Cooperative hunting in a discrete predator-prey system

We propose and investigate a discrete-time predator-prey system with cooperative hunting in the predator population. The model is constructed from the classical Nicholson-Bailey host-parasitoid system with density dependent growth rate. A sufficient condition based on the model parameters for which both populations can coexist is derived, namely that the predator's maximal reproductive number exceeds one. We study existence of interior steady states and their stability in certain parameter regimes. It is shown that the system behaves asymptotically similar to the model with no cooperative hunting if the degree of cooperation is small. Large cooperative hunting, however, may promote persistence of the predator for which the predator would otherwise go extinct if there were no cooperation

On the Penrose Inequality for general horizons

For asymptotically flat initial data of Einstein's equations satisfying an energy condition, we show that the Penrose inequality holds between the ADM mass and the area of an outermost apparent horizon, if the data are restricted suitably. We prove this by generalizing Geroch's proof of monotonicity of the Hawking mass under a smooth inverse mean curvature flow, for data with non-negative Ricci scalar. Unlike Geroch we need not confine ourselves to minimal surfaces as horizons. Modulo smoothness issues we also show that our restrictions on the data can locally be fulfilled by a suitable choice of the initial surface in a given spacetime.Comment: 4 pages, revtex, no figures. Some comments added. No essential changes. To be published in Phys. Rev. Let

Droop models of nutrient–plankton interaction with intratrophic predation

Droop models of nutrient–phytoplankton–zooplankton interaction with intratrophic predation of zooplankton are introduced and investigated. The models proposed in this study are open ecosystems which include both a constant and a periodic input nutrient models. A simple stochastic model mimics a randomly varying nutrient input is also presented. For the deterministic models it is shown analytically that intratrophic predation has no effect on the global asymptotic dynamics of the systems if either one of the populations has a negative growth rate. Numerical simulations are also used to investigate the effects of intratrophic predation. Unlike the deterministic models for which both populations can coexist with each other if populations’ net growth rates are positive, plankton populations can become extinct if the input nutrient concentration is varied randomly

Raman amplification and pulsed lasing in cladding-pumped germanosilicate fiber

We report for the first time Raman amplification in a cladding-pumped fiber. The double-clad germanosilicate fiber was pumped by a Q-switched Er-Yb co-doped fiber laser at 1570 nm. The power conversion efficiency was up to 36%, with a slope of 64%

Free energy barrier for molecular motions in bistable [2]rotaxane molecular electronic devices

Donor−acceptor binding of the π-electron-poor cyclophane cyclobis(paraquat-p-phenylene) (CBPQT^(4+)) with the π-electron-rich tetrathiafulvalene (TTF) and 1,5-dioxynaphthalene (DNP) stations provides the basis for electrochemically switchable, bistable [2]rotaxanes, which have been incorporated and operated within solid-state devices to form ultradense memory circuits (ChemPhysChem 2002, 3, 519−525; Nature 2007, 445, 414−417) and nanoelectromechanical systems. The rate of CBPQT^(4+) shuttling at each oxidation state of the [2]rotaxane dictates critical write-and-retention time parameters within the devices, which can be tuned through chemical synthesis. To validate how well computational chemistry methods can estimate these rates for use in designing new devices, we used molecular dynamics simulations to calculate the free energy barrier for the shuttling of the CBPQT^4+ ring between the TTF and the DNP. The approach used here was to calculate the potential of mean force along the switching pathway, from which we calculated free energy barriers. These calculations find a turn-on time after the rotaxane is doubly oxidized of ~10^9−7) s (suggesting that the much longer experimental turn-on time is determined by the time scale of oxidization). The return barrier from the DNP to the TTF leads to a predicted lifetime of 2.1 s, which is compatible with experiments

Effect of contact statistics on electrical contact resistance

The flow of electrical current through a microscopic actual contact spot between two conductors is influenced by the flow through adjacent contact spots. A smoothed version of this interaction effect is developed and used to predict the contact resistance when the statistical size and spatial distribution of contact spots is known. To illustrate the use of the method, an idealized fractal rough surface is defined using the random midpoint displacement algorithm, and the size distribution of contact spots is assumed to be given by the intersection of this surface with a constant height plane. With these assumptions, it is shown that including finer scale detail in the fractal surface, equivalent to reducing the sampling length in the measurement of the surface, causes the predicted resistance to approach the perfect contact limit. © 2003 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70949/2/JAPIAU-94-11-7215-1.pd

Isometric Representations of Totally Ordered Semigroups

Let S be a subsemigroup of an abelian torsion-free group G. If S is a positive cone of G, then all C*-algebras generated by faithful isometrical non-unitary representations of S are canonically isomorphic. Proved by Murphy, this statement generalized the well-known theorems of Coburn and Douglas. In this note we prove the reverse. If all C*-algebras generated by faithful isometrical non-unitary representations of S are canonically isomorphic, then S is a positive cone of G. Also we consider G = Z\times Z and prove that if S induces total order on G, then there exist at least two unitarily not equivalent irreducible isometrical representation of S. And if the order is lexicographical-product order, then all such representations are unitarily equivalent.Comment: February 21, 2012. Kazan, Russi

B -> Xs l_i^+ l_j^+ Decays with R-parity Violation

We derive the upper bounds on certain products of R-parity- and lepton-flavor-violating couplings from B \ra X_s {l_i}^+ {l_j}^- decays. These modes of B-meson decays can constrain the product combinations of the couplings with one or more heavy generation indices which are comparable with or stronger than the present bounds. From the studies of the invariant dilepton mass spectrum and the forward backward asymmetry of the emitted leptons we note the possibility of detecting R-parity-violating signals even when the total decay rate due to R-parity violating couplings is comparable with that in the standard model and discriminating two types of R-parity-violating signals. The general expectation of the enhancement of the forward backward asymmetry of the emitted leptons in the minimal supersymmetric standard model with R-parity may be corrupted by R-parity violation.Comment: 10 pages, Revtex, 1 table and 2 figure