase transition. In a general conclusion, the phase difference of adjacent channels isalways static in the APT symmetric phase, while it dynamically evolves or oscillates when the APT symmetry is broken.     

Resonant diffusive radiation in random multilayered systems

We have theoretically shown that the yield of diffuse radiation generated by relativistic electrons passing random multilayered systems can be increased when a resonant condition is met. The resonant condition can be satisfied for the wavelength region representing visible light as well as soft X rays. The intensity of diffusive soft X rays for specific multilayered systems consisting of two components is compared with the intensity of Cherenkov radiation. For radiation at a photon energy of 99.4 eV, the intensity of resonant diffusive radiation (RDR) generated by 5-MeV electrons passing a Be/Si multilayer exceeds the intensity of Cherenkov radiation by a factor of ≈60 for electrons with the same energy passing a Si foil. For a photon energy of 453 eV and 13 MeV, electrons passing a Be/Ti multilayer generate RDR exceeding the Cherenkov radiation generated by electrons passing Ti foils by a factor ≈130.     

Onset of diffusive behavior in confined transport systems

We investigate the onset of diffusive behavior in polygonal channels for disks of finite size, modeling simple microporous membranes. It is well established that the point-particle case displays anomalous transport, because of slow correlation decay in the absence of defocusing collisions. We investigate which features of point-particle transport survive in the case of finite-sized particles (which undergo defocusing collisions). A similar question was investigated by Lansel, Porter, and Bunimovich [Chaos 16, 013129 (2006)], who found that certain integrals of motion and multiple ergodic components, characteristic of the point-particle case, remain in "mushroom"-like systems with few finite-sized particles. We quantify the time scales over which the transport of disks shows features typical of the point particles, or is driven toward diffusive behavior. In particular, we find that interparticle collisions drive the system toward diffusive behavior more strongly than defocusing boundary collisions. We illustrate how, and at what stage, typical thermodynamic behavior (consistent with kinetic theory) is observed, as particle numbers grow and mean free paths diminish. These results have both applied (e.g., nanotechnological) and theoretical interest.