Computation of the contact temperature and wear during braking

We propose a model for determining the surface temperature and wear during braking. We take account of the change of heat flux caused by frictional forces over time. We obtain good agreement with known experimental data.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 3, 1997, pp. 108–112.     

Simulation and Analysis of Thermal Fatigue Based on Imperfection Model of Brake Discs

A non-linear FEM model of brake discs of high-speed trains with thermal-mechanical coupling has been established in ANSYS. The simulation and analysis of 3-D transient temperature field and stress field of brake discs have been carried out for the braking process. According to typical imperfections of brake discs, some imperfection models of brake discs have been developed and the thermal stresses of different models are obtained through simulation and analysis. By comparing results of different models, the influence of imperfection parameters, including the position, depth and size, is resulted for the thermal resistance of brake discs. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Microscopic theory of superconductivity in MgB<Subscript>2</Subscript>-type systems in a magnetic field: A neighborhood of <Emphasis Type="Italic">H</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis>2</Subscript>

We calculate the upper critical magnetic field H _c2 in the framework of a microscopic superconductivity theory with two energy bands of different dimensions on the Fermi surface with the cavity topology typical of the compound MgB₂ taken into account (an anisotropic system). We assume an external magnetic field parallel to the crystallographic z axis. We obtain analytic formulas in the low-temperature range (T/T_c ≪ 1) and also near the critical temperature ((T-T_c)/T_c ≪ 1). We compare the temperature dependence of H_c2 for a two-band anisotropic system with that of H _c2 ⁰ corresponding to a two-band isotropic system (with Fermi-surface cavities of the same topology). We determine the role of the band-structure anisotropy, the positive curvature of the upper critical field near the critical temperature, and the important role of the ratio v₁/v₂ of the velocities on the Fermi surface in determining H_c2. We also obtain the values of the parameters Δ₁ and Δ₂ along the line of the critical magnetic field. This paper is dedicated to the 90th birthday of Professor D. N. Zubarev __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 1, pp. 113–128, January, 2008.     

A study of the thermoelastic behavior of a cylinder of low electrical conductivity in a uniform steady external electromagnetic field

We determine and study the temperature fields and stresses in a cylinder of low electrical conductivity resulting from force and thermal actions on it by a uniform external electromagnetic field. We study resonance phenomena and the behavior of the unknown fields in the vicinity of the resonance frequencies of the electromagnetic field. Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 80–86.     

Sur les équations de la magnétothermoélasticité

Summary Writing the MTE equations in non-dimensional variables, the author points out the essential parameters and the structure of the equations. The equation of the MTE system characteristics is determined, as well as the displacement velocities of the waves of weak discontinuity. Furthermore, the equation which is satisfied by the current density vectorJ is determined.The paper considers the Cauchy problem for the infinite perfectly conductive plane, in the presence of a temperature and of a magnetic field. The general solution for the current density and the magnetic field are determined from Maxwell's equation. The solution obtained permits one to determine the displacement and the temperature fields by means of the classical thermoelasticity.The method of solving the Cauchy problem is based upon the representation of the general solution by a continous superposition of plane waves.     

Return to Equilibrium for Pauli-Fierz Systems

We study ergodic properties of Pauli-Fierz systems – W*-dynamical systems often used to describe the interaction of a small quantum system with a bosonic free field at temperature $ T \geq 0 $. We prove that, for a small coupling constant uniform as the positive temperature $ T \downarrow 0 $, a large class of Pauli-Fierz systems has the property of return to equilibrium. Most of our arguments are general and deal with mathematical theory of Pauli-Fierz systems for an arbitrary density of bosonic field. Communicated by Gian Michele Graf submitted 22/09/02, accepted: 06/05/03     

On the determination of the parameters that describe a quasistatic electromagnetic field in an electrically conducting shell

We state the initial equations and the boundary conditions for determining the parameters that describe a quasistatic electromagnetic field perturbed by the action of external electric currents in a this nonferromagnetic shell. Translated fromMatematichni Metody i Fiziko-Mekhanichni Polya, Vol. 38, 1995.     

Minimizers near the first critical field for the nonself-dual Chern–Simons–Higgs energy

The Chern–Simons–Higgs energy serves as a model for high temperature superconductivity. We show the existence of weak solutions to the CSH equations that are minimizers of the CSH energy. The solutions are vortexless for an applied magnetic field h _ex below the critical field strength, whereas vortices appear when h _ex exceeds the critical field strength. D. Spirn was supported in part by NSF grants DMS-0510121 and DMS-0707714. X. Yan was supported in part by NSF grants DMS-0700966 and DMS-0401048.     

Numerical study of forced and free convective boundary layer flow of a magnetic fluid over a flat plate under the action of a localized magnetic field

The two-dimensional, steady, laminar, forced and free convective boundary layer flow of a magnetic fluid over a semi-infinite vertical plate, under the action of a localized magnetic field, is numerically studied. The magnetic fluid is considered to be water-based with temperature dependent viscosity and thermal conductivity. The study of the boundary layer is separated into two cases. In case I the boundary layer is studied near the leading edge, where it is dominated by the large viscous forces, whereas in case II the boundary layer is studied far from the leading edge of the plate where the effects of buoyancy forces increase. The numerical solution, for these two different cases, is obtained by an efficient numerical technique based on the common finite difference method. Numerical calculations are carried out for the value of Prandl number Pr =  49.832 (water-based magnetic fluid) and for different values of the dimensionless parameters entering into the problem and especially for the magnetic parameter Mn, the viscosity/temperature parameter Θ _r and the thermal/conductivity parameter S*. The analysis of the obtained results show that the flow field is influenced by the application of the magnetic field as well as by the variation of the viscosity and the thermal conductivity of the fluid with temperature. It is hoped that they could be interesting for engineering applications.     

Deconfinement phase transition in mirror of symmetries

We argue that the deconfinement phase transition in Yang-Mills theories can be viewed as a change of effective non-perturbative degrees of freedom and of symmetries of their interactions. In short, the strings in four dimensions (4d) at temperatures below the critical temperature T _c are replaced by particles, or field theories in 3d at T > T _c. The picture emerges within various approaches based on dual models, lattice data and effective field theoretic models. We concentrate mostly on the lattice data, or the language of quantum geometry.     

The influence of a spherical defect on the temperature field in a half-space under local heating

We study the nonlinear axisymmetric problem of determining the temperature field near a spherical defect irradiated by a heat flux. The solution is constructed by the Fourier method using the Kirchhoff transform in a bipolar coordinate system. We carry out a numerical analysis of two special cases of boundary conditions. Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 47–50.     

Dimensional Regularization and the n-Wave Procedure for Scalar Fields in Many-Dimensional Quasi-Euclidean Spaces

We obtain the vacuum expectation values of the energy–momentum tensor for a scalar field arbitrarily coupled to a curvature in the case of an N-dimensional quasi-Euclidean space–time; the vacuum is defined in accordance with the Hamiltonian diagonalization method. We extend the n-wave procedure to the many-dimensional case. We find all the counterterms in the case N=5 and the counterterms for the conformal scalar field in the cases N=6,7. We determine the geometric structure of the first three counterterms in the N-dimensional case. We show that all the subtractions in the four-dimensional case and the first three subtractions in the many-dimensional case correspond to the renormalization of the parameters in the bare gravitational Lagrangian. We discuss the geometric structure of the other counterterms in the many-dimensional case and the problem of eliminating the conformal anomaly in the four-dimensional case.     

Thermodynamic properties of two-layer quasi-two-dimensional antiferromagnets

For two-layer quasi-two-dimensional antiferromagnets of type YBaCuO in the Tyablikov approximation, we investigate the dependences of the energy spectrum and the temperature of transition into an ordered state on both the quasi-two-dimensionality parameter and the intensity of the exchange coupling of spin moments located in two close planes. We assume that the exchange parameters inside the CuO ₂ planes are much greater than the exchange parameters resulting in coupling between a spin located on a plane of an elementary cell and a spin on another plane of a different elementary cell. The obtained expressions for the Néel temperature and for the sublattice magnetic moment at zero temperature describe the dependences of these quantities on the parameters of interplane exchange interactions.     

Solution of the two-dimensional integrodifferential equation of the heat conduction problem for an unbounded body with a thin thermally conducting inclusion

We determine the temperature field in an unbounded body with a thin heat-conducting foreign inclusion. We propose a method of solution of the corresponding two-dimensional singular integrodifferenlial equation of the problem based on the study of the behavior of the solution in a neighborhood of the boundary of the inclusion.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 28, 1988, pp. 78–83.     

Synthesis scheme for hybrid methods of solving boundary problems

A scheme is proposed for the development of a numericoanalytic boundary problem technique that can synthesize the mesh-projective method with the integral transform method to yield an effective hybrid method for the determination of the temperature field in a body from a moving heat source with given dependences of the thermophysical parameters on temperature.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 25, pp. 19–22, 1987.     

Rational regimes for induction heating of cylindrical articles for graphitation

We develop a method of computing regimes for induction heating of cylindrical carbon devices during graphitation. We study the electromagnetic, temperature, and mechanical fields as functions of the parameters of the heating regime.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 33, 1991, pp. 27–31.     

Control of thermoelastic stresses in a cylinder in the case of a two-dimensional nonaxisymmetric temperature field

We obtain new functional relations among the components of thermal stresses, and also their dependence on the temperature field. Using these relations we find solutions of a control problem that we pose. We state necessary conditions for the existence of the required optimal control which must be satisfied by the given distribution function of the control of thermal stresses.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 36, 1992, pp. 56–60.     

Stochastic nonstationary temperature fields in a solid circular-cylindrical two-layer plate

We determine the nonstationary temperature field in a solid two-layer plate subject to heat sources whose power is a random function of time and the radial variable. The probability characteristics constructed for the stochastic nonstationary temperature fields are sufficient for engineering computations. Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 37, 1994, pp. 104–108.     

A phenomenological description of temperature dependence of magnetoresistance in La2/3Ca1/3MnO3-δ thin films

The electrical resistance in zero magnetic field and magnetoresistance in different external magnetic fields have been measured in a temperature range of 77—300 K. It is found that the temperature dependence of magnetoresistance can be well described by a phenomenofogical formula of

Valuation theory of exponential Hardy fields I

We describe the valuation theoretic properties of the Hardy fields associated to models of , where T is the theory of a polynomially bounded o-minimal expansion of the reals and is the real exponential function. We deduce that has levels with parameters and is exponentially bounded. We establish a maximality property of , the Hardy field of the expansion by the restricted analytic functions and power functions. Received: 10 July 2000 ; in final form: 15 April 2002/Published online: 24 February 2003 RID="*" ID="*" This paper was written while both authors were partially supported by a Canadian NSERC research grant.