Symmetric Volume Maps: Order-invariant Volumetric Mesh Correspondence with Free Boundary

Volume-preserving maps with an invariant.

Several families of volume-preserving maps on R(3) that have an integral are constructed using techniques due to Suris. We study the dynamics of these maps as the topology of the two-dimensional level sets of the invariant changes. (c) 2002 American Institute of Physics.

Compact combinatorial maps: A volume mesh data structure

We propose a compact data structure for volumetric meshes of arbitrary topology and bounded valence that offers cell-face, face-edge, and edge-vertex incidence queries in constant time. Our structure is simple to implement, easy to use, and allows for arbitrary, user-defined 3-cells such as prisms and hexahedra, while remaining very efficient in memory usage compared to previous work. Its time ...

A New Type of Free Boundary Problem with Volume Constraint

We consider a free boundary problem arising from a polymer dispersed Liquid Crystal model. This variational problem can be viewed as a coupling between harmonic mappings into manifold and area minimization with given volume. In this paper, the existence of the solution together with some regularity and partial regularity results are presented.

Quadratic Volume-Preserving Maps: Invariant Circles and Bifurcations

We study the dynamics of the five-parameter quadratic family of volume-preserving diffeomorphisms of R. This family is the unfolded normal form for a bifurcation of a fixed point with a triple-one multiplier and is also the general form of a quadratic three-dimensional map with a quadratic inverse. Much of the nontrivial dynamics of this map occurs when its two fixed points are saddle-foci with...

On the Rate of the Volume Growth for Symmetric Viscous Heat-conductinggas Flows with a Free Boundary