On the properties and stability of thermally evaporated Ge–As–Se thin films

Thin films of Ge–As–Se chalcogenide glasses have been deposited by thermal evaporation from bulk material and submitted to thermal treatments. The linear refractive index and optical band-gap for as-deposited and annealed films have been analyzed as function of the deposition parameters, chemical composition and mean coordination number (MCN). The chemical composition of the films was found to be directly affected by deposition rate, with low rates producing films with elevated Ge and reduced As content, whilst at high rates the Ge content was generally reduced and As levels increased compared with the bulk starting material. As a result films with close to the same stoichiometry as the bulk glass could be obtained by choosing appropriate deposition conditions. As-deposited films with MCN in between 2.44 and 2.55 showed refractive indices and optical band-gaps very close to those of the bulk glass whereas outside this range the film indices were higher and the optical gaps lower than those of the bulk glass. Upon annealing at close to their glass transition temperature, high MCN films evolved such that their indices and band-gaps approached the bulk glass values whereas at low MCN films resulted in no changes to the film properties.     

On stability of the elliptical “orbits” of diamagnetic positronium

The stability of the elliptical orbits of diamagnetic positronium is studied and it is found to depend only on the eccentricity ε and the combination of parameters λ = B²r_0c³ (where B is the magnetic field strength and r_0c the conserved guiding center). For small and large values of λ the orbits remain stable while at approximately λ = 1 unstable behavior appears when the eccentricity becomes larger than ε = 0.25.     

On radiative corrections to the strangeness-conserving β-decay of free baryons

In the work presented, the effect of electromagnetic interactions on the strangeness-conserving β-decay of baryons: neutron, $n \to p + e^ - + \bar \nu + \gamma $ , and hyperon, $\Sigma ^ \pm \to \Lambda ^0 + e^ \pm + \nu (\bar \nu ) + \gamma $ , is visualized. The polarized baryon decay studied, the total decay probability modification, as well as the modifications of the e ^± spectrum and the angular distribution with respect to the polarization vector ξ of the initial baryon (coefficient A), have been calculated. Dependence of the results on the value of the ultraviolet cut-off parameter Λ is elucidated. The spectrum and yield of the γ-radiation accompanying the β-decay is acquired, with special attention being paid to the infrared (soft-photon) radiation. The photon radiation of pions constituting the baryon's “pion cloud” is investigated. The radiative corrections to the total β-decay probability and to the electron energy and angular distributions found in this work proves to be of pivotal importance for obtaining the main characteristics of the weak interaction from experimental data processing.     

On the stability of two superposed Walters B′ viscoelastic liquids

The stability of the plane interface separating two viscoelastic (Walters B) superposed fluids of uniform densities has been studied. The stability analysis has been carried out, for mathematical simplicity, for two highly viscoelastic fluids of equal kinematic viscosities and equal kinematic viscoelasticities. For the stable configuration, the system is found to be stable or unstable for the wave-number range k < or > (2ev)^-1/2, depending on kinematic viscoelasticity v. However, the system is found to be unstable for the unstable configuration. The behaviour of growth rates with respect to kinematic viscosity and kinematic viscoelasticity are examined analytically.     

On sufficient stability conditions of the Couette — Poiseuille flow of monodisperse mixture

The stability of the Couette — Poiseuille flow of a monodisperse mixture is considered. Sufficient stability conditions are derived. Results of the computation of the spectrum are presented. A considerable stabilization of the flow with particles admixture to small disturbances is observed. It is found that the regions of instability generation may have complex geometry. The influence of the main velocity profile and admixture parameters on the stability conditions is considered.     

On the Hausdorff Dimension of the Spectrum of the Thue–Morse Hamiltonian

We show that the Hausdorff dimension of the spectrum of the Thue–Morse Hamiltonian has a common positive lower bound for all coupling.     

On the modulation equations and stability of periodic generalized Korteweg–de Vries waves via Bloch decompositions

In this paper, we consider the relation between Evans-function-based approaches to the stability of periodic travelling waves and other theories based on long-wavelength asymptotics together with Bloch wave expansions. In previous work it was shown by rigorous Evans function calculations that the formal slow modulation approximation resulting in the linearized Whitham averaged system accurately describes the spectral stability to long-wavelength perturbations. To clarify the connection between Bloch-wave-based expansions and Evans-function-based approaches, we reproduce this result without reference to the Evans function by using direct Bloch expansion methods and spectral perturbation analysis. One of the novelties of this approach is that we are able to calculate the relevant Bloch waves explicitly for arbitrary finite-amplitude solutions. Furthermore, this approach has the advantage of being applicable in the more general multi-periodic setting where no conveniently computable Evans function has yet been devised.     

On the algebraic types of the Bel–Robinson tensor

The Bel–Robinson tensor is analyzed as a linear map on the space of the traceless symmetric tensors. This study leads to an algebraic classification that refines the usual Petrov–Bel classification of the Weyl tensor. The new classes correspond to degenerate type I space-times which have already been introduced in literature from another point of view. The Petrov–Bel types and the additional ones are intrinsically characterized in terms of the sole Bel–Robinson tensor, and an algorithm is proposed that enables the different classes to be distinguished. Results are presented that solve the problem of obtaining the Weyl tensor from the Bel–Robinson tensor in regular cases.     

On the Non-Integrability of the Stark–Zeeman Hamiltonian System

In this paper we present a proof of the non-integrability in the Liouvillian sense of the Stark–Zeeman Hamiltonian. In particular, we generalize the result of Kummer and Saenz about the non-integrability of the pure Zeeman Hamiltonian. The proof we give is an application of the theorem of Morales and Ramis (1998) about non-integrability, based on differential Galois theory. Received: 30 March 1999 / Accepted: 16 May 1999     

On the Diffuse Structure of the Toluene–Water Interface

The electric density profile along the normal to the phase interface between aromatic hydrocarbon toluene and water has been studied by X-ray reflectometry using synchrotron radiation. According to the experimental data, the width of the interface under normal conditions is (3.9 ± 0.1) Å. This value is much larger than a theoretical value of (5.7 ± 0.2) Å predicted by the theory of capillary waves with an interphase tension of (36.0 ± 0.1) mN/m. The observed broadening of the interface is attributed to its own diffuse near-surface structure with a width no less than Å, which is about the value previously discussed for (high-molecular-weight saturated hydrocarbon–water) and (1,2-dichloroethane–water) interfaces.     

On the Eigenstates of the Elliptic Calogero–Moser Model

It is known that the trigonometric Calogero–Sutherland model is obtained by the trigonometric limit (–1) of the elliptic Calogero–Moser model, where (1, ) is a basic period of the elliptic function. We show that for all square-integrable eigenstates and eigenvalues of the Hamiltonian of the Calogero–Sutherland model, if exp(2–1) is small enough then there exist square-integrable eigenstates and eigenvalues of the Hamiltonian of the elliptic Calogero–Moser model which converge to the ones of the Calogero–Sutherland model for the 2-particle and the coupling constant l is positive integer cases and the 3-particle and l=1 case. In other words, we justify the regular perturbation with respect to the parameter exp(2–1). With some assumptions, we show analogous results for N-particle and l is positive integer cases.     

On the Instability Intervals of the Mathieu–Hill Operator

Consider the Mathieu–Hill operator

On the zero fluctuation of the “microscopic free energy” and its potential use

The fluctuations of the microscopic free energy calculated with the ensemble probability are shown to be zero. We suggest that this result be used for estimating approximate free energies calculated on the basis of the minimum free energy principle. As an example the estimation is performed with respect to a certain computer simulation of the square Ising lattice. The zero fluctuations also can be used to obtain relations among fluctuations with the accurate ensemble probability distribution.     

On the Effect of Stochastic Fluctuations in the Dynamics of the Lifshitz–Slyozov–Wagner Model

In this paper the dynamics of a system of spherical particles that fill a small volume fraction of the space and that evolves in a concentration field is discussed. Corrections to the Lifshitz–Slyozov–Wagner (LSW) model that take into account the stochastic character of the problem are computed. It is proved, under suitable smallness assumptions for the volume fraction filled by the particles, that the effect of these corrections does not modify much the dynamics of the self-similar solutions of the LSW system of equations.     

On the level-dependence of Wess–Zumino–Witten three-point functions

Three-point functions of Wess–Zumino–Witten models are investigated. In particular, we study the level-dependence of three-point functions in the models based on algebras su(3) and su(4). We find a correspondence with Berenstein–Zelevinsky triangles. Using previous work connecting those triangles to the fusion multiplicities, and the Gepner–Witten depth rule, we explain how to construct the full three-point functions. We show how their level-dependence is similar to that of the related fusion multiplicity. For example, the concept of threshold level plays a prominent role, as it does for fusion.     

On the Orthocomplementation of State–Property–Systems of Contextual Systems

We adopt an operational approach to quantum mechanics in which a physical system is defined by the mathematical structure of its set of states and properties. We present a model in which the maximal change of state of the system due to interaction with the measurement context is controlled by a parameter which corresponds with the number N of possible outcomes in an experiment. In the case N=2 the system reduces to a model for the spin measurements on a quantum spin-1/2 particle. In the limit N→∞ the system is classical, i.e. the experiments are deterministic and its set of properties is a Boolean lattice. For intermediate situations the change of state due to measurement is neither ‘maximal’ (i.e. quantum) nor ‘zero’ (i.e. classical). We show that two of the axioms used in Piron’s representation theorem for quantum mechanics are violated, namely the covering law and weak modularity. Next, we discuss a modified version of the model for which it is even impossible to define an orthocomplementation on the set of properties. Another interesting feature for the intermediate situations of this model is that the probability of a state transition in general not only depends on the two states involved, but also on the measurement context which induces the state transition.