Forest-Pest Interaction Dynamics: The Simplest Mathematical Models

This paper is devoted to the investigation of the simplest mathematical models of non-even-aged forests affected by insect pests. Two extremely simple situations are considered: (1) the pest feeds only on young trees; (2) the pest feeds only on old trees. The parameter values of the second model are estimated for the case of balsam fir forests and the eastern spruce budworm. It is shown that an invasion of a small number of pests into a steady-state forest ecosystem could result in intensive oscillations of its age structure. Possible implications of environmental changes on forest ecosystems are also considered

The Response of the Balsam Fir Forest to a Spruce Budworm Invasion: A Simple Dynamical Model

The parameter values of a simple dynamical model of a non-even age forest-insect ecosystem are estimated for the case of balsam fir forests and the eastern spruce budworm. It is shown that, despite its extreme simplicity, the model can reproduce time series of a real budworm outbreak and can be considered a compact presentation of available forest data. Strengths and weaknesses of the model are discussed and some directions for further research proposed

Forest-Pest Interaction Dynamics: The Simplest Mathematical Models

This report is devoted to the investigation of the simplest mathematical models of non-even-aged forests affected by insect pests. Two extremely simple situations are considered: (1) the pest feeds only on young trees; (2) the pest feeds only on old trees. The parameter values of the second model are estimated for the case of balsam fir forests and the eastern spruce budworm. It is shown that an invasion of a small number of pests into a steady-state forest ecosystem could result in intensive oscillations of its age structure. Possible implications of environmental changes in forest ecosystems are also considered

Abnormal phenomena in a one-dimensional periodic structure containing left-handed materials

The explicit dispersion equation for a one-dimensional periodic structure with alternative layers of left-handed material (LHM) and right-handed material (RHM) is given and analyzed. Some abnormal phenomena such as spurious modes with complex frequencies, discrete modes and photon tunnelling modes are observed in the band structure. The existence of spurious modes with complex frequencies is a common problem in the calculation of the band structure for such a photonic crystal. Physical explanation and significance are given for the discrete modes (with real values of wave number) and photon tunnelling propagation modes (with imaginary wave numbers in a limited region).Comment: 10 pages, 4 figure

Potentials of stable processes

For a stable process, we give an explicit formula for the potential measure of the process killed outside a bounded interval and the joint law of the overshoot, undershoot and undershoot from the maximum at exit from a bounded interval. We obtain the equivalent quantities for a stable process reflected in its infimum. The results are obtained by exploiting a simple connection with the Lamperti representation and exit problems of stable processes.Comment: 10 page

Nonlinear coupled Alfv\'{e}n and gravitational waves

In this paper we consider nonlinear interaction between gravitational and electromagnetic waves in a strongly magnetized plasma. More specifically, we investigate the propagation of gravitational waves with the direction of propagation perpendicular to a background magnetic field, and the coupling to compressional Alfv\'{e}n waves. The gravitational waves are considered in the high frequency limit and the plasma is modelled by a multifluid description. We make a self-consistent, weakly nonlinear analysis of the Einstein-Maxwell system and derive a wave equation for the coupled gravitational and electromagnetic wave modes. A WKB-approximation is then applied and as a result we obtain the nonlinear Schr\"{o}dinger equation for the slowly varying wave amplitudes. The analysis is extended to 3D wave pulses, and we discuss the applications to radiation generated from pulsar binary mergers. It turns out that the electromagnetic radiation from a binary merger should experience a focusing effect, that in principle could be detected.Comment: 20 pages, revtex4, accepted in PR

The geometry of spontaneous spiking in neuronal networks

The mathematical theory of pattern formation in electrically coupled networks of excitable neurons forced by small noise is presented in this work. Using the Freidlin-Wentzell large deviation theory for randomly perturbed dynamical systems and the elements of the algebraic graph theory, we identify and analyze the main regimes in the network dynamics in terms of the key control parameters: excitability, coupling strength, and network topology. The analysis reveals the geometry of spontaneous dynamics in electrically coupled network. Specifically, we show that the location of the minima of a certain continuous function on the surface of the unit n-cube encodes the most likely activity patterns generated by the network. By studying how the minima of this function evolve under the variation of the coupling strength, we describe the principal transformations in the network dynamics. The minimization problem is also used for the quantitative description of the main dynamical regimes and transitions between them. In particular, for the weak and strong coupling regimes, we present asymptotic formulas for the network activity rate as a function of the coupling strength and the degree of the network. The variational analysis is complemented by the stability analysis of the synchronous state in the strong coupling regime. The stability estimates reveal the contribution of the network connectivity and the properties of the cycle subspace associated with the graph of the network to its synchronization properties. This work is motivated by the experimental and modeling studies of the ensemble of neurons in the Locus Coeruleus, a nucleus in the brainstem involved in the regulation of cognitive performance and behavior

Photoproduction of mesons off nuclei

Recent results for the photoproduction of mesons off nuclei are reviewed. These experiments have been performed for two major lines of research related to the properties of the strong interaction. The investigation of nucleon resonances requires light nuclei as targets for the extraction of the isospin composition of the electromagnetic excitations. This is done with quasi-free meson photoproduction off the bound neutron and supplemented with the measurement of coherent photoproduction reactions, serving as spin and/or isospin filters. Furthermore, photoproduction from light and heavy nuclei is a very efficient tool for the study of the interactions of mesons with nuclear matter and the in-medium properties of hadrons. Experiments are currently rapidly developing due to the combination of high quality tagged (and polarized) photon beams with state-of-the-art 4pi detectors and polarized targets