Symmetric random walks in random environments

We consider a random walk on thed-dimensional lattice ^d where the transition probabilitiesp(x,y) are symmetric,p(x,y)=p(y,x), different from zero only ify–x belongs to a finite symmetric set including the origin and are random. We prove the convergence of the finite-dimensional probability distributions of normalized random paths to the finite-dimensional probability distributions of a Wiener process and find our an explicit expression for the diffusion matrix.     

On Effective Conductivity on ℤ d Lattice

We study the effective conductivity _e for a random wire problem on the d-dimensional cubic lattice ^d , d2 in the case when random conductivities on bonds are independent identically distributed random variables. We give exact expressions for the expansion of the effective conductivity in terms of the moments of the disorder parameter up to the 5th order. In the 2D case using the duality symmetry we also derive the 6th order expansion. We compare our results with the Bruggeman approximation and show that in the 2D case it coincides with the exact solution up to the terms of 4th order but deviates from it for the higher order terms.     

Size effects upon phase transitions in vanadium oxide nanocomposites

A phenomenological model has been proposed for the formation of the major thermal hysteresis loop of optical parameters upon the semiconductor-metal phase transition in vanadium oxide nanocomposites. It has been demonstrated that the effects associated with the influence of nanocrystallite sizes on the phase transition temperature in an individual nanocrystallite, which is determined by the width of the elementary hysteresis loop and the position of the phase equilibrium temperature on the temperature scale, manifest themselves in the form of pronounced features in the loop shape. In particular, the size effects for VO₂ polycrystalline films are observed in the formation of a trapezoidal shape of the optical thermal hysteresis loop with a wide lower base, whereas these effects for nanocomposites based on porous glasses with VO₂ nanocrystals are revealed in the form of the optical hysteresis loop with a narrow lower base (wide upper base). The proposed model also explains the symmetric shape of the major hysteresis loop for vanadium oxide nanocomposites based on opals. The size effects in opal nanocomposites with strictly fixed sizes of pores and, therefore, nanocrystallite sizes manifest themselves in the form of well-defined steps in the heating and cooling branches of the major hysteresis loop.     

Chemical Composition of Glass and Traditions of Enamellers in Eastern Europe in the Late Roman Period (a Case Study of the Bryansk Hoard)

Crystallography Reports - The chemical composition of Bryansk hoard enamels (late II?III century) has been investigated by scanning electron microscopy and electron probe microanalysis. Raw...     

Observation of Spin and Valley Splitting of Landau Levels under Magnetic Tunneling in Graphene/Boron Nitride/Graphene Structures

Resonance magnetic tunneling in heterostructures formed by graphene single sheets separated by a hexagonal boron nitride barrier and bounded by two gates has been investigated in a strong magnetic field, which has allowed observing transitions between spin- and valley-split Landau levels with various indices belonging to different graphene sheets. An unexpected increase with the temperature in the interlayer tunneling conductance owing to transitions between the Landau levels in strong magnetic fields cannot be explained by existing theories.     

Switching Channel Development Dynamics in Planar Structures on the Basis of Vanadium Dioxide

The results of the experimental studies and numerical simulation of the switching channel development dynamics in planar structures on the basis of vanadium dioxide are reported. The obtained data on the variation of the temperature in the channel with time and of the current arisen after the pulsed load, and on the times of transition from the high-resistance to the low-resistance state and back are analyzed in order to determine the switching mechanism and to predict the functional characteristics of the switchable vanadium- oxide structures as promising materials for the creation of relaxation generators that can serve as prototypes of neural oscillators. It is shown that the switching behavior is associated with the metal–semiconductor phase transition in vanadium dioxide, which is stimulated by the emission of Joule heat.     

The Use of Galvanic Displacement for Synthesizing Pt/Carbide (Mo2C,ZrC, NbC) Catalysts Highly Active in the Hydrogen Evolution Reaction

Russian Journal of Electrochemistry - The composite materials involving platinum nanoparticles on the surface of carbides of Mo, Zr, and Nb are synthesized by the currentless redox reaction between...     

Herman’s theory revisited

We prove that a C ^2+α -smooth orientation-preserving circle diffeomorphism with rotation number in Diophantine class D _δ , 0≤δ<α≤1, α−δ≠1, is C ^1+α−δ -smoothly conjugate to a rigid rotation. This is the first sharp result on the smoothness of the conjugacy. We also derive the most precise version of Denjoy’s inequality for such diffeomorphisms.     

Polarization dynamics of intracavity frequency-doubled Nd:YAG laser

Experimental study of low-frequency dynamics of an intracavity frequency-doubled Nd:YAG laser demonstrates the influence of the interaction of orthogonally polarized modes, participating in frequency doubling (type II phase matching), on the stability of the laser output. At a sufficiently low pump rate and low conversion efficiency, the laser shows stable operation with a low noise level at the frequencies of relaxation oscillations. At a high pump power and/or a high conversion efficiency, the laser emission becomes unstable as a result of Hopf bifurcation at the frequencies of relaxation oscillations that are responsible for the anti-phase polarization dynamics of the laser.     

Multidimensional Continued Fractions,Dynamical Renormalization and KAM Theory

The disadvantage of ‘traditional’ multidimensional continued fraction algorithms is that it is not known whether they provide simultaneous rational approximations for generic vectors. Following ideas of Dani, Lagarias and Kleinbock-Margulis we describe a simple algorithm based on the dynamics of flows on the homogeneous space (the space of lattices of covolume one) that indeed yields best possible approximations to any irrational vector. The algorithm is ideally suited for a number of dynamical applications that involve small divisor problems. As an example, we explicitly construct a renormalization scheme for the linearization of vector fields on tori of arbitrary dimension.