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Hans J Herrmann

Publications and source records attributed to Hans J Herrmann.

At least 19 recordsLinked to original sources
PubMed2006

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 theta which is the ratio between the dune characteristic erosion rate and vegetation growth velocity. We find a fixation index theta(c) below which the dunes are stabilized, characterized by scaling laws.

Ecosystem↗
PubMed2006

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.

Journal Article↗
PubMed2006

Shear viscosity of claylike colloids in computer simulations and experiments.

Dense suspensions of small strongly interacting particles are complex systems that are rarely understood on the microscopic level. We investigate properties of dense suspensions and sediments of small spherical Al2O3 particles in a shear cell by means of a combined molecular-dynamics and stochastic rotation dynamics 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 with experimental data, the relation between the bulk pH value and surface charge of spherical colloidal particles is modeled by Debye-Hückel theory in conjunction with a 2 pK charge regulation model.

Journal Article↗
PubMed2006

Distribution of local fluxes in diluted porous media.

We study the distributions of channel openings, local fluxes, and velocities in a two-dimensional random medium of nonoverlapping disks. We present theoretical arguments supported by numerical data of high precision and find scaling laws as functions of the porosity. For the channel openings we observe a crossover to a highly correlated regime at small porosities. The distribution of velocities through these channels scales with the square of the porosity. The fluxes turn out to be the convolution of velocity and channel width corrected by a geometrical factor. Furthermore, while the distribution of velocities follows a Gaussian form, the fluxes are distributed according to a stretched exponential with exponent 1/2. Finally, our scaling analysis allows us to express the tortuosity and pore shape factors from the Kozeny-Carman equation as direct average properties from microscopic quantities related to the geometry as well as the flow through the disordered porous medium.

Journal Article↗
PubMed2006

Failure process of a bundle of plastic fibers.

We present an extension of fiber bundle models considering that failed fibers still carry a fraction 0 < or = alpha < or = 1 of their failure load. The value of alpha interpolates between the perfectly brittle failure (alpha = 0) and perfectly plastic behavior (alpha = 1) of fibers. We show that the finite load bearing capacity of broken fibers has a substantial effect on the failure process of the bundle. In the case of global load sharing it is found that for alpha --> 1 the macroscopic response of the bundle becomes perfectly plastic with a yield stress equal to the average fiber strength. On the microlevel, the size distribution of avalanches has a crossover from a power law of exponent approximately 2.5 to a faster exponential decay. For localized load sharing, computer simulations revealed a sharp transition at a well-defined value alpha(c) from a phase where macroscopic failure occurs due to localization as a consequence of local stress enhancements, to another one where the disordered fiber strength dominates the damage process. Analyzing the microstructure of damage, the transition proved to be analogous to percolation. At the critical point alpha(c), the spanning cluster of damage is found to be compact with a fractal boundary. The distribution of bursts of fiber breakings shows a power-law behavior with a universal exponent approximately 1.5 equal to the mean-field exponent of fiber bundles of critical strength distributions. The model can be relevant to understand the shear failure of glued interfaces where failed regions can still transmit load by remaining in contact.

Journal Article↗
PubMed2006

System of mobile agents to model social networks.

We propose a model of mobile agents to construct social networks, based on a system of moving particles by keeping track of the collisions during their permanence in the system. We reproduce not only the degree distribution, clustering coefficient, and shortest path length of a large database of empirical friendship networks recently collected, but also some features related with their community structure. The model is completely characterized by the collision rate, and above a critical collision rate we find the emergence of a giant cluster in the universality class of two-dimensional percolation. Moreover, we propose possible schemes to reproduce other networks of particular social contacts, namely, sexual contacts.

Algorithms↗
PubMed2006

Self-organized criticality model for brain plasticity.

Networks of living neurons exhibit an avalanche mode of activity, experimentally found in organotypic cultures. Here we present a model that is based on self-organized criticality and takes into account brain plasticity, which is able to reproduce the spectrum of electroencephalograms (EEG). The model consists of an electrical network with threshold firing and activity-dependent synapse strengths. The system exhibits an avalanche activity in a power-law distribution. The analysis of the power spectra of the electrical signal reproduces very robustly the power-law behavior with the exponent 0.8, experimentally measured in EEG spectra. The same value of the exponent is found on small-world lattices and for leaky neurons, indicating that universality holds for a wide class of brain models.

Algorithms↗
PubMed2006

Aeolian transport layer.

We investigate the airborne transport of particles on a granular surface by the saltation mechanism through numerical simulation of particle motion coupled with turbulent flow. We determine the saturated flux q(s) and show that its behavior is consistent with classical empirical relations obtained from wind tunnel measurements. Our results also allow one to propose and explain a new relation valid for small fluxes, namely, q(s) = a(u*-u(t))alpha, where u* and u(t) are the shear and threshold velocities of the wind, respectively, and the scaling exponent is alpha approximately 2. We obtain an expression for the velocity profile of the wind distorted by the particle motion due to the feedback and discover a novel dynamical scaling relation. We also find a new expression for the dependence of the height of the saltation layer as a function of the wind velocity.

Journal Article↗
PubMed2005

Cycles and clustering in bipartite networks.

We investigate the clustering coefficient in bipartite networks where cycles of size three are absent and therefore the standard definition of clustering coefficient cannot be used. Instead, we use another coefficient given by the fraction of cycles with size four, showing that both coefficients yield the same clustering properties. The new coefficient is computed for two networks of sexual contacts, one bipartite and another where no distinction between the nodes is made (monopartite). In both cases the clustering coefficient is similar. Furthermore, combining both clustering coefficients we deduce an expression for estimating cycles of larger size, which improves previous estimations and is suitable for either monopartite and multipartite networks, and discuss the applicability of such analytical estimations.

Journal Article↗
PubMed2005

Random bearings and their stability.

Self-similar space-filling bearings have been proposed some time ago as models for the motion of tectonic plates and appearance of seismic gaps. These models have two features which, however, seem unrealistic, namely, high symmetry in the arrangement of the particles, and lack of a lower cutoff in the size of the particles. In this work, an algorithm for generating random bearings in both two and three dimensions is presented. Introducing a lower cutoff for the sizes of the particles, the instabilities of the bearing under an external force such as gravity, are studied.

Journal Article↗
PubMed2005

Simulation of claylike colloids.

We investigate the properties of dense suspensions and sediments of small spherical silt particles by means of a combined molecular dynamics and stochastic rotation dynamics (SRD) simulation. We include van der Waals and effective electrostatic interactions between the colloidal particles, as well as Brownian motion and hydrodynamic interactions which are calculated in the SRD part. We present the simulation technique and first results. We have measured velocity distributions, diffusion coefficients, sedimentation velocity, spatial correlation functions, and we have explored the phase diagram depending on the parameters of the potentials and on the volume fraction.

Journal Article↗
PubMed2005

Magnetic models on Apollonian networks.

Thermodynamic and magnetic properties of Ising models defined on the triangular Apollonian network are investigated. This and other similar networks are inspired by the problem of covering a Euclidian domain with circles of maximal radii. Maps for the thermodynamic functions in two subsequent generations of the construction of the network are obtained by formulating the problem in terms of transfer matrices. Numerical iteration of this set of maps leads to very precise values for the thermodynamic properties of the model. Different choices for the coupling constants between only nearest neighbors along the lattice are taken into account. For both ferromagnetic and antiferromagnetic constants, long-range magnetic ordering is obtained. With exception of a size-dependent effective critical behavior of the correlation length, no evidence of asymptotic criticality was detected.

Journal Article↗
PubMed2005

Apollonian networks: simultaneously scale-free, small world, euclidean, space filling, and with matching graphs.

We introduce a new family of networks, the Apollonian networks, that are simultaneously scale-free, small-world, Euclidean, space filling, and with matching graphs. These networks describe force chains in polydisperse granular packings and could also be applied to the geometry of fully fragmented porous media, hierarchical road systems, and area-covering electrical supply networks. Some of the properties of these networks, namely, the connectivity exponent, the clustering coefficient, and the shortest path are calculated and found to be particularly rich. The percolation, the electrical conduction, and the Ising models on such networks are also studied and found to be quite peculiar. Consequences for applications are also discussed.

Journal Article↗
PubMed2004

Coherence in scale-free networks of chaotic maps.

We study fully synchronized states in scale-free networks of chaotic logistic maps as a function of both dynamical and topological parameters. Three different network topologies are considered: (i) a random scale-free topology, (ii) a deterministic pseudofractal scale-free network, and (iii) an Apollonian network. For the random scale-free topology we find a coupling strength threshold beyond which full synchronization is attained. This threshold scales as k(-mu) , where k is the outgoing connectivity and mu depends on the local nonlinearity. For deterministic scale-free networks coherence is observed only when the coupling strength is proportional to the neighbor connectivity. We show that the transition to coherence is of first order and study the role of the most connected nodes in the collective dynamics of oscillators in scale-free networks.

Journal Article↗
PubMed2003

Time evolution of damage under variable ranges of load transfer.

We study the time evolution of damage in a fiber bundle model in which the range of interaction of fibers varies through an adjustable stress transfer function recently introduced. We find that the lifetime of the material exhibits a crossover from mean-field to short-range behavior as in the static case. Numerical calculations showed that the value at which the transition takes place depends on the system's disorder. Finally, we have performed a microscopic analysis of the failure process. Our results confirm that the growth dynamics of the largest crack is radically different in the two limiting regimes of load transfer during the first stages of breaking.

Journal Article↗
PubMed2003

Scaling laws of creep rupture of fiber bundles.

We study the creep rupture of fiber composites in the framework of fiber bundle models. Two fiber bundle models are introduced based on different microscopic mechanisms responsible for the macroscopic creep behavior. Analytical and numerical calculations show that above a critical load the deformation of the creeping system monotonically increases in time resulting in global failure at a finite time t(f), while below the critical load the system suffers only partial failure and the deformation tends to a constant value giving rise to an infinite lifetime. It is found that approaching the critical load from below and above the creeping system is characterized by universal power laws when the fibers have long-range interaction. The lifetime of the composite above the critical point has a universal dependence on the system size.

Journal Article↗
PubMed2002

Evolution of percolating force chains in compressed granular media.

The evolution of effective force chains percolating through a compressed granular system is investigated. We compressed an ensemble of spherical particles monitoring the macroscopic constitutive behavior and the acoustic signals emitted by microscopic rearrangements of particles. We applied the continuous damage model of fiber bundles to describe the evolution of the array of force chains. The model provides a nonlinear constitutive behavior in good quantitative agreement with the experimental results. The amplitude distribution of acoustic signals was found experimentally to follow a power law of an exponent delta=1.15+/-0.05, which is in good agreement with the analytic solution of the model.

Journal Article↗