Machian Origin of the Entropic Gravity and Cosmic Acceleration

We discuss the emergence of relativistic effects in the Machian universe with a global preferred frame and use thermodynamic considerations to clarify the origin of gravity as an entropic force and the origin of dark energy/cosmic acceleration as related to the Hawking-Unruh temperature at the universe’s horizon.     

Information-Probabilistic Description of the Universe

We describe the universe as a single entangled ensemble of quantum particles. The total entropy of this world ensemble, which can be expressed as a sum of information, thermodynamic and entanglement components, is assumed to be always zero. This condition suggests information quantization, which we associate with the Planck’s action. Then the entropy neutrality condition for the universe leads to the zero-action principle. We show that the main concepts of classical space-time and gravity naturally emerge in this picture. A generalized least action principle, which embraces the maximal entropy principles of information theory, is introduced.     

Gravitational repulsion of spherical domain walls

We consider the disagreements in gravitational properties of planar and spherical domain walls (bubbles). We argue that if the spherical domain walls are described by the same equation of state as the planar walls are, then they also exhibit gravitational repulsion just as the planar walls are assumed to do. In the thin-wall approximation we show the existence of the solution of Einstein equations with negative gravitational mass of bubbles and the reversed direction of time flow on the shell. The equilibrium radius and critical mass of such objects are found for realistic models.     

The boundary value problems of the full coupled theory of poroelasticity for materials with double porosity

In this paper the full coupled quasi-static theory of poroelasticity for materials with double porosity is considered. The basic boundary value problems (BVPs) of the steady vibrations are investigated. The uniqueness theorems of the internal BVPs of steady vibrations are proved. The basic properties of elastopotentials are established. The existence of regular solutions of the BVPs by means of the boundary integral equations method and the theory of singular integral equations is proved. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fundamental solutions in the linear theory of consolidation for elastic solids with double porosity

This paper concerns the theory of consolidation for elastic solids with double porosity, and the governing fully coupled linear quasi-static equations are considered. The system of these equations is based on the equilibrium equations for a solid, conservation of fluid mass, the effective stress concept, and Darcy’s law for material with double porosity. Two levels of spatial cases of consolidation theory for a solid with double porosity are considered: equations of steady vibrations and equations of equilibrium. The fundamental solutions of these equations are constructed by means of elementary functions. Finally, the basic properties of these solutions are established.     

Boundary value problems in the theory of thermomicrostretch elastic solids

In this paper the linear theory of thermomicrostretch elastic solids is considered. The basic properties of wave numbers of the longitudinal and transverse plane waves are established.The existence of eigenfrequencies of the interior homogeneous boundary value problem (BVP) of steady oscillations is studied. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Boundary value problems in the theory of binary mixtures

In this paper, the boundary value problems of steady oscillation (vibration) of the linear theory of thermoelasticity for binary mixtures are investigated by means of the boundary integral equation method (potential method). The uniqueness and existence theorems of solutions of the exterior boundary value problems by means potential method and multidimensional singular integral equations are proved. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Plane Waves and Eigenfrequencies in the Linear Theory of Binary Mixtures of Thermoelastic Solids

In this paper some basic properties of wave numbers of the longitudinal and transverse plane waves are treated. The existence theorems of eigenfrequencies of the interior homogeneous boundary-value problems of steady oscillations of binary mixtures for thermoelastic solids are proved. The connection between plane waves and eigenfrequencies is established. This paper dedicated to my teacher Professor Mikheil Basheleishvili on the occasion of his 80th birthday.     

Uniqueness theorems in the theory of thermoelasticity for solids with double porosity

In this paper the coupled linear theory of thermoelasticity for solids with double porosity is considered. The governing system of field equations of this theory is based on motion equations, conservation of fluid mass, constitutive equations, extended Darcy’s law for materials with double porosity and Fourier’s law for heat conduction. A wide class of the basic internal and external boundary value problems (BVPs) of steady vibrations is formulated and uniqueness theorems for regular (classical) solutions of these BVPs are proved.     

Potential Method in the Linear Theory of Viscoelastic Materials with Voids

In the present paper the linear theory of viscoelasticity for Kelvin–Voigt materials with voids is considered and some basic results of the classical theory of elasticity are generalized. Indeed, the basic properties of plane harmonic waves are established. The explicit expression of fundamental solution of the system of equations of steady vibrations is constructed by means of elementary functions. The Green’s formulas in the considered theory are obtained. The uniqueness theorems of the internal and external basic boundary value problems (BVPs) are proved. The representation of Galerkin type solution is obtained and the completeness of this solution is established. The formulas of integral representations of Somigliana type of regular vector and regular (classical) solution are obtained. The Sommerfeld-Kupradze type radiation conditions are established. The basic properties of elastopotentials and singular integral operators are given. Finally, the existence theorems for classical solutions of the internal and external basic BVPs of steady vibrations are proved by using of the potential method (boundary integral method) and the theory of singular integral equations.