43 research outputs found
Pattern Formation of Ion Channels with State Dependent Electrophoretic Charges and Diffusion Constants in Fluid Membranes
A model of mobile, charged ion channels in a fluid membrane is studied. The
channels may switch between an open and a closed state according to a simple
two-state kinetics with constant rates. The effective electrophoretic charge
and the diffusion constant of the channels may be different in the closed and
in the open state. The system is modeled by densities of channel species,
obeying simple equations of electro-diffusion. The lateral transmembrane
voltage profile is determined from a cable-type equation. Bifurcations from the
homogeneous, stationary state appear as hard-mode, soft-mode or hard-mode
oscillatory transitions within physiologically reasonable ranges of model
parameters. We study the dynamics beyond linear stability analysis and derive
non-linear evolution equations near the transitions to stationary patterns.Comment: 10 pages, 7 figures, will be submitted to Phys. Rev.
Phase Transitions in Operational Risk
In this paper we explore the functional correlation approach to operational
risk. We consider networks with heterogeneous a-priori conditional and
unconditional failure probability. In the limit of sparse connectivity,
self-consistent expressions for the dynamical evolution of order parameters are
obtained. Under equilibrium conditions, expressions for the stationary states
are also obtained. The consequences of the analytical theory developed are
analyzed using phase diagrams. We find co-existence of operational and
non-operational phases, much as in liquid-gas systems. Such systems are
susceptible to discontinuous phase transitions from the operational to
non-operational phase via catastrophic breakdown. We find this feature to be
robust against variation of the microscopic modelling assumptions.Comment: 13 pages, 7 figures. Accepted in Physical Review
Low energy excitations in crystalline perovskite oxides: Evidence from noise experiments
In this paper we report measurements of 1/f noise in a crystalline metallic
oxide with perovskite structure down to 4.2K. The results show existence of
localized excitations with average activation energy 70-80 meV which
produce peak in the noise at T 35-40K. In addition, it shows clear
evidence of tunnelling type two-level-systems (as in glasses) which show up in
noise measurements below 30K.Comment: 11 pages, 4 figures, to appear in Phys Rev B, vol 58, 1st Dec issu
New Kernels in Quantum Gravity
Recent work in the literature has proposed the use of non-local boundary
conditions in Euclidean quantum gravity. The present paper studies first a more
general form of such a scheme for bosonic gauge theories, by adding to the
boundary operator for mixed boundary conditions of local nature a two-by-two
matrix of pseudo-differential operators with pseudo-homogeneous kernels. The
request of invariance of such boundary conditions under infinitesimal gauge
transformations leads to non-local boundary conditions on ghost fields. In
Euclidean quantum gravity, an alternative scheme is proposed, where non-local
boundary conditions and the request of their complete gauge invariance are
sufficient to lead to gauge-field and ghost operators of pseudo-differential
nature. The resulting boundary conditions have a Dirichlet and a
pseudo-differential sector, and are pure Dirichlet for the ghost. This approach
is eventually extended to Euclidean Maxwell theory.Comment: 19 pages, plain Tex. In this revised version, section 5 is new,
section 3 is longer, and the presentation has been improve
Topological Evolution of Dynamical Networks: Global Criticality from Local Dynamics
We evolve network topology of an asymmetrically connected threshold network
by a simple local rewiring rule: quiet nodes grow links, active nodes lose
links. This leads to convergence of the average connectivity of the network
towards the critical value in the limit of large system size . How
this principle could generate self-organization in natural complex systems is
discussed for two examples: neural networks and regulatory networks in the
genome.Comment: 4 pages RevTeX, 4 figures PostScript, revised versio
Statistical properties of phases and delay times of the one-dimensional Anderson model with one open channel
We study the distribution of phases and of Wigner delay times for a
one-dimensional Anderson model with one open channel. Our approach, based on
classical Hamiltonian maps, allows us an analytical treatment. We find that the
distribution of phases depends drastically on the parameter where is the variance of the disorder distribution and
the wavevector. It undergoes a transition from uniformity to singular
behaviour as increases. The distribution of delay times shows
universal power law tails , while the short time behaviour is
- dependent.Comment: 4 pages, 2 figures, Submitted to PR
Field theory for a reaction-diffusion model of quasispecies dynamics
RNA viruses are known to replicate with extremely high mutation rates. These
rates are actually close to the so-called error threshold. This threshold is in
fact a critical point beyond which genetic information is lost through a
second-order phase transition, which has been dubbed the ``error catastrophe.''
Here we explore this phenomenon using a field theory approximation to the
spatially extended Swetina-Schuster quasispecies model [J. Swetina and P.
Schuster, Biophys. Chem. {\bf 16}, 329 (1982)], a single-sharp-peak landscape.
In analogy with standard absorbing-state phase transitions, we develop a
reaction-diffusion model whose discrete rules mimic the Swetina-Schuster model.
The field theory representation of the reaction-diffusion system is
constructed. The proposed field theory belongs to the same universality class
than a conserved reaction-diffusion model previously proposed [F. van Wijland
{\em et al.}, Physica A {\bf 251}, 179 (1998)]. From the field theory, we
obtain the full set of exponents that characterize the critical behavior at the
error threshold. Our results present the error catastrophe from a new point of
view and suggest that spatial degrees of freedom can modify several mean field
predictions previously considered, leading to the definition of characteristic
exponents that could be experimentally measurable.Comment: 13 page
Field theory of absorbing phase transitions with a non-diffusive conserved field
We investigate the critical behavior of a reaction-diffusion system
exhibiting a continuous absorbing-state phase transition. The
reaction-diffusion system strictly conserves the total density of particles,
represented as a non-diffusive conserved field, and allows an infinite number
of absorbing configurations. Numerical results show that it belongs to a wide
universality class that also includes stochastic sandpile models. We derive
microscopically the field theory representing this universality class.Comment: 13 pages, 1 eps figure, RevTex styl