this article concerned on the study of signature submanifolds for curves under lie group actions se(2), sa(2) and for surfaces under se(3). signature submanifold is a regular submanifold which its coordinate components are dierential invariants of an associated manifold under lie group action, and therefore signature submanifold is a key for solving equivalence problems.

In this paper, solutions of one-phase direct and inverse Stefan problems are presented. The direct problem consists in a calculation of temperature distribution and of a function which describes the position of the moving interface, whilst the inverse problem consists in a calculation of temperature distribution as well as in the reconstruction of the function which describes the temperature di...

a fundamental topic in computational fluid dynamics is the role of coordinate particularly for searching optimized coordinates. the objective of this study is the numerical modeling of supersonic flows using a new coordinate system i.e. unified coordinate system (ucs) uses moving mesh with motionless viewing window technique. ucs has an advantage over traditional coordinate systems (eulerian an...

The aim of this paper is to show the global existence of weak solutions for a moving boundary problem arising in the non-isothermal crystallization of polymers. The main features of our works are (i) the moving interface is shown to be of co-dimension one; (ii)finite Hölder continuous propagation speed yields an intrinsic estimate of finite co-dimension one Hausdorff measure of the moving inter...

<p style='text-indent:20px;'>In this article, we develop a new mixed immersed finite element discretization for two-dimensional unsteady Stokes interface problems with unfitted meshes. The proposed IFE spaces use conforming linear elements one velocity component and non-conforming the other component. pressure is approximated by piecewise constant. Unisolvency, among fundamental propertie...

Abstract. Using method of matched asymptotic expansions, we derive the sharp interface limit for the diffusive interface model with the generalized Navier boundary condition recently proposed by Qian, Wang and Sheng in [9, 11] for the moving contact line problem. We show that the leading order problem satisfies a boundary value problem for a coupled Hale-Shaw and Navier-Stokes equations with th...

A diffuse interface method is used to simulate two-phase flows with moving contact lines in 3D. The specific numerical issue is the validation of the method regarding the dynamics of moving contact lines in 3D. In particular, we aim to use the method to extend previous (2D and/or creeping-flow) work on sheardriven motion of a droplet on a wall to the full 3D problem, accounting for inertial eff...

Abstract. We study a moving boundary value problem consisting of a viscous incompressible fluid moving and interacting with a nonlinear elastic shell. The fluid motion is governed by the Navier-Stokes equations, while the shell is modeled by the nonlinear St. Venant-Kirchhoff constitutive law, and they are coupled together by continuity of displacement and traction (stress) along the moving mat...

Abstract. We study a moving boundary value problem consisting of a viscous incompressible fluid moving and interacting with a nonlinear elastic solid shell. The fluid motion is governed by the Navier-Stokes equations, while the shell is modeled by the nonlinear Koiter shell model, consisting of both bending and membrane tractions. The fluid is coupled to the solid shell through continuity of di...

We study a moving boundary value problem consisting of a viscous incompressible fluid moving and interacting with a nonlinear elastic solid shell. The fluid motion is governed by the Navier–Stokes equations, while the shell is modeled by the nonlinear Koiter shell model, consisting of bending and membrane tractions as well as inertia. The fluid is coupled to the solid shell through continuity o...