Numerical investigations on vortical structures of viscous film flows along periodic rectangular corrugations

Two-dimensional gravity-driven film flows along a substrate with rectangular corrugations are studied numerically by using Finite Volume Method. The volume of fluid (VOF) method is utilized to capture the evolution of free surfaces. The film flows down an inclined plate are simulated to validate the numerical implementation of the present study. Results obtained indicate that the phase shift between the surface wave and the wall corrugation increases as the Reynolds number. The parametric studies on the interesting resonant phenomenon indicate that the peak Reynolds numbers increase as the raise of the wall depth or the decline of the inclination angle. The dependence of the flow fields is analyzed on the Reynolds numbers and wall depth in details. It is found that the vortical structures in the steady flows, either produced by the interaction between capillary wrinkling and inertia, or by the rectangular geometry, are closely related to the remarkable deformation of the free surfaces. This conclusion is also confirmed by the transient flow development of two typical simulations, i.e., flows in capillary–inertial regime and in inertial regime.     

Three-dimensional dynamic Green’s functions for a multilayered transversely isotropic half-space

With the aid of a method of displacement potentials, an efficient and accurate analytical derivation of the three-dimensional dynamic Green’s functions for a transversely isotropic multilayered half-space is presented. Constituted by proper algebraic factorizations, a set of generalized transmission–reflection matrices and internal source fields that are free of any numerically unstable exponential terms are proposed for effective computations of the potential solution. Three-dimensional point-load Green’s functions for stresses and displacements are given, for the first time, in the complex-plane line-integral representations. The present formulations and solutions are analytically in exact agreement with the existing solutions given by Pak and Guzina (2002) for the isotropic case. For the numerical computation of the integrals, a robust and effective methodology which gives the necessary account of the presence of singularities including branch points and poles on the path of integration is laid out. A comparison with the existing numerical solutions for multilayered isotropic half-space is made to confirm the accuracy of the numerical solutions.     

Key Word Index of Volume 36 – 2001

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Key Word Index of Volume 36 – 2001     

Covariants of the symmetric group and its analogs in Weyl algebras

Lomonosov State University, Moscow. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 24, No. 3, pp. 9–13, July–September, 1990.     

Stationary Problem of Radiative Heat Transfer with Cauchy Boundary Conditions

Computational Mathematics and Mathematical Physics - A stationary problem of radiative-conductive heat transfer in a three-dimensional domain is studied in the $${{P}_{1}}$$ -approximation of the...     

Field-induced phase transitions in magnetooptical films with a small positive anisotropy constant

We study phase transitions induced by a static magnetic field in magnetically uniaxial films with a small positive anisotropy constant. The phase diagram of these objects is determined in the H _∥-H _⊥ plane, where H _∥ and H _⊥ are, respectively, the components of the magnetizing field along and perpendicular to the surface normal. The stability boundary is located for all of the main types of domain configurations observed: a simple stripe domain structure, a stripe domain structure with periodic bending by surface distortions in the profile of the domain walls, and hexagonal lattices of cylindrical magnetic bubbles. Zh. éksp. Teor. Fiz. 111, 283–297 (January 1997)     

Luminescence of 4,7-diphenyl-1,10-phenanthroline forms bound in NAFION membrane

The fixation of 4,7-diphenyl-1,10-phenanthroline on walls of nanosized cavities of a Nafion perfluorosulfonic membrane was realized by two methods: by sorption of molecules on the sulfo groups of the membrane and by coordination attachment to previously grafted La³⁺ and Tb³⁺ cations. The bright luminescence of the molecule forms bound in the membrane is recorded at room temperature in the range of 400–500 nm.