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 $\approx$ 70-80 meV which produce peak in the noise at T $\approx$ 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 $K_c =2$ in the limit of large system size $N$. 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 $\sigma_A = \sigma/sin k$ where $\sigma^2$ is the variance of the disorder distribution and $k$ the wavevector. It undergoes a transition from uniformity to singular behaviour as $\sigma_A$ increases. The distribution of delay times shows universal power law tails $~ 1/\tau^2$, while the short time behaviour is $\sigma_A$- 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