arXiv subjects
Publications and source records attributed to H. J. Herrmann.
We report experimental measurements of density waves in granular materials flowing down in a capillary tube. The density wave regime occurs at intermediate flow rates between a low density free fall regime and a high compactness slower flow.
We study the shape of the tail of a heap of granular material. A simple theoretical argument shows that the tail adds a logarithmic correction to the slope given by the angle of repose. This expression is in good agreement with experiments. We present a cellular automaton that contains gravity, dissipation and surface roughness and its simulation also gives the predicted shape.
Using 20 months of CPU time on our special purpose computer ``Percola'' we determined the exponent for the normal conductivity at the threshold of three-dimensional site and bond percolation. The extrapolation analysis taking into account the first correction to scaling gives a value of $t/ν= 2.26\pm 0.04$ and a correction exponent $ω$ around 1.4.
A simple growth model for DNA evolution is introduced which is analytically solvable and reproduces the observed statistical behavior of real sequences.
We propose a heterogeneous reaction-diffusion model for the hydration and setting of cement. The model is based on diffusional ion transport and on cement specific chemical dissolution/precipitation reactions under spatial heterogeneous solid/liquid conditions. We simulate the spatial and temporal evolution of precipitated micro structures starting from initial random configurations of anhydrous cement particles. Though the simulations have been performed for two dimensional systems, we are able to reproduce qualitatively basic features of the cement hydration problem. The proposed model is also applicable to general water/mineral systems.
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.
We present a numerical method to deal efficiently with large numbers of particles in incompressible fluids. The interactions between particles and fluid are taken into account by a physically motivated ansatz based on locally defined drag forces. We demonstrate the validity of our approach by performing numerical simulations of sedimenting non-Brownian spheres in two spatial dimensions and compare our results with experiments. Our method reproduces essential aspects of the experimental findings, in particular the strong anisotropy of the hydrodynamic bulk self-diffusivities.
We present various Lattice Boltzmann Models which reproduce the effects of rough walls, shear thinning and granular flow. We examine the boundary layers generated by the roughness of the walls. Shear thinning produces plug flow with a sharp density contrast at the boundaries. Density waves are spontaneously generated when the viscosity has a nonlinear dependence on density which characterizes granular flow.
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.
We investigate random lattices where the connectivities are determined by the Voronoi construction, while the location of the points are the dynamic degrees of freedom. The Voronoi random lattices with an associated energy are immersed in a heat bath and investigated using a Monte Carlo simulation algorithm. In thermodynamic equilibrium we measure coordination number distributions and test the Aboav-Weaire and Lewis laws.
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.
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