Abstract:
A thermodynamic formulation for moving granular material is proposed. The fluctuations due to the constant flux and dissipation of energy are controlled in a `granular' ensemble by a pressure $\wp$ (`compression') which is conjugate to a contact volume (`contactopy'). The corresponding response function (`dissipativity') describes how dissipation increases with $\wp$ and should serve to identify the fluidization transition and 1/f noise. In the granular ensemble one can consider the granular medium as a gas of elastically colliding particles and define a ``granular'' temperature and other standard thermodynamic quantities. PACS: 05.70, 46.10

Abstract:
We study the phenomena associated with the low-velocity impact of two solid discs of equal size using a cell model of brittle solids. The fragment ejection exhibits a jet-like structure the direction of which depends on the impact parameter. We obtain the velocity and the mass distribution of the debris. Varying the radius and the initial velocity of the colliding particles, the velocity components of the fragments show anomalous scaling. The mass distribution follows a power law in the region of intermediate masses.

Abstract:
Recent experiments by Baxter et al. showed the existence of density waves in granular material flowing out of a hopper. We show, using Molecular Dynamics Simulations, that this effect is a consequence of static friction and find that these density fluctuations follow a $1/f$ spectrum. The effect is enhanced when the opening angle of the hopper decreases.

Abstract:
We present a simple model for the friction of two solid bodies moving against each other. In a self consistent way we can obtain the dependence of the macroscopic friction force as a function of the driving velocity, the normal force and the ruggedness of the surfaces in contact. Our results are discussed in the context of friction laws used in earthquake models.

Abstract:
We consider a two dimensional lattice model to describe the opening of a crack in hydraulic fracturing. In particular we consider that the material only breaks under tension and the fluid has no pressure drop inside the crack. For the case in which the material is completely homogeneous (no disorder) we present results for pressure and elastic energy as a function of time and compare our findings with some analytic results from continuum fracture mechanics. Then we investigate fracture processes in strongly heterogeneous cohesive environments. We determine the cummulative probability distribution for breaking events of a given energetical magnitude (acoustic emission). Further we estimate the probabilty distribution of emission free time intervals. %We present results for a scaling relation between the amount of %injected fluids, the crack pressures, the time dependent crack %extensions and the system sizes. Finally we determine the fractal dimension(s) of the cracks.

Abstract:
We present exact results for the contact forces in a three dimensional static piling of identical, stiff and frictionless spheres. The pile studied is a pyramid of equilateral triangular base (``stack of cannonballs'') with a FCC (face centered cubic) structure. We show in particular that, as for the two dimensional case, the pressure on the base of such a pile is uniform.

Abstract:
In many applications to biophysics and environmental engineering, sedimentation of non-spherical particles for example: ellipsoids, is an important problem. In our work, we simulate the dynamics of oblate ellipsoids under gravity. We study the settling velocity and the average orientation of the ellipsoids as a function of volume fraction. We see that the settling velocity shows a local maximum at the intermmediate densities unlike the spheres. The average orientation of the ellipsoids also shows a similar local maximum and we observe that this local maximum disappears as the Reynolds number is increased. Also, at small volume fractions, we observe that the oblate ellipsoids exhibit an orientational clustering effect in alignment with gravity accompanied by strong density fluctuations. The vertical and horizontal fluctuations of the oblate ellipsoids are small compared to that of the spheres.

Abstract:
We present calculations of forces for two dimensional static sandpile models. Using a symbolic calculation software we obtain exact results for several different orientations of the lattice and for different types of supporting surfaces. The model is simple, supposing spherical, identical, rigid particles on a regular triangular lattice, without friction and with unilateral spring-like contacts. Special attention is given to the stress tensor and pressure on the base of the pile. We show that orientation of the lattice and the characteristics of the supporting surface have a strong influence on the physical properties of the pile. Our results agree well with numerical simulations done on similar systems and show, in some specific cases, a dip i.e. a depression under the apex of the pile. We also estimate that the algorithm we have developed can be easily adapted to other configurations and models of granulates and can be used in other physical cases where piecewise linear systems are encountered.

Abstract:
The intruder segregation dependence on size and density is investigated in the framework of a hydrodynamic theoretical model for vibrated granular media. We propose a segregation mechanism based on the difference of densities between different regions of the granular system, which give origin to a buoyant force that acts on the intruder. From the analytic solution of the segregation velocity we can analyze the transition from the upward to downward intruder's movement.

Abstract:
We have numerically investigated a reaction-diffusion model for the hydration of calciumsulphate (gypsum). The simulations were conducted for two and three dimensional systems. While the dissolution of anhydrous gypsum is considered irreversible at a finite rate the precipitation/dissolution reaction for the calciumdihydrate is considered reversible. The latter reaction is assumed to be controlled by the dihydrate's equilibrium solubility {\em and} the abillity of the system to react on supersaturation only at a certain velocity described by the reaction rate constant of precipitation. For $d=2$ we find at early times an accelerated hydration period followed by a maximum and a decreasing hydration rate. For large times the ionic product of involved species assumes closely the value of the di-hydrate equilibrium solubility. Calculated model micro-structures exhibit typical features such as inner and outer hydrate products, induction and dormant period as well as bridging. Furthermore we find that the overall chemical reactivity as a function of initial anhydrous (volume) concentration $p$ exhibits a maximum close to the percolation point of the underlying lattice. Employing a rescaling procedure we find {\em two} percolation thresholds in $d=2$, $p_c^{min}=0.44\pm 0.015$ and $p_c^{max}=0.77\pm 0.02$, for the initial anhydrous gypsum concentration {\em between} which percolating dihydrate structures can be attained. For $d=3$ we find $p_c^{min}=0.10\pm 0.02$ and $p_c^{max}=0.95 \pm 0.02$.