Modeling Method of C/C-ZrC Composites and Prediction of Equivalent Thermal Conductivity Tensor Based on Asymptotic Homogenization

This article proposes a modeling method for C/C-ZrC composite materials.According to the superposition of Gaussian random field,the original gray model is obtained,and the threshold segmentation method is used to generate the C-ZrC inclusion model.Finally,the fiber structure is added to construct the microstructure of the three-phase plain weave composite.The reconstructed inclusions can meet the randomness of the shape and have a uniform distribution.Using an algorithm based on asymptotic homogenization and finite element method,the equivalent thermal conductivity prediction of the microstructure finite element model was carried out,and the influence of component volume fraction on material thermal properties was explored.The sensitivity of model parameters was studied,including the size,mesh sensitivity,Gaussian complexity,and correlation length of the RVE model,and the optimal calculation model was selected.The results indicate that the volume fraction of the inclusion phase has a significant impact on the equivalent thermal conductivity of the material.As the volume fraction of carbon fiber and ZrC increases,the equivalent thermal conductivity tensor gradually decreases.This model can be used to explore the impact of materialmicrostructure on the results,and numerical simulations have studied the relationship between structure and performance,providing the possibility of designing microstructure based on performance.

Analytical solution for the effective elastic properties of rocks with the tilted penny-shaped cracks in the transversely isotropic background

Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.

Recent advancements in thermal conductivity of magnesium alloys

As highly integrated circuits continue to advance,accompanied by a growing demand for energy efficiency and weight reduction,materials are confronted with mounting challenges pertaining to thermal conductivity and lightweight properties.By virtue of numerous intrinsic mechanisms,as a result,the thermal conductivity and mechanical properties of the Mg alloys are often inversely related,which becomes a bottleneck limiting the application of Mg alloys.Based on several effective modification methods to improve the thermal conductivity of Mg alloys,this paper describes the law of how they affect the mechanical properties,and clearly indicates that peak aging treatment is one of the best ways to simultaneously enhance an alloy's thermal conductivity and mechanical properties.As the most frequently used Mg alloy,cast alloys exhibit substantial potential for achieving high thermal conductivity.Moreover,recent reports indicate that hot deformation can significantly improve the mechanical properties while maintaining,and potentially slightly enhancing,the alloy's thermal conductivity.This presents a meaningful way to develop Mg alloys for applications in the field of small-volume heat dissipation components that require high strength.This comprehensive review begins by outlining standard testing and prediction methods,followed by the theoretical models used to predict thermal conductivity,and then explores the primary influencing factors affecting thermal conductivity.The review summarizes the current development status of Mg alloys,focusing on the quest for alloys that offer both high thermal conductivity and high strength.It concludes by providing insights into forthcoming prospects and challenges within this field.

Development of Multilayer Models of Globular Star Clusters and Study of Their Evolution

Usually, models of globular star clusters are created by analyzing their luminosity and other observation parameters. The goal of this work is to create stable models of globular clusters based on the laws of mechanics. It is necessary to set the coordinates, velocities and masses of the stars so that as a result of their gravitational interaction the globular cluster is not destroyed. This is not an easy task, and it has been solved in this paper. Using an exact solution of the axisymmetric gravitational interaction of N-bodies, single-layer spherical structures were created. They are combined into multilayer models of globular clusters. An algorithm and a program for their creation is described. As a result of solving the problem of gravitational interaction of N bodies, evolution of 5-, 10-, and 15-layer structures was studied. During the inter-body interaction, there proceeds a transition from the initial specially organized structure to a structure with bodies, uniformly distributed in space. The number of inter-body collisions decreases, and the globular cluster model passes into the stable form of its existence. The collisions of bodies and the acquisition of rotational motion and thermal energy by them are considered. As a result of the passage to scaled dimensions, the results were recalculated to the conditions of globular star clusters. The periods of rotation and the temperatures of merged stars are calculated. Attention is paid to a decreased central-body mass in the analyzed models of globular star clusters.

Mathematical Wave Functions and 3D Finite Element Modelling of the Electron and Positron

The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.

Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schr?dinger equation

We make a quantitative study on the soliton interactions in the nonlinear Schro¨dinger equation(NLSE) and its variable–coefficient(vc) counterpart. For the regular two-soliton and double-pole solutions of the NLSE, we employ the asymptotic analysis method to obtain the expressions of asymptotic solitons, and analyze the interaction properties based on the soliton physical quantities(especially the soliton accelerations and interaction forces);whereas for the bounded two-soliton solution, we numerically calculate the soliton center positions and accelerations, and discuss the soliton interaction scenarios in three typical bounded cases. Via some variable transformations, we also obtain the inhomogeneous regular two-soliton and double-pole solutions for the vcNLSE with an integrable condition. Based on the expressions of asymptotic solitons, we quantitatively study the two-soliton interactions with some inhomogeneous dispersion profiles,particularly discuss the influence of the variable dispersion function f(t) on the soliton interaction dynamics.

Asymptotic solution of a weak nonlinear model for the mid-latitude stationary wind field of a two-layer barotropic ocean

A weak nonlinear model of a two-layer barotropic ocean with Rayleigh dissipation is built.The analytic asymptotic solution is derived in the mid-latitude stationary wind field,and the physical meaning of the corresponding problem is discussed.

FLUID-SOLID COUPLING MATHEMATICAL MODEL OF CONTAMINANT TRANSPORT IN UNSATURATED ZONE AND ITS ASYMPTOTICAL SOLUTION

The process of contaminant transport is a problem of multicomponent and multiphase flow in unsaturated zone. Under the presupposition that gas existence affects water transport, a coupled mathematical model of contaminant transport in unsaturated zone has been established based on fluid_solid interaction mechanics theory. The asymptotical solutions to the nonlinear coupling mathematical model were accomplished by the perturbation and integral transformation method. The distribution law of pore pressure, pore water velocity and contaminant concentration in unsaturated zone has been presented under the conditions of with coupling and without coupling gas phase. An example problem was used to provide a quantitative verification and validation of the model. The asymptotical solution was compared with Faust model solution. The comparison results show reasonable agreement between asymptotical solution and Faust solution, and the gas effect and media deformation has a large impact on the contaminant transport. The theoretical basis is provided for forecasting contaminant transport and the determination of the relationship among pressure_saturation_permeability in laboratory.

ON THE ASYMPTOTICAL BEHAVIOUR OF SOLUTIONS OF A CLASS OF NONLINEAR CONTROL SYSTEMS

In this paper, the asymptotical behaviour solutions of a class of nonlinear control systems are studied. By establishing infinite integrals along solutions of the system and drawing support from a LaSalle's invariance principle of integral form, criteria of dichotomy and global asymptotical behaviour of solutions are obtained. This work is an improvement and further extension of research methods and results of A. S. Aisagaliev.

Asymptotic solution for a perturbed mechanism of western boundary undercurrents in the Pacific

This paper consider a class of perturbed mechanism for the western boundary undercurrents in the Pacific. The model of generalized governing equations is studied. Using the perturbation method, it constructs the asymptotic solution of the model. And the accuracy of asymptotic solution is proved by the theory of differential inequalities. Thus the uniformly valid asymptotic expansions of the solution are obtained.

EXISTENCE AND ASYMPTOTIC BEHAVIOR OF THE SOLUTIONS FOR A NONLINEAR ELLIPTIC EQUATION ARISING IN ASTROPHYSICS

The author first analyzes the existence of ground state solutions and cylindrically symmetric solutions and then the asymptotic behavior of the ground state solution of the equation -△u =φ（r）u^p-1, u 〉 0 in R^N, u ∈ D^1,2（R^N）, where N ≥ 3, x = （x^1,z） ∈ R^K×R^N-K,2 ≤ K ≤ N,r = ｜x′｜. It is proved that for 2（N-s）/（N-2） 〈 p 〈 2^＊ = 2N/（N - 2）, 0 〈 s 〈 2, the above equation has a ground state solution and a cylindrically symmetric solution. For p = 2^＊, the above equation does not have a ground state solution but a cylindrically symmetric.solution, and when p close to 2^＊, the ground state solutions are not cylindrically symmetric. On the other hand, it is proved that as p close to 2＊, the ground state solution Up has a unique maximum point xp = （x′p, Zp） and as p → 2^＊, ｜x′p｜ → r0 which attains the maximum of φ on R^N. The asymptotic behavior of ground state solution Up is also given, which also deduces that the ground state solution is not cylindrically symmetric as p goes to 2^＊.

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO THE HEAT EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

The purpose of this paper is to investigate the stability and asymptotic behavior of the time-dependent solutions to a linear parabolic equation with nonlinear boundary condition in relation to their corresponding steady state solutions. Then, the above results are extended to a semilinear parabolic equation with nonlinear boundary condition by analyzing the corresponding eigenvalue problem and using the method of upper and lower solutions.

ASYMPTOTIC PROPERTY STUDY OF THE LEAST SQUARE ESTIMATES OF 2-D EXPONENTIAL SIGNALS VIA COMPLEX SIGNAL PROCESSING APPROACH

By use of the approach of complex random signal processing, the asymptotic statistical properties of the least square estimates of 2-D exponential signals are studied. In doing so it is found that the representation is considerably more intuitive, and is analytically more tractable.

ON THE ASYMPTOTIC SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR A CLASS OF SYSTEMS OF NONLINEAR DIFFERENTIAL EQUATIONS (Ⅰ)

A new method is applied to study the asymptotic behavior of solutions of boundary value problems for a class of systems of nonlinear differential equations u' = nu, epsilon nu' + f(x, u, u')nu' - g(x, u, u') nu = 0 (0 < epsilon much less than 1). The asymptotic expansions of solutions are constructed, the remainders are estimated. The former works are improved and generalized.

ASYMPTOTIC SOLUTION OF SINGULAR PERTURBATION PROBLEMS FOR THE FOURTH-ORDER ELLIPTIC DIFFERENTIAL EQUATIONS

In this paper we consider the singularly perturbed boundary value problem for the fourth-order elliptic differential equation, establish the energy estimates of the solutionand its derivatives and construct the formal asymptotic solution by Lyuternik- Vishik 's method. Finally, by means of the energy estimates we obtain the bound of the remainder of the asymptotic solution.

L^2 ASYMPTOTIC FOR THE EQUILIBRIUM SOLUTION OF THE F-M EQUATIONS IN THE SPACE-PERIODIC CASE

The L2 exponetial asymptotical stability for the equilibrium solution of the F-M equations in the space-periodic case (n=2) is considered. Under some assumptions on the external force, it can be shown that the weak solution of F-M equations with initial and boundary conditions in space-periodic case approaches the stationary solution of the system exponetially when time t goes to infinite.

A COMPLETE EXPRESSION OF THE ASYMPTOTIC SOLUTION OF DIFFERENTIAL EQUATION WITH THREE_TURNING POINTS

In this paper, a second order linear ordinary differential equation with three-turning points is studied. This equation is as follows (dx2)/(d2y) + [lambda(2)q(1)(x) + lambda q(2)(x, lambda)]y = 0, where q(1) (x) = (x - mu(1))(x - mu(2))(x - mu(3))f(x), f(x) not equal 0, mu(1) < mu(2) < mu(3) and lambda is a large parameter, but q(2)(x, lambda) = Sigma(i = 0)(epsilon a) g(i)(x)lambda(-i) (here g(0)(x) not equivalent to 0). By using JL function, the complete expression of the formal uniformly, valid asymptotic solutions of the equation near turning point is obtained.

THE ASYMPTOTIC BEHAVIOR OF SOLUTION FOR THE NONLINEAR HEAT-CONDUCTION EQUATION AND ITS APPLICATION

In this paper the nonlinear heat-conduction equations rhoc partial derivativew/partial derivativet = partial derivative/partial derivativex (k partial derivativew/partial derivativex) with Dirichlet boundary condition and the nonlinear boundary condition are studied. The asymptotic behavior of the global of solution are analyzed by using Lyapuunov function. As its application, the approximate solutions are constructed.

Asymptotic Behavior of the Solutions to the One-Dimensional Nonisentropic Hydrodynamic Model for Semiconductors

In this paper, the asymptotic behavior of the global smooth solutions to the Cauchy problem for the one-dimensional nonisentropic Euler-Poisson （or full hydrodynamic） model for semiconductors, where the energy equation with non-zero thermal conductivity coefficient are contained, is discussed. The global existence of smooth solutions for the Cauchy problem with small perturbed initial data is proved. In particular, that the solutions converge to the corresponding stationary solutions exponentially fast as t → ∞ is showed.

Asymptotic stability of solutions to the nonisentropic hydrodynamic model for semiconductors

In this paper, the asymptotic stability of smooth solutions to the multidimensional nonisentropic hydrodynamic model for semiconductors is established, under the assumption that the initial data are a small perturbation of the stationary solutions for the thermal equilibrium state, whose proofs mainly depend on the basic energy methods.