In a continuum approach to the simulation of granular materials self intersection between particles becomes an issue. Even with a solution to incompressible flow, the incompressibility constraint won’t prevent particles from intersecting each other. The unilateral incompressibility constraint [1] provides a constraint to prevent most of these self-intersections that are visually obvious and can...

Finding the shortest vector of a lattice is one of the most important problems in computational lattice theory. For a random lattice, one can estimate the length of the shortest vector using the Gaussian heuristic. However, no rigorous proof can be provided for some classes of lattices, as the Gaussian heuristic may not hold for them. In this paper, we propose a general method to estimate lower...

In parameterized complexity each problem instance comes with a parameter k, and a parameterized problem is said to admit a polynomial kernel if there are polynomial time preprocessing rules that reduce the input instance to an instance with size polynomial in k. Many problems have been shown to admit polynomial kernels, but it is only recently that a framework for showing the non-existence of p...

The saturation properties of neutron-rich matter are investigated in a relativistic mean-field formalism using two accurately calibrated models: NL3 and FSUGold. The saturation properties—density, binding energy per nucleon, and incompressibility coefficient—are calculated as a function of the neutron-proton asymmetry α ≡ (N − Z)/A to all orders in α. Good agreement (at the 10% level or better)...

Simulations of biomembranes have gained an increasing interest in the past years. Specifities of these membranes propose new challenges for the numerics. In particular, vesicle dynamics are governed by bending forces as well as a surface incompressibility constraint. A method to compute the bending force density resultant onto piecewise linearly triangulated surface meshes is described. This me...

We develop a parallel computational algorithm for simulating models of gel dynamics where the gel is described by two phases, a networked polymer and a fluid solvent. The models consist of transport equations for the two phases, two coupled momentum equations, and a volumeaveraged incompressibility constraint. Multigrid with Vanka-type box relaxation scheme is used as preconditioner for the Kry...