The gradient-flow dynamics of an arbitrary geometric quantity is derived using a generalization of Darcy’s Law. We consider flows in both Lagrangian and Eulerian formulations. The Lagrangian formulation includes a dissipative modification of fluid mechanics. Eulerian equations for self-organization of scalars, 1-forms and 2-forms are shown to reduce to nonlocal characteristic equations. We iden...

An important part of the Arbitrary Lagrangian-Eulerian method is the rezoning or mesh improvement step after completion of the Lagrangian step where the mesh is deformed according to the flow. A procedure is presented here to optimize the quality of elements in 3D solid meshes by node repositioning. The procedure aims to improve the quality of boundary mesh faces and interior mesh regions while...

The 1–loop effective Lagrangian for a massive scalar field on an arbitrary causality violating spacetime is calculated using the methods of Euclidean quantum field theory in curved spacetime. Fields of spin 12 , spin 1 and twisted field configurations are also considered. In general, we find that the Lagrangian diverges to minus infinity at each of the nth polarised hypersurfaces of the spaceti...

This paper deals with the extension to the cylindrical geometry of the recently introduced Reconnection algorithm for Arbitrary-Lagrangian-Eulerian (ReALE) framework. The main elements in standard ALE methods are an explicit Lagrangian phase, a rezoning phase, and a remapping phase. Usually the new mesh provided by the rezone phase is obtained by moving grid nodes without changing connectivity ...

W present a new adaptive reconnection-based arbitrary Lagrangian Eulerian: A-ReALE method. The main elements in a A-ReALE method are: An explicit Lagrangian phase on arbitrary polygonal mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined number of mesh cells, their location and connectivity (it is based on using Voronoi tessellatio...

preprint numerics no. 3/2008 norwegian university of science and technology trondheim, norway We present a new method for tracking an interface immersed in a given velocity field. The method is particularly relevant to the simulation of unsteady free surface problems using the arbitrary Lagrangian-Eulerian (ALE) framework. The new method has been constructed with two goals in mind: (i) to be ab...

Lagrangian codes with mesh moving with the fluid suffer in many cases by mesh distortion leading to tangled mesh which in principle stops the computation as basic assumptions of the numerical method as e.g. positive volume of cells are not valid any more. Arbitrary LagrangianEulerian (ALE) method overcomes this difficulty by untangling or smoothing the mesh and conservative remapping of conserv...

Title of dissertation: CAPTURING MICRO-EMULSIONS AND MICRO-FOAMS WITH THE ARBITRARY LAGRANGIAN EULERIAN METHOD Andrew Brandon, Doctor of Philosophy, 2015 Dissertation directed by: Professor Konstantina Trivisa Department of Mathematics The goal of this work is to develop a 2D, heterogenous model for the purpose of studying liquid drainage from micro-foams and micro-emulsions. Liquid drainage wi...

We propose a superfield formalism of Lagrangian BRST–antiBRST quantization of arbitrary gauge theories in general coordinates with the base manifold of fields and antifields described in terms of both bosonic and fermionic variables.

It is shown that the phase space path integral for a system with arbitrary second class constraints (primary, secondary ...) can be rewritten as a configuration space path integral of the exponent of the Lagrangian action with some local measure.