141 research outputs found
Anomalously slow phase transitions in self-gravitating systems
Kinetics of collapse and explosion transitions in microcanonical
self-gravitating ensembles is analyzed. A system of point particles interacting
via an attractive soft Coulomb potential and confined to a spherical container
is considered. We observed that for 100--200 particles collapse takes --
particle crossing times to complete, i. e., it is by 2-3 orders of
magnitude slower than velocity relaxation. In addition, it is found that the
collapse time decreases rapidly with the increase of the softcore radius. We
found that such an anomalously long collapse time is caused by the slow energy
exchange between a higher-temperature compact core and relatively cold diluted
halo. The rate of energy exchange between the faster modes of the core
particles and slower-moving particles of the halo is exponentially small in the
ratio of the frequencies of these modes. As the softcore radius increases, and
the typical core modes become slower, the ratio of core and halo frequencies
decreases and the collapse accelerates. Implications to astrophysical systems
and phase transition kinetics are discussed.Comment: 6 pages, 5 figure
Finding mesoscopic communities in sparse networks
We suggest a fast method to find possibly overlapping network communities of
a desired size and link density. Our method is a natural generalization of the
finite- superparamegnetic Potts clustering introduced by Blatt, Wiseman, and
Domany (Phys. Rev. Lett. v.76, 3251 (1996) and the recently suggested by
Reichard and Bornholdt (Phys. Rev. Lett. v.93, 21870 (2004)) annealing of Potts
model with global antiferromagnetic term. Similarly to both preceding works,
the proposed generalization is based on ordering of ferromagnetic Potts model;
the novelty of the proposed approach lies in the adjustable dependence of the
antiferromagnetic term on the population of each Potts state, which
interpolates between the two previously considered cases. This adjustability
allows to empirically tune the algorithm to detect the maximum number of
communities of the given size and link density. We illustrate the method by
detecting protein complexes in high-throughput protein binding networks.Comment: 8 pages, 2 figure, typos corrected, 1 figure adde
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
Collapses and explosions in self-gravitating systems
Collapse and reverse to collapse explosion transition in self-gravitating
systems are studied by molecular dynamics simulations. A microcanonical
ensemble of point particles confined to a spherical box is considered; the
particles interact via an attractive soft Coulomb potential. It is observed
that the collapse in the particle system indeed takes place when the energy of
the uniform state is put near or below the metastability-instability threshold
(collapse energy), predicted by the mean-field theory. Similarly, the explosion
in the particle system occurs when the energy of the core-halo state is
increased above the explosion energy, where according to the mean field
predictions the core-halo state becomes unstable. For a system consisting of
125 -- 500 particles, the collapse takes about single particle crossing
times to complete, while a typical explosion is by an order of magnitude
faster. A finite lifetime of metastable states is observed. It is also found
that the mean-field description of the uniform and the core-halo states is
exact within the statistical uncertainty of the molecular dynamics data.Comment: 9 pages, 14 figure
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