63 research outputs found
Self-organized critical and synchronized states in a nonequilibrium percolation model
We introduce a nonequilibrium percolation model which shows a self-organized
critical (SOC) state and several periodic states. In the SOC state, the
correlation length diverges slower than the system size, and the corresponding
exponent depends non universally on the parameter of the model. The periodic
states contain an infinite cluster covering only part of the system.Comment: 10 pages, Revtex, two uuencoded figure
Elastically coupled molecular motors
We study the influence of filament elasticity on the motion of collective
molecular motors. It is found that for a backbone flexibility exceeding a
characteristic value (motor stiffness divided through the mean displacement
between attached motors), the ability of motors to produce force reduces as
compared to rigidly coupled motors, while the maximum velocity remains
unchanged. The force-velocity-relation in two different analytic approximations
is calculated and compared with Monte-Carlo simulations. Finally, we extend our
model by introducing motors with a strain-dependent detachment rate. A
remarkable crossover from the nearly hyperbolic shape of the Hill curve for
stiff backbones to a linear force-velocity relation for very elastic backbones
is found. With realistic model parameters we show that the backbone flexibility
plays no role under physiological conditions in muscles, but it should be
observable in certain in vitro assays.Comment: REVTeX, 13 pages, 11 figures; presentation improved; to appear in
European Physical Journal B; a Java applet showing the simulation is
accessible at http://www.physik.tu-muenchen.de/~avilfan/ecmm
Superconductivity Controlled by Polarization in Field-Effect Devices of Confined Geometry
We propose a concept for superconducting electric field-effect devices based
on superconducting films sandwiched between ferroelectric layers. We provide
theoretical calculations that indicate how the field effect in these devices
could be amplified, which can be experimentally probed even at the current
stage of film fabrication techniques.Comment: to appear in Applied Physics Letters, 3 pages RevTeX4, 3 figure
Dipolar Interactions in Superconductor-Ferromagnet Heterostructures
We consider a simple model for a superlattice composed of a thin magnetic
film placed between two bulk superconductors. The magnetic film is modelled by
a planar but otherwise arbitrary distribution of magnetic dipoles and the
superconductors are treated in the London approximation. Due to the linearity
of the problem, we are able to compute the magnetic energy of the film in the
presence of the superconductors. We show that in the case of small wavenumbers
compared to the inverse London penetration depth, the magnetic energy resembles
the energy of a distribution of magnetisation in a two dimensional space.
Possible experimental applications of these results are discussed.Comment: RevTeX, 29 pages, 3 figures. To be published in Phys. Rev. B. Changes
were made (including adding fig. 3), to conform with the referee's report.
Reference 54 was also adde
Finite-size effects in the self-organized critical forest-fire model
We study finite-size effects in the self-organized critical forest-fire model
by numerically evaluating the tree density and the fire size distribution. The
results show that this model does not display the finite-size scaling seen in
conventional critical systems. Rather, the system is composed of relatively
homogeneous patches of different tree densities, leading to two qualitatively
different types of fires: those that span an entire patch and those that don't.
As the system size becomes smaller, the system contains less patches, and
finally becomes homogeneous, with large density fluctuations in time.Comment: 10 pages, 11 figure
Statistical mechanics
The completely revised new edition of the classical book on Statistical Mechanics covers the basic concepts of equilibrium and non-equilibrium statistical physics. In addition to a deductive approach to equilibrium statistics and thermodynamics based on a single hypothesis - the form of the microcanonical density matrix - this book treats the most important elements of non-equilibrium phenomena. Intermediate calculations are presented in complete detail. Problems at the end of each chapter help students to consolidate their understanding of the material. Beyond the fundamentals, this text demonstrates the breadth of the field and its great variety of applications. Modern areas such as renormalization group theory, percolation, stochastic equations of motion and their applications to critical dynamics, kinetic theories, as well as fundamental considerations of irreversibility, are discussed. The text will be useful for advanced students of physics and other natural sciences; a basic knowledge of quantum mechanics is presumed
Exact Results for the One-Dimensional Self-Organized Critical Forest-Fire Model
We present the analytic solution of the self-organized critical (SOC)
forest-fire model in one dimension proving SOC in systems without conservation
laws by analytic means. Under the condition that the system is in the steady
state and very close to the critical point, we calculate the probability that a
string of neighboring sites is occupied by a given configuration of trees.
The critical exponent describing the size distribution of forest clusters is
exactly and does not change under certain changes of the model
rules. Computer simulations confirm the analytic results.Comment: 12 pages REVTEX, 2 figures upon request, dro/93/
Crossover from Percolation to Self-Organized Criticality
We include immunity against fire as a new parameter into the self-organized
critical forest-fire model. When the immunity assumes a critical value,
clusters of burnt trees are identical to percolation clusters of random bond
percolation. As long as the immunity is below its critical value, the
asymptotic critical exponents are those of the original self-organized critical
model, i.e. the system performs a crossover from percolation to self-organized
criticality. We present a scaling theory and computer simulation results.Comment: 4 pages Revtex, two figures included, to be published in PR
Forest fires and other examples of self-organized criticality
We review the properties of the self-organized critical (SOC) forest-fire
model. The paradigm of self-organized criticality refers to the tendency of
certain large dissipative systems to drive themselves into a critical state
independent of the initial conditions and without fine-tuning of the
parameters. After an introduction, we define the rules of the model and discuss
various large-scale structures which may appear in this system. The origin of
the critical behavior is explained, critical exponents are introduced, and
scaling relations between the exponents are derived. Results of computer
simulations and analytical calculations are summarized. The existence of an
upper critical dimension and the universality of the critical behavior under
changes of lattice symmetry or the introduction of immunity are discussed. A
survey of interesting modifications of the forest-fire model is given. Finally,
several other important SOC models are briefly described.Comment: 37 pages RevTeX, 13 PostScript figures (Figs 1, 4, 13 are of reduced
quality to keep download times small
The self-organized critical forest-fire model on large scales
We discuss the scaling behavior of the self-organized critical forest-fire
model on large length scales. As indicated in earlier publications, the
forest-fire model does not show conventional critical scaling, but has two
qualitatively different types of fires that superimpose to give the effective
exponents typically measured in simulations. We show that this explains not
only why the exponent characterizing the fire-size distribution changes with
increasing correlation length, but allows also to predict its asymptotic value.
We support our arguments by computer simulations of a coarse-grained model, by
scaling arguments and by analyzing states that are created artificially by
superimposing the two types of fires.Comment: 26 pages, 7 figure
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