Reconstruction of scattering properties of rough air-dielectric boundary

The article is devoted to elaboration of the method of reconstruction of rough surface scattering properties. The object with rough surface is made of transparent dielectric material. Typically these properties are described with bi-directional scattering distribution function (BSDF). Direct measurement of such function is either impossible or very expensive. The suggested solution provides physically reasonable method for the rough surface BSDF reconstruction. The method is based on Monte-Carlo ray tracing simulation for BSDF calculation. Optimization technique is further applied to correctly reconstruct the BSDF. The results of the BSDF reconstruction together with measurement results are presented in the article as well.     

Calculation of thermal stresses in profiled single crystals taking into account the temperature dependence of thermal expansion

Approximate expressions for stress tensor components in cylindrical and ribbon crystals are obtained taking into account the temperature dependence of the thermal expansion coefficient. These expressions are used for estimating the effect of the thermal expansion nonlinearity factor on the stress level. It is shown that the stresses emerging in linear temperature fields due to this factor are comparable with critical stresses for defect formation.     

Shape of the surface of a vertical liquid bridge between two parallel solid planes taking into account the gravity force for small Bond numbers

A variational formulation has given the problem of the shape of the lateral surface of a small vertical liquid θ bridge between two parallel solid surfaces that take into account the gravity force in the axisymmetric case. An algorithm has been constructed for the iterative solution of the problem for small Bond numbers. The dependence of the number of solutions on the liquid bridge height has been analyzed.     

Analysis of the development concepts and methods of visual data representation in computational physics

Main steps in the development of scientific visualization as a branch of science are discussed. The evolution and prospects of the development of concepts, methods, and approaches of visual representation of numerical results obtained in computational physics (mainly, in computational fluid dynamics) are discussed.     

The Problem of the Shape of a Vertical Liquid Bridge between Convex Surfaces Taking the Gravity Force into Account

Technical Physics - The solution to the problem of the shape of the lateral surface of a vertical 3D catenoidal liquid bridge of small volume between two arbitrary convex solid surfaces in the...     

Calculation of the thermal effect of an electron probe on a sample of GaN

Stationary temperature fields due to the interaction of an electron probe with a GaN sample are examined. In order to calculate the density of generated heat, the process of electron energy loss is modeled by the Monte Carlo method. The heat generation region is assumed to have the shape of a half-ellipsoid. In the case of uniform heat generation in the ellipsoid, an analytical solution to the heat conduction problem is found and expressed in terms of elementary functions. It is shown that the maximum heating temperature and the temperature field distribution depend only slightly on the shape of the heat generation region. An approximation of the density of heat sources by a uniform distribution over a hemisphere of radius equal to the ultimate range of electrons leads to a considerably underestimated maximum heating temperature. An expression is derived for determining the characteristic size of the heat generation region in GaN; this expression allows one to calculate the maximum heat temperature with an accuracy of 3% in a wide range of electron beam energies.     

Hermitian Spectral Theory and Blow‐Up Patterns for a Fourth‐Order Semilinear Boussinesq Equation

Two families of asymptotic blow‐up patterns of nonsimilarity and similarity kinds are studied in the Cauchy problem for the fourth‐order semilinear wave, or Boussinesq‐type, equation The first countable family is constructed by matching with linearized patterns obtained via eigenfunctions (generalized Hermite polynomials) of a related quadratic pencil of linear operators. The second family comprises nonlinear blow‐up patterns given by self‐similar solutions. The results have their counterparts in the classic second‐order semilinear wave equation which was known to admit blow‐up solutions since Keller's work in 1957.