On the recovery factor in free-molecular flow

The equilibrium temperature in free-molecular flow can be lower than the stagnation temperature, i.e. the recovery factor smaller than one, if two distinct accommodation coefficients are assumed for the tangential and the normal translational energy of the molecules. Moreover the equilibrium temperature turns out to be dependent on a parameter which is a function of these accommodation coefficients and therefore is related to the physical nature of the surface and of the gas. The connection of this theory with a gas-surface interaction model previously proposed by the authors is shown.

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Riassunto La temperatura di equilibrio nel regime di molecole libere può essere minore della temperatura di ristagno, e cioè il fattore di recupero minore di uno, se si introducono due distinti coefficienti di accomodamento per l'energia normale e tangenziale delle molecole. Inoltre la temperatura di equilibrio risulta dipendere da un parametro funzione di questi coefficienti di accomodamento e quindi è influenzata dalla natura fisica del gas e della superficie solida. Questa teoria è connessa con un modello di interazione gas-superficie precedentemente proposto dagli Autori.

     

The hydrodynamic equations for chemically equilibrium flows of a multielement plasma with exact transport coefficients

Explicit expressions for all of the effective transport coefficients are derived for thermochemically equilibrium flows using the exact mass and heat transfer equations, which are resolved with respect to the “forces” (the gradients of the hydrodynamic variables) via the flukes. It is shown that, in a mixture where the components have different diffusion properties, separation (diffusion) of the chemical elements occurs which leads to a state of affairs where the equilibrium concentrations, and together with them, the effective transport coefficients will be functions not only of the pressure and temperature but will also depend on the concentrations of the elements, determined when solving the problem (self-consistent concentrations of the elements). It is shown that the existence of an electric current and lack of quasineutrality (flow around electrically conducting walls—electrodes) does not change the structure of the expressions for the effective transport coefficients and does not add anything new. The approximate and incomplete treatment of thermochemically equilibrium flows of multicomponent gas mixtures and a plasma in previously published papers are especially noted. Numerical estimates of the effective transport coefficients are presented for an air plasma and the domains in the pressure-temperature plane with the required number of approximations in order to obtain results with an error of no worse than 5% are indicated.     

Smoluchowski's problem for molecular gases taking the accommodation coefficients of the translational and rotational energy of the molecules into account

The effect of the accommodation coefficients of the energy of translational and rotational motion of molecules on the temperature jump in the classical Smoluchowski problem is investigated. Using the extension of the well-known kinetic BKW (Boltzmann-Krook-Welander) equation to the case of molecular gases, an analytical solution of this problem is obtained for diatomic and polyatomic gases taking the rotational degrees of freedom into account. A numerical analysis of the results obtained is carried out.     

Phase transitions in multi-phase media

Two problems on phase transitions in a continuous medium are considered. The first problem deals with an elastic medium admitting more than two phases. Necessary conditions for equilibrium states are derived. The dependence of equilibrium states on the surface tension coefficients and temperature is studied for one model of a three-phase elastic medium such that each phase has a quadratic energy density. The second problem deals with phase transitions under some restrictions on the vector field under consideration. These restrictions imply that this vector field is solenoidal and its normal component vanishes on the boundary of the interfaces of phases. The equilibrium equations are deduced. Bibliography: 5 titles. Translated fromProblemy Matematicheskogo Analiza, No. 20, 2000, pp. 120–170.     

Two-dimensional thermoelastic analysis of beams with variable thickness subjected to thermo-mechanical loads

Two-dimensional thermoelastic analysis for simply supported beams with variable thickness and subjected to thermo-mechanical loads is investigated. An approximate analytical method is proposed. Firstly, the heat conduction equation is analytically solved to obtain the temperature distributions for two kinds of boundary conditions at the beam ends, which are the harmonic series with unknown coefficients. Then the two-dimensional equilibrium differential equations are analytically solved to obtain the displacement component series with unknown coefficients and the stress component series is obtained. The unknown coefficients in the temperature series and the stress component series are approximately determined by using the upper surface and lower surface conditions of the beam. With the proposed procedure, the solutions satisfy the governing differential equations, the loading conditions, and the simply supported end conditions. The proposed solution method shows a good convergence and the results agree well with those obtained from the commercial finite element software ANSYS. Several examples are used to demonstrate the effectiveness of the proposed solution method. The simultaneous effects of temperature change and applied mechanical load on the behavior of the beam are examined.     

Effect of fillers on the structure and properties of cured resins

The elastic (modulus of elasticity and equilibrium high-elastic modulus) and thermal (volume coefficients of thermal expansion below and above the glass transition temperature) properties of compositions based on ÉD-5 epoxy resin cured with polyethylenepolyamine have been investigated. Quartz powder and aluminoborosilicate glass powder were employed as fillers at concentrations from 0 to 0.413. The thermal expansion coefficients of the compositions were studied in a dilatometer, in which the specimen is free of mechanical loads. The Young's modulus at 25°C and the equilibrium high-elastic modulus at 125°C of the compositions were determined in the compression regime in an instrument based on the IZV-2 optical length gage. The thermal expansion coefficients of the polymer matrix were calculated with allowance for the elastic properties of the resin and the filler. It is shown that, as the filler concentration increases, the thermal and elastic properties of the resin in the filled system change. This can be interpreted as a change in the properties of the resin as it approaches the surface of the filler particles. Increased interaction between the filler surface and the epoxy resin tends to stiffen the polymer network.Scientific Research Institute of Precision Technology, Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1018–1022, November–December, 1969.     

The stability of generalized Volterra equations

In this paper, a particular type of a system of generalized Volterra equations [1], whose solutions are assured to be nonnegative for arbitrary nonnegative initial values, is considered. The extended stability theorem of LaSalle is used for deriving conditions for a nonnegative equilibrium point to be stable with respect to a certain subset of the Euclidean space. The obtained stability theorem has a close relation with Lyapunov's stability condition for linear systems with constant coefficients and is generally less restrictive than conditions known so far.     

Queueing models for a flexible machining station Part II: The method of Coxian phases

A work station of a flexible manufacturing system (fms) is modeled as a multi-server queue with finite waiting room. The interarrival/service time distributions have squared coefficients of variations not less than 0.5 and are modeled as Coxian laws of two phases. A recursive scheme is developed to calculate the equilibrium queue length distribution. The model, together with the diffusion approximation model of Part I, can be used to aid the design of fms work stations.     

The Influence of Human Behavior on Heroin Dynamics

In this paper, considering the influence of human behavior on heroin abuse, we establish a mathematical model to describe the spread of heroin. When the basic reproduction number is less than one, the heroin-free abuse equilibrium point is globally asymptotically stable. When the basic re- production number is greater than one, the model has a unique heroin abuse equilibrium point which is globally asymptotically stable, and the heroin-free abuse equilibrium point is unstable. Finally, based on the partial rank corre- lation coefficients (PRCCs) and numerical simulations, the dynamic behavior of the model is further revealed. Our results show that human behavior can reduce the heroin abuse level.     

Dynamics of a Mutualistic Model with Diffusion

This article is concerned with a system of semilinear parabolic equations with no-flux boundary condition in a mutualistic ecological model. Stability result of the equilibrium about relevant ODE problem is proved by discussing its Jacobian matrix, we give two priori estimates and prove that the model is permanent when ε_1+ ε_2 ≠ 0. Moreover sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the model are obtained. Nonexistence of nonconstant positive steady states of the model is also given. When ε_1+ε_2= 0, grow up property is derived if the geometric mean of the interaction coefficients is greater than 1(α_1α_2 1),while if the geometric mean of the interaction coefficients is less than 1(α_1α_2 1), there exists a global solution. Finally, numerical simulations are given.     

热弹性材料的自由能表达式及其与物性系数的关系*

本文中,自由能的表达式展开成幂级数,其中,温度增量θ*取到三阶,应变张量γ_ij只取到二阶.由这个表达式可以导出物性系数随温度增量的变化规律.这些规律与参考文献中的实验图线是相符的.不过,自由能表达式中的常数须由实验数据确定.文中指出,变化的弹性模量E和剪切弹性模量G是彼此独立的,而其它的物性系数则与它们相关.     

Controlling hyperchaos in hyperchaotic Lorenz system using feedback controllers

In this paper, the control strategies for hyperchaotic Lorenz system is investigated. The ordinary, dislocated, enhancing and speed feedback controls are used to suppress hyperchaos to unstable equilibrium. The Routh-Hurwitz criterion is used to derive the conditions of stability of the controlled hyperchaotic systems. It is found that the coefficients of enhancing feedback control and dislocated feedback control may be smaller than those of ordinary feedback control, so, the complexity and cost of the system control are reduced. Numerical simulations are given to illustrate the effectiveness of the proposed controllers.     

Saint-Venant decay rates for an inhomogeneous isotropic linear thermoelastic strip

In this paper we consider the state of plane strain in an isotropic and inhomogeneous thermoelastic material occupying a rectangular strip. Such a strip is maintained in equilibrium under self-equilibrated traction applied on one of the heated edges, while the other three edges are thermally insulated and traction-free. Our aim is to derive some explicit spatial estimates describing how certain appropriate measures of the Airy stress function and temperature evolve with respect to the distance from the loaded and heated edge, provided specific assumptions are made upon the derivatives of the thermoelastic coefficients. The results of the present paper prove how the spatial decay rate varies with the inhomogeneous constitutive profile.     

Applied general equilibrium modeling for environmental policy analysis

Incorporating environmental regulation and its impact in general equilibrium models has by now a twenty years long tradition. In 1970, Leontief extended his input-output approach to quantify environmental repercussions on the economic structure. The shortcomings of this model, such as fixed coefficients in technological processes or zero price and income elasticities of demand, can be resolved by using a quantitative general equilibrium model. The objective of this paper is to employ such a model to quantify the economic effects of environmental policy and to present a cost-effectiveness analysis of different market instruments in environmental policy.     

Solutions of one-dimensional problems of elasticity and thermoelasticity for cylindrical piecewise-homogeneous bodies

We propose a method of direct integration of the equilibrium and continuity equations in stresses for one-dimensional problems of elasticity and thermoelasticity for piecewise-homogeneous cylinders and disks with an arbitrary number of layers. The solutions are reduced to finding the constants of systems of algebraic equations with nearly triangular matrices of coefficients, making it possible to find the unknown constants in a closed form that is functionally dependent on the bulk forces and temperature field.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 139–148.     

Stagnation point flow of dusty Casson fluid with thermal radiation and buoyancy effects

The aim of the study is to examine the stagnation point flow of a dusty Casson fluid over a stretching sheet with thermal radiation and buoyancy effects. The governing boundary layer equations are represented by a system of partial differential equation. After applying suitable similarity transformations, the resulting boundary layer equations are solved numerically using the Runge Kutta Fehlberg fourth-fifth order method (RKF-45 method). The behaviors of velocity, temperature and concentration profiles of fluid and dusty particles with respect to change in fluid particle interaction parameter, Casson paramter, Grashof number, radiation parameter, Prandtl number, number density, thermal equilibrium time, relaxation time, specific heat of fluid and dusty particles, ratio of diffusion coefficients, Schmidt number and Eckert number are analysed graphically and discussed. Our computed results interpret that velocity distribution decays for higher estimation of Casson parameter while temperature distribution shows increasing behavior for larger radiation parameter.     

Convergence in competition models with small diffusion coefficients

It is well known that for reaction-diffusion 2-species Lotka-Volterra competition models with spatially independent reaction terms, global stability of an equilibrium for the reaction system implies global stability for the reaction-diffusion system. This is not in general true for spatially inhomogeneous models. We show here that for an important range of such models, for small enough diffusion coefficients, global convergence to an equilibrium holds for the reaction-diffusion system, if for each point in space the reaction system has a globally attracting hyperbolic equilibrium. This work is planned as an initial step towards understanding the connection between the asymptotics of reaction-diffusion systems with small diffusion coefficients and that of the corresponding reaction systems.     

Dissociation effects in hypersonic flow past a circular cone at an angle of attack

The analytical solution to the steady, compressible, non-viscous, inviscid hypersonic flow past a circular cone at an angle of incidence, with an attached Shockwave, in the presence of dissociation of air in the shock layer, has been obtained here under the assumption of thermal equilibrium. Expression for the velocity, pressure, temperature, density, velocity of air, Mach number, pressure, drag and lift coefficients have been obtained both in the shocklayer outside the vortical layer and on the surface of the cone inside the vortical layer.     

Complex dynamics of an eco-epidemiological model with different competition coefficients and weak Allee in the predator

The paper explores an eco-epidemiological model with weak Allee in predator, and the disease in the prey population. We consider a predator-prey model with type II functional response. The curiosity of this paper is to consider different competition coefficients within the prey population, which leads to the emergent carrying capacity. We perform the local and global stability analysis of the equilibrium points and the Hopf bifurcation analysis around the endemic equilibrium point. Further we pay attention to the chaotic dynamics which is produced by disease. Our numerical simulations reveal that the three species eco-epidemiological system without weak-Allee induced chaos from stable focus for increasing the force of infection, whereas in the presence of the weak-Allee effect, it exhibits stable solution. We conclude that chaotic dynamics can be controlled by the Allee parameter as well as the competition coefficients. We apply basic tools of non-linear dynamics such as Poincare section and maximum Lyapunov exponent to identify chaotic behavior of the system.