We develop a general formalism for the construction of (supersymmetric) gauge theories of volume-preserving diffeomorphisms (SDiff), focusing on the D = 3 superconformal SDiff3 invariant ‘BLG’ theory describing a condensate of M2-branes. 1 igor [email protected]; supported by the Basque Science Foundation Ikerbasque. 2 [email protected]

We consider the effect of noise on the dynamics generated by volume-preserving maps on a d-dimensional torus. The quantity we use to measure the irreversibility of the dynamics is the dissipation time. We focus on the asymptotic behaviour of this time in the limit of small noise. We derive universal lower and upper bounds for the dissipation time in terms of various properties of the map and it...

This paper presents an efficient and novel geometric flow-driven method for mesh optimization of segmented tetrahedral meshes with non-manifold boundary surfaces. The presented method is composed of geometric optimization and topological transformation techniques, so that both location and topology of vertices are optimized. Non-manifold boundary can be divided into manifold surface patches hav...

Let Fd be the collection of all d-dimensional probability distribution functions on [0, 1]d, d ≥ 2. The metric entropy of Fd under the L2([0, 1]d) norm is studied. The exact rate is obtained for d = 1, 2 and bounds are given for d > 3. Connections with small deviation probability for Brownian sheets under the sup-norm are established.

We present a straightforward, yet effective approach to volume-preserving mesh skinning. After each skinned mesh deformation, a volume correction is applied which moves the vertices along an automatically constructed displacement field. The volume correction is exact and is computed directly by a closed-form solution. The animator can control the volume correction interactively to achieve custo...

In this work, we consider the Lie's method of infinitesimal transformation groups and discrete symmetries method for Burgers equation with time dependent flux at the origin. Following the Lie's method of infinitesimal transformation groups we determine the symmetry reductions and similarity solutions of the governing equation. By applying discrete symmetries analysis we have obtained three grou...

Let φt be a three dimensional contact Anosov flow. Then we prove that its cohomological pressure coincides with its metric entropy if and only if φt is C ∞ flow equivalent to a special time change of a three dimensional algebraic contact Anosov flow.

Let T be a measure-preserving transformation acting on a probability space (a, Sr, P). This T induces a linear isometry V on &(a, F, P) defined by V(f) = f o T. The analysis of T by using properties of V is referred to as spectral analysis. It is often profitable to consider the action of V on certain closed linear invariant subspaces 9 of L,(O, ST, P). In this note we make the following assump...

In a recent paper [1], the authors suggest a novel Riemannian framework for comparing shapes. In this framework, a simple closed surface is represented by a field of metric tensors and curvatures. A product Riemannian metric is developed based on the L norm on symmetric positive definite matrices and scalar fields. Taken as a quotient space under the group of volume-preserving diffeomorphisms, ...

The metric entropy of absolute convex hulls of sets in Hilbert spaces is studied for the general case when the metric entropy of the sets is arbitrary. Under some regularity assumptions, the results are sharp.