Linear oscillations of a compressible hemispherical bubble on a solid substrate

The linear natural and forced oscillations of a hemispherical bubble on a solid substrate are under theoretical consideration. The contact line dynamics is taken into account with the Hocking condition, which eventually leads to interaction of the shape and volume oscillations. Resonant phenomena, mostly pronounced for the bubble with the fixed contact line or with the fixed contact angle, are found out. The limiting case of weakly compressible bubble is studied. The general criterion identifying whether the compressibility of a bubble can be neglected is obtained.Comment: new slightly extended version with some minor changes, added journal reference and DOI information; 12 pages, 8 figures, published in Physics of Fluid

Intersection of triangles in space based on cutting off segment

The article proposes a new method for finding the triangle-triangle intersection in 3D space, based on the use of computer graphics algorithms -- cutting off segments on the plane when moving and rotating the beginning of the coordinate axes of space. This method is obtained by synthesis of two methods of cutting off segments on the plane -- Cohen-Sutherland algorithm and FC-algorithm. In the proposed method, the problem of triangle-triangle intersection in 3D space is reduced to a simpler and less resource-intensive cut-off problem on the plane. The main feature of the method is the developed scheme of coding the points of the cut-off in relation to the triangle segment plane. This scheme allows you to get rid of a large number of costly calculations. In the article the cases of intersection of triangles at parallelism, intersection and coincidence of planes of triangles are considered. The proposed method can be used in solving the problem of tetrahedron intersection, using the finite element method, as well as in image processing.Comment: Convergent Cognitive Information Technologies. Convergent 2019. Communications in Computer and Information Science, in press, Springer, Cham. http://it-edu.oit.cmc.msu.ru/index.php/convergent/convergent2019 (14 pages, 11 figures

Electrostatics in Fractal Geometry: Fractional Calculus Approach

The electrostatics properties of composite materials with fractal geometry are studied in the framework of fractional calculus. An electric field in a composite dielectric with a fractal charge distribution is obtained in the spherical symmetry case. The method is based on the splitting of a composite volume into a fractal volume $V_d\sim r^d$ with the fractal dimension $d$ and a complementary host volume $V_h=V_3-V_d$. Integrations over these fractal volumes correspond to the convolution integrals that eventually lead to the employment of the fractional integro-differentiation

Dynamics of pulse waves in bubble liquids: Comparison between theory and experiment

The fundamentals of mechanics and thermal physics of bubble liquids and the most essential results on studying the wave processes in such media are presented. The sample is placed in a vessel with water between an acoustic signal source (the piezoelectric converter) and a hydrophone. On the basis of the analysis of the parameters of sound waves transmitted through a sample, the data on its properties are found. Although the second condition is not completely fulfilled, the theoretical curve of the dependence of the pressure at the hydrophone on the reduced time agrees well with the experiment. Thus, the theory under consideration can be used confidently for calculation of the distortion of the acoustic signal in the diagnostics of multilayer samples with bubble inclusions

Dynamics of pulse waves in bubble liquids: Comparison between theory and experiment

The fundamentals of mechanics and thermal physics of bubble liquids and the most essential results on studying the wave processes in such media are presented. The sample is placed in a vessel with water between an acoustic signal source (the piezoelectric converter) and a hydrophone. On the basis of the analysis of the parameters of sound waves transmitted through a sample, the data on its properties are found. Although the second condition is not completely fulfilled, the theoretical curve of the dependence of the pressure at the hydrophone on the reduced time agrees well with the experiment. Thus, the theory under consideration can be used confidently for calculation of the distortion of the acoustic signal in the diagnostics of multilayer samples with bubble inclusions

Capture of particles of dust by convective flow

Interaction of particles of dust with vortex convective flows is under theoretical consideration. It is assumed that the volume fraction of solid phase is small, variations of density due to nonuniform distribution of particles and those caused by temperature nonisothermality of medium are comparable. Equations for the description of thermal buoyancy convection of a dusty medium are developed in the framework of the generalized Boussinesq approximation taking into account finite velocity of particle sedimentation. The capture of a cloud of dust particles by a vortex convective flow is considered, general criterion for the formation of such a cloud is obtained. The peculiarities of a steady state in the form of a dust cloud and backward influence of the solid phase on the carrier flow are studied in detail for a vertical layer heated from the sidewalls. It is shown that in the case, when this backward influence is essential, a hysteresis behavior is possible. The stability analysis of the steady state is performed. It turns out that there is a narrow range of governing parameters, in which such a steady state is stable.Comment: 14 pages, 10 figures, published in Physics of Fluid