7,189 research outputs found
Self-Organization of Balanced Nodes in Random Networks with Transportation Bandwidths
We apply statistical physics to study the task of resource allocation in
random networks with limited bandwidths along the transportation links. The
mean-field approach is applicable when the connectivity is sufficiently high.
It allows us to derive the resource shortage of a node as a well-defined
function of its capacity. For networks with uniformly high connectivity, an
efficient profile of the allocated resources is obtained, which exhibits
features similar to the Maxwell construction. These results have good
agreements with simulations, where nodes self-organize to balance their
shortages, forming extensive clusters of nodes interconnected by unsaturated
links. The deviations from the mean-field analyses show that nodes are likely
to be rich in the locality of gifted neighbors. In scale-free networks, hubs
make sacrifice for enhanced balancing of nodes with low connectivity.Comment: 7 pages, 8 figure
Dynamics underlying Box-office: Movie Competition on Recommender Systems
We introduce a simple model to study movie competition in the recommender
systems. Movies of heterogeneous quality compete against each other through
viewers' reviews and generate interesting dynamics of box-office. By assuming
mean-field interactions between the competing movies, we show that run-away
effect of popularity spreading is triggered by defeating the average review
score, leading to hits in box-office. The average review score thus
characterizes the critical movie quality necessary for transition from
box-office bombs to blockbusters. The major factors affecting the critical
review score are examined. By iterating the mean-field dynamical equations, we
obtain qualitative agreements with simulations and real systems in the
dynamical forms of box-office, revealing the significant role of competition in
understanding box-office dynamics.Comment: 8 pages, 6 figure
Tracing the Evolution of Physics on the Backbone of Citation Networks
Many innovations are inspired by past ideas in a non-trivial way. Tracing
these origins and identifying scientific branches is crucial for research
inspirations. In this paper, we use citation relations to identify the
descendant chart, i.e. the family tree of research papers. Unlike other
spanning trees which focus on cost or distance minimization, we make use of the
nature of citations and identify the most important parent for each
publication, leading to a tree-like backbone of the citation network. Measures
are introduced to validate the backbone as the descendant chart. We show that
citation backbones can well characterize the hierarchical and fractal structure
of scientific development, and lead to accurate classification of fields and
sub-fields.Comment: 6 pages, 5 figure
Models of Financial Markets with Extensive Participation Incentives
We consider models of financial markets in which all parties involved find
incentives to participate. Strategies are evaluated directly by their virtual
wealths. By tuning the price sensitivity and market impact, a phase diagram
with several attractor behaviors resembling those of real markets emerge,
reflecting the roles played by the arbitrageurs and trendsetters, and including
a phase with irregular price trends and positive sums. The positive-sumness of
the players' wealths provides participation incentives for them. Evolution and
the bid-ask spread provide mechanisms for the gain in wealth of both the
players and market-makers. New players survive in the market if the
evolutionary rate is sufficiently slow. We test the applicability of the model
on real Hang Seng Index data over 20 years. Comparisons with other models show
that our model has a superior average performance when applied to real
financial data.Comment: 17 pages, 16 figure
Coarsening Dynamics of a One-Dimensional Driven Cahn-Hilliard System
We study the one-dimensional Cahn-Hilliard equation with an additional
driving term representing, say, the effect of gravity. We find that the driving
field has an asymmetric effect on the solution for a single stationary
domain wall (or `kink'), the direction of the field determining whether the
analytic solutions found by Leung [J.Stat.Phys.{\bf 61}, 345 (1990)] are
unique. The dynamics of a kink-antikink pair (`bubble') is then studied. The
behaviour of a bubble is dependent on the relative sizes of a characteristic
length scale , where is the driving field, and the separation, ,
of the interfaces. For the velocities of the interfaces are
negligible, while in the opposite limit a travelling-wave solution is found
with a velocity . For this latter case () a set of
reduced equations, describing the evolution of the domain lengths, is obtained
for a system with a large number of interfaces, and implies a characteristic
length scale growing as . Numerical results for the domain-size
distribution and structure factor confirm this behavior, and show that the
system exhibits dynamical scaling from very early times.Comment: 20 pages, revtex, 10 figures, submitted to Phys. Rev.
Dynamics of Ordering of Heisenberg Spins with Torque --- Nonconserved Case. I
We study the dynamics of ordering of a nonconserved Heisenberg magnet. The
dynamics consists of two parts --- an irreversible dissipation into a heat bath
and a reversible precession induced by a torque due to the local molecular
field. For quenches to zero temperature, we provide convincing arguments, both
numerically (Langevin simulation) and analytically (approximate closure scheme
due to Mazenko), that the torque is irrelevant at late times. We subject the
Mazenko closure scheme to systematic numerical tests. Such an analysis, carried
out for the first time on a vector order parameter, shows that the closure
scheme performs respectably well. For quenches to , we show, to , that the torque is irrelevant at the Wilson-Fisher fixed
point.Comment: 13 pages, REVTEX, and 19 .eps figures, compressed, Submitted to Phys.
Rev.
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