Kinetic theory of adsorption and desorption

In this paper we use stochastic methods to discuss adsorption and desorption. The paper derives generalized coefficients of sticking and accomodation depending on surface temperatureT _s and gas temperatureT _g and shows, that for additive Markov processes, these kinetic coefficients are identical. Furthermore, exact solutions of the kinetic equations for certain simple transition probabilitiesP(, ) are found and an approximation method for more complicatedP(, ) is given. The comparison of the theory with experimental results for noble gas-metal systems indicate a quadratic relationship between the first moment of the transition probabilityP(, ) and the well depth of the physisorption system.     

The Statistics of the Trajectory of a Certain Billiard in a Flat Two-Torus

We consider a billiard in the punctured torus obtained by removing a small disk of radius >0 from the flat torus ², with trajectory starting from the center of the puncture. In this case the phase space is given by the range of the velocity only. Let (), and respectively R(), denote the first exit time (length of the trajectory), and respectively the number of collisions with the side cushions when ² is being identified with [0,1)². We prove that the probability measures on [0, ) associated with the random variables and R are weakly convergent as 0⁺ and explicitly compute the densities of the limits. Research partially supported by ANSTI grant C6189/2000.     

Lattice and continuum wavelets and the block renormalization group

We obtain a resolution of the identity operator, for functions on a latticeZ ^d, which is derived from the block renormalization group. We use eigenfunctions of the terms of the decomposition to form a basis forl ₂(Z^d) and show how the basis is generated from lattice wavelets. The lattice spacing is taken to zero and continuum wavelets are obtained.     

Accurate calculation of functional determinants

A dependence of the functional determinant of the operator from the family D() satisfying the condition D()=fD()+D()f on the parameter m² of infrared regularization is found in the regularization method using a generalized function.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 27–32, June, 1988.     

P-polarized nonlinear surface polaritons near the surface of a saturable self-defocusing medium: Threshold case

We have obtained the solution of the stationary problem for P-polarized nonlinear surface polaritons (NLSP) near the interface of two media, one of which is optically linear and the other having an optical nonlinearity with saturation and a dielectric function of the form: =_xx=_zz=₀+a|E|²/(1+b|E|²), where E is the amplitude of the electric field. On this basis the NLSP energy and propagation properties, the polarization structure and the localization depth of the NLSP field as well as the physically allowed region in the parameter space have been investigated for the case in which the parameter ₀ is positive, b is non-negative, and a and ₁ are negative (₁ is the dielectric function of the linear medium); ₀>|₁|.     

Effect of quenching temperature on the components of the permeability tensor and the complex dielectric constant of microwave magnesium ferrites

We report an investigation of the effect of the quenching temperature (from 900 °C, 700 °C, and for self-cooling) on the components of the permeability tensor and on the complex dielectric constant * of magnesium-aluminum, magnesium-chromium and magnesium-manganese, ferrites of fixed composition. The measuring apparatus and measurement procedure are described and an estimate of the errors is given. It is shown that due to quenching the gyrotropic properties of the ferrites are increased ( falls and _a increases), while the dielectric constant is unchanged. Quenching leads to an increase in the magnetic and dielectric losses.Translated from Izvestiya VUZ. Fizika, Vol. 11, No. 11, pp. 41–47, November, 1968.     

Retardation of electromagnetic waves by helices of large diameters

This paper is devoted to the study of the wave retardation by helices of large diameters, when the lengthL of one turn of the helix is larger than the vacuum wavelength, i.e.L/>1. The dispersion equation of the tape helix wound up on a dielectric cylinder was derived and the dependence of the phase velocity of slowed-down waves on the diameter of helix was calculated. The theory was verified experimentally at a frequencyf=2·385 GHz. Helices were wound up on polyfoam (=1·04) and plexiglass (=2·55) cylinders of various diameters. For the helix wound up on plexiglass cylinders it was found that the wave retardation depends on the form of conductor from which the helix is made. The retardation of waves is determined by an effective dielectric constant _ef which is equal either ( _i + _e)/2 for the tape helix or ( _{i e}) for the helix made from a wire of the circular cross-section; here _i is the dielectric constant of inner dielectric rod and _e is that of outer space.     

The ɛ-expansion for the Hierarchical Model

In this paper, the Hierarchical Model is studied near a non-trivial fixed point of its renormalization group. Our analysis is an extension of work of Bleher and Sinai. We prove the validity of the -expansion for . We then show that the renormalization transformations around have an unstable manifold which is completely characterized by the tangent map and can be brought to normal form. We then establish relations between this result and the critical behaviour of the model in the thermodynamic limit.     

Asymptotic theory of multidimensional chaos

A delay-differential equationu(t)+u(t)=f(u(t–1)), 0t < , and its generalization are investigated in the limit 0, when the attractor's dimension increases infinitely. It is shown that a number of statistical characteristics are asymptotically independent of. As for the attractor, it can be regarded as a direct product ofO(1/) equivalent subattractors, their statistical characteristics being asymptotically independent of . The results enable one to predict some characteristics of the attractor with fractal dimensionD 1 for the case 1, when they are inaccessible numerically. The approach developed seems to be applicable for a wide class of spatiotemporal systems.     

Static and dynamic properties of XY systems with extended defects in cubic anisotropic crystallines

Static and dynamic critical behavior ofXY systems in cubic anisotropic crystallines, with extended defects (or quenched nonmagnetic impurities) strongly correlated along _d -dimensional space and randomly distributed ind – _d dimensions, were studied. These extended defects make the systems coordinate anisotropic, resulting in unique critical behavior due to competition between the cubic anisotropy and the coordinate anisotropy. The systems were analyzed by an ^1/2 (4 – d) type of expansion with double expansion parameters based on a renormalization-group (RG) approach. Critical exponents were calculated near the second-order phase transition point and the behavior of the first-order transition was evaluated near the tricritical point.     

Spectral behavior of quasi periodic potentials

Spectral properties of Schrödinger operators of the typeH =–+V, where is the Laplacian,V a quasiperiodic potential and a coupling constant, are developed.V is taken to be finite sum of exponentials with generic frequencies. For small a strong stability is shown. On the other hand, examples (in the finite diffeence case) are given, for which a transition in the type of spectrum occurs, as is increased.Research supported in part by grant NSF MCS 7900813     

Effect of ultrasonic vibrations on the parameters of the hardening curve for copper single crystals

The variations induced in the parameters of the hardening curve for copper single crystals by ultrasonic vibrations at a frequency of 20 kHz are investigated. It is shown that the application of ultrasound to the samples under tension significantly lowers the critical yield stress (₀) and increases the duration of the first hardening stage (₂). Preliminary ultrasonic irradiation is accompanied by an increase in ₀ and an appreciable increase in ₂. The magnitude of the variations oft ₀ and ₂ depends on the ultrasonic intensity. Experimental results are given for the time dependence of the recovery of the yield point for the irradiated copper samples at 20 and –50 °C.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 51–56, February, 1972.     

Natural boundaries for area-preserving twist maps

We consider KAM invariant curves for generalizations of the standard map of the form (x, y)=(x+y, y+f(x)), wheref(x) is an odd trigonometric polynomial. We study numerically their analytic properties by a Padé approximant method applied to the function which conjugates the dynamics to a rotation +. In the complex plane, natural boundaries of different shapes are found. In the complex plane the analyticity region appears to be a strip bounded by a natural boundary, whose width tends linearly to 0 as tends to the critical value.     

Critical (Φ4)3,ε

The Euclidean (⁴)_3, model in R³ corresponds to a perturbation by a ⁴ interaction of a Gaussian measure on scalar fields with a covariance depending on a real parameter in the range 01. For =1 one recovers the covariance of a massless scalar field in R³. For =0, ⁴ is a marginal interaction. For 0<1 the covariance continues to be Osterwalder-Schrader and pointwise positive. We consider the infinite volume critical theory with a fixed ultraviolet cutoff at the unit length scale and we prove that for >0, sufficiently small, there exists a non-gaussian fixed point (with one unstable direction) of the Renormalization Group iterations. We construct the stable critical manifold near this fixed point and prove that under Renormalization Group iterations the critical theories converge to the fixed point. Partially supported by NSERC of CanadaLaboratoire Associé au CNRS. UMR 5825Partially supported by CNR, G.N.F.M. and MURST     

Simulation calculation of dielectric constants: Comparison of methods on an exactly solvable model

A mean spherical model of classical dipoles on a simple cubic lattice of sideM=2N+1 sites is considered. Exact results are obtained for finite systems using periodic boundary conditions with an external dielectric constant and using reaction field boundary conditions with a cutoff radiusR _c N and an external dielectric constant. The dielectric constant in the disordered phase is calculated using a variety of fluctuation formulas commonly implemented in Monte Carlo and molecular dynamics simulations of dipolar systems. The coupling in the system is measured by the parametery=4 ²/9kT, where ² is the fixed mean square value of the dipole moments on the lattice. The system undergoes a phase transition aty2.8, so that very high dielectric constants cannot be obtained in the disordered phase. The results show clearly the effects of system size, cutoff radius, external dielectric constant, and different measuring techniques on a dielectric constant estimate. It is concluded that with periodic boundary conditions, the rate of approach of the dielectric constant estimate to its thermodynamic limit is asN ^–2/3 and depends only weakly on. Methods of implementing reaction field boundary conditions to give rapid convergence to the thermodynamic limit are discussed.     

Measurement of superhigh-frequency dielectric permittivity for paraelectrics (Ba,Sr) TiO3 in a transverse bias field

An improved apparatus for measuring dielectric permittivity in the shf range by the dielectric-resonance method is described. A cylindrical sample is placed at the antinode of a waveguide magnetic field. A measurement-line probe, placed at the minimum of the standing wave, is used to indicate resonance. Dielectric resonances are traversed by varying the sample temperature and dielectric permittivity. Results of measuring temperature dependences of and tan are given for BaTiO₃ ceramics and BaTiO₃ SrTiO₃ solid solutions in the paraelectric phase. The dependences of on a bias electric field perpendicular to the measuring field are found. It is shown that in a transverse bias field decreases though to a smaller extent than in a longitudinal field. It is concluded that the basic mechanism of paraelectric nonlinearity is the saturation of electron-ion polarization.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 9, pp. 20–25, September, 1971.     

Gap exponents for percolation processes with triangle condition

A study is made of the gap exponents for percolation processes with the triangle condition in the subcritical region. It is show that the gaps are given by _t =2 fort=2, 3,. Scaling theory predicts thatP _p (¦C ₀¦S(p))–(p _c –p) andE _p (1/¦C ₀¦; ¦C ₀¦S(p))–(p _c –p)³, whereS(p) is the typical cluster size. It is found that (p _c –p)P _p (|C ₀S(p) ^1–)(p _c –p)^1–2 and (p _c –p)³E _p (1/|C ₀|;|C ₀|S(p) ^1–))(p _c –p)^3–4.     

More on the τ-μ-e problem: The process e+e−→l+l− in the region of the z-resonance

Theoretical and experimental aspects of the study of the e-- problem in effects of neutral weak currents in colliding e⁺e^– beams in the region of the Z resonance are discussed. Quantities that describe the degree of violation of e-- universality are analyzed. In particular, it is shown that by measuring the spin asymmetry for angles 160° it is possible to determine the degree of violation ofl-e universality =g _A ^e g _V ^l –g _V ^e g _A ^l to an accuracy of up to 0.01.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 88-91, May, 1989.     

Dispersion of the permittivity of high-resistance semiconductors

We consider the mechanism of macroscopic polarization of semiconducting plates owing to the interaction of free carriers with an impurity level, in which role the level of the residual impurity of compensated semiconductors may appear. This mechanism, in combination with the diffusion-drift mechanism of polarization, results in additional dispersion of the real () and imaginary () parts of the dielectric permittivity, this being particularly significant for semiconductors of thickness smaller than the screening length L_s of free carriers. The character of the behavior of and depends on the relation between the Maxwell relation time _M and the times of carrier capture: _c and ejection _e by an impurity center. For _cetm and (/L_s) _e/_c1 the dispersion of and is the same as for thick plates (/L_s1). For _{c m e} and (/L_s)_e/_c1 the () curve has a characteristic kink in the region 1/_e, indicating additional absorption associated with the ejection of carriers into the surface region.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 11–13, October, 1981.     

Continuity of type-I intermittency from a measure-theoretical point of view

We study a simple dynamical system which displays a so-called type-I intermittency bifurcation. We determine the Bowen-Ruelle measure and prove that the expectation (g) of any continuous functiong and the Kolmogoroff-Sinai entropyh() are continuous functions of the bifurcation parameter. Therefore the transition is continuous from a measure-theoretical point of view. Those results could be generalized to any similar dynamical system.