The kinetic theory of gases implies an independent evolution equation for the momentum flux tensor that closely resembles an evolution equation for the elastic stress in continuum descriptions of viscoelastic liquids. However, kinetic theory leads to a non-objective convected derivative for the evolution of the deviatoric stress, and a fixed relation between the stress relaxation rate and the v...

We consider general torsion components in three-dimensional Einstein-Cartan gravity, providing a geometrical interpretation for matter, and find new solutions of the corresponding equations Riemann curvature torsion. These geometries involve peculiar interplay between vector $(\beta_i)$ singlet $(\tau)$ irreducible which, under conditions, feature formal analogy with equation Beltrami fluid. In...

It is proved that the action for nonlinear Beltrami equation (quasi-classical ¯ ∂-problem) evaluated on its solution gives a τ-function for dis-persionless KP hierarchy. Infinitesimal transformations of τ-function corresponding to variations of ¯ ∂-data are found. Determinant equations for the function generating these transformations are derived. They represent a dispersionless analogue of sin...

We report on a new general class of solutions of the Beltrami equation, with special characteristics. We also provide examples of solutions that also satisfy Maxwell equations. A subset of these solutions can be isolated which corresponds to " gauge " fields. A special projective geometry of vacuum fields is also revealed and discussed. 1. Introduction The notion of a force-free field comes dir...

A numerical method for quasiconformal mapping of doubly connected domains onto annuli is presented. The ratio R of the radii of the annulus is not known a priori and is determined as part of the solution procedure. The numerical method presented in this paper requires solving iteratively a sequence of inhomogeneous Beltrami equations, each for a diierent R. R is updated using a procedure based ...

We develop on estimation method, for the derivative field of an image based on Bayesian approach which is formulated in a geometric way. The Maximum probability configuration of the derivative field is found by a gradient descent method which leads to a non-linear diffusion type equation with added constraints. The derivatives are assumed to be piecewise smoothe and the Beltrami framework is us...

In this paper, the Neumann boundary value problem for Beltrami operator is explicitly solved in a circular ring domain, solvability conditions are also given explicit forms. Moreover, second-order operators with Bitsadze/Laplace as main part combinations of Cauchy-Riemann and investigated.