264 research outputs found

### Self-Organized Criticality and Synchronization in the Forest-Fire Model

Depending on the rule for tree growth, the forest-fire model shows either
self-organized criticality with rule-dependent exponents, or synchronization,
or an intermediate behavior. This is shown analytically for the one-dimensional
system, but holds evidently also in higher dimensions.Comment: Latex 4 pages, 4 figure

### Self--organized criticality due to a separation of energy scales

Certain systems with slow driving and avalanche-like dissipation events are
naturally close to a critical point when the ratio of two energy scales is
large. The first energy scale is the threshold above which an avalanche is
triggered, the second scale is the threshold above which a site is affected by
an avalanche. I present results of computer simulations, and a mean-field
theory.Comment: This paper is very different from the old version which had an error
in the simulation code. Please destroy the old version if you have i

### Extinction events and species lifetimes in a simple ecological model

A model for large-scale evolution recently introduced by Amaral and Meyer is
studied analytically and numerically. Species are located at different trophic
levels and become extinct if their prey becomes extinct. It is proved that this
model is self-organized critical in the thermodynamic limit, with an exponent 2
characterizing the size distribution of extinction events. The lifetime
distribution of species, cutoffs due to finite-size effects, and other
quantities are evaluated. The relevance of this model to biological evolution
is critically assessed.Comment: 4 pages RevTex, including 3 postscript figure

### On the relation between the second law of thermodynamics and classical and quantum mechanics

In textbooks on statistical mechanics, one finds often arguments based on
classical mechanics, phase space and ergodicity in order to justify the second
law of thermodynamics. However, the basic equations of motion of classical
mechanics are deterministic and reversible, while the second law of
thermodynamics is irreversible and not deterministic, because it states that a
system forgets its past when approaching equilibrium. I argue that all
"derivations" of the second law of thermodynamics from classical mechanics
include additional assumptions that are not part of classical mechanics. The
same holds for Boltzmann's H-theorem. Furthermore, I argue that the
coarse-graining of phase-space that is used when deriving the second law cannot
be viewed as an expression of our ignorance of the details of the microscopic
state of the system, but reflects the fact that the state of a system is fully
specified by using only a finite number of bits, as implied by the concept of
entropy, which is related to the number of different microstates that a closed
system can have. While quantum mechanics, as described by the Schroedinger
equation, puts this latter statement on a firm ground, it cannot explain the
irreversibility and stochasticity inherent in the second law.Comment: Invited talk given on the 2012 "March meeting" of the German Physical
Society To appear in: B. Falkenburg and M. Morrison (eds.), Why more is
different (Springer Verlag, 2014

### Random Boolean Networks

This review explains in a self-contained way the properties of random Boolean
networks and their attractors, with a special focus on critical networks. Using
small example networks, analytical calculations, phenomenological arguments,
and problems to solve, the basic concepts are introduced and important results
concerning phase diagrams, numbers of relevant nodes and attractor properties
are derived.Comment: This is a review on Random Boolean Networks. The new version now
includes a proper title page. The main body is unchange

### Ten reasons why a thermalized system cannot be described by a many-particle wave function

It is widely believed that the underlying reality behind statistical
mechanics is a deterministic and unitary time evolution of a many-particle wave
function, even though this is in conflict with the irreversible, stochastic
nature of statistical mechanics. The usual attempts to resolve this conflict
for instance by appealing to decoherence or eigenstate thermalization are
riddled with problems. This paper considers theoretical physics of thermalized
systems as it is done in practise and shows that all approaches to thermalized
systems presuppose in some form limits to linear superposition and
deterministic time evolution. These considerations include, among others, the
classical limit, extensivity, the concepts of entropy and equilibrium, and
symmetry breaking in phase transitions and quantum measurement. As a
conclusion, the paper argues that the irreversibility and stochasticity of
statistical mechanics should be taken as a true property of nature. It follows
that a gas of a macroscopic number $N$ of atoms in thermal equilibrium is best
represented by a collection of $N$ wave packets of a size of the order of the
thermal de Broglie wave length, which behave quantum mechanically below this
scale but classically sufficiently far beyond this scale. In particular, these
wave packets must localize again after scattering events, which requires
stochasticity and indicates a connection to the measurement process.Comment: Drastically rewritten version, with more explanations, with three new
reasons added and three old ones merged with other parts of the tex

### Critical Boolean networks with scale-free in-degree distribution

We investigate analytically and numerically the dynamical properties of
critical Boolean networks with power-law in-degree distributions. When the
exponent of the in-degree distribution is larger than 3, we obtain results
equivalent to those obtained for networks with fixed in-degree, e.g., the
number of the non-frozen nodes scales as $N^{2/3}$ with the system size $N$.
When the exponent of the distribution is between 2 and 3, the number of the
non-frozen nodes increases as $N^x$, with $x$ being between 0 and 2/3 and
depending on the exponent and on the cutoff of the in-degree distribution.
These and ensuing results explain various findings obtained earlier by computer
simulations.Comment: 5 pages, 1 graph, 1 sketch, submitte

### Winding angles for two-dimensional polymers with orientation dependent interactions

We study winding angles of oriented polymers with orientation-dependent
interaction in two dimensions. Using exact analytical calculations, computer
simulations, and phenomenological arguments, we succeed in finding the variance
of the winding angle for most of the phase diagram. Our results suggest that
the winding angle distribution is a universal quantity, and that the
$\theta$--point is the point where the three phase boundaries between the
swollen, the normal collapsed, and the spiral collapsed phase meet. The
transition between the normal collapsed phase and the spiral phase is shown to
be continuous.Comment: 21 pages (incl 5 figures

### Scaling laws in critical random Boolean networks with general in- and out-degree distributions

We evaluate analytically and numerically the size of the frozen core and
various scaling laws for critical Boolean networks that have a power-law in-
and/or out-degree distribution. To this purpose, we generalize an efficient
method that has previously been used for conventional random Boolean networks
and for networks with power-law in-degree distributions. With this
generalization, we can also deal with power-law out-degree distributions. When
the power-law exponent is between 2 and 3, the second moment of the
distribution diverges with network size, and the scaling exponent of the
nonfrozen nodes depends on the degree distribution exponent. Furthermore, the
exponent depends also on the dependence of the cutoff of the degree
distribution on the system size. Altogether, we obtain an impressive number of
different scaling laws depending on the type of cutoff as well as on the
exponents of the in- and out-degree distributions. We confirm our scaling
arguments and analytical considerations by numerical investigations

### Dynamics of a single particle in a horizontally shaken box

We study the dynamics of a particle in a horizontally and periodically shaken
box as a function of the box parameters and the coefficient of restitution. For
certain parameter values, the particle becomes regularly chattered at one of
the walls, thereby loosing all its kinetic energy relative to that wall. The
number of container oscillations between two chattering events depends in a
fractal manner on the parameters of the system. In contrast to a vertically
vibrated particle, for which chattering is claimed to be the generic fate, the
horizontally shaken particle can become trapped on a periodic orbit and follow
the period-doubling route to chaos when the coefficient of restitution is
changed. We also discuss the case of a completely elastic particle, and the
influence of friction between the particle and the bottom of the container.Comment: 11 pages RevTex. Some postscript files have low resolution. We will
send the high-resolution files on reques

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