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

Simultaneous message framing and error detection

Circuitry simultaneously inserts message framing information and detects noise errors in binary code data transmissions. Separate message groups are framed without requiring both framing bits and error-checking bits, and predetermined message sequence are separated from other message sequences without being hampered by intervening noise

Long-range and many-body effects in coagulation processes

We study the problem of diffusing particles which coalesce upon contact. With the aid of a nonperturbative renormalization group, we first analyze the dynamics emerging below the critical dimension two, where strong fluctuations imply anomalously slow decay. Above two dimensions, the long-time, low-density behavior is known to conform with the law of mass action. For this case, we establish an exact mapping between the physics at the microscopic scale (lattice structure, particle shape and size) and the macroscopic decay rate in the law of mass action. In addition, we identify a term violating this classical law. It originates in long-range and many-particle fluctuations and is a simple, universal function of the macroscopic decay rate. DOI: 10.1103/PhysRevE.87.02213

El Hermanito: El Niño's overlooked little brother in the Atlantic

An oscillation with a period of about 30 months has been identified in the equatorial Atlantic by analyzing sea surface temperature (SST) observations for the period 1949-1991. The 30-month time scale was also found in numerical simulations with an atmospheric general circulation model (AGCM) that was forced by these SSTs and a coupled ocean atmosphere general circulation model (CGCM). Consistent with the theory of tropical air-sea interactions, the Atlantic oscillation (El Hermanito) is an inherently coupled air-sea mode and can be viewed as the Atlantic analogon of the El Nino/Southern Oscillation (ENSO) phenomenon in the equatorial Pacific. El Hermanito is an internal Atlantic mode and appears to be independent of the quasi-biennial (QB) variability observed in the tropical Indian and Pacific Oceans. The discovery of El Hermanito is important to the prediction of Atlantic climate anomalies. (orig.

Understanding Collective Dynamics of Soft Active Colloids by Binary Scattering

Collective motion in actively propelled particle systems is triggered on the very local scale by nucleation of coherently moving units consisting of just a handful of particles. These units grow and merge over time, ending up in a long-range ordered, coherently-moving state. So far, there exists no bottom-up understanding of how the microscopic dynamics and interactions between the constituents are related to the system's ordering instability. In this paper, we study a class of models for propelled colloids allowing an explicit treatment of the microscopic details of the collision process. Specifically, the model equations are Newtonian equations of motion with separate force terms for particles' driving, dissipation and interaction forces. Focusing on dilute particle systems, we analyze the binary scattering behavior for these models, and determine-based on the microscopic dynamics-the corresponding collision-rule, i.e., the mapping of pre-collisional velocities and impact parameter on post-collisional velocities. By studying binary scattering we also find that the considered models for active colloids share the same principle for parallel alignment: the first incoming particle (with respect to the center of collision) is aligned to the second particle as a result of the encounter. This behavior is distinctively different to alignment in non-driven dissipative gases. Moreover, the obtained collision rule lends itself as a starting point to apply kinetic theory for propelled particle systems in order to determine the phase boundary to a long-range ordered, coherently-moving state. The microscopic origin of the collision rule offers the opportunity to quantitatively scrutinize the predictions of kinetic theory for propelled particle systems through direct comparison with multi-particle simulations.Comment: 19 pages, 12 figure

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

Role of particle conservation in self-propelled particle systems

Actively propelled particles undergoing dissipative collisions are known to develop a state of spatially distributed coherently moving clusters. For densities larger than a characteristic value, clusters grow in time and form a stationary well-ordered state of coherent macroscopic motion. In this work we address two questions. (i) What is the role of the particles’ aspect ratio in the context of cluster formation, and does the particle shape affect the system’s behavior on hydrodynamic scales? (ii) To what extent does particle conservation influence pattern formation? To answer these questions we suggest a simple kinetic model permitting us to depict some of the interaction properties between freely moving particles and particles integrated in clusters. To this end, we introduce two particle species: single and cluster particles. Specifically, we account for coalescence of clusters from single particles, assembly of single particles on existing clusters, collisions between clusters and cluster disassembly. Coarse graining our kinetic model, (i) we demonstrate that particle shape (i.e. aspect ratio) shifts the scale of the transition density, but does not impact the instabilities at the ordering threshold and (ii) we show that the validity of particle conservation determines the existence of a longitudinal instability, which tends to amplify density heterogeneities locally, and in turn triggers a wave pattern with wave vectors parallel to the axis of macroscopic order. If the system is in contact with a particle reservoir, this instability vanishes due to a compensation of density heterogeneities

A Critical Assessment of the Boltzmann Approach for Active Systems

Generic models of propelled particle systems posit that the emergence of polar order is driven by the competition between local alignment and noise. Although this notion has been confirmed employing the Boltzmann equation, the range of applicability of this equation remains elusive. We introduce a broad class of mesoscopic collision rules and analyze the prerequisites for the emergence of polar order in the framework of kinetic theory. Our findings suggest that a Boltzmann approach is appropriate for weakly aligning systems but is incompatible with experiments on cluster forming systems.Comment: 11 pages, 3 figure