cc sd - 0 00 00 57 7 ( v er si on 4 ) : 1 6 Ja n 20 04 Three - dimensional bubble clusters : shape , packing and growth - rate

cc sd - 0 00 83 03 4 , v er si on 1 - 2 9 Ju n 20 06 On symmetric sandpiles ∗

A symmetric version of the well-known SPM model for sandpiles is introduced. We prove that the new model has fixed point dynamics. Although there might be several fixed points, a precise description of the fixed points is given. Moreover, we provide a simple closed formula for counting the number of fixed points originated by initial conditions made of a single column of grains.

ar X iv : 0 80 1 . 25 00 v 1 [ co nd - m at . o th er ] 1 6 Ja n 20 08 Making , probing and understanding ultracold Fermi

Regular three-dimensional bubble clusters: shape, packing and growth-rate

We consider three-dimensional clusters of equal-volume bubbles packed around a central bubble and calculate their energy and optimal shape. We obtain the surface area and bubble pressures to improve on existing growth laws for three-dimensional bubble clusters. We discuss the possible number of bubbles that can be packed around a central one: the “kissing problem”, here adapted to deformable ob...

cc sd - 0 00 87 28 5 , v er si on 1 - 2 1 Ju l 2 00 6 FAST ALGORITHMS FOR COMPUTING THE BOLTZMANN COLLISION OPERATOR

The development of accurate and fast numerical schemes for the five fold Boltzmann collision integral represents a challenging problem in scientific computing. For a particular class of interactions, including the so-called hard spheres model in dimension three, we are able to derive spectral methods that can be evaluated through fast algorithms. These algorithms are based on a suitable represe...

cc sd - 0 00 22 70 4 , v er si on 1 - 1 3 A pr 2 00 6 Time - Changed Bessel Processes and Credit Risk ∗ Marc

The Constant Elasticity of Variance (CEV) model is mathematically presented and then used in a Credit-Equity hybrid framework. Next, we propose extensions to the CEV model with default: firstly by adding a stochastic volatility diffusion uncorrelated from the stock price process, then by more generally time changing Bessel processes and finally by correlating stochastic volatility moves to the ...