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Efficient Collision Detection for MD-Simulations

The most time consuming part in molecular dynamics simulations is the collision detection. Usually, this problem is solved by restricting theshape of the particles to spheres. I will present an algorithm, originally developed for virtual reality visualizations by D.Baraff and M.C.Lin, that enables us to use complex polyhedra  (up to 920 faces and more). The expected run time is  O(N), where N is the number of particles in the simulation. Neither complexity nor shape of the particles affect the run time.

Dynamics of a Sliding Particle in a Rotating DrumPrimary tabs

The motion of a sliding particle, influenced by friction, in a rotating drum is investigated. A differential equation is formulated for general friction laws. Assuming a constant coefficient of friction, the equation is exactly solvable. For a velocity dependent coefficient of friction, perturbation methods may be used. The nonperturbed system is solved and with the help of the averaging method, the perturbed system can be examined for periodic motions.

Pressure Distribution and stresses under granular heaps with the Distinct Element Method

We investigate the stresses and pressures under a 2-dimensional heap using a simulation of convex polygonal particles. Former Experiments and simulations on granular cones strongly suggest that for cones no generic pressure distribution exists but that the pressure and stress distribution is highly sensitive to the size distribution of the grains and the building history of the heap.

Shared Memory Parallelization for Molecular Dynamics Simulations of Non-spherical Granular Materials

The problem of granular materials is not alone a problem of material properties, but also a problem of structures. To examine these  interesting systems, one uses molecular dynamics simulations. The objective of the work presented here was to have a program which can run on cheap high-end shared memory workstations. Therefore we have developed  a fast thread-based simulation of polygonal particles.

Stress in Static Sandpiles

We are interested in the stress distribution in static granular matter. Experiments have found a minimum of the vertical normal stress beneath the apex of a sandpile. Because of the indeterminacy of static friction force even in the simplest sandpile and the ensuing absence of a constitutive relation between stress and strain (Hooke's law) there is no closed set of equations. Continuum theories, trying to describe the dip, have to make assumptions on the existence of constitutive relations among the components of the stress tensor itself.

Rotation and Reptation

In order to understand the peculiar behavior of granular matter, it is oftenelucidating to observe the physics of only a few grains. We present twosetups which fall into this class: The motion of a single particle in arotating drum, and the collective behavior of a few particles under theinfluence of a swirling motion.

Insertion Sort and Closest Features

I want to introduce two algorithms, useful for fast collision detection in granular medium simulations. We all know that the  most time consuming part in molecular dynamics simulations is the collision detection. Usually, this problem can be solved by restricting the shape of the particles to spheres. But if you want to use arbitrary convex polygons you need faster algorithms.

At first, a little bit of philosophy:

Stress in Static Sandpiles

We are interested in the stress distribution in static granular matter. Experiments have found a minimum of the vertical normal stress beneath the apex of a sandpile.

Because of the indeterminacy of static friction force even in the simplest sandpile and the ensuing absence of a constitutive relation between stress and strain (Hooke's law) there is no closed set of equations. Continuum theories, trying to describe the "dip", have to make assumptions on the existence of constitutive relations among the components of the stress tensor itself.

Data Mining – Detection and isolation of events using transformations

There is a variety of tools to filter packets from a network. One of the most popular ones is the Berkeley Packet Filter (BPF). All such filters are based on static descriptions, e.g., fixed source ports or fixed subnets of IP addresses. These methods work well for most types of network traffic, but there are cases in which a wider variety of applications may be appropriate. In this paper we will introduce a new analysis tool which will allow us to do a time-dependent analysis.

Influence of the geometry on the pressure distribution of granular heaps

We investigate the effect of the geometry of granular heaps on the pressure distribution. For given pressure distributions under cones we compute the pressuredistribution under wedges using linear superposition. For cones with a pressure minimum, the pressure minimum for the corresponding wedge vanishes. Comparisons with experimental data gives good qualitative aggreement, but the total pressure is overestimated.

Towards a micromechanic understanding of the pressure distribution under heaps

The pressure distribution under heaps has found to be dependent on the builing hostory of the heap both in experiments and simulations. Up to now, theoretical models and analysis assume that the packing of the heap is homogeneous. We show new experimental and simulational results which indicate that the packing is inhomogeneous and that this packing property is likley causing the pressure minimum under the heap.

Elastic material properties of sand piles of soft convex poly-gonal particles

We investigate the effective material properties of sand piles of soft convex polygonal particles numerically using the discrete element method (DEM). We first construct two types of sand piles by two different procedures. We then measure averaged stress and strain, thelatter via imposing a 10% reduction of gravity, as well as the fabric tensor. Furthermore, we compare the vertical normal strain tensor between sand piles qualitatively and show how the construction history of the piles affects their strain distribution as well as the stress distribution.

Micro and macro aspects of the elastoplastic behaviour of sand pilesPrimary tabs

We use a discrete element method to simulate the dynamics of granulates made up from arbitrarily shaped particles. Static and dynamic friction are accounted for in our force laws, which enables us to simulate the relaxation of (two-dimensional) sand piles to their final static state. Depending on the growth history, a dip in the pressure under a heap may or may not appear. Properties of the relaxed state are measured and averaged numerically to obtain the values of field quantitities pertinent for a continuum description.

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