73 research outputs found
NUMERICAL SIMULATIONS OF MAGNETIC BRUSH FORMATION PHENOMENA
We have developed models capable of describing magnetic brush formation phenomena.
In particular, we investigate the effects of physical parameters (applied magnetic field,
etc.) on the correlations and the structure. Three models are presented, which point out
different aspects of the brush growth process
Driven Interface Depinning in a Disordered Medium
The dynamics of a driven interface in a medium with random pinning forces is
analyzed. The interface undergoes a depinning transition where the order
parameter is the interface velocity , which increases as for driving forces close to its threshold value . We
consider a Langevin-type equation which is expected to be valid close to the
depinning transition of an interface in a statistically isotropic medium. By a
functional renormalization group scheme the critical exponents characterizing
the depinning transition are obtained to the first order in ,
where is the interface dimension. The main results were published earlier
[T. Nattermann et al., J. Phys. II France {\bf 2} (1992) 1483]. Here, we
present details of the perturbative calculation and of the derivation of the
functional flow equation for the random-force correlator. The fixed point
function of the correlator has a cusp singularity which is related to a finite
value of the threshold , similar to the mean field theory. We also present
extensive numerical simulations and compare them with our analytical results
for the critical exponents. For the numerical and analytical
results deviate from each other by only a few percent. The deviations in lower
dimensions are larger and suggest that the roughness exponent
is somewhat larger than the value of an interface in
thermal equilibrium.Comment: 32 pages, 14 figures, REVTeX, to be published in Annalen der Physi
Explicit isomorphisms of quaternion algebras over quadratic global fields
Let L be a separable quadratic extension of either {\mathbb {Q}} Q or {\mathbb {F}}_q(t) F q ( t ) . We exhibit efficient algorithms for finding isomorphisms between quaternion algebras over L . Our techniques are based on computing maximal one-sided ideals of the corestriction of a central simple L -algebra
On the relation between Vicsek and Kuramoto models of spontaneous synchronization
The Vicsek model for the self-propelled particles is investigated with the
respect to the introduction of the stochastic perturbation of the dynamics. It
is shown that such a dependence can be thought in terms of the isomorphism of
the Vicsek model with the Kuramoto model of spontaneous synchronization. They
are isomorphic at least within the mean-field approach. The isomorphism between
two models allows to state the dependence of the type of the transition in
Vicsek model on the noise perturbation. Two types of noise the scalar and the
vector ones lead to qualitatively different behavior with continuous and the
discontinuous transition to ordered state correspondingly. New type of the
stochastic perturbation - ``mixed`` noise is proposed. It is the weighted
superposition of the scalar and vector noises. The corresponding phase diagram
``noise amplitude vs. interaction strength`` is obtained and the tricritical
behavior for Vicsek model is demonstrated.Comment: 11 pages, 5 figure
New aspects of the continuous phase transition in the scalar noise model (SNM) of collective motion
In this paper we present our detailed investigations on the nature of the
phase transition in the scalar noise model (SNM) of collective motion. Our
results confirm the original findings of Vicsek et al. [Phys. Rev. Lett. 75
(1995) 1226] that the disorder-order transition in the SNM is a continuous,
second order phase transition for small particle velocities ().
However, for large velocities () we find a strong anisotropy in the
particle diffusion in contrast with the isotropic diffusion for small
velocities. The interplay between the anisotropic diffusion and the periodic
boundary conditions leads to an artificial symmetry breaking of the solutions
(directionally quantized density waves) and a consequent first order transition
like behavior. Thus, it is not possible to draw any conclusion about the
physical behavior in the large particle velocity regime of the SNM.Comment: 13 pages, 11 figure
Collective behavior of interacting self-propelled particles
We discuss biologically inspired, inherently non-equilibrium self-propelled
particle models, in which the particles interact with their neighbours by
choosing at each time step the local average direction of motion. We summarize
some of the results of large scale simulations and theoretical approaches to
the problem
Dynamics of a Driven Single Flux Line in Superconductors
We study the low temperature dynamics of a single flux line in a bulk type-II
superconductor, driven by a surface current, both near and above the onset of
an instability which sets in at a critical driving. We found that above the
critical driving, the velocity profile of the flux line develops a
discontinuity.Comment: 10 pages with 4 figures, REVTE
Sample-Dependent Phase Transitions in Disordered Exclusion Models
We give numerical evidence that the location of the first order phase
transition between the low and the high density phases of the one dimensional
asymmetric simple exclusion process with open boundaries becomes sample
dependent when quenched disorder is introduced for the hopping rates.Comment: accepted in Europhysics Letter
Explicit isomorphisms of quaternion algebras over quadratic global fields
Let L be a separable quadratic extension of either {\mathbb {Q}} Q or {\mathbb {F}}_q(t) F q ( t ) . We exhibit efficient algorithms for finding isomorphisms between quaternion algebras over L . Our techniques are based on computing maximal one-sided ideals of the corestriction of a central simple L -algebra
Mean-field analysis of a dynamical phase transition in a cellular automaton model for collective motion
A cellular automaton model is presented for random walkers with biologically
motivated interactions favoring local alignment and leading to collective
motion or swarming behavior. The degree of alignment is controlled by a
sensitivity parameter, and a dynamical phase transition exhibiting spontaneous
breaking of rotational symmetry occurs at a critical parameter value. The model
is analyzed using nonequilibrium mean field theory: Dispersion relations for
the critical modes are derived, and a phase diagram is constructed. Mean field
predictions for the two critical exponents describing the phase transition as a
function of sensitivity and density are obtained analytically.Comment: 4 pages, 4 figures, final version as publishe
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