Cooling dynamics of a dilute gas of inelastic rods: a many particle simulation

We present results of simulations for a dilute gas of inelastically colliding particles. Collisions are modelled as a stochastic process, which on average decreases the translational energy (cooling), but allows for fluctuations in the transfer of energy to internal vibrations. We show that these fluctuations are strong enough to suppress inelastic collapse. This allows us to study large systems for long times in the truely inelastic regime. During the cooling stage we observe complex cluster dynamics, as large clusters of particles form, collide and merge or dissolve. Typical clusters are found to survive long enough to establish local equilibrium within a cluster, but not among different clusters. We extend the model to include net dissipation of energy by damping of the internal vibrations. Inelatic collapse is avoided also in this case but in contrast to the conservative system the translational energy decays according to the mean field scaling law, E(t)\propto t^{-2}, for asymptotically long times.Comment: 10 pages, 12 figures, Latex; extended discussion, accepted for publication in Phys. Rev.

A microscopic 2D lattice model of dimer granular compaction with friction

We study by Monte Carlo simulation the compaction dynamics of hard dimers in 2D under the action of gravity, subjected to vertical and horizontal shaking, considering also the case in which a friction force acts for horizontal displacements of the dimers. These forces are modeled by introducing effective probabilities for all kinds of moves of the particles. We analyze the dynamics for different values of the time $\tau$ during which the shaking is applied to the system and for different intensities of the forces. It turns out that the density evolution in time follows a stretched exponential behavior if $\tau$ is not very large, while a power law tail develops for larger values of $\tau$. Moreover, in the absence of friction, a critical value $\tau^*$ exists which signals the crossover between two different regimes: for $\tau < \tau^*$ the asymptotic density scales with a power law of $\tau$, while for $\tau > \tau^*$ it reaches logarithmically a maximal saturation value. Such behavior smears out when a finite friction force is present. In this situation the dynamics is slower and lower asymptotic densities are attained. In particular, for significant friction forces, the final density decreases linearly with the friction coefficient. We also compare the frictionless single tap dynamics to the sequential tapping dynamics, observing in the latter case an inverse logarithmic behavior of the density evolution, as found in the experiments.Comment: 10 pages, 15 figures, to be published in Phys. Rev.

A model for collisions in granular gases

We propose a model for collisions between particles of a granular material and calculate the restitution coefficients for the normal and tangential motion as functions of the impact velocity from considerations of dissipative viscoelastic collisions. Existing models of impact with dissipation as well as the classical Hertz impact theory are included in the present model as special cases. We find that the type of collision (smooth, reflecting or sticky) is determined by the impact velocity and by the surface properties of the colliding grains. We observe a rather nontrivial dependence of the tangential restitution coefficient on the impact velocity.Comment: 11 pages, 2 figure

Metallo-cryptophanes decorated with Bis-N-heterocyclic carbene ligands: self-assembly and guest uptake into a nonporous crystalline lattice

Pd3L2 metallo-cryptophane cages with cyclotriveratrylene-type L ligands can be stabilized by use of a bis-N-heterocyclic carbene as an auxiliary cis-protecting ligand, while use of more common protecting chelating ligands such as ethylenediamine saw a Pd3L2 to Pd6L8 rearrangement occur in solution. The crystalline Pd3L2 complexes act as sponges, taking up 1,2-dichorobenzene or iodine in a single-crystal-to-single-crystal fashion despite not exhibiting conventional porosity

Cellular model for the compaction of a vertically tapped granular column

A cellular model for the compaction of granular material is described. It takes into account horizontal redistribution as well as vertical transfer of particles. Parameters are the width of the horizontal redistribution and the settling probability. Numerical simulations of the behaviour of a granular column in a container are shown as an example, and the evolution of some characteristic features over time has been followed for some typical configurations. Experimental results for the time evolution of the density can be reproduced for a settling probability proportional to the unoccupied spaces for particles in the lower cells

Streulichtmessanordnung zur Untersuchung der Oberflaechenrauheit

Scattered light measuring setup to analyze surface roughness based on the principle of angular-resolution scattered light measurement by means of one or several receiver arrays, characterized by the fact that the individual receivers of the arrays are arranged on curved supports in such a way that the geometric expansion of the individual receivers corresponds in each case to an equidistant interval within the local frequency range

Experimental study and numerical simulation of the vertical bounce of a polymer ball over a wide temperature range

The dependence to temperature of the rebound of a solid polymer ball on a rigid slab is investigated. An acrylate polymer ball is brought to a wide range of temperatures, covering its glass to rubbery transition, and let fall on a granite slab while the coe cient of restitution, duration of contact, and force history are measured experimentally. The ball fabrication is controlled in the lab, allowing the mechanical characterization of the material by classic dynamic mechanical analysis (DMA). Finite element simulations of the rebound at various temperatures are run, consider- ing the material as viscoelatic and as satisfying a WLF equation for its time-temperature superposition property. A comparison between the experiments and the simulations shows the strong link between viscoelasticity and time-temperature superposition properties of the material and the bounce characteristics of the ball