231 research outputs found
Dynamical surface structures in multi-particle-correlated surface growths
We investigate the scaling properties of the interface fluctuation width for
the -mer and -particle-correlated deposition-evaporation models. These
models are constrained with a global conservation law that the particle number
at each height is conserved modulo . In equilibrium, the stationary
roughness is anomalous but universal with roughness exponent ,
while the early time evolution shows nonuniversal behavior with growth exponent
varying with models and . Nonequilibrium surfaces display diverse
growing/stationary behavior. The -mer model shows a faceted structure, while
the -particle-correlated model a macroscopically grooved structure.Comment: 16 pages, 10 figures, revte
Theoretical approach and impact of correlations on the critical packet generation rate in traffic dynamics on complex networks
Using the formalism of the biased random walk in random uncorrelated networks
with arbitrary degree distributions, we develop theoretical approach to the
critical packet generation rate in traffic based on routing strategy with local
information. We explain microscopic origins of the transition from the flow to
the jammed phase and discuss how the node neighbourhood topology affects the
transport capacity in uncorrelated and correlated networks.Comment: 6 pages, 5 figure
Search for Kosterlitz-Thouless transition in a triangular Ising antiferromagnet with further-neighbour ferromagnetic interactions
We investigate an antiferromagnetic triangular Ising model with anisotropic
ferromagnetic interactions between next-nearest neighbours, originally proposed
by Kitatani and Oguchi (J. Phys. Soc. Japan {\bf 57}, 1344 (1988)). The phase
diagram as a function of temperature and the ratio between first- and second-
neighbour interaction strengths is thoroughly examined. We search for a
Kosterlitz-Thouless transition to a state with algebraic decay of correlations,
calculating the correlation lengths on strips of width up to 15 sites by
transfer-matrix methods. Phenomenological renormalization, conformal invariance
arguments, the Roomany-Wyld approximation and a direct analysis of the scaled
mass gaps are used. Our results provide limited evidence that a
Kosterlitz-Thouless phase is present. Alternative scenarios are discussed.Comment: 10 pages, RevTeX 3; 11 Postscript figures (uuencoded); to appear in
Phys. Rev. E (1995
Scaling of mean first-passage time as efficiency measure of nodes sending information on scale-free Koch networks
A lot of previous work showed that the sectional mean first-passage time
(SMFPT), i.e., the average of mean first-passage time (MFPT) for random walks
to a given hub node (node with maximum degree) averaged over all starting
points in scale-free small-world networks exhibits a sublinear or linear
dependence on network order (number of nodes), which indicates that hub
nodes are very efficient in receiving information if one looks upon the random
walker as an information messenger. Thus far, the efficiency of a hub node
sending information on scale-free small-world networks has not been addressed
yet. In this paper, we study random walks on the class of Koch networks with
scale-free behavior and small-world effect. We derive some basic properties for
random walks on the Koch network family, based on which we calculate
analytically the partial mean first-passage time (PMFPT) defined as the average
of MFPTs from a hub node to all other nodes, excluding the hub itself. The
obtained closed-form expression displays that in large networks the PMFPT grows
with network order as , which is larger than the linear scaling of
SMFPT to the hub from other nodes. On the other hand, we also address the case
with the information sender distributed uniformly among the Koch networks, and
derive analytically the entire mean first-passage time (EMFPT), namely, the
average of MFPTs between all couples of nodes, the leading scaling of which is
identical to that of PMFPT. From the obtained results, we present that although
hub nodes are more efficient for receiving information than other nodes, they
display a qualitatively similar speed for sending information as non-hub nodes.
Moreover, we show that the location of information sender has little effect on
the transmission efficiency. The present findings are helpful for better
understanding random walks performed on scale-free small-world networks.Comment: Definitive version published in European Physical Journal
Constrained spin dynamics description of random walks on hierarchical scale-free networks
We study a random walk problem on the hierarchical network which is a
scale-free network grown deterministically. The random walk problem is mapped
onto a dynamical Ising spin chain system in one dimension with a nonlocal spin
update rule, which allows an analytic approach. We show analytically that the
characteristic relaxation time scale grows algebraically with the total number
of nodes as . From a scaling argument, we also show the
power-law decay of the autocorrelation function C_{\bfsigma}(t)\sim
t^{-\alpha}, which is the probability to find the Ising spins in the initial
state {\bfsigma} after time steps, with the state-dependent non-universal
exponent . It turns out that the power-law scaling behavior has its
origin in an quasi-ultrametric structure of the configuration space.Comment: 9 pages, 6 figure
The triangular Ising antiferromagnet in a staggered field
We study the equilibrium properties of the nearest-neighbor Ising
antiferromagnet on a triangular lattice in the presence of a staggered field
conjugate to one of the degenerate ground states. Using a mapping of the ground
states of the model without the staggered field to dimer coverings on the dual
lattice, we classify the ground states into sectors specified by the number of
``strings''. We show that the effect of the staggered field is to generate
long-range interactions between strings. In the limiting case of the
antiferromagnetic coupling constant J becoming infinitely large, we prove the
existence of a phase transition in this system and obtain a finite lower bound
for the transition temperature. For finite J, we study the equilibrium
properties of the system using Monte Carlo simulations with three different
dynamics. We find that in all the three cases, equilibration times for low
field values increase rapidly with system size at low temperatures. Due to this
difficulty in equilibrating sufficiently large systems at low temperatures, our
finite-size scaling analysis of the numerical results does not permit a
definite conclusion about the existence of a phase transition for finite values
of J. A surprising feature in the system is the fact that unlike usual glassy
systems, a zero-temperature quench almost always leads to the ground state,
while a slow cooling does not.Comment: 12 pages, 18 figures: To appear in Phys. Rev.
An Interface View of Directed Sandpile Dynamics
We present a directed unloading sand box type avalanche model, driven by
slowly lowering the retaining wall at the bottom of the slope. The avalanche
propagation in the two dimensional surface is related to the space-time
configurations of one dimensional Kardar-Parisi-Zhang (KPZ) type interface
growth dynamics. We express the scaling exponents for the avalanche cluster
distributions into that framework. The numerical results agree closely with KPZ
scaling, but not perfectly.Comment: 4 pages including 5 figure
Recursive graphs with small-world scale-free properties
We discuss a category of graphs, recursive clique trees, which have
small-world and scale-free properties and allow a fine tuning of the clustering
and the power-law exponent of their discrete degree distribution. We determine
relevant characteristics of those graphs: the diameter, degree distribution,
and clustering parameter. The graphs have also an interesting recursive
property, and generalize recent constructions with fixed degree distributions.Comment: 4 pages, 2 figure
Effective dimensions and percolation in hierarchically structured scale-free networks
We introduce appropriate definitions of dimensions in order to characterize
the fractal properties of complex networks. We compute these dimensions in a
hierarchically structured network of particular interest. In spite of the
nontrivial character of this network that displays scale-free connectivity
among other features, it turns out to be approximately one-dimensional. The
dimensional characterization is in agreement with the results on statistics of
site percolation and other dynamical processes implemented on such a network.Comment: 5 pages, 5 figure
Exact scaling properties of a hierarchical network model
We report on exact results for the degree , the diameter , the
clustering coefficient , and the betweenness centrality of a
hierarchical network model with a replication factor . Such quantities are
calculated exactly with the help of recursion relations. Using the results, we
show that (i) the degree distribution follows a power law with , (ii) the diameter grows
logarithmically as with the number of nodes , (iii) the
clustering coefficient of each node is inversely proportional to its degree, , and the average clustering coefficient is nonzero in the infinite
limit, and (iv) the betweenness centrality distribution follows a power law
. We discuss a classification scheme of scale-free networks
into the universality class with the clustering property and the betweenness
centrality distribution.Comment: 4 page
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