arXiv subjects

Hans J. Herrmann

Publications and source records attributed to Hans J. Herrmann.

At least 163 records · Page 9Linked to original sources

arXiv2007

Numerical Improvement of the Discrete Element Method applied to Shear of Granular Media

We present a detailed analysis of the bounds on the integration step in Discrete Element Method (DEM) for simulating collisions and shearing of granular assemblies. We show that, in the numerical scheme, the upper limit for the integration step, usually taken from the average time $t_c$ of one contact, is in fact not sufficiently small to guarantee numerical convergence of the system during relaxation. In particular, we study in detail how the kinetic energy decays during the relaxation stage and compute the correct upper limits for the integration step, which are significantly smaller than the ones commonly used. In addition, we introduce an alternative approach, based on simple relations to compute the frictional forces, that converges even for integration steps above the upper limit.

cond-mat.mtrl-sci↗

arXiv2007

Spreading gossip in social networks

We study a simple model of information propagation in social networks, where two quantities are introduced: the spread factor, which measures the average maximal fraction of neighbors of a given node that interchange information among each other, and the spreading time needed for the information to reach such fraction of nodes. When the information refers to a particular node at which both quantities are measured, the model can be taken as a model for gossip propagation. In this context, we apply the model to real empirical networks of social acquaintances and compare the underlying spreading dynamics with different types of scale-free and small-world networks. We find that the number of friendship connections strongly influences the probability of being gossiped. Finally, we discuss how the spread factor is able to be applied to other situations.

physics.soc-ph↗

arXiv2007

Minimal size of a barchan dune

Barchans are dunes of high mobility which have a crescent shape and propagate under conditions of unidirectional wind. However, sand dunes only appear above a critical size, which scales with the saturation distance of the sand flux [P. Hersen, S. Douady, and B. Andreotti, Phys. Rev. Lett. {\bf{89,}} 264301 (2002); B. Andreotti, P. Claudin, and S. Douady, Eur. Phys. J. B {\bf{28,}} 321 (2002); G. Sauermann, K. Kroy, and H. J. Herrmann, Phys. Rev. E {\bf{64,}} 31305 (2001)]. It has been suggested by P. Hersen, S. Douady, and B. Andreotti, Phys. Rev. Lett. {\bf{89,}} 264301 (2002) that this flux fetch distance is itself constant. Indeed, this could not explain the proto size of barchan dunes, which often occur in coastal areas of high litoral drift, and the scale of dunes on Mars. In the present work, we show from three dimensional calculations of sand transport that the size and the shape of the minimal barchan dune depend on the wind friction speed and the sand flux on the area between dunes in a field. Our results explain the common appearance of barchans a few tens of centimeter high which are observed along coasts. Furthermore, we find that the rate at which grains enter saltation on Mars is one order of magnitude higher than on Earth, and is relevant to correctly obtain the minimal dune size on Mars.

cond-mat.other↗

arXiv2007

Saltation transport on Mars

We present the first calculation of saltation transport and dune formation on Mars and compare it to real dunes. We find that the rate at which grains are entrained into saltation on Mars is one order of magnitude higher than on Earth. With this fundamental novel ingredient, we reproduce the size and different shapes of Mars dunes, and give an estimate for the wind velocity on Mars.

cond-mat.other↗

arXiv2007

Dune formation on the present Mars

We apply a model for sand dunes to calculate formation of dunes on Mars under the present Martian atmospheric conditions. We find that different dune shapes as those imaged by Mars Global Surveyor could have been formed by the action of sand-moving winds occuring on today's Mars. Our calculations show, however, that Martian dunes could be only formed due to the higher efficiency of Martian winds in carrying grains into saltation. The model equations are solved to study saltation transport under different atmospheric conditions valid for Mars. We obtain an estimate for the wind speed and migration velocity of barchan dunes at different places on Mars. From comparison with the shape of bimodal sand dunes, we find an estimate for the timescale of the changes in Martian wind regimes.

cond-mat.other↗

arXiv2007

A Stability Diagram for Dense Suspensions of Model Colloidal Al2O3-Particles in Shear Flow

In Al2O3 suspensions, depending on the experimental conditions very different microstructures can be found, comprising fluid like suspensions, a repulsive structure, and a clustered microstructure. For technical processing in ceramics, the knowledge of the microstructure is of importance, since it essentially determines the stability of a workpiece to be produced. To enlighten this topic, we investigate these suspensions under shear by means of simulations. We observe cluster formation on two different length scales: the distance of nearest neighbors and on the length scale of the system size. We find that the clustering behavior does not depend on the length scale of observation. If inter-particle interactions are not attractive the particles form layers in the shear flow. The results are summarized in a stability diagram.

cond-mat.soft↗

arXiv2007

The Strange Man in Random Networks of Automata

We have performed computer simulations of Kauffman's automata on several graphs such as the regular square lattice and invasion percolation clusters in order to investigate phase transitions, radial distributions of the mean total damage (dynamical exponent $z$) and propagation speeds of the damage when one adds a damaging agent, nicknamed "strange man". Despite the increase in the damaging efficiency, we have not observed any appreciable change at the transition threshold to chaos neither for the short-range nor for the small-world case on the square lattices when the strange man is added in comparison to when small initial damages are inserted in the system. The propagation speed of the damage cloud until touching the border of the system in both cases obeys a power law with a critical exponent $α$ that strongly depends on the lattice. Particularly, we have ckecked the damage spreading when some connections are removed on the square lattice and when one considers special invasion percolation clusters (high boundary-saturation clusters). It is seen that the propagation speed in these systems is quite sensible to the degree of dilution.

cond-mat.dis-nn↗

arXiv2007

Analytical approach to directed sandpile models on the Apollonian network

We investigate a set of directed sandpile models on the Apollonian network, which are inspired on the work by Dhar and Ramaswamy (PRL \textbf{63}, 1659 (1989)) for Euclidian lattices. They are characterized by a single parameter $q$, that restricts the number of neighbors receiving grains from a toppling node. Due to the geometry of the network, two and three point correlation functions are amenable to exact treatment, leading to analytical results for the avalanche distributions in the limit of an infinite system, for $q=1,2$. The exact recurrence expressions for the correlation functions are numerically iterated to obtain results for finite size systems, when larger values of $q$ are considered. Finally, a detailed description of the local flux properties is provided by a multifractal scaling analysis.

cond-mat.stat-mech↗

arXiv2007

Formation and growth of clusters in colloidal suspensions

Depending on the pH value and salt concentration of Al2O3 suspensions different microstructures can form. Especially the clustered one is of major interest for industrial purposes as found in the production of ceramics. In this paper we investigate the clustered microstructure by means of a coupled Stochastic Rotation Dynamics (SRD) and Molecular Dynamics (MD) simulation. In order to gain statistics within a system containing numerous clusters, large simulation volumes are needed. We present our parallel implementation of the simulation algorithm as well as a newly developed cluster detection and tracking algorithm. We then show first results of measured growth rates and cluster size distributions to validate the applicability of our method.

cond-mat.soft↗

arXiv2007

New approaches to model and study social networks

We describe and develop three recent novelties in network research which are particularly useful for studying social systems. The first one concerns the discovery of some basic dynamical laws that enable the emergence of the fundamental features observed in social networks, namely the nontrivial clustering properties, the existence of positive degree correlations and the subdivision into communities. To reproduce all these features we describe a simple model of mobile colliding agents, whose collisions define the connections between the agents which are the nodes in the underlying network, and develop some analytical considerations. The second point addresses the particular feature of clustering and its relationship with global network measures, namely with the distribution of the size of cycles in the network. Since in social bipartite networks it is not possible to measure the clustering from standard procedures, we propose an alternative clustering coefficient that can be used to extract an improved normalized cycle distribution in any network. Finally, the third point addresses dynamical processes occurring on networks, namely when studying the propagation of information in them. In particular, we focus on the particular features of gossip propagation which impose some restrictions in the propagation rules. To this end we introduce a quantity, the spread factor, which measures the average maximal fraction of nearest neighbors which get in contact with the gossip, and find the striking result that there is an optimal non-trivial number of friends for which the spread factor is minimized, decreasing the danger of being gossiped.

physics.soc-ph↗

arXiv2006

Vegetation against dune mobility

Vegetation is the most common and most reliable stabilizer of loose soil or sand. This ancient technique is for the first time cast into a set of equations of motion describing the competition between aeolian sand transport and vegetation growth. Our set of equations is then applied to study quantitatively the transition between barchans and parabolic dunes driven by the dimensionless fixation index $θ$ which is the ratio between dune characteristic erosion rate and vegetation growth velocity. We find a fixation index $θ_c$ below which the dunes are stabilized characterized by scaling laws.

cond-mat.other↗

arXiv2006

Shear Viscosity of Clay-like Colloids in Computer Simulations and Experiments

Dense suspensions of small strongly interacting particles are complex systems, which are rarely understood on the microscopic level. We investigate properties of dense suspensions and sediments of small spherical Al_2O_3 particles in a shear cell by means of a combined Molecular Dynamics (MD) and Stochastic Rotation Dynamics (SRD) simulation. We study structuring effects and the dependence of the suspension's viscosity on the shear rate and shear thinning for systems of varying salt concentration and pH value. To show the agreement of our results to experimental data, the relation between bulk pH value and surface charge of spherical colloidal particles is modeled by Debye-Hueckel theory in conjunction with a 2pK charge regulation model.

cond-mat.soft↗

arXiv2006

Local load sharing fiber bundles with a lower cutoff of strength disorder

We study the failure properties of fiber bundles with a finite lower cutoff of the strength disorder varying the range of interaction between the limiting cases of completely global and completely local load sharing. Computer simulations revealed that at any range of load redistribution there exists a critical cutoff strength where the macroscopic response of the bundle becomes perfectly brittle, i.e. linearly elastic behavior is obtained up to global failure, which occurs catastrophically after the breaking of a small number of fibers. As an extension of recent mean field studies [Phys. Rev. Lett. 95, 125501 (2005)], we demonstrate that approaching the critical cutoff, the size distribution of bursts of breaking fibers shows a crossover to a universal power law form with an exponent 3/2 independent of the range of interaction.

cond-mat.stat-mech↗

arXiv2006

Lattice Boltzmann simulations of apparent slip in hydrophobic microchannels

Various experiments have found a boundary slip in hydrophobic microchannel flows, but a consistent understanding of the results is still lacking. While Molecular Dynamics (MD) simulations cannot reach the low shear rates and large system sizes of the experiments, it is often impossible to resolve the needed details with macroscopic approaches. We model the interaction between hydrophobic channel walls and a fluid by means of a multi-phase lattice Boltzmann model. Our mesoscopic approach overcomes the limitations of MD simulations and can reach the small flow velocities of known experiments. We reproduce results from experiments at small Knudsen numbers and other simulations, namely an increase of slip with increasing liquid-solid interactions, the slip being independent of the flow velocity, and a decreasing slip with increasing bulk pressure. Within our model we develop a semi-analytic approximation of the dependence of the slip on the pressure.

physics.flu-dyn↗

arXiv2006

Computer Simulation of Particle Suspensions

Particle suspensions are ubiquitous in our daily life, but are not well understood due to their complexity. During the last twenty years, various simulation methods have been developed in order to model these systems. Due to varying properties of the solved particles and the solvents, one has to choose the simulation method properly in order to use the available compute resources most effectively with resolving the system as well as needed. Various techniques for the simulation of particle suspensions have been implemented at the Institute for Computational Physics allowing us to study the properties of clay-like systems, where Brownian motion is important, more macroscopic particles like glass spheres or fibers solved in liquids, or even the pneumatic transport of powders in pipes. In this paper we will present the various methods we applied and developed and discuss their individual advantages.

cond-mat.soft↗

arXiv2006

Networks based on collisions among mobile agents

We investigate in detail a recent model of colliding mobile agents [Phys. Rev. Lett.~96, 088702], used as an alternative approach to construct evolving networks of interactions formed by the collisions governed by suitable dynamical rules. The system of mobile agents evolves towards a quasi-stationary state which is, apart small fluctuations, well characterized by the density of the system and the residence time of the agents. The residence time defines a collision rate and by varying the collision rate, the system percolates at a critical value, with the emergence of a giant cluster whose critical exponents are the ones of two-dimensional percolation. Further, the degree and clustering coefficient distributions and the average path length show that the network associated with such a system presents non-trivial features which, depending on the collision rule, enables one not only to recover the main properties of standard networks, such as exponential, random and scale-free networks, but also to obtain other topological structures. Namely, we show a specific example where the obtained structure has topological features which characterize accurately the structure and evolution of social networks in different contexts, ranging from networks of acquaintances to networks of sexual contacts.

physics.soc-ph↗

arXiv2006

The Kauffman model on Small-World Topology

We apply Kauffman's automata on small-world networks to study the crossover between the short-range and the infinite-range case. We perform accurate calculations on square lattices to obtain both critical exponents and fractal dimensions. Particularly, we find an increase of the damage propagation and a decrease in the fractal dimensions when adding long-range connections.

cond-mat.stat-mech↗

arXiv2006

Plurality Voting: the statistical laws of democracy in Brazil

We explore the statistical laws behind the plurality voting system by investigating the election results for mayor held in Brazil in 2004. Our analysis indicate that the vote partition among mayor candidates of the same city tends to be "polarized" between two candidates, a phenomenon that can be closely described by means of a simple fragmentation model. Complex concepts like "government continuity" and "useful vote" can be identified and even statistically quantified through our approach.

physics.soc-ph↗