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K. D. Usadel

Publications and source records attributed to K. D. Usadel.

35 records · Page 2Linked to original sources
arXiv1998

SOC in a class of sandpile models with stochastic dynamics

We have studied one-dimensional cellular automata with updating rules depending stochastically on the difference of the heights of neighbouring cells. The probability for toppling depends on a parameter lambda which goes to one with increasing slope, i.e. the dynamics can be varied continuously. We have investigated the scaling properties of the model using finite-size scaling analysis. A robust power-law behavior is observed for the probability density of the size of avalanches in a certain range of lambda values. The two exponents which determine the dependence of the probability density on time and system size both depend continuously on lambda, i.e. the model exhibits nonuniversal behavior. We also measured the roughness of the surface of the sandpile and here we obtained an universal behavior, i.e. a roughness exponent of about 1.75 for all values of lambda. For the temporal behavior of the mass a $f^{-ϕ}$ spectrum is obtained with an exponent phi close to 2 again for all lambda-values.

cond-mat.stat-mech↗
arXiv1998

Investigation of the dynamical structure factor of the Nagel-Schreckenberg traffic flow model

The Nagel-Schreckenberg traffic flow model shows a transition from a free flow regime to a jammed regime for increasing car density. The measurement of the dynamical structure factor offers the chance to observe the evolution of jams without the necessity to define a car to be jammed or not. Above the jamming transition the dynamical structure factor $S(k,ω)$ exhibits for a given $k$-value two maxima corresponding to the separation of the system into the free flow phase and jammed phase. Analyzing the $k$-dependence of these maxima the backward velocity of the jams is measured. We find that the jam velocity neither depends on the global density of the cars nor the maximal velocity of the model.

cond-mat.stat-mech↗
arXiv1998

Density fluctuations and phase separation in a traffic flow model

Within the Nagel-Schreckenberg traffic flow model we consider the transition from the free flow regime to the jammed regime. We introduce a method of analyzing the data which is based on the local density distribution. This analyzes allows us to determine the phase diagram and to examine the separation of the system into a coexisting free flow phase and a jammed phase above the transition. The investigation of the steady state structure factor yields that the decomposition in this phase coexistence regime is driven by density fluctuations, provided they exceed a critical wavelength.

cond-mat.stat-mech↗
arXiv1997

Density Fluctuations and Phase Transition in the Nagel-Schreckenberg Traffic Flow Model

We consider the transition of the Nagel-Schreckenberg traffic flow model from the free flow regime to the jammed regime. We examine the inhomogeneous character of the system by introducing a new method of analysis which is based on the local density distribution. We investigated the characteristic fluctuations in the steady state and present the phase diagram of the system.

cond-mat.stat-mech↗
arXiv1997

Reorientation transition of ultrathin ferromagnetic films

We demonstrate that the reorientation transition from out-of-plane to in-plane magnetization with decreasing temperature as observed experimentally in Ni-films on Cu(001) can be explained on a microscopic basis. Using a combination of mean field theory and perturbation theory, we derive an analytic expression for the temperature dependent anisotropy. The reduced magnetization in the film surface at finite temperatures plays a crucial role for this transition as with increasing temperature the influence of the uniaxial anisotropies is reduced at the surface and is enhanced inside the film.

cond-mat.stat-mech↗
arXiv1997

Modified Scaling Relation for the Random-Field Ising Model

We investigate the low-temperature critical behavior of the three dimensional random-field Ising ferromagnet. By a scaling analysis we find that in the limit of temperature $T \to 0$ the usual scaling relations have to be modified as far as the exponent $α$ of the specific heat is concerned. At zero temperature, the Rushbrooke equation is modified to $α+ 2 β+ γ= 1$, an equation which we expect to be valid also for other systems with similar critical behavior. We test the scaling theory numerically for the three dimensional random field Ising system with Gaussian probability distribution of the random fields by a combination of calculations of exact ground states with an integer optimization algorithm and Monte Carlo methods. By a finite size scaling analysis we calculate the critical exponents $ν\approx 1.0$, $β\approx 0.05$, $\barγ \approx 2.9$ $γ\approx 1.5$ and $α\approx -0.55$.

cond-mat.dis-nn↗
arXiv1997

The Bak-Tang-Wiesenfeld sandpile model around the upper critical dimension

We consider the Bak-Tang-Wiesenfeld sandpile model on square lattices in different dimensions (D>=6). A finite size scaling analysis of the avalanche probability distributions yields the values of the distribution exponents, the dynamical exponent, and the dimension of the avalanches. Above the upper critical dimension D_u=4 the exponents equal the known mean field values. An analysis of the area probability distributions indicates that the avalanches are fractal above the critical dimension.

cond-mat↗
arXiv1997

Numerical Determination of the Avalanche Exponents of the Bak-Tang-Wiesenfeld Model

We consider the Bak-Tang-Wiesenfeld sandpile model on a two-dimensional square lattice of lattice sizes up to L=4096. A detailed analysis of the probability distribution of the size, area, duration and radius of the avalanches will be given. To increase the accuracy of the determination of the avalanche exponents we introduce a new method for analyzing the data which reduces the finite-size effects of the measurements. The exponents of the avalanche distributions differ slightly from previous measurements and estimates obtained from a renormalization group approach.

cond-mat.stat-mech↗
arXiv1997

Non-exponential relaxation in diluted antiferromagnets

Diluted Ising antiferromagnets in a homogenous magnetic field have a disordered phase for sufficiently large values of the field and for low temperatures. Here, the system is in a domain state with a broad size-distribution of fractal domains. We study the relaxation dynamics of this domain state after removing the external field for two and three dimensions. Using Monte Carlo simulation techniques, we measure the decay of the remanent magnetization. Its temperature dependence can be understood as thermal activation. All data can be described by a unique generalized power law for a wide range of temperatures in two and three dimensions. The question wether the exponent of the generalized power law is universal remains open.

cond-mat.dis-nn↗
arXiv1996

Domain wall roughening in three dimensional magnets at the depinning transition

The kinetic roughening of a driven interface between three dimensional spin-up and spin-down domains in a model with non-conserved scalar order parameter and quenched disorder is studied numerically within a discrete time dynamics at zero temperature. The exponents characterizing the morphology of the interface are obtained close to the depinning-transition

cond-mat.dis-nn↗
arXiv1996

Exact Ground State Properties of Disordered Ising-Systems

Exact ground states are calculated with an integer optimization algorithm for two and three dimensional site-diluted Ising antiferromagnets in a field (DAFF) and random field Ising ferromagnets (RFIM). We investigate the structure and the size-distribution of the domains of the ground state and compare it to earlier results from Monte Carlo simulations for finite temperature. Although DAFF and RFIM are thought to be in the same universality class we found essential differences between these systems as far as the domain properties are concerned. For the DAFF the ground states consist of fractal domains with a broad size distribution that can be described by a power law with exponential cut-off. For the RFIM the limiting case of the size distribution and structure of the domains for strong random fields is the size distribution and structure of the clusters of the percolation problem with a field dependent lower cut-off. The domains are fractal and in three dimensions nearly all spins belong to two large infinite domains of up- and down spins - the system is in a two-domain state.

cond-mat.dis-nn↗
arXiv1996

Nonequilibrium Phase Transition and Self-Organized Criticality in a Sandpile Model with Stochastic Dynamics

We introduce and study numerically a directed two-dimensional sandpile automaton with probabilistic toppling (probability parameter p) which provides a good laboratory to study both self-organized criticality and the far-from-equilibrium phase transition. In the limit p=1 our model reduces to the critical height model in which the self-organized critical behavior was found by exact solution [D. Dhar and R. Ramaswamy, Phys. Rev. Lett. 63, 1659 (1989)]. For 0<p<1 metastable columns of sand may be formed, which are relaxed when one of the local slopes exceeds a critical value sigma _c. By varying the probability of toppling p we find that a continuous phase transition occurs at the critical probability p_c, at which the steady states with zero average slope (above p_c) are replaced by states characterized by a finite average slope (below p_c). We study this phase transition in detail by introducing an appropriate order parameter and the order-parameter susceptibility chi. In a certain range of p<1 we find the self- organized critical behavior which is characterized by nonuniversal p-dependent scaling exponents for the probability distributions of size and length of avalanches. We also calculate the anisotropy exponent zeta and the fractal dimension d_f of relaxation clusters in the entire range of values of the toppling parameter p. We show that the relaxation clusters in our model are anisotropic and can be described as fractals for values of $p$ above the transition point. Below the transition they are isotropic and compact.

cond-mat↗
arXiv1996

Dynamics of Domains in Diluted Antiferromagnets

We investigate the dynamics of two-dimensional site-diluted Ising antiferromagnets. In an external magnetic field these highly disordered magnetic systems have a domain structure which consists of fractal domains with sizes on a broad range of length scales. We focus on the dynamics of these systems during the relaxation from a long-range ordered initial state to the disordered fractal-domain state after applying an external magnetic field. The equilibrium state with applied field consists of fractal domains with a size distribution which follows a power law with an exponential cut-off. The dynamics of the system can be understood as a growth process of this fractal-domain state in such a way that the equilibrium distribution of domains develops during time. Following these ideas quantitatively we derive a simple description of the time dependence of the order parameter. The agreement with simulations is excellent.

cond-mat↗
arXiv1995

Characterization of the reorientation transition in classical Heisenberg models with dipole interaction

In this paper the thermodynamics of thin ferromagnetic films are studied in the framework of the classical Heisenberg model with uniaxial anisotropy and long--range dipole interaction. The dependence of the order of the reorientation transition in these systems on the number of layers and on the distribution of anisotropies is investigated using both mean field theory and Monte-Carlo simulations.

cond-mat↗
arXiv1995

Fractal properties of relaxation clusters and phase transition in a stochastic sandpile automaton

We study numerically the spatial properties of relaxation clusters in a two dimensional sandpile automaton with dynamic rules depending stochastically on a parameter p, which models the effects of static friction. In the limiting cases p=1 and p=0 the model reduces to the critical height model and critical slope model, respectively. At p=p_c, a continuous phase transition occurs to the state characterized by a nonzero average slope. Our analysis reveals that the loss of finite average slope at the transition is accompanied by the loss of fractal properties of the relaxation clusters.

cond-mat↗