The application of the Gaussian moment closure to micron-scale flows is considered. The mathematical formulation of the closure is reviewed as well as an extension to allow for diatomic gases and treatment for solid wall boundaries. A parallel upwind finite-volume scheme with adaptive mesh refinement (AMR) using Roe and HLLE-type flux functions is described for solving the hyperbolic system of ...

We derive a simple criterion for transverse instabilities along a general invariant manifold of a multidimensional dynamical system. The criterion requires an appropriately defined normal infinitesimal Lyapunov exponent (NILE) to be positive over regions of transverse instability on the manifold. Unlike classic Lyapunov-type numbers in the theory of normally hyperbolic invariant manifolds, the ...

We present a computer assisted proof or diffusion in the Planar Elliptic Restricted Three Body Problem. treat elliptic problem as perturbation of circular problem, where parameter is eccentricity primaries. The unperturbed system preserves energy, and we show that for sufficiently small perturbations have orbits with explicit energy changes, independent from size perturbation. result based on s...

In this paper we present a new kind of B-splines, called hyperbolic B-splines generated over the space spanned by hyperbolic functions and we use it to interpolate an arbitrary function on a set of points. Numerical tests for illustrating hyperbolic B-spline are presented.

Abstract A fully coupled high order discontinuous Galerkin (DG) solver for viscoelastic Oldroyd B fluid flow problems is presented. Contrary to known methods combining DG the discretization of convective terms material model with standard finite element (FEM) and using elastic viscous stress splitting (EVSS) its derivatives, a local (LDG) formulation first described hyperbolic convection‐diffus...

‎The aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]‎. ‎In [1]‎, ‎Ungar and Chen showed that the algebra of the group $SL(2,mathbb C)$ naturally leads to the notion of gyrogroups ‎and gyrovector spaces for dealing with the Lorentz group and its ‎underlying hyperbolic geometry‎. ‎They defined the Chen addition and then Chen model of hyperbolic geomet...

the aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]. in [1], ungar and chen showed that the algebra of the group sl(2,c) naturally leads to the notion of gyrogroups and gyrovector spaces for dealing with the lorentz group and its underlying hyperbolic geometry. they defined the chen addition and then chen model of hyperbolic geometry. in this paper,...

А new closed-loop solution for the coupled nonstationary problem of thermoelectric elasticity is designed a long piezoceramic radially polarized cylinder. The case load acting on its inner cylindrical surface considered as function temperature change at given law convection heat exchange outer face wall (boundary conditions conductivity 1st and 3rd types). Electrodynamic cylinder surfaces are c...

This paper concerns the structural stability of smooth cylindrically symmetric transonic flows in a concentric cylinder. Both cylindrical and axi-symmetric perturbations are considered. The governing system here is mixed elliptic–hyperbolic changes type suitable formulation boundary conditions at boundaries great importance. First, we establish existence uniqueness spiral solutions with nonzero...