32 research outputs found

### Time distribution and loss of scaling in granular flow

Two cellular automata models with directed mass flow and internal time scales
are studied by numerical simulations. Relaxation rules are a combination of
probabilistic critical height (probability of toppling $p$) and deterministic
critical slope processes with internal correlation time $t_c$ equal to the
avalanche lifetime, in Model A, and $t_c\equiv 1$, in Model B. In both cases
nonuniversal scaling properties of avalanche distributions are found for $p\ge
p^\star$, where $p^\star$ is related to directed percolation threshold in
$d=3$. Distributions of avalanche durations for $p\ge p^\star$ are studied in
detail, exhibiting multifractal scaling behavior in model A, and finite size
scaling behavior in model B, and scaling exponents are determined as a function
of $p$. At $p=p^\star$ a phase transition to noncritical steady state occurs.
Due to difference in the relaxation mechanisms, avalanche statistics at
$p^\star$ approaches the parity conserving universality class in Model A, and
the mean-field universality class in Model B. We also estimate roughness
exponent at the transition

### Adaptive Random Walks on the Class of Web Graph

We study random walk with adaptive move strategies on a class of directed
graphs with variable wiring diagram. The graphs are grown from the evolution
rules compatible with the dynamics of the world-wide Web [Tadi\'c, Physica A
{\bf 293}, 273 (2001)], and are characterized by a pair of power-law
distributions of out- and in-degree for each value of the parameter $\beta$,
which measures the degree of rewiring in the graph. The walker adapts its move
strategy according to locally available information both on out-degree of the
visited node and in-degree of target node. A standard random walk, on the other
hand, uses the out-degree only. We compute the distribution of connected
subgraphs visited by an ensemble of walkers, the average access time and
survival probability of the walks. We discuss these properties of the walk
dynamics relative to the changes in the global graph structure when the control
parameter $\beta$ is varied. For $\beta \geq 3$, corresponding to the
world-wide Web, the access time of the walk to a given level of hierarchy on
the graph is much shorter compared to the standard random walk on the same
graph. By reducing the amount of rewiring towards rigidity limit \beta \to
\beta_c \lesss im 0.1, corresponding to the range of naturally occurring
biochemical networks, the survival probability of adaptive and standard random
walk become increasingly similar. The adaptive random walk can be used as an
efficient message-passing algorithm on this class of graphs for large degree of
rewiring.Comment: 8 pages, including 7 figures; to appear in Europ. Phys. Journal

### Switching current noise and relaxation of ferroelectric domains

We simulate field-induced nucleation and switching of domains in a
three-dimensional model of ferroelectrics with quenched disorder and varying
domain sizes. We study (1) bursts of the switching current at slow driving
along the hysteresis loop (electrical Barkhausen noise) and (2) the
polarization reversal when a strong electric field was applied and
back-switching after the field was removed. We show how these processes are
related to the underlying structure of domain walls, which in turn is
controlled by the pinning at quenched local electric fields.
When the depolarization fields of bound charges are properly screened we find
that the fractal switching current noise may appear with two distinct universal
behaviors. The critical depinning of plane domain walls determines the
universality class in the case of weak random fields, whereas for large
randomness the massive nucleation of domains in the bulk leads to different
scaling properties.
In both cases the scaling exponents decay logarithmically when the driving
frequency is increased. The polarization reverses in the applied field as a
power-law, while its relaxation in zero field is a stretch exponential function
of time. The stretching exponent depends on the strength of pinning. The
results may be applicable for uniaxial relaxor ferroelectrics, such as doped
SBN:Ce.Comment: Revtex, 7 Figures, to appear in EPJ

### Exploring Complex Graphs by Random Walks

We present an algorithm to grow a graph with scale-free structure of {\it
in-} and {\it out-links} and variable wiring diagram in the class of the
world-wide Web. We then explore the graph by intentional random walks using
local next-near-neighbor search algorithm to navigate through the graph. The
topological properties such as betweenness are determined by an ensemble of
independent walkers and efficiency of the search is compared on three different
graph topologies. In addition we simulate interacting random walks which are
created by given rate and navigated in parallel, representing transport with
queueing of information packets on the graph.Comment: Latex, 4 figure

### Voltage Distribution in Growing Conducting Networks

We investigate by random-walk simulations and a mean-field theory how growth
by biased addition of nodes affects flow of the current through the emergent
conducting graph, representing a digital circuit. In the interior of a large
network the voltage varies with the addition time $s<t$ of the node as
$V(s)\sim \ln (s)/s^\theta$ when constant current enters the network at last
added node $t$ and leaves at the root of the graph which is grounded. The
topological closeness of the conduction path and shortest path through a node
suggests that the charged random walk determines these global graph properties
by using only {\it local} search algorithms. The results agree with mean-field
theory on tree structures, while the numerical method is applicable to graphs
of any complexity