arXiv subjects

G. L. Buchbinder

Publications and source records attributed to G. L. Buchbinder.

9 recordsLinked to original sources

arXiv2021

Kinetic phase diagram for a binary system near the transition to diffusionless solidification

The rapid solidification of a binary mixture in the region of the interface velocities $V$ close to the diffusion speed in the bulk of the liquid phase $V_D$ is considered within the framework of the local nonequilibrium approach. In this high-speed region the derivation of the analytical expression for the response function "temperature-velocity" representing kinetic phase diagram is given without using the concept of the equilibrium phase diagram. The modes of movement of the interface both without and with the drag effect are analyzed. It is shown that the drag effect can be accompanied by a local interface temperature maximum at $V = V_D$.

cond-mat.mtrl-sci↗

arXiv2019

Boundary interface conditions and solute trapping near the transition to diffusionless solidification

The process of rapid solidification of a binary mixture is considered in the framework of local nonequilibrium model (LNM) based on the assumption that there is no local equilibrium in solute diffusion in the bulk liquid and at the solid-liquid interface. According to LNM the transition to complete solute trapping and diffusionless solidification occurs at a finite interface velocity $V=V_D$, where $V_D$ is the diffusion speed in bulk liquid. In the present work, the boundary conditions at the phase interface moving with the velocity $V$ close to $V_D$ ($V \lesssim V_D$) have been derived to find the non-equilibrium solute partition coefficient. In the high-speed region, its comparison with the partition coefficient from the work [Phys. Rev. E 76 (2007) 031606] is given.

cond-mat.mtrl-sci↗

arXiv2012

Heat transfer in rapidly solidifying supercooled pure melt during final transient

The heat transfer model for a one-dimensional supercooled melt during the final stage of solidification is considered. The Stefan problem for the determination of the temperature distribution is solved under the condition that (i) the interface approaches the specimen surface with a constant velocity $V$; (ii) the latent heat of solidification linearly depends on the interface temperature; (iii) all the physical quantities given at the phase boundary are presented by linear combinations of the exponential functions of the interface position. First we find the solution of the corresponding hyperbolic Stefan problem within the framework of which the heat transfer is described by the telegraph equation. The solution of the initial parabolic Stefan problem is then found as a result of the limiting transition $V/V_H \rightarrow 0$ $(V_H \rightarrow \infty)$, where $ V_H $ is the velocity of the propagation of the heat disturbances, in which the hyperbolic heat model teds to the parabolic one.

cond-mat.mtrl-sci↗

arXiv2009

Model for solute diffusion during rapid solidification of binary alloy in semi-infinite volume

On the basis of local nonequilibrium approach, the one-dimensional model of the solute diffusion during rapid solidification of the binary alloy in the semi-infinite volume is considered. Within the scope of the model it is supposed that mass transport is described by the telegrapher equation. The basic assumption concerns the behavior of the diffusion flux and the solute concentration at the interface. Under the condition that these quantities are given by the superposition of the exponential functions the solutions of the telegrapher equation determining the flux and the solute distributions in the melt have been found. On the basis of these solutions different regimes of the solidification in the near surface region and the behavior of the partition coefficient have been investigated. The concentration profiles in the solid after complete solidification are analyzed depending on the model parameters.

cond-mat.mtrl-sci↗

arXiv2008

Market dynamics after large financial crash

The model describing market dynamics after a large financial crash is considered in terms of the stochastic differential equation of Ito. Physically, the model presents an overdamped Brownian particle moving in the nonstationary one-dimensional potential $U$ under the influence of the variable noise intensity, depending on the particle position $x$. Based on the empirical data the approximate estimation of the Kramers-Moyal coefficients $D_{1,2}$ allow to predicate quite definitely the behavior of the potential introduced by $D_1 = - \partial U /\partial x$ and the volatility $\sim \sqrt{D_2}$. It has been shown that the presented model describes well enough the best known empirical facts relative to the large financial crash of October 1987. \

q-fin.ST↗

arXiv2006

Multiple time scales and the empirical models for stochastic volatility

The most common stochastic volatility models such as the Ornstein-Uhlenbeck (OU), the Heston, the exponential OU (ExpOU) and Hull-White models define volatility as a Markovian process. In this work we check of the applicability of the Markovian approximation at separate times scales and will try to answer the question which of the stochastic volatility models indicated above is the most realistic. To this end we consider the volatility at both short (a few days) and long (a few months)time scales as a Markovian process and estimate for it the coefficients of the Kramers-Moyal expansion using the data for Dow-Jones Index. It has been found that the empirical data allow to take only the first two coefficients of expansion to be non zero that define form of the volatility stochastic differential equation of Ito. It proved to be that for the long time scale the empirical data support the ExpOU model. At the short time scale the empirical model coincides with ExpOU model for the small volatility quantities only.

physics.soc-ph↗

arXiv2002

Mass transfer in field of fast-moving deformation disturbance

The mass transfer of interstitial impurities in a crystalline lattice under the influence of the fast-moving deformation disturbance of the type of a shock wave is considered. The velocity of the movement of the disturbance is supposed to be compared with the characteristic velocity of the relaxation of the diffusion flux to its local equilibrium value determined by the Fick's law. The similar situation occurs in a number of experiments on the exposure of a solid to dynamical external loads giving rise to such fast hydrodynamical processes in a sample that the local equilibrium assumption, normally assumed for the macroscopic description of transport processes, is no longer valid. Considering the diffusion flux among the set of independent variables we have derived a set of coupled hydrodynamic equations describing nonequilibrium behavior of a solid in the absence of local equilibrium in the system. Within the scope of the proposed model it has been shown that in comparison with the local equilibrium system an enhanced mass transfer occurs under local nonequilibrium conditions.

cond-mat.mtrl-sci↗

arXiv2000

Hydrodynamics of crystals with interstitials

The hydrodynamic equations for a crystals with interstitials, taking into account the dissipative processes of the viscosity, heat conduction and the interstitial diffusion are derived. To achieve that we use the phenomenological approach has originally been applied in the theory of the superfluids for the derivation of equations of the two-fluid hydrodynamics. On the basis of the obtained equations the problem of the propagation of plane waves in the crystals with low interstitial concentration has been considered. For the case when effects of the viscosity and the heat conduction are absent and the diffusion mobility of interstitials is small the absorption coefficient of longitudinal sound wave has been calculated.

cond-mat.mtrl-sci↗

arXiv1999

Quantum diffusion at high interstitial concentrations: Application to surface diffusion

In this work we first study the quantum diffusion in a volume of a crystalline solid at high interstitial concentrations when the effects of the short-range interactions between the diffusing particles are to be factors. Within the scope of the small-polaron formalism the transition rate depending on both the temperature and the interstitial concentration has been calculated. Then, using the obtained result, we consider the model of surface diffusion that reproduces qualitatively the diffusion behaviour of the hydrogen isotopes on W(110) surface, observed in the lowtemperature experiments [S.C. Wang and R. Gomer, J.Chem.Phys. v.83, 4193 (1985)]. The coverage dependence of the diffusion coefficient is determined by Monte Carlo simulation. The model allows to suppose that substantially the different diffusion of hydrogen (tritium) and deuterium can be the outcome of their different quantum statistic and the direct interactions between the adparticles.

cond-mat.mtrl-sci↗