Hard-hexagon model: Calculation of anisotropic interfacial tension from asymptotic degeneracy of largest eigenvalues of row-row transfer matrix

To find the directional dependence of the interfacial tension of the hard-hexagon model, an inhomogeneous system is studied. This system is defined on a square lattice with (1+v)M columns so that the lhs of the (M+1)th column is the hard-hexagon model and the rhs of the (M+1)th column works as the operator which shifts the particle configuration of a column downward. A triplet of the largest eigenvalues of the row-row transfer matrix are asymptotically degenerate asM under the conditions that (1–v)M0 (mod 3), withv being fixed to be constant. The interfacial tension of a tilted interface is calculated from the finite correction terms in this limit.     

Low-frequency stimulated emission and induced absorption in a three-level atom

Investigations of the motion of conventional negative ions (electron bubbles) in He II under pressures above 11 bar have provided the only means of measuring the Landau critical velocity for roton creation,v _L, and for studying supercritical dissipation at higher velocities. Earlier work on roton creation is reviewed and it is pointed out that there is still no generally agreed explanation of the fact that the rotons seem to be emitted from the moving ionin pairs; nor is it known why the matrix element characterising the pair emission process should decrease rapidly with pressure. The possibility of studying these phenomena through use either of the fast ion (whose nature remains unknown), or of selected ions from the large variety of species that can be injected into He II by the recently developed technique of laser ablation, is discussed.     

Trajectory attractors for dissipative 2D Euler and Navier-Stokes equations

A trajectory attractor is constructed for the 2D Euler system containing an additional dissipation term −ru, r > 0, with periodic boundary conditions. The corresponding dissipative 2D Navier-Stokes system with the same term −ru and with viscosity v > 0 also has a trajectory attractor, . Such systems model large-scale geophysical processes in atmosphere and ocean (see [1]). We prove that → as v → 0+ in the corresponding metric space. Moreover, we establish the existence of the minimal limit of the trajectory attractors as v → 0+. We prove that is a connected invariant subset of . The connectedness problem for the trajectory attractor by itself remains open. Dedicated to the memory of Leonid Volevich Partially supported by the Russian Foundation for Basic Research (projects no 08-01-00784 and 07-01-00500). The first author has been partially supported by a research grant from the Caprio Foundation, Landau Network-Cento Volta.     

Influence of second kind collisions on the electron distribution function in the positive column of low pressure nitrogen discharge

A numerical solution of the Boltzmann equation for the electron gas in the positive column of a DC discharge in nitrogen is presented. The Boltzmann equation was solved with the inclusion of the second kind (superelastic) collisions proceeding from the first six excited vibrational levels of molecular nitrogen. The vibrational level population is supposed to follow a Boltzmann distribution for a given vibrational temperatureT _v, with a possible deviation of the ground level, which can be overpopulated in a given ratio. Apart from the electron distribution functions, which were gained for various values ofE/p ₀,T _v and, the values of some production frequencies and kinetic coefficients are presented in form of tables and plots. It is found that the electron distribution (and also the corresponding production rates) depends above a certain energy limit onT _v and through the normalization constant only.     

Quadratic Lagrangians and the Reissner-Nordström-de Sitter metric

The purpose of this note is to point out that the Einstein-Maxwell equations with cosmological constant can be derived from the quadratic Lagrangians R² and F F . The linear combination R R + ²+k ₂F F leads to field equations not satisfied by the Reissner-Nordström-de Sitter metric.     

Highly excited rovibrational states of HNC

The emission spectrum of HCN has been recorded at 1463 K using hot gas molecular emission (HOTGAME) spectroscopy in the wavenumber region of 2900–3500 cm⁻¹ with a resolution of 0.01 cm⁻¹. The dense emission spectrum was analyzed with the spectrum analysis software SyMath™ implemented in the Mathematica™ computer algebra system. This work reports the analysis of the band series up to v₂ = 8 and of the band series up to v₂ = 6.36 rovibronic (v₁, v₂, l, e/f, v₃) substates of HCN including all l = 0, 2, 4, 6, 8 sublevels of the highly excited bending combination mode have been characterized for the first time and for the 22 known vibrational sublevels it was possible to improve the existing spectroscopic constants substantially. 18 (v₁, v₂, l, v₃) vibrational sublevels are located for the first time relative to the 00⁰0 state. The analysis reported here includes rovibrational states up to very large rotational excitations of J = 60–80. For the combination states the rotational states have been determined up to J = 86 which corresponds to 7000 cm⁻¹ rotational excitation energy, this state is only 2000 cm⁻¹ below the isomerization barrier. It was possible to determine for the first time the L_v high order rotational constant for many states reported in this work.     

Angle and speed distributions of hydrogen desorbing thermally from metal surfaces

A quantum theoretical treatment of the angle and speed distributions of recombinatively desorbing hydrogen from metal surfaces is proposed. The desorption rate is discussed in the framework of the transition state theory. The recombinative reaction process of hydrogen due to thermal activation leads to the formation of an activated complex in the transition state. In the vicinity of a saddle point on a three-dimensional potential energy surface, the translational motion of the activated complex in the direction perpendicular to the metal surface is accompanied by its center-of-mass vibrational motion parallel to the metal surface. In order to carry out the quantum mechanical calculation, the potential surface is replaced by a simplified model potential, which provides a square potential barrier along the surface normal. It is shown that, on leaving the potential barrier, the activated complex is reflected by the boundary of the potential barrier with a certain probability and, at the same time, the center-of-mass modes of vibration with frequencies v ₁ and v ₂ are coupled with the translational motion along the surface normal. Vibrational wave functions in the momentum representation are used to calculate the transmission coefficient, which is incorporated into the conventional rate formula. The angle-dependent speed distributions of desorbing molecules are derived from the rate formula.     

Induced geometry and confinement

A classical, Poincaré invariant dynamical system is developed which contains, besides the natural metric _v , an induced metricg _v that is generated by a real scalar dynamical field. It is shown that scalar fields whose dynamics are governed by the induced metric can be consistently introduced. Also, point particles which follow timelike quasi-geodesic trajectories can be introduced. The reaction forces acting ong _v due to the presence of these fields and particles are computed. A discussion of causality and geometrical confinement is given.     

Motion of vortex lines and mutual friction in superfluid4He nearT λ

The motion of a single vortex line in superfluid⁴He nearT is studied within modelF. The linear response of the vortex-line velocityv _L to a homogeneous counterflowv _s –v _n is calculated up to lowest order of renormalized perturbation theory. The critical temperature dependence is taken into account via the renormalizationgroup theory. Non-asymptotic critical effects are found to be important. The results are generalized to describe collective vortex motion and mutual friction in rotating superfluid⁴He. The phenomenological mutual-friction coefficientsB andB of Hall and Vinen are determined without adjustment of parameters. ForB quantitative agreement with experiments nearT is found whereas forB the agreement is only semiquantiative.     

Quantization and instability of the damped harmonic oscillator subject to a time-dependent force

We consider the one-dimensional motion of a particle immersed in a potential field U(x) under the influence of a frictional (dissipative) force linear in velocity () and a time-dependent external force (K(t)). The dissipative system subject to these forces is discussed by introducing the extended Bateman’s system, which is described by the Lagrangian: which leads to the familiar classical equations of motion for the dissipative (open) system. The equation for a variable y is the time-reversed of the x motion. We discuss the extended Bateman dual Lagrangian and Hamiltonian by setting specifically for a dual extended damped–amplified harmonic oscillator subject to the time-dependent external force. We show the method of quantizing such dissipative systems, namely the canonical quantization of the extended Bateman’s Hamiltonian ?. The Heisenberg equations of motion utilizing the quantized Hamiltonian surely lead to the equations of motion for the dissipative dynamical quantum systems, which are the quantum analog of the corresponding classical systems. To discuss the stability of the quantum dissipative system due to the influence of an external force K(t) and the dissipative force, we derived a formula for transition amplitudes of the dissipative system with the help of the perturbation analysis. The formula is specifically applied for a damped–amplified harmonic oscillator subject to the impulsive force. This formula is used to study the influence of dissipation such as the instability due to the dissipative force and/or the applied impulsive force.     

Electrodynamics Under a Possible Alternative to the Lorentz Transformation

A generalization of the classical electrodynamics for systems in absolute motion in presented using a possible alternative to the Lorentz transformation. The main hypothesis assumed in this work are: a) The inertial transformations relate two inertial frames: the privileged frame S and the moving frame S with velocity v with respect to S. b) The transformation of the fields from S to the moving frame S is given by H = a(H – v × D) and E = a(E + v × B), where a is a matrix whose elements depend of the absolute velocity of the system. c) The constitutive relations in the moving frame S are given by D = E, B = H and J = E. It is found that Maxwell's equations, which are transformed to the moving frame, take a new form depending on the absolute velocity of the system. Moreover, differing from classical electrodynamics, it is proven that the electrodynamics proposed explains satisfactorily the Wilson effect.     

Polymer models and generalized Potts-Kasteleyn models

The well-established relation between Potts models withv spin values and random-cluster models (with intracluster bonding favored over intercluster bonding by a factorv) is explored, but with the random-cluster model replaced by a much generalized polymer model, implying a corresponding generalization of the Potts model. The analysis is carried out in terms a given defined functionR(), an entropy/free-energy density for the polymer model in the casev=1, expressed as a function of the density of units. The aim of the analysis is to determine the analogR _v () ofR() for general nonnegativev in terms ofR(), and thence to determine the critical value of density _vg at which gelation occurs. This critical value is independent ofv up to a valuev _P, the Potts-critical value. What is principally required ofR() is that it should show a certain given concave/convex behavior, although differentiability and another regularizing condition are required for complete conclusions. Under these conditions the unique evaluation ofR _v () in terms ofR() is given in a form known to hold for integralv but not previously extended. The analysis is carried out in terms of the Legendre transforms of these functions, in terms of which the phenomena of criticality (gelation) and Potts criticality appear very transparently andv _P is easily determined. The value ofv _P is 2 under mild conditions onR. Special interest attaches to the functionR ₀(), which is shown to be the greatest concave minorant ofR(). The naturalness of the approach is demonstrated by explicit treatment of the first-shell model.     

On an internal symmetry for arbitrary dislocations in solids

We discuss an arbitrary distribution of dislocations moving in an anisotropic finite linear elastic solid. The field equations for theelastic strain tensor are decomposed into two independent systems of equations, the equations for acompatible elastic displacement fields and the equations for anincompatible elastic strain ^v . This can be done in such a way thats contains the full information on anisotropy, external forces, and boundaries, whereas ^v contains only a single material constant , which is related to a signal velocity , wherep is the mass density. In order to understand the symmetries of the ^v -field equations we introduce ac _T -relativistic space-time. As a consequence of certain hypothesis concerning the balance of eigenstresses for moving dislocations the Lorentz group becomes the symmetry group for the ^v -field equations. We call this aninternal symmetry. Thematerial symmetry of the field equations for the elastic displacement vectors which is defined by Hooke's tensor breaks this Lorentz symmetry for the complete elastic strain . Some conclusions for the dynamics of dislocations are discussed. It is found that Seeger's theory of kinks on dislocations describes elementary processes of this dynamics. Within the limits of the continuum model plasticity becomes a field theory with broken Lorentz symmetry.     

Multifractal Spectra of Fragmentation Processes

Let (S(t),t0) be a homogeneous fragmentation of ]0,1[ with no loss of mass. For x]0,1[, we say that the fragmentation speed of x is v if and only if, as time passes, the size of the fragment that contains x decays exponentially with rate v. We show that there is v _typ>0 such that almost every point x]0,1[ has speed v _typ. Nonetheless, for v in a certain range, the random set _v of points of speed v, is dense in ]0,1[, and we compute explicitly the spectrum vDim( _v ) where Dim is the Hausdorff dimension.     

Uniform boundedness of the solutions for a one-dimensional isentropic model system of compressible viscous gas

This paper studies an initial boundary value problem for a one-dimensional isentropic model system of compressible viscous gas with large external forces, represented by v _t –u _x =0,u _t +(av ^–) _x =(u _x /v) _x +f( ₀ ^x vdx,t), with (v(x, 0),u(x, 0))= (v ₀(x),u ₀(x)),u(0,t)=u(1,t)=0. Especially, the uniform boundedness of the solution in time is investigated. It is proved that for arbitrary large initial data and external forces, the problem uniquely has an uniformly bounded, global-in-time solution with also uniformly positive mass density, provided the adiabatic constant (>1) is suitably close to 1. The proof is based on L ²-energy estimates and a technique used in [9].     

Noise Induced Dissipation in Lebesgue-Measure Preserving Maps on d-Dimensional Torus

We consider dissipative systems resulting from the Gaussian and alpha-stable noise perturbations of measure-preserving maps on the d dimensional torus. We study the dissipation time scale and its physical implications as the noise level vanishes. We show that nonergodic maps give rise to an O(1/) dissipation time whereas ergodic toral automorphisms, including cat maps and their d-dimensional generalizations, have an O(ln(1/)) dissipation time with a constant related to the minimal, dimensionally averaged entropy among the automorphism's irreducible blocks. Our approach reduces the calculation of the dissipation time to a nonlinear, arithmetic optimization problem which is solved asymptotically by means of some fundamental theorems in theories of convexity, Diophantine approximation and arithmetic progression. We show that the same asymptotic can be reproduced by degenerate noises as well as mere coarse-graining. We also discuss the implication of the dissipation time in kinematic dynamo.     

Linewidth studies on the Kr+ 469.4 nm and 473.9 nm lines excited in a helium-krypton hollow cathode discharge

Collisional and Doppler linewidths (v _C and v _D ) of the 469.4 nm and 473.9 nm Kr ion lines were measured in a He-Kr hollow cathode discharge using Fabry-Perot technique. A linear dependence of v _C on He pressure was found for both lines. Significant differences were found between the temperature values deduced from the v _D -s of the two lines, and an unexpected temperature dependence of the broadening parameter for the Kr⁺ 469 nm line was also observed. The temperature difference between the two lines is explained by excitation of the upper level of the 469 nm line by second kind collisions between metastable He atoms and ground-state Kr ions, while the temperature dependence of the broadening parameter of the Kr⁺ 469 nm line is suggested to be due to the inverse process.     

Large time behavior of the vorticity of two-dimensional viscous flow and its application to vortex formation

We consider the Cauchy problem for the two-dimensional vorticity equation. We show that the solution behaves like a constant multiple of the Gauss kernel having the same total vorticity as time tends to infinity. No particular structure of initial data ₀=(x, 0) is assumed except the restriction that the Reynolds numberR=|₀|dx/v is small, wherev is the kinematic viscosity. Applying a time-dependent scale transformation, we show a stability of Burgers' vortex, which physically implies formation of a concentrated vortex.Partly supported by Grant-in-Aid for Scientific Research No. B60460042, the Japan Ministry of Education, Science and Culture     

On the Initial Boundary Value Problems for the Enskog Equation in Irregular Domains

The paper is concerned with the Enskog equation with a constant high density factor for large initial data in L ¹(R ⁿ). The initial boundary value problem is investigated for bounded domains with irregular boundaries. The proof of an H-theorem for the case of general domains and boundary conditions is given. The main result guarantees the existence of global solutions of boundary value problems for large initial data with all v-moments initially finite and domains having boundary with finite Hausdorff measure and satisfying a cone condition. Existence and uniqueness are first proved for the case of bounded velocities. The solution has finite norm where q = (t ₀, x) is taken on all possible n-dimensional planes Q(v) in R ^n+l intersecting a fixed point and orthogonal to vectors (1, v), v R ⁿ.