On the Collision between two PNG Droplets

In this article we study the interface generated by the collision between two crystals growing layer by layer on a one-dimensional substrate through random decomposition of particles. We relate this interface with the notion of β-path in an equivalent directed polymer model and, by using asymptotics results from J. Baik and E. Rains, J. Stat. Phys., 100:523–541 (2000). and some hydrodynamic tools introduced by E. Cator and P. Groeneboom, Ann. Probab., 33:879–903 (2005), we derive a law of large numbers for such a path and obtain some bounds for its fluctuations. 2000 Mathematics Subject Classification: 60C05, 60K35     

Theorem on the kinetic energy in an elastic continuum with defects

An expression of the theorem on the kinetic energy for an elastic continuum with dislocations is derived on the basis of the dynamical equations of a gauge model of the medium. This relation shows that the work performed by internal surface stresses in the volume is redistributed between the work performed by the effective stresses at the rates of the effective elastic distortions and plastic distortions. In phenomenological theories of plasticity the latter quantity, representing the rate of energy dissipation, governs the dissipative processes. An expression is obtained which relates the rate of energy dissipation with the self-energy density of the field of the defects and the energy flux of the defects. Zh. Tekh. Fiz. 68, 82–83 (March 1998)     

Cooling Process for Inelastic Boltzmann Equations for Hard Spheres, Part I: The Cauchy Problem

We develop the Cauchy theory of the spatially homogeneous inelastic Boltzmann equation for hard spheres, for a general form of collision rate which includes in particular variable restitution coefficients depending on the kinetic energy and the relative velocity as well as the sticky particles model. We prove (local in time) non-concentration estimates in Orlicz spaces, from which we deduce weak stability and existence theorem. Strong stability together with uniqueness and instantaneous appearance of exponential moments are proved under additional smoothness assumption on the initial datum, for a restricted class of collision rates. Concerning the long-time behaviour, we give conditions for the cooling process to occur or not in finite time. Mathematics Subject Classification (2000): 76P05 Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05].     

Symmetry of the nonlinear collision operator matrix and new prospects in the moment method for solving the Boltzmann equation

Traditionally, the moment method has been used in kinetic theory to calculate transport coefficients. Its application to the solution of more complicated problems runs into enormous difficulties associated with calculating the matrix elements of the collision operator. The corresponding formulas for large values of the indices are either lacking or are very cumbersome. In this paper relations between matrix elements are derived from very general principles, and these can be employed as simple recurrence relations for calculating all the nonlinear and linear anisotropic matrix elements from assigned linear isotropic matrix elements. Efficient programs which implement this algorithm are developed. The possibility of calculating the distribution function out to 8–10 thermal velocities is demonstrated. The results obtained open up prospects for solving many topical problems in kinetic theory. Zh. Tekh. Fiz. 69, 6–9 (September 1999)     

Quantum kinetic equation for nonequilibrium dense systems

Using the density matrix method in the form developed by Zubarev, equations of motion for nonequilibrium quantum systems with continuous short range interactions are derived which describe kinetic and hydrodynamic processes in a consistent way. The T-matrix as well as the two-particle density matrix determining the nonequilibrium collision integral are obtained in the ladder approximation including the Hartree-Fock corrections and the Pauli blocking for intermediate states. It is shown that in this approximation the total energy is conserved. The developed approach to the kinetic theory of dense quantum systems is able to reproduce the virial corrections consistent with the generalized Beth-Uhlenbeck approximation in equilibrium. The contribution of many-particle correlations to the drift term in the quantum kinetic equation for dense systems is discussed.     

Critical dynamics of slightly disordered spin systems

A new approach to the analysis of magnetic dipole motion in external magnetic field and fields generated by neighboring magnetic dipoles is suggested, and original general kinetic equations for the dipole density are derived. Special cases of these general equations are the Bloch, Redfield, and Provotorov equations, which are widely used in NMR theory. A comparison between NMR spectra calculated with the new theory and published experimental data also shows good agreement in regions to which the equations listed above do not apply. Zh. éksp. Teor. Fiz. 113, 967–980 (March 1998)     

Observation of ^1H tunneling diffusion in crystalline Si

H diffusion in crystalline Si has been measured in the temperature range of 50–220 K. The temperature dependence of the diffusion coefficient follows a power law of the type , . D(H) values range between 10– cm/s up to about 200 K, where a transition to thermally activated diffusion is indicated. The low-temperature transport mechanism is attributed to tunneling. Received: 15 October 1996 / Accepted: 11 November 1996     

Kinetics of dense matter: Correlations and memory

A link between correlation contributions to kinetic equations for dense quantum systems and the energy conservation is considered. In order that the energy be conserved by an approximate collision integral, the one-particle density matrix and the mean interaction energy are treated as independent state parameters. It is shown how the density operator method can be used to derive non-Markovian kinetic equations including the correlation effect associated with the energy conservation. A quantum generalization of the Enskog theory is discussed. The text was submitted by the author in English.     

Stationary nonequilibrium solutions of model Boltzmann equation

We give an explicit solution of a model Boltzmann kinetic equation describing a gas between two walls maintained at different temperatures. In the model, which is essentially one-dimensional, there is a probability for collisions to reverse the velocities of particles traveling in opposite directions. Particle number and speeds (but not momentum) are collision invariants. The solution, which depends on the stochastic collision kernels at the walls, has a linear density profile and the energy flux satisfies Fourier's law.This paper is dedicated to Peter Gabriel Bergmann with affection and admiration on the occasion of his 70th birthday.     

Electrodynamics of hard superconductors in crossed magnetic fields

A model systematically accounting for the cutting of Abrikosov flux lines has been developed for the critical state of a hard superconductor in crossed dc and ac magnetic fields. The electrodynamic equations have been derived by minimizing the Gibbs free energy calculated using the proposed two-velocity hydrodynamic model. One velocity describes the motion of the vortex lattice as a whole, and the other describes the relative motion of the two intersecting sublattices. The resulting equations yield as special cases the previously known electrodynamic equations for hard superconductors. The model provides a natural explanation for the suppression of dc magnetization by a transverse ac magnetic field observed in our experiments. Zh. éksp. Teor. Fiz. 111, 1071–1084 (March 1997)     

Ion conductivity and dielectric relaxation behavior in FIC silver based phospho-molybdate glasses

Electrical conductivity and dielectric relaxation studies of silver ion-conducting glasses have been prepared using xAg₂SO₄-15Ag₂O-(90-x)(90P₂O₅-10MoO₃) glass system over a temperature range of 298–353 K and frequencies of 10 Hz to 10 MHz. DC conductivities exhibit Arrhenius behavior over the entire temperature range with a single activation barrier. The ac conductivity behavior of these glasses has been analyzed using single power law; conductivity increases linearly in logarithmic scale with Ag₂SO₄ concentration. The power law exponent (s) decreases, while stretched exponent (β) is insensitive to increase of temperature. Scaling behavior has also been carried out using the reduced plots of conductivity and frequency, which suggest that ion transport mechanism remains unaffected at all temperatures and compositions.     

Around Multicolour Disordered Lattice Gas

We consider a system of multicolour disordered lattice gas, following closely the (monocolour) introduced by Faggionato and Martinelli^(3,4). We study the projection on the monocolour system and we derive an estimate of the closeness between grand canonical and canonical Gibbs measures. AMS Classification: Primary: 60K35, 82C20, 82C22     

Structural stability of disperse systems and finite nature of a coagulation front

A new discrete model of coagulation, which is a discrete analog of the Oort-van de Hulst-Safronov equation, is derived. It is shown that the familiar version, in contrast with Smoluchowski’s equation, can be used to calculate the propagation of a coagulation front. The relationship between compliance to the mass conservation law and the finite nature of the coagulation front is established, and then estimates of the time of violation of the mass conservation law are made for several classes of coagulation kernels. One of the conclusions is that the mass conservation law can be violated in cases where particles of roughly equal mass cannot coagulate, as occurs, for example, in gravitational coagulation. Estimates of the time for the appearance of structural instability of the system are made for multiplicative coagulation kernels. Zh. éksp. Teor. Fiz. 116, 717–730 (August 1999)     

Scaling and Expansion of Moment Equations in Kinetic Theory

The set of generalized 13 moment equations for molecules interacting with power law potentials [Struchtrup, Multiscale Model. Simul. 3:211 (2004)] forms the base for an investigation of expansion methods in the Knudsen number and other scaling parameters. The scaling parameters appear in the equations by introducing dimensionless quantities for all variables and their gradients. Only some of the scaling coefficients can be chosen independently, while others depend on these chosen scales–their size can be deduced from a Chapman–Enskog expansion, or from the principle that a single term in an equation cannot be larger in size by one or several orders of magnitude than all other terms.It is shown that for the least restrictive scaling the new order of magnitude expansion method [Struchtrup, Phys. Fluids 16(11):3921 (2004)] reproduces the original equations after only two expansion steps, while the classical Chapman–Enskog expansion would require an infinite number of steps. Both methods yield the Euler and Navier–Stokes–Fourier equations to zeroth and first order. More restrictive scaling choices, which assume slower time scales, small velocities, or small gradients of temperature, are considered as well.     

Limiting Dynamics for Spherical Models of Spin Glasses at High Temperature

We analyze the coupled non-linear integro-differential equations whose solution is the thermodynamical limit of the empirical correlation and response functions in the Langevin dynamics for spherical p−spin disordered mean-field models. We provide a mathematically rigorous derivation of their FDT solution (for the high temperature regime) and of certain key properties of this solution, which are in agreement with earlier derivations based on physical grounds. AMS (2000) Subject Classification: Primary: 82C44, Secondery: 82C31, 60H10, 60F15, 60K35     

Fine structure of the permittivity spectrum of a fluorite crystal

The experimental curve of the permittivity of fluorite is decomposed, for the first time, into 11 components in the range 10.5–18 eV (90 K) and 18 components in the range 10–35 eV (300 K) by the Argand diagram method. Three parameters are determined for each component: the energy at band maximum, the half-width of the band, and the oscillator strength. A scheme is proposed for the nature of the components of the permittivity of fluorite. Fiz. Tverd. Tela (St. Petersburg) 41, 1614–1615 (September 1999)     

Statistical symmetries and its impact on new decay modes and integral invariants of decaying turbulence

Classical decay laws of isotropic turbulence usually derived from the von Kármán–Howarth equation are essentially based on two paradigms. First, scaling symmetries of space and time, both tracing back to the Navier–Stokes equations in the limit of large Reynolds numbers (or r?η), give rise to a temporal power-law decay for the turbulent kinetic energy and at the same time an algebraic growth of the integral length scale at an exponent that is uniquely coupled to the latter energy decay. Second, global invariants such as Birkhoff or Loitsianskii integrals determine the exponent of both power laws. We presently show that this class of decay laws may be considerably extended considering the entire set of multi-point correlation equations that admit a much wider class of symmetries. It was recently shown that these new symmetries are of paramount importance, e.g. in deriving the logarithmic law of the wall being an analytic solution of the multi-point equations. For the present case, it is particularly an additional scaling group, which we call statistical scaling group, that gives rise to two additional families of ‘canonical’ decay laws including those with an exponential characteristic for both the kinetic energy and the integral length scale. Finally, a second rather generic group admitted by all linear differential equations corresponding to the superposition principle induces an infinite set of scaling laws of rather complex form that may match rather generic initial conditions. All scaling laws are analyzed in the light of the above-mentioned integral invariants that have been further extended in the present contribution to an exponential-type invariant.