Solution of the Boltzmann Kinetic Equation in the Problem on Calculation of Heat Flux from a Spherical Particle at Arbitrary Values of Knudsen Number

The problem on calculation of the heat flux from a uniformly heated spherical particle in an arbitrary range of the Knudsen number is solved. Numerical calculations are performed for a model of molecules interacting as elastic hard spheres under the condition that their reflection from the surface of the particle is purely diffuse.     

Scattering of surface water waves involving a vertical barrier with a gap

A mixed boundary-value problem associated with scattering of surface water waves by a vertical barrier with a gap of an arbitrary length is solved completely by the aid of the solution of a special logarithmic singular integral equation in the domain (a,b), which has bounded behaviour at both the end points a(>0) and b. The reflection coefficient is obtained analytically and its numerical values are presented graphically, for different values of the ratio of the width of the gap to the position of the gap. The present method of solution replaces the existing methods, which are either more elaborate or approximate in nature.     

Harmonic generation from ionization-damped two-level system in the framework of nonlinear Riccati-type equation

We formulate the problem of harmonic generation by a two-level system with ionization in terms of a nonlinear Riccati-type differential equation. Different simplified forms of this equation are solved analytically and the resulting photon-emission spectra are compared with those obtained by others along different lines. For the complete-form Riccati-type equation, we give an iterative code solving this equation for arbitrary laser pulses. The code is used to study the effect of ionization and turn-on of the laser pulse on the harmonic spectrum.     

An approximated closed-form solution for inhomogeneous planar layers

An approximated closed-form analytic solution is introduced for arbitrary inhomogeneous planar layers (IPLs). First, the differential equations of IPLs are written as a suitable matrix differential equation. Then, the matrix differential equation is solved to obtain the chain parameter matrix of IPLs. Afterwards, the electric and magnetic fields at any point and also the reflection and transmission coefficients are obtained using the chain parameter matrix. The validation of the introduced solution is studied finally.     

Two-dimensional scattering of a plane wave from a periodic array of dielectric cylinders with arbitrary shape

A two-dimensional scattering of a plane wave from a periodic array of dielectric cylinders with arbitrary shape using the multigrid-moment method is examined. The scattered field is expressed in terms of the integral form by an infinite summation of the surface integral over the cross section of the reference cylinder. The integral form is converted into the matrix equation by using the moment method. The integration in the elements of the matrix equation is evaluated by the lattice-sums technique to obtain a precise solution. The multigrid method is applied to the matrix equation to improve the CPU time. The CPU time and the residual norm are examined numerically for a given number of iterations and cycle indices. Then the effects of shape and material of the periodic structure on the power reflection coefficient of the fundamental Floquet mode are shown. In addition, the results indicate the effect of changing the relative permittivity of the dielectric coated body and the reflection coefficient.     

Effect of the interaction of gases with a surface on thermal creep in a flat channel

The dependence of the thermal creep in a flat channel on the coefficient of accommodation of tangential momentum with an arbitrary mode of gas flow is studied. The problem is solved on the basis of a linearized kinetic equation using the BGK (Bhatnager-Gross-Krook) model for the molecular collision operator. The Maxwell specular-diffuse system is taken as the boundary conditions.     

Gradient-based shape optimisation of conformal array antennas

We present and test a gradient-based shape optimisation method for the minimisation of the active reflection coefficient for conformal array antennas. The goal function is an average of the active reflection coefficient with respect to all antenna elements, a prespecified frequency interval, and a set of excitation modes. The sensitivity of the goal function with respect to changes of the antenna's shape is based on the continuum form of Maxwell's equations, which provides good flexibility for the choice of field solver. The sensitivity is formulated in terms of the field solution of the original antenna problem and a similar adjoint field problem, which gives the sensitivity for an arbitrary number of design parameters given the solution of Maxwell's equations. We test the optimisation method in two dimensions for array antennas that conform to a circular cylinder, where both uniform arrays and arrays that occupy a part of the cylinder's circumference are considered. For some cases, we find that it is feasible to reduce the active reflection coefficient for arrays that partially cover the circumference of the cylinder by means of end elements that differ from the bulk elements of the array. In general, substantial reductions in the active reflection coefficient can be achieved by relatively small shape changes of the antenna elements. For the test cases considered in this article, the optimisation method typically converges to an optimised design within 5-15 iterations.     

Radiative properties of snow for clear sky solar radiation

Spectral and integrated radiative properties (reflection, transmission, and the rate of heating) of finegrained wind-packed snow typical of subpolar regions are studied through a model taking into account surface reflection and volumetric multiple scattering. The surface reflection is modeled by a bidirectional reflectance distribution function applicable to powdered dielectric material. For the volumetric multiple scattering, the radiative transfer equation designed for strongly asymmetric scattering is solved. All multiple scattering parameters (single scattering albedo, various moments of the scattering phase function, and optical depth) are related to measurable physical characteristics (density, grain size, and the absorption coefficient of pure ice).Parameterized atmospheric spectral transmission coefficients for scattering and absorption by aerosols and gases are used to obtain the direct and diffuse components of solar flux, incident on the snow-cover. Calculated values of spectral and integrated visible and near infrared reflection and flux attenuation coefficients of snow are compared with observations. The rate of radiative heating at different depths within the snowcover is calculated from the net flux divergence. It is shown that the conventional method of calculating this rate using measured bulk extinction coefficients grossly underestimates the amount of heating within the top few millimeters. This study provides a better overall understanding of the radiative properties of snow under clear sky conditions in terms of the physical characteristics of the snowcover.     

Calculation of the heat flux from a spherical particle in a molecular gas

The problem of calculating the heat flux from a uniformly heated spherical particle in a molecular gas is considered. The results of numerical calculations performed within the framework of the Hanson-Morse model using the linearized Wang Chang-Uhlenbeck equation are presented, which are obtained under the condition of purely diffuse reflection of gas molecules from the particle surface. The values of the temperature jump coefficient for particular gases have been determined.     

Microstructure dependence of diffusional transport

A simple and effective numerical method is proposed for simulating the temporal diffusive mass transport process through a microstructure with arbitrary complexity described by a phase-field approach. The mass diffusion through a given microstructure is modeled by a diffusion equation with a variable diffusion coefficient, which is solved by an efficient and accurate semi-implicit spectral method. It is shown that it is possible to extract the effective diffusion coefficient for any given microstructure from the temporal concentration profiles. The method is used to simulate the grain boundary diffusion in a single-phase polycrystalline grain structure and the heterogeneous diffusion in a two-phase microstructure with different diffusion coefficient in each phase. Results are compared with existing analytical theories and computer simulations.     

A green's function method for large deflection analysis of plates

Summary An integral equation method is presented for large deflection analysis of thin elastic plates, whose behaviour is governed by the von Kármán equations. The method uses the Green function of the biharmonic equation to establish integral representations of the deflection and stress function for the linear part of the governing operator while the nonlinearities are treated as loading forces. Six nonlinear domain integral equations are formulated which are solved to yield the curvature tensors of the deflection and stress function surfaces and thereby the deflections and stress resultants. The nonlinear integral equations are solved numerically by developing an effective technique based on Gaussian quadrature over domains of arbitrary shape. For domains of simple geometry ready-to-use Green functions are employed whereas for regions of arbitrary shape the Green function is established numerically using BEM. The efficiency of the method is demonstrated and attested by analyzing a circular clamped plate with movable edge.With 4 Figures     

A direct integral equation method for the potential flow about arbitrary bodies

The velocity on the surface of an arbitrary three-dimensional body in the potential flow of an ideal fluid is determined by means of an integral equation method. The equations to be solved are a pair of singular integral equations of the second kind, the unknowns being the desired velocity components. The integral equations are approximated by a set of linear equations, which are solved numerically. For ellipsoids the results are compared with the analytic solutions.     

General case of specular-ditfuse reflection of radiation on the bound-aries of a plane layer under radiative-conductive heat exchange conditions

Linear integral equations describing the angular distribution of the radiation intensity at the boundaries of a semitransparent plane layer are formulated for arbitrary reflection indices. The simpler models of specular and diffuse reflection investigated earlier are obtained as particular cases of the general construction mentioned.     

渐变截面梁波透射反射系数求解的数值验证

推导任意截面形状的预应力Timoshenko梁波动微分方程,对预应力箱板梁渐变截面段弹性波透(反)射系数矩阵进行计算,为求得小端传播到大端的透射波幅值,将渐变截面梁近似当作具有一系列截面间断的阶梯梁,按层状结构波传播的传递矩阵法求波幅在大小端间的透(反)射系数矩阵,通过基于Maple软件平台编写子程序对梁截面尺寸及渐变段分段数目对透(反)射系数矩阵精确性的影响进行数值分析。在波动微分方程伽辽金近似解基础上,对渐变截面段梁波透(反)射系数矩阵的求解法进行数值验证,验证中以第一类贝塞尔函数组合作为系数具有高次项幂级数函数的高阶常微分方程伽辽金法近似解的试函数,该试函数对这类方程具有普遍的适用性。     

Self-consistent approach to the solution of the light transfer problem for irradiances in marine waters with arbitrary turbidity, depth, and surface illumination. I. Case of absorption and elastic scattering

A self-consistent variant of the two-flow approximation that takes into account strong anisotropy of light scattering in seawater of finite depth and arbitrary turbidity is presented. To achieve an appropriate accuracy, this approach uses experimental dependencies between downward and total mean cosines. It calculates irradiances, diffuse attenuation coefficients, and diffuse reflectances in waters with arbitrary values of scattering, backscattering, and attenuation coefficients. It also takes into account arbitrary conditions of illumination and reflection from the bottom with the Lambertian albedo. This theory can be used for the calculation of apparent optical properties in both open and coastal oceanic waters, lakes, and rivers. It can also be applied to other types of absorbing and scattering medium such as paints, photographic emulsions, and biological tissues.     

Improvement of anisotropy sensitivity in the scanning acoustic microscope

The response of the conventional scanning acoustic microscope (SAM) to anisotropic materials is theoretically investigated. For this purpose, the reflection coefficient of plane acoustic waves incident on a liquid-solid interface is numerically calculated for a general anisotropic solid oriented in any arbitrary direction. In general, the reflection coefficient depends on polar and azimuthal angles of incidence. For the case of a circularly symmetric acoustic microscope lens, a mean reflectance function can be defined that depends only on the polar angle. With this mean reflectance function, it is very easy to predict the anisotropic material response of the acoustic microscope. It is found that, under certain conditions, the amplitude response of the acoustic microscope can depend heavily on the orientation of the solid material under investigation. The amplitude of the acoustic microscope signal is influenced by the orientation of the material because there is a cancellation of acoustic rays reflected from the object surface at different azimuthal angles. This cancellation is revealed as a minimum in the mean reflectance function. It is shown by numerical simulation that the sensitivity to orientation can be increased by the use of a ring-shaped insonification at the back of the acoustic lens.     

Influence of the parameters of sweet-water flow in littoral sea zones on the dimensions of a saline-water tongue

Consideration is given to the model of motion of sweet groundwater in a trapezoidal pressure water-bearing stratum to a sea with saline water. For studying this model, a mixed multiparametric boundary-value problem of the theory of analytical functions is formulated and solved using the P. Ya. Polubarinova-Kochina method. The algorithm of calculation of the intrusion of seawater into the sweet-water layer in the case where its right-hand boundary modeling the littoral zone of the sea floor makes an arbitrary angle with the horizon is developed based on this scheme. The characteristic features of the modeled process and the influence of all determining physical parameters on the character and degree of intrusion are analyzed using the exact analytical dependences obtained and numerical calculations. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 3, pp. 427–433, May–June, 2008.     

小斜率近似方法分析粗糙界面声散射问题

利用小斜率近似方法计算了起伏海面的声散射特性,得到了具有高斯分布粗糙海面的平均反射系数（即镜反射系数）计算公式,并与微扰法和Kirchhoff近似做了比较,结果表明小斜率近似是一种非常有效的分析起伏表面散射特性的近似方法。最后讨论了海面镜反射系数随海面的不平整度（波浪的均方根高度）、声波频率和声波入射方向的变化关系,得出了只有在声波波长和起伏波浪高度可比拟时,才有明显的镜反射的结论。这为分析浅海目标声散射特性时,选择是否需要考虑海面（海底）所引起的多途效应提供了理论依据。     

New scalar potential method for computation of electromagnetic variables in multilayer slab conductors

We present a new scalar potential method for computing the electromagnetic variables in multilayer slab conductors, excited by waves of arbitrary shape. In this method a large number of layers can be modeled separately, and it is possible to consider the arbitrary shape exciters in between the conductor layers. We use the scalar potential method to solve the Helmholtz equation in three dimensions. For the solution of this problem, two-dimensional fast Fourier transform and exponential functions are used with scalar potential variables. We verify the method by comparing the results of an example problem solved both by the new method and the finite-element method.     

Effect of surface roughness on determination of tissue optical properties obtained by diffusion approximation

A nylon bar with different surface roughness is used as a simulation sample of biological tissue for the determination of optical properties by using the spatially resolved steady-state diffuse reflection technique. The results obtained indicate that surface roughness has some effects on the determination of the optical properties of the nylon bar. The determined reduced scattering coefficient decreases with the decrease of the surface roughness of the nylon bar and goes to a constant for the lower surface roughness, and the determined absorption coefficient increases with the decrease of the surface roughness of the nylon bar. Consequently, the optical properties of the tissues obtained by the spatially resolved steady-state diffuse reflection technique should be modified.