A study of the influence of physico-chemical processes in a metal base/nonmetallic coating system on the operational properties of coatings in a chemically active medium

We propose a method for the analytic computation and prediction of the lifetime of electrically nonconducting coatings in chemically active media. We study the role that the quantity of passivating additives in the coating and other parameters of the medium-coating-base system play in the destruction of the coating. We investigate the influence of passivating components on the process of corrosive destruction of the metal under the coating.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 31, 1990, pp. 30–36.     

Mathematical modeling and the study of the heat exchange process in color kinescopes

We propose a mathematical model for computing the heat exchange in a masked color kinescope taking account of the specific geometry of its shell and the actual three-dimensional character of the heat emission in the mask. We study the temperature field in the mask and determine the size of the integral degree of blackness in the cone coating that guarantees a stable operation of the kinescope. Three figures. Bibliography: 7 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 57–63.     

FEM simulation of oxidation induced stresses in a simplified thermal barrier coating system

To study the behaviour of the complex failure mechanisms in thermal barrier coatings, a simplified model system is used to reduce the number of system parameters. The artificial system consists of a bond-coat material (fast creeping Fecralloy or slow creeping MA956) as the substrate with a Y₂O₃ partially stabilized plasma sprayed zircon oxide TBC on top and a TGO between the two layers. A FEM simulation was developed to calculate the stress distribution inside the coating system. The simulation permits the identification of compression and tension areas which are established by the growth of the oxide layer and the stresses which occur during the heating and cooling processes. Full thermal cycles, including heating from RT to 1000°C, dwelling for 2 hours and cooling to RT, were simulated. The stress distributions provide an insight into the possible failure mechanisms in the coating and allow to draw conclusions for optimizing real thermal barrier coating systems. It is shown that the failure mechanism depends on the creep properties of the bond-coat. Therefore, optimizing the creep properties may adjust lifetime of the whole coating system. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical Calculation of the Stationary Distribution of the Main Multiserver Retrial Queue

We are concerned with the main multiserver retrial queue of M/M/c type with exponential repeated attempts. It is known that an analytical solution of this queueing model is difficult and does not lead to numerical implementation. Based on appropriate understanding of the physical behavior, an efficient and numerically stable algorithm for computing the stationary distribution of the system state is developed. Numerical calculations are done to compare our approach with the existing approximations.     

Numerical calculation of directional diagrams and profiles of evaporators with an accelerating nozzle

We investigate the possibility of achieving optimal directional diagrams of molecular flow and optimal profiles in evaporators with an accelerating nozzle. The numerical calculations elucidate the factors that have an essential effect on the thickness and uniformity of the coating formed by metal vapors on the substrate.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 59, pp. 70–76, 1986.     

Asymptotic analysis and scaling of friction parameters

We consider an eigenvalue problem associated to the antiplane shearing on a system of collinear faults under a slip-dependent friction law. Firstly we consider a periodic system of faults in the whole plane. We prove that the first eigenvalues/eigenfunctions of different physical periodicity are all equal and that the other eigenvalues converge to this first common eigenvalue as their physical period becomes indefinitely large. Secondly we consider a large scale fault system composed on a small scale collinear faults periodically disposed. If β₀^* is the first eigenvalue of the periodic problem in the whole plane, we prove that the first eigenvalue of the microscopic problem behaves as β₀^*/∈ when ∈→ 0 regardless the geometry of the domain (here ∈ is the scale quotient). The geophysical implications of this result is that the macroscopic critical slip D_c scales with D_c^∈/∈ (here D_c^∈ is the small scale critical slip).     

Destruction of dissipative structures under random actions

We consider random-parameter chemical kinetic systems that are important in numerous physical, chemical, and biological applications. Random parameters describe the action of ambient medium fluctuations on the system. We estimate the probability that the system state remains in a given domain of the phase space during a time interval [0, T] under the condition that the state at the initial instant was in u ₀ , where u ₀ is the equilibrium solution describing a dissipative structure. We show that in some cases, the problem of maximizing this probability is reducible to the known problem of minimizing the Hopfield Hamiltonian.     

Exact solutions of the spherically symmetric gravitational field equations

The Einstein gravitational equations in the spherically symmetric case and for the dust model (i.e., p = 0) have been studied by several authors. However, the solutions obtained by them are not completed yet, and the corresponding metric is written in implicit forms which is inconvenient for physical problems. In the present paper we make the following improvements: (1) We obtain all spherical solutions for the dust model with explicit expressions which consist of three classes and an exceptional case; (2) All these solutions contain singularities which are analyzed together with their physical properties. __________ Translated from Journal of Fudan University (Natural Science), 1974, 1: 92–98 An erratum to this article is available at .     

Semilinear perturbation of powers of the mizohata operators

ABSTRACT

We study the Cauchy Problem associated to a class of quasilinear Schrödinger equations which have been derived as models of several physical phenomenas. We prove local existence in arbitrary space dimension N without any smallness condition on the initial data.     

A mathematical and physical Study of multiscale deconvolution models of turbulence

This work presents a rigorous analysis of mathematical and physical properties for solutions of multiscale deconvolution turbulence models. We show that solutions of these models exactly conserve model quantities for the integral invariants of fundamental physical importance: kinetic energy, helicity, and (in two dimensions) enstrophy. The kinetic energy conservation is the key that allows us to next apply the phenomenology of homogeneous, isotropic turbulence to establish the existence of a model energy cascade and, in particular, that the cascade exhibits enhanced energy dissipation in a secondary accelerated cascade, which ends at the model's microscale (which we establish is larger than the Kolmogorov microscale). We also prove that the model dissipates energy at the same rate as true turbulent flow, ～ O(U³ ∕ L), independent of Reynolds number. Lastly, we prove the existence of global attractors for the model solutions; the proof of which also shows that solutions are actually one degree of regularity higher than previously known. Copyright © 2012 John Wiley & Sons, Ltd.     

Noncritical W-strings and minimal models

We perform a BRST analysis of the physical states described by a general noncriticalW-string. A crucial feature of our analysis is that we introduce a special basis in the Hilbert space of physical states in which the BRST operator splits into a nested sum of nilpotent BRST operators. We argue that the cohomology of each nilpotent BRST operator occurring in the nested sum is closely related to a specificW mimimal model. We discuss in detail the special case of the noncriticalW ₃-string.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98, No. 3, pp. 343–357, March, 1994.     

Computation of the lifetime of metal cathode coatings

We propose a method of computing the service time of protective coatings as functions of the geometric and physical characteristics of the aggressive medium-coating-base system. The method is based on representing the destruction process as a series of successive time stages. We analyze the possibility of loss of protective properties of a metallic cathode covering both as a consequence of mechanical failure and as a result of flaking.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 24–34.     

Representation and interpretation of quantum mixtures in the ESR model

The interpretation of mixtures is problematic in quantum mechanics (QM) because physical properties are nonobjective in this theory. An extended semantic realism model was recently developed, restoring objectivity by reinterpreting quantum probabilities as conditional on detection and embodying the QM mathematical formalism in a broader noncontextual (hence local) framework. In this model, each generalized observable is represented by a family of positive operator-valued measures parameterized by the pure states of the considered physical system Ω. We here propose a new proof that each proper mixture is represented by a family of density operators parameterized by the macroscopic properties characterizing Ω. We then show that this representation implies some predictions differing from the QM predictions and avoids the problems following from the standard QM representation of proper mixtures. We also recall that the state transformations induced by idealized nondestructive measurements can be obtained using a nontrivial generalization of the Lüders postulate.     

Identifying initial condition of the Rayleigh‐Stokes problem with random noise

We investigate a backward problem for the Rayleigh‐Stokes problem, which aims to determine the initial status of some physical field such as temperature for slow diffusion from its present measurement data. This problem is well‐known to be ill‐posed because of the rapid decay of the forward process. We construct a regularized solution using the filter regularization method in the Gaussian random noise. Under some a priori assumptions on the exact solution, we establish the expectation between the exact solution and the regularized solution in the L² and H^m norms.     

The elastoplastic stressed state of a half-plane under local nonstationary heating

We solve the thermoplastic problem for a semi-infinite plate under local nonstationary heating by heat sources. The physical equations are taken to be the relations of the nonisothermic theory of plastic flow associated with the Mises fluidity condition. The solution of the problem is constructed by the method of integral equations and the self-correcting method of sequential loading, where time is taken as the loading parameter. We carry out numerical computations of the stresses in the case of heating a plate with heat output by normal-circular heat sources. We study the problem of optimization of heating regimes in order to introduce favorable residual compressive stresses (from the point of view of hardness) in a given region of a half-plane. Two figures.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 29–34.     

New degrees of freedom for high-order Whitney approximations of Darcy’s flows

We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. We propose a high-order discretisation based on Whitney finite elements, namely, Raviart-Thomas finite elements of degree r +?1 for the discharge and discontinuous piecewise polynomial finite elements of degree r for the pressure, with r ≥?0. We comment on the use of new degrees of freedom that have a clear physical meaning, the so-called weights on the small simplices, for the involved discharge and pressure fields. We describe a new numerical strategy to solve the discrete problem based on a tree-cotree block-decomposition of the unknowns that is natural when considering these new degrees of freedom. Preliminary numerical tests in two dimensions confirm the stability of the adopted method and the effectiveness of the new degrees of freedom.

     

Analysis of the Adhesion and Adhesion Strength of Two-Layer Polymer Films and Coatings

The formation of adhesion bonds during the creation of two-layer polymer films and coatings capable of acid–base interaction is considered. The coatings are obtained from polymer solutions, and the second layer is formed from the polymer solutions and their mixtures on a hard polymer coating. As a result of absorption by the coating of a considerable amount of solvents (to 14%), polymer macrochains are able to approach one another at a distance necessary for the formation of acid–base (hydrogen) bonds and a transition layer. The polar component of the work of adhesion is equal to about 50% of the whole work W _a. There is no interrelation of the thermodynamic work W _a between the films and the work of their separation into layers. The main part of the external work upon the separation is spent (if strong donor–acceptor bonds are formed) for extracting the segments and macrochains of polymers out of the films.     

Asymptotic Behavior of the Nonlinear Schrödinger Equation with Harmonic Trapping

We consider the cubic nonlinear Schrödinger equation with harmonic trapping on ?^D (1 ≤ D ≤ 5). In the case when all directions but one are trapped (aka “cigar‐shaped trap”), we prove modified scattering and construct modified wave operators for small initial and final data, respectively. The asymptotic behavior turns out to be a rather vigorous departure from linear scattering and is dictated by the resonant system of the NLS equation with full trapping on ?D?1. In the physical dimension D = 3, this system turns out to be exactly the (CR) equation derived by Faou, Germain, and the first author as the large box limit of the resonant NLS equation in the homogeneous (zero potential) setting. The special dynamics of the latter equation, combined with the above modified scattering results, allow us to justify and extend some physical approximations in the theory of Bose‐Einstein condensates in cigar‐shaped traps.© 2016 Wiley Periodicals, Inc.     

A theorem on geometric rigidity and the derivation of nonlinear plate theory from three‐dimensional elasticity

The energy functional of nonlinear plate theory is a curvature functional for surfaces first proposed on physical grounds by G. Kirchhoff in 1850. We show that it arises as a Γ‐limit of three‐dimensional nonlinear elasticity theory as the thickness of a plate goes to zero. A key ingredient in the proof is a sharp rigidity estimate for maps v : U → ?ⁿ, U ? ?ⁿ. We show that the L²‐distance of ?v from a single rotation matrix is bounded by a multiple of the L²‐distance from the group SO(n) of all rotations. © 2002 Wiley Periodicals, Inc.     

The mathematical theory of defects in a Cosserat continuum

We give a survey of the theory of dislocations and disclinations in moment media. We study the theory of incompatible deformations of three- and two-dimensional Cosserat continua. In the context of a differential-geometric approach we give a physical interpretation of the geometric quantities in terms of the continuous theory of defects.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 34–40.