257 research outputs found
Fluctuation spectrum of quasispherical membranes with force-dipole activity
The fluctuation spectrum of a quasi-spherical vesicle with active membrane
proteins is calculated. The activity of the proteins is modeled as the proteins
pushing on their surroundings giving rise to non-local force distributions.
Both the contributions from the thermal fluctuations of the active protein
densities and the temporal noise in the individual active force distributions
of the proteins are taken into account. The noise in the individual force
distributions is found to become significant at short wavelengths.Comment: 9 pages, 2 figures, minor changes and addition
Entropy Production of Brownian Macromolecules with Inertia
We investigate the nonequilibrium steady-state thermodynamics of single
Brownian macromolecules with inertia under feedback control in isothermal
ambient fluid. With the control being represented by a velocity-dependent
external force, we find such open systems can have a negative entropy
production rate and we develop a mesoscopic theory consistent with the second
law. We propose an equilibrium condition and define a class of external forces,
which includes a transverse Lorentz force, leading to equilibrium.Comment: 10 pages, 1 figur
Can kinomics and proteomics bridge the gap between pediatric cancers and newly designed kinase inhibitors?
status: publishe
Compositionality, stochasticity and cooperativity in dynamic models of gene regulation
We present an approach for constructing dynamic models for the simulation of
gene regulatory networks from simple computational elements. Each element is
called a ``gene gate'' and defines an input/output-relationship corresponding
to the binding and production of transcription factors. The proposed reaction
kinetics of the gene gates can be mapped onto stochastic processes and the
standard ode-description. While the ode-approach requires fixing the system's
topology before its correct implementation, expressing them in stochastic
pi-calculus leads to a fully compositional scheme: network elements become
autonomous and only the input/output relationships fix their wiring. The
modularity of our approach allows to pass easily from a basic first-level
description to refined models which capture more details of the biological
system. As an illustrative application we present the stochastic repressilator,
an artificial cellular clock, which oscillates readily without any cooperative
effects.Comment: 15 pages, 8 figures. Accepted by the HFSP journal (13/09/07
Cluster approximations for infection dynamics on random networks
In this paper, we consider a simple stochastic epidemic model on large
regular random graphs and the stochastic process that corresponds to this
dynamics in the standard pair approximation. Using the fact that the nodes of a
pair are unlikely to share neighbors, we derive the master equation for this
process and obtain from the system size expansion the power spectrum of the
fluctuations in the quasi-stationary state. We show that whenever the pair
approximation deterministic equations give an accurate description of the
behavior of the system in the thermodynamic limit, the power spectrum of the
fluctuations measured in long simulations is well approximated by the
analytical power spectrum. If this assumption breaks down, then the cluster
approximation must be carried out beyond the level of pairs. We construct an
uncorrelated triplet approximation that captures the behavior of the system in
a region of parameter space where the pair approximation fails to give a good
quantitative or even qualitative agreement. For these parameter values, the
power spectrum of the fluctuations in finite systems can be computed
analytically from the master equation of the corresponding stochastic process.Comment: the notation has been changed; Ref. [26] and a new paragraph in
Section IV have been adde
Dynamic Mean-Field Glass Model with Reversible Mode Coupling and Trivial Hamiltonian
Often the current mode coupling theory (MCT) of glass transitions is compared
with mean field theories. We explore this possible correspondence. After
showing a simple-minded derivation of MCT with some difficulties we give a
concise account of our toy model developed to gain more insight into MCT. We
then reduce this toy model by adiabatically eliminating rapidly varying
velocity-like variables to obtain a Fokker-Planck equation for the slowly
varying density-like variables where diffusion matrix can be singular. This
gives a room for nonergodic stationary solutions of the above equation.Comment: 9 pages, contribution to the Proceedings of the Merida Satellite
Meeting to STATPHYS21 (Merida, Mexico, July 9-14, 2001). To appear in J.
Phys. Condens. Matte
Information spreading and development of cultural centers
The historical interplay between societies are governed by many factors,
including in particular spreading of languages, religion and other symbolic
traits. Cultural development, in turn, is coupled to emergence and maintenance
of information spreading. Strong centralized cultures exist thanks to attention
from their members, which faithfulness in turn relies on supply of information.
Here, we discuss a culture evolution model on a planar geometry that takes into
account aspects of the feedback between information spreading and its
maintenance. Features of model are highlighted by comparing it to cultural
spreading in ancient and medieval Europe, where it in particular suggests that
long lived centers should be located in geographically remote regions.Comment: 7 pages, 5 figure
Mapping between dissipative and Hamiltonian systems
Theoretical studies of nonequilibrium systems are complicated by the lack of
a general framework. In this work we first show that a transformation
introduced by Ao recently (J. Phys. A {\bf 37}, L25 (2004)) is related to
previous works of Graham (Z. Physik B {\bf 26}, 397 (1977)) and Eyink {\it et
al.} (J. Stat. Phys. {\bf 83}, 385 (1996)), which can also be viewed as the
generalized application of the Helmholtz theorem in vector calculus. We then
show that systems described by ordinary stochastic differential equations with
white noise can be mapped to thermostated Hamiltonian systems. A steady-state
of a dissipative system corresponds to the equilibrium state of the
corresponding Hamiltonian system. These results provides a solid theoretical
ground for corresponding studies on nonequilibrium dynamics, especially on
nonequilibrium steady state. The mapping permits the application of established
techniques and results for Hamiltonian systems to dissipative non-Hamiltonian
systems, those for thermodynamic equilibrium states to nonequilibrium steady
states. We discuss several implications of the present work.Comment: 18 pages, no figure. final version for publication on J. Phys. A:
Math & Theo
Conservation Laws and Integrability of a One-dimensional Model of Diffusing Dimers
We study a model of assisted diffusion of hard-core particles on a line. The
model shows strongly ergodicity breaking : configuration space breaks up into
an exponentially large number of disconnected sectors. We determine this
sector-decomposion exactly. Within each sector the model is reducible to the
simple exclusion process, and is thus equivalent to the Heisenberg model and is
fully integrable. We discuss additional symmetries of the equivalent quantum
Hamiltonian which relate observables in different sectors. In some sectors, the
long-time decay of correlation functions is qualitatively different from that
of the simple exclusion process. These decays in different sectors are deduced
from an exact mapping to a model of the diffusion of hard-core random walkers
with conserved spins, and are also verified numerically. We also discuss some
implications of the existence of an infinity of conservation laws for a
hydrodynamic description.Comment: 39 pages, with 5 eps figures, to appear in J. Stat. Phys. (March
1997
Mobility and stochastic resonance in spatially inhomogeneous system
The mobility of an overdamped particle, in a periodic potential tilted by a
constant external field and moving in a medium with periodic friction
coefficient is examined. When the potential and the friction coefficient have
the same periodicity but have a phase difference, the mobility shows many
interesting features as a function of the applied force, the temperature, etc.
The mobility shows stochastic resonance even for constant applied force, an
issue of much recent interest. The mobility also exhibits a resonance like
phenomenon as a function of the field strength and noise induced slowing down
of the particle in an appropriate parameter regime.Comment: 14 pages, 12 figures. Submitted to Phys. Rev.
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