arXiv subjects

H. J. Herrmann

Publications and source records attributed to H. J. Herrmann.

At least 163 records · Page 9Linked to original sources

arXiv2004

Transport Phenomena and Structuring in Shear Flow of Suspensions near Solid Walls

In this paper we apply the lattice-Boltzmann method and an extension to particle suspensions as introduced by Ladd et al. to study transport phenomena and structuring effects of particles suspended in a fluid near sheared solid walls. We find that a particle free region arises near walls, which has a width depending on the shear rate and the particle concentration. The wall causes the formation of parallel particle layers at low concentrations, where the number of particles per layer decreases with increasing distance to the wall.

cond-mat.soft↗

arXiv2004

Multiple Invaded Consolidating Materials

We study a multiple invasion model to simulate corrosion or intrusion processes. Estimated values for the fractal dimension of the invaded region reveal that the critical exponents vary as function of the generation number $G$, i.e., with the number of times the invasion process takes place. The averaged mass $M$ of the invaded region decreases with a power-law as a function of $G$, $M\sim G^β$, where the exponent $β\approx 0.6$. We also find that the fractal dimension of the invaded cluster changes from $d_{1}=1.887\pm0.002$ to $d_{s}=1.217\pm0.005$. This result confirms that the multiple invasion process follows a continuous transition from one universality class (NTIP) to another (optimal path). In addition, we report extensive numerical simulations that indicate that the mass distribution of avalanches $P(S,L)$ has a power-law behavior and we find that the exponent $τ$ governing the power-law $P(S,L)\sim S^{-τ}$ changes continuously as a function of the parameter $G$. We propose a scaling law for the mass distribution of avalanches for different number of generations $G$.

cond-mat.dis-nn↗

arXiv2004

Indeterminacy, Memory, and Motion in a Simple Granular Packing

We apply two theoretical and two numerical methods to the problem of a disk placed in a groove and subjected to gravity and a torque. Methods assuming rigid particles are indeterminate -- certain combinations of forces cannot be calculated, but only constrained by inequalities. In methods assuming deformable particles, these combinations of forces are determined by the history of the packing. Thus indeterminacy in rigid particles becomes memory in deformable ones. Furthermore, the torque needed to rotate the particle was calculated. Two different paths to motion were identified. In the first, contact forces change slowly, and the indeterminacy decreases continuously to zero, and vanishes precisely at the onset of motion, and the torque needed to rotate the disk is independent of method and packing history. In the second way, this torque depends on method and on the history of the packing, and the forces jump discontinuously at the onset of motion.

cond-mat.other↗

arXiv2004

Break-up of shells under explosion and impact

A theoretical and experimental study of the fragmentation of closed thin shells made of a disordered brittle material is presented. Experiments were performed on brown and white hen egg-shells under two different loading conditions: fragmentation due to an impact with a hard wall and explosion by a combustion mixture giving rise to power law fragment size distributions. For the theoretical investigations a three-dimensional discrete element model of shells is constructed. Molecular dynamics simulations of the two loading cases resulted in power law fragment mass distributions in satisfactory agreement with experiments. Based on large scale simulations we give evidence that power law distributions arise due to an underlying phase transition which proved to be abrupt and continuous for explosion and impact, respectively. Our results demonstrate that the fragmentation of closed shells defines a universality class different from that of two- and three-dimensional bulk systems.

cond-mat.stat-mech↗

arXiv2004

Shakedown of unbound granular material

Compacted unbound granular materials are extensively used as sub-layer in pavement design. Most pavement design guides assume that they are responsible for the degradation and deformation of the roads and railways that they support. Biaxial tests are usually employed to investigate the elasto-plastic response of these materials to cyclic loading. A particularly interesting question is whether a limit load exists, below which the excitations shake down, in the sense that the material does not accumulate further deformations. We have carried out a detailed study of the elasto-plastic behavior of a simple model of unbound granular matter submitted to cyclic loading. The dissipated energy through out the simulation has been used for the characterization of the different regimes of responses.

cond-mat.mtrl-sci↗

arXiv2004

Investigation of the incremental response of soils using a discrete element model

The incremental stress-strain relation of dense packings of polygons is investigated here by using molecular dynamics simulations. The comparison of the simulation results to the continuous theories is performed using explicit expressions for the averaged stress and strain over a representative volume element. The discussion of the incremental response raises two important questions of soil deformation: Is the incrementally non-linear theory appropriate to describe the soil mechanical response? Does a purely elastic regime exists in the deformation of granular materials?. In both cases our answer will be "no". The question of stability is also discussed in terms of the Hill condition of stability for non-associated materials.

cond-mat.mtrl-sci↗

arXiv2004

The anisotropy of granular materials

The effect of the anisotropy on the elastoplastic response of two dimensional packed samples of polygons is investigated here, using molecular dynamics simulation. We show a correlation between fabric coefficients, characterizing the anisotropy of the granular skeleton, and the anisotropy of the elastic response. We also study the anisotropy induced by shearing on the subnetwork of the sliding contacts. This anisotropy provides an explanation to some features of the plastic deformation of granular media.

cond-mat.mtrl-sci↗

arXiv2004

Sedimentation of Oblate Ellipsoids at low and Moderate Reynolds numbers

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.

cond-mat.soft↗

arXiv2004

Scaling of the propagation of epidemics in a system of mobile agents

For a two-dimensional system of agents modeled by molecular dynamics, we simulate epidemics spreading, which was recently studied on complex networks. Our resulting network model is time-evolving. We study the transitions to spreading as function of density, temperature and infection time. In addition, we analyze the epidemic threshold associated to a power-law distribution of infection times.

cond-mat.stat-mech↗

arXiv2003

Space-filling bearings in three dimensions

We present the first space-filling bearing in three dimensions. It is shown that a packing which contains only loops with even number of spheres can be constructed in a self-similar way and that it can act as a three dimensional bearing in which spheres can rotate without slip and with negligible torsion friction.

cond-mat↗

arXiv2003

Ratcheting of granular materials

We investigate the quasi-static mechanical response of soils under cyclic loading using a discrete model of randomly generated convex polygons. This response exhibits a sequence of regimes, each one characterized by a linear accumulation of plastic deformation with the number of cycles. At the grain level, a quasi-periodic ratchet-like behavior is observed at the contacts, which excludes the existence of an elastic regime. The study of this slow dynamics allows to explore the role of friction in the permanent deformation of unbound granular materials supporting railroads and streets.

cond-mat↗

arXiv2003

Opinion Formation on a Deterministic Pseudo-fractal Network

The Sznajd model of socio-physics, that only a group of people sharing the same opinion can convince their neighbors, is applied to a scale-free random network modeled by a deterministic graph. We also study a model for elections based on the Sznajd model and the exponent obtained for the distribution of votes during the transient agrees with those obtained for real elections in Brazil and India. Our results are compared to those obtained using a Barabasi-Albert scale-free network.

cond-mat.stat-mech↗

arXiv2003

Segregation in a fluidized binary granular mixture: Competition between buoyancy and geometric forces

Starting from the hydrodynamic equations of binary granular mixtures, we derive an evolution equation for the relative velocity of the intruders, which is shown to be coupled to the inertia of the smaller particles. The onset of Brazil-nut segregation is explained as a competition between the buoyancy and geometric forces: the Archimedean buoyancy force, a buoyancy force due to the difference between the energies of two granular species, and two geometric forces, one compressive and the other-one tensile in nature, due to the size-difference. We show that inelastic dissipation strongly affects the phase diagram of the Brazil nut phenomenon and our model is able to explain the experimental results of Breu et al. (PRL, 2003, vol. 90, p. 01402).

cond-mat.soft↗

arXiv2002

A note on the upward and downward intruder segregation in granular media

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.

cond-mat.stat-mech↗

arXiv2002

A reaction-diffusion model for the hydration of calciumsulphate (gypsum) and microstructure percolation

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 $p_c^{max}=0.95 \pm 0.02$.

cond-mat.mtrl-sci↗

arXiv2002

Analysis of the elasto-plastic response of a polygonal packing

We investigate the constitutive response of two-dimensional packed samples of polygons using molecular dynamics simulation. The incremental elasto-plastic response is examined in the pre-failure regime. Besides the Young modulus and the Poisson ratio, an additional parameter must be included, which takes into account the anisotropy of the elastic response. The plastic deformations are described by the introduction of the yield and the flow directions. These directions do not agree, which reproduces the non-associated feature of realistic soils. In order to detect the yield surface, different loading-unloading-reloading tests were performed. During the reload path, it is found that the yielding develops continuously with the amplitude of loading, which does not allow to identify a purely elastic regime.

cond-mat↗

arXiv2002

Calculation of the incremental stress-strain relation of a polygonal packing

The constitutive relation of the quasi-static deformation on two dimensional packed samples of polygons is calculated using molecular dynamic simulations. The stress values at which the system remains stable are bounded by a failure surface, that shows a power law dependence on the pressure. Below the failure surface, non linear elasticity and plastic deformation are obtained, which are evaluated in the framework of the incremental linear theory. The results shows that the stiffness tensor can be directly related to the micro-contact rearrangements. The plasticity obeys a non-associated flow rule, with a plastic limit surface that does not agree with the failure surface.

cond-mat.mtrl-sci↗

arXiv2002

Modelling a Dune Field

We present a model to describe the collective motion of barchan dunes in a field. Our model is able to reproduce the observation that a typical dune stays confined within a stripe. We also obtain some of the pattern structures which ressemble those observed from aerial photos which we do analyse and compare with the specific field of Laâyounne.

cond-mat↗