We investigate the experimental limits of validity of the Stokes–Einstein equation. There is an important difference between diffusion and self-diffusion. The experimental evidences show, that in the case of selfdiffusion the product Dg/T is constant and the Stokes–Einstein equation is still valid. On the other hand, comparison of existing experimental data, on viscosity g and diffusion coeffic...

‎the notion of quasi-einstein metric in physics is equivalent to the notion of ricci soliton in riemannian spaces‎. ‎quasi-einstein metrics serve also as solution to the ricci flow equation‎. ‎here‎, ‎the riemannian metric is replaced by a hessian matrix derived from a finsler structure and a quasi-einstein finsler metric is defined‎. ‎in compact case‎, ‎it is proved that the quasi-einstein met...

We study the spectrum of the scalar Laplacian on the five-dimensional toric Sasaki-Einstein manifolds Y . The eigenvalue equation reduces to Heun’s equation, which is a Fuchsian equation with four regular singularities. We show that the ground states, which are given by constant solutions of Heun’s equation, are identified with BPS states corresponding to the chiral primary operators in the dua...

The quantum gravity is formulated based on gauge principle. The model discussed in this paper has local gravitational gauge symmetry and gravitational field is represented by gauge potential. A preliminary study on gravitational gauge group is presented. Path integral quantization of the theory is discussed in the paper. A strict proof on the renormalizability of the theory is also given. In le...

The system of two coupled Bose-Einstein condensates is mapped onto a uniaxial spin with an applied magnetic field. The mean-field interaction, the coupling and the asymmetry or the detuning correspond to the anisotropy, the transverse field, and the longitudinal field, respectively. A generalized Bloch equation is derived. In the low barrier limit for the quasi-spin model, the tunneling rate is...

Vacuum gravitational fields invariant for a bidimensional non Abelian Lie algebra of Killing fields, are explicitly described. They are parameterized either by solutions of a transcendental equation (the tortoise equation) or by solutions of a linear second order differential equation on the plane. Gravitational fields determined via the tortoise equation, are invariant for a 3-dimensional Lie ...

Extended Einstein-Maxwell model and its application to the problem of evolution of magnetized Bianchi-I Universe are considered. The evolution of medium magnetization is governed by a relaxation type extended constitutive equation. The series of exact solutions to the extended master equations is obtained and discussed. The anisotropic expansion of the Bianchi-I Universe is shown to become non-...

The antecedent of Einstein field equations with Euclidean signature is the complex elliptic Monge-Ampère equation, CMA2. For elliptic CMA2 solutions determine hyper-Kähler, self-dual and therefore Ricci-flat metrics with Euclidean signature. We shall consider a symmetry reduction of CMA2 to solutions that admit only a single Killing vector. Systematic studies of vacuum metrics with one Killing ...