External boundary value problems of steady vibrations in the theory of rigid bodies with a double porosity structure

This paper concerns with the linear 3D theory of rigid solids with a double porosity structure. Basic external boundary value problems (BVPs) of steady vibrations are formulated. The uniqueness and existence theorems for regular (classical) solutions of these BVPs are established. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dark matter in the framework of the shell-universe

We show that the shell-universe model (used to explain the observed expansion rate of the universe without a dark energy component) provides a natural mechanism for local increasing of the brane tension leading to the modified Newtons law alternative to galactic dark matter.     

Black Hole Information Problem and Wave Bursts

By reexamination of the boundary conditions of wave equation on a black hole horizon it is found not harmonic, but real-valued exponentially time-dependent solutions. This means that quantum particles probably do not cross the Schwarzschild horizon, but are absorbed and some are reflected by it, what potentially can solve the famous black hole information paradox. To study this strong gravitational lensing we are introducing an effective negative cosmological constant between the Schwarzschild and photon spheres. It is shown that the reflected particles can obtain their additional energy in this effective AdS space and could explain properties of some unusually strong signals, like LIGO events, gamma ray and fast radio bursts.     

New class of N-dimensional braneworlds

The new class of the non-stationary solutions to the system of N-dimensional equations for coupled gravitational and massless scalar field is found. The model represents a single (N-1)-brane in a space-time with one large (infinite) and (N-5) small (compact) space-like extra dimensions. In some particular cases the model corresponds to the gravitational and scalar field standing waves bounded by the brane. These braneworlds can be relevant in string and other higher dimensional models.     

Plane waves and vibrations in the theory of micropolar thermoelasticity for materials with voids

The present paper concerns with the linear theory of micropolar thermoelasticity for materials with voids. Some basic properties of wave numbers of the longitudinal and transverse plane harmonic waves are treated. The existence theorems of non-trivial solutions and eigenfrequencies of the interior homogeneous boundary value problems of steady vibrations are proved. The connection between plane harmonic waves and eigenfrequencies of the aforementioned problems is established.     

Fundamental Solution of the System of Equations of Steady Oscillations in the Theory of Fluid-Saturated Porous Media

In the present paper the linear theory of the liquid-saturated porous medium consisting of a microscopically incompressible solid skeleton containing microscopically incompressible liquid is considered. The fundamental solution of the system of linear coupled partial differential equations of the steady oscillations of the porous solids is constructed in terms of elementary functions and some basic properties are established.     

Boundary value problems in the theory of thermoporoelasticity for materials with double porosity

In this paper the linear quasi-static theory of thermoelasticity for solids with double porosity is considered. The system of equations of this theory is based on the equilibrium equations for solids with double porosity, conservation of fluid mass, constitutive equations, Darcy's law for materials with double porosity and Fourier's law for heat conduction. The basic internal and external boundary value problems (BVPs) of steady vibrations are formulated. The uniqueness and existence theorems for classical solutions of the above mentioned BVPs are proved by means of the potential method (boundary integral equation method) and the theory of singular integral equations. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Coriolis force and Sagnac effect

The optical Sagnac effect is considered, when the fictitious gravitational field simulates the reflections from the mirrors. It is shown that no contradiction exists between the conclusions of the laboratory and rotated observers. Because of the acting of a gravity-like Coriolis force, the trajectories of coand anti-rotating photons have different radii in the rotating reference frame, while in the case of equal radii the effective gravitational potentials for the photons have to be different.     

Localization of gauge bosons in the 5D standing wave braneworld

We investigate the problem of localization of gauge fields within the 5D standing wave braneworld model and show that in the case of increasing warp factor there exist normalizable vector field zero modes on the brane.