Extinction in neutrally stable stochastic Lotka-Volterra models

Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes leading to extinction of species, whose understanding is a key component in the study of evolution and biodiversity, are influenced by both of these factors. In this paper, we investigate a class of stochastic population dynamics models based on generalized Lotka-Volterra systems. In the case of neutral stability of the underlying deterministic model, the impact of intrinsic noise on the survival of species is dramatic: it destroys coexistence of interacting species on a time scale proportional to the population size. We introduce a new method based on stochastic averaging which allows one to understand this extinction process quantitatively by reduction to a lower-dimensional effective dynamics. This is performed analytically for two highly symmetrical models and can be generalized numerically to more complex situations. The extinction probability distributions and other quantities of interest we obtain show excellent agreement with simulations.Comment: 14 pages, 7 figure

Driven lattice gas of dimers coupled to a bulk reservoir

We investigate the non-equilibrium steady state of a one-dimensional (1D) lattice gas of dimers. The dynamics is described by a totally asymmetric exclusion process (TASEP) supplemented by attachment and detachment processes, mimicking chemical equilibrium of the 1D driven transport with the bulk reservoir. The steady-state phase diagram, current and density profiles are calculated using both a refined mean-field theory and extensive stochastic simulations. As a consequence of the on-off kinetics, a new phase coexistence region arises intervening between low and high density phases such that the discontinuous transition line of the TASEP splits into two continuous ones. The results of the mean-field theory and simulations are found to coincide. We show that the physical picture obtained in the corresponding lattice gas model with monomers is robust, in the sense that the phase diagram changes quantitatively, but the topology remains unaltered. The mechanism for phase separation is identified as generic for a wide class of driven 1D lattice gases.Comment: 15 pages, 10 figures, 1tabl

The effect of internal and global modes on the radial distribution function of confined semiflexible polymers

The constraints imposed by nano- and microscale confinement on the conformational degrees of freedom of thermally fluctuating biopolymers are utilized in contemporary nano-devices to specifically elongate and manipulate single chains. A thorough theoretical understanding and quantification of the statistical conformations of confined polymer chains is thus a central concern in polymer physics. We present an analytical calculation of the radial distribution function of harmonically confined semiflexible polymers in the weakly bending limit. Special emphasis has been put on a proper treatment of global modes, i.e. the possibility of the chain to perform global movements within the channel. We show that the effect of these global modes significantly impacts the chain statistics in cases of weak and intermediate confinement. Comparing our analytical model to numerical data from Monte Carlo simulations we find excellent agreement over a broad range of parameters.Comment: 6 pages, 3 figures typo corrected, slightly revised line of reasoning, results unchange

Phase perturbation measurements through a heated ionosphere

High frequency radiowaves incident on an overdense (i.e., HF-frequency penetration frequency) ionosphere produce electron density irregularities. The effect of such ionospheric irregularities on the phase of UHF-radiowaves was determined. For that purpose the phase of radiowaves originating from celestial radio sources was observed with two antennas. The radiosources were chosen such that the line of sight to at least one of the antennas (usually both) passed through the modified volume of the ionosphere. Observations at 430 MHz and at 2380 MHz indicate that natural irregularities have a much stronger effect on the UHF phase fluctuations than the HF-induced irregularities for presently achieved HF-power densities of 20-80 uW/sq m. It is not clear whether some of the effects observed are the result of HF-modification of the ionosphere. Upper limits on the phase perturbations produced by HF-modification are 10 deg at 2380 MHz and 80 deg at 430 MHz

Identification of Potential Weak Target Radio Quasars for ASTRO-G In-Beam Phase-Referencing

We apply an efficient selection method to identify potential weak Very Long Baseline Interferometry (VLBI) target quasars simply using optical (SDSS) and low-resolution radio (FIRST) catalogue data. Our search is restricted to within 12" from known compact radio sources that are detectable as phase-reference calibrators for ASTRO-G at 8.4 GHz frequency. These calibrators have estimated correlated flux density >20 mJy on the longest ground-space VLBI baselines. The search radius corresponds to the primary beam size of the ASTRO-G antenna. We show that ~20 quasars with at least mJy-level expected flux density can be pre-selected as potential in-beam phase-reference targets for ASTRO-G at 8.4 GHz frequency. Most of them have never been imaged with VLBI. The sample of these dominantly weak sources offers a good opportunity to study their radio structures with unprecedented angular resolution provided by Space VLBI. The method of in-beam phase-referencing is independent from the ability of the orbiting radio telescope to do rapid position-switching manoeuvres between the calibrators and the nearby reference sources, and less sensitive to the satellite orbit determination uncertainties.Comment: 5 pages, accepted for the Publ. Astron. Soc. Japan (Vol. 61, No. 1, Feb 2009

Dipolar Interactions in Superconductor-Ferromagnet Heterostructures

We consider a simple model for a superlattice composed of a thin magnetic film placed between two bulk superconductors. The magnetic film is modelled by a planar but otherwise arbitrary distribution of magnetic dipoles and the superconductors are treated in the London approximation. Due to the linearity of the problem, we are able to compute the magnetic energy of the film in the presence of the superconductors. We show that in the case of small wavenumbers compared to the inverse London penetration depth, the magnetic energy resembles the energy of a distribution of magnetisation in a two dimensional space. Possible experimental applications of these results are discussed.Comment: RevTeX, 29 pages, 3 figures. To be published in Phys. Rev. B. Changes were made (including adding fig. 3), to conform with the referee's report. Reference 54 was also adde

Dynamic Light Scattering from Semidilute Actin Solutions: A Study of Hydrodynamic Screening, Filament Bending Stiffness and the Effect of Tropomyosin/Troponin-Binding

Quasi-elastic light scattering (QELS) is applied to investigate the effect of the tropomyosin/troponin complex (Tm/Tn) on the stiffness of actin filaments. The importance of hydrodynamic screening in semidilute solutions is demonstrated. A new concentration dependent expression for the dynamic structure factor $g(\bm k,t)$ of semiflexible polymers in semidilute solutions is used to analyze the experimental QELS data. A concentration independent value for the bending modulus $\kappa$ is thus obtained. It increases by 50\% as a consequence of Tm/Tn binding in a 7:1:1 molar ratio of actin/Tm/Tn. In addition a new expression for the initial slope of the dynamic structure factor of a semiflexible polymer is used to determine the effective hydrodynamic diameter of the actin filament. Our results confirm the general relevance of the concept of (intrinsic) semiflexibility to polymer dynamics.Comment: 9 pages, RevTeX, 9 figures, all uuencoded gzipe

Exact results for the Kardar--Parisi--Zhang equation with spatially correlated noise

We investigate the Kardar--Parisi--Zhang (KPZ) equation in $d$ spatial dimensions with Gaussian spatially long--range correlated noise --- characterized by its second moment $R(\vec{x}-\vec{x}') \propto |\vec{x}-\vec{x}'|^{2\rho-d}$ --- by means of dynamic field theory and the renormalization group. Using a stochastic Cole--Hopf transformation we derive {\em exact} exponents and scaling functions for the roughening transition and the smooth phase above the lower critical dimension $d_c = 2 (1+\rho)$. Below the lower critical dimension, there is a line $\rho_*(d)$ marking the stability boundary between the short-range and long-range noise fixed points. For $\rho \geq \rho_*(d)$, the general structure of the renormalization-group equations fixes the values of the dynamic and roughness exponents exactly, whereas above $\rho_*(d)$, one has to rely on some perturbational techniques. We discuss the location of this stability boundary $\rho_* (d)$ in light of the exact results derived in this paper, and from results known in the literature. In particular, we conjecture that there might be two qualitatively different strong-coupling phases above and below the lower critical dimension, respectively.Comment: 21 pages, 15 figure