143 research outputs found
Ballistic Coalescence Model
We study statistical properties of a one dimensional infinite system of
coalescing particles. Each particle moves with constant velocity
towards its closest neighbor and merges with it upon collision. We propose a
mean-field theory that confirms a concentration decay obtained in
simulations and provides qualitative description for the densities of growing,
constant, and shrinking inter-particle gaps.Comment: 4 pages, 2 column Revtex, 5 figures include
Wealth Distributions in Models of Capital Exchange
A dynamical model of capital exchange is introduced in which a specified
amount of capital is exchanged between two individuals when they meet. The
resulting time dependent wealth distributions are determined for a variety of
exchange rules. For ``greedy'' exchange, an interaction between a rich and a
poor individual results in the rich taking a specified amount of capital from
the poor. When this amount is independent of the capitals of the two traders, a
mean-field analysis yields a Fermi-like scaled wealth distribution in the
long-time limit. This same distribution also arises in greedier exchange
processes, where the interaction rate is an increasing function of the capital
difference of the two traders. The wealth distribution in multiplicative
processes, where the amount of capital exchanged is a finite fraction of the
capital of one of the traders, are also discussed. For random multiplicative
exchange, a steady state wealth distribution is reached, while in greedy
multiplicative exchange a non-steady power law wealth distribution arises, in
which the support of the distribution continuously increases. Finally,
extensions of our results to arbitrary spatial dimension and to growth
processes, where capital is created in an interaction, are presented.Comment: 10 pages, RevTeX, 4 figures, to be submitted to PR
Propagation of fluctuations in interaction networks governed by the law of mass action
Using an example of physical interactions between proteins, we study how
perturbations propagate in interconnected networks whose equilibrium state is
governed by the law of mass action. We introduce a comprehensive matrix
formalism which predicts the response of this equilibrium to small changes in
total concentrations of individual molecules, and explain it using a heuristic
analogy to a current flow in a network of resistors. Our main conclusion is
that on average changes in free concentrations exponentially decay with the
distance from the source of perturbation. We then study how this decay is
influenced by such factors as the topology of a network, binding strength, and
correlations between concentrations of neighboring nodes. An exact analytic
expression for the decay constant is obtained for the case of uniform
interactions on the Bethe lattice. Our general findings are illustrated using a
real biological network of protein-protein interactions in baker's yeast with
experimentally determined protein concentrations.Comment: 4 pages; 2 figure
Binaries and core-ring structures in self-gravitating systems
Low energy states of self-gravitating systems with finite angular momentum
are considered. A constraint is introduced to confine cores and other condensed
objects within the system boundaries by gravity alone. This excludes previously
observed astrophysically irrelevant asymmetric configurations with a single
core. We show that for an intermediate range of a short-distance cutoff and
small angular momentum, the equilibrium configuration is an asymmetric binary.
For larger angular momentum or for a smaller range of the short distance
cutoff, the equilibrium configuration consists of a central core and an
equatorial ring. The mass of the ring varies between zero for vanishing
rotation and the full system mass for the maximum angular momentum a
localized gravitationally bound system can have. The value of scales
as , where is a ratio of a short-distance cutoff range
to the system size. An example of the soft gravitational potential is
considered; the conclusions are shown to be valid for other forms of
short-distance regularization.Comment: 6 pages, 3 figure
Particle Systems with Stochastic Passing
We study a system of particles moving on a line in the same direction.
Passing is allowed and when a fast particle overtakes a slow particle, it
acquires a new velocity drawn from a distribution P_0(v), while the slow
particle remains unaffected. We show that the system reaches a steady state if
P_0(v) vanishes at its lower cutoff; otherwise, the system evolves
indefinitely.Comment: 5 pages, 5 figure
Ensemble inequivalence: A formal approach
Ensemble inequivalence has been observed in several systems. In particular it
has been recently shown that negative specific heat can arise in the
microcanonical ensemble in the thermodynamic limit for systems with long-range
interactions. We display a connection between such behaviour and a mean-field
like structure of the partition function. Since short-range models cannot
display this kind of behaviour, this strongly suggests that such systems are
necessarily non-mean field in the sense indicated here. We further show that a
broad class of systems with non-integrable interactions are indeed of
mean-field type in the sense specified, so that they are expected to display
ensemble inequivalence as well as the peculiar behaviour described above in the
microcanonical ensemble.Comment: 4 pages, no figures, given at the NEXT2001 conference on
non-extensive thermodynamic
On the evolution of decoys in plant immune systems
The Guard-Guardee model for plant immunity describes how resistance proteins
(guards) in host cells monitor host target proteins (guardees) that are
manipulated by pathogen effector proteins. A recently suggested extension of
this model includes decoys, which are duplicated copies of guardee proteins,
and which have the sole function to attract the effector and, when modified by
the effector, trigger the plant immune response. Here we present a
proof-of-principle model for the functioning of decoys in plant immunity,
quantitatively developing this experimentally-derived concept. Our model links
the basic cellular chemistry to the outcomes of pathogen infection and
resulting fitness costs for the host. In particular, the model allows
identification of conditions under which it is optimal for decoys to act as
triggers for the plant immune response, and of conditions under which it is
optimal for decoys to act as sinks that bind the pathogen effectors but do not
trigger an immune response.Comment: 15 pages, 6 figure
Nonconcave entropies from generalized canonical ensembles
It is well-known that the entropy of the microcanonical ensemble cannot be
calculated as the Legendre transform of the canonical free energy when the
entropy is nonconcave. To circumvent this problem, a generalization of the
canonical ensemble which allows for the calculation of nonconcave entropies was
recently proposed. Here, we study the mean-field Curie-Weiss-Potts spin model
and show, by direct calculations, that the nonconcave entropy of this model can
be obtained by using a specific instance of the generalized canonical ensemble
known as the Gaussian ensemble.Comment: 5 pages, RevTeX4, 3 figures (best viewed in ps
Cliques and duplication-divergence network growth
A population of complete subgraphs or cliques in a network evolving via
duplication-divergence is considered. We find that a number of cliques of each
size scales linearly with the size of the network. We also derive a clique
population distribution that is in perfect agreement with both the simulation
results and the clique statistic of the protein-protein binding network of the
fruit fly. In addition, we show that such features as fat-tail degree
distribution, various rates of average degree growth and non-averaging,
revealed recently for only the particular case of a completely asymmetric
divergence, are present in a general case of arbitrary divergence.Comment: 7 pages, 6 figure
Generalized canonical ensembles and ensemble equivalence
This paper is a companion article to our previous paper (J. Stat. Phys. 119,
1283 (2005), cond-mat/0408681), which introduced a generalized canonical
ensemble obtained by multiplying the usual Boltzmann weight factor of the canonical ensemble with an exponential factor involving a continuous
function of the Hamiltonian . We provide here a simplified introduction
to our previous work, focusing now on a number of physical rather than
mathematical aspects of the generalized canonical ensemble. The main result
discussed is that, for suitable choices of , the generalized canonical
ensemble reproduces, in the thermodynamic limit, all the microcanonical
equilibrium properties of the many-body system represented by even if this
system has a nonconcave microcanonical entropy function. This is something that
in general the standard () canonical ensemble cannot achieve. Thus a
virtue of the generalized canonical ensemble is that it can be made equivalent
to the microcanonical ensemble in cases where the canonical ensemble cannot.
The case of quadratic -functions is discussed in detail; it leads to the
so-called Gaussian ensemble.Comment: 8 pages, 4 figures (best viewed in ps), revtex4. Changes in v2: Title
changed, references updated, new paragraph added, minor differences with
published versio
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