A complete analytic theory for structure and dynamics of populations and communities spanning wide ranges in body size

The prediction and management of ecosystem responses to global environmental change would profit from a clearer understanding of the mechanisms determining the structure and dynamics of ecological communities. The analytic theory presented here develops a causally closed picture for the mechanisms controlling community and population size structure, in particular community size spectra, and their dynamic responses to perturbations, with emphasis on marine ecosystems. Important implications are summarised in non-technical form. These include the identification of three different responses of community size spectra to size-specific pressures (of which one is the classical trophic cascade), an explanation for the observed slow recovery of fish communities from exploitation, and clarification of the mechanism controlling predation mortality rates. The theory builds on a community model that describes trophic interactions among size-structured populations and explicitly represents the full life cycles of species. An approximate time-dependent analytic solution of the model is obtained by coarse graining over maturation body sizes to obtain a simple description of the model steady state, linearising near the steady state, and then eliminating intraspecific size structure by means of the quasi-neutral approximation. The result is a convolution equation for trophic interactions among species of different maturation body sizes, which is solved analytically using a novel technique based on a multiscale expansion.

Plasma surface dynamics and smoothing in the relativistic few-cycle regime

Efficient production of coherent harmonic radiation from solid targets relies critically on the formation of smooth, short density scalelength plasmas. Recent experimental results (Dromey et al 2009 Nat. Phys. 5 146) suggest, however, that the target roughness on the scale of the emitted harmonic wavelength does not result in diffuse reflection-in apparent contradiction to the Rayleigh criterion for coherent reflection. In this paper we show, for the first time, using analytic theory and 2D PIC simulations, that the interaction of relativistically strong laser pulses with corrugated target surfaces results in a highly effective smoothing of the interaction surface and consequently the generation of highly collimated and temporally confined XUV pulses from rough targets, in excellent agreement with experimental observations.

Three-Dimensional Dynamics of Breakout Afterburner Ion Acceleration Using High-Contrast Short-Pulse Laser and Nanoscale Targets

Breakout afterburner (BOA) laser-ion acceleration has been demonstrated for the first time in the laboratory. In the BOA, an initially solid-density target undergoes relativistically induced transparency, initiating a period of enhanced ion acceleration. First-ever kinetic simulations of the BOA in three dimensions show that the ion beam forms lobes in the direction orthogonal to laser polarization and propagation. Analytic theory presented for the electron dynamics in the laser ponderomotive field explains how azimuthal symmetry breaks even for a symmetric laser intensity profile; these results are consistent with recent experiments at the Trident laser facility. © 2011 American Physical Society.

Mono-energetic ion beam acceleration in solitary waves during relativistic transparency using high-contrast circularly polarized short-pulse laser and nanoscale targets

In recent experiments at the Trident laser facility, quasi-monoenergetic ion beams have been obtained from the interaction of an ultraintense, circularly polarized laser with a diamond-like carbon target of nm-scale thickness under conditions of ultrahigh laser pulse contrast. Kinetic simulations of this experiment under realistic laser and plasma conditions show that relativistic transparency occurs before significant radiation pressure acceleration and that the main ion acceleration occurs after the onset of relativistic transparency. Associated with this transition are a period of intense ion acceleration and the generation of a new class of ion solitons that naturally give rise to quasi-monoenergetic ion beams. An analytic theory has been derived for the properties of these solitons that reproduces the behavior observed in kinetic simulations and the experiments. © 2011 American Institute of Physics.

The Last Minutes of Oxygen Shell Burning in a Massive Star

We present the first 3D simulation of the last minutes of oxygen shell burning in an 18 solar mass supernova progenitor up to the onset of core collapse. A moving inner boundary is used to accurately model the contraction of the silicon and iron core according to a 1D stellar evolution model with a self-consistent treatment of core deleptonization and nuclear quasi-equilibrium. The simulation covers the full solid angle to allow the emergence of large-scale convective modes. Due to core contraction and the concomitant acceleration of nuclear burning, the convective Mach number increases to ~0.1 at collapse, and an l=2 mode emerges shortly before the end of the simulation. Aside from a growth of the oxygen shell from 0.51 to 0.56 solar masses due to entrainment from the carbon shell, the convective flow is reasonably well described by mixing length theory, and the dominant scales are compatible with estimates from linear stability analysis. We deduce that artificial changes in the physics, such as accelerated core contraction, can have precarious consequences for the state of convection at collapse. We argue that scaling laws for the convective velocities and eddy sizes furnish good estimates for the state of shell convection at collapse and develop a simple analytic theory for the impact of convective seed perturbations on shock revival in the ensuing supernova. We predict a reduction of the critical luminosity for explosion by 12--24% due to seed asphericities for our 3D progenitor model relative to the case without large seed perturbations.

Linguistics and Information Theory: Analytic advantages

The analytic advantages of central concepts from linguistics and information theory, and the analogies demonstrated between them, for understanding patterns of retrieval from full-text indexes to documents are developed. The interaction between the syntagm and the paradigm in computational operations on written language in indexing, searching, and retrieval is used to account for transformations of the signified or meaning between documents and their representation and between queries and documents retrieved. Characteristics of the message, and messages for selection for written language, are brought to explain the relative frequency of occurrence of words and multiple word sequences in documents. The examples given in the companion article are revisited and a fuller example introduced. The signified of the sequence stood for, the term classically used in the definitions of the sign, as something standing for something else, can itself change rapidly according to its syntagm. A greater than ordinary discourse understanding of patterns in retrieval is obtained.

Analogies between linguistics and information theory

An analogy is established between the syntagm and paradigm from Saussurean linguistics and the message and messages for selection from the information theory initiated by Claude Shannon. The analogy is pursued both as an end itself and for its analytic value in understanding patterns of retrieval from full text systems. The multivalency of individual words when isolated from their syntagm is contrasted with the relative stability of meaning of multi-word sequences, when searching ordinary written discourse. The syntagm is understood as the linear sequence of oral and written language. Saussureâ??s understanding of the word, as a unit which compels recognition by the mind, is endorsed, although not regarded as final. The lesser multivalency of multi-word sequences is understood as the greater determination of signification by the extended syntagm. The paradigm is primarily understood as the network of associations a word acquires when considered apart from the syntagm. The restriction of information theory to expression or signals, and its focus on the combinatorial aspects of the message, is sustained. The message in the model of communication in information theory can include sequences of written language. Shannonâ??s understanding of the written word, as a cohesive group of letters, with strong internal statistical influences, is added to the Saussurean conception. Sequences of more than one word are regarded as weakly correlated concatenations of cohesive units.

Magnetically quantized continuum distorted-wave theory in atomic and molecular collisions

The continuum distorted-wave eikonal initial-state (CDW-EIS) theory of Crothers and McCann (J Phys B 1983, 16, 3229) used to describe ionization in ion-atom collisions is generalized (G) to GCDW-EIS to incorporate the azimuthal angle dependence of each CDW in the final-state wave function. This is accomplished by the analytic continuation of hydrogenic-like wave functions from below to above threshold, using parabolic coordinates and quantum numbers including magnetic quantum numbers, thus providing a more complete set of states. At impact energies lower than 25 keVu(-1), the total ionization cross-section falls off, with decreasing energy, too quickly in comparison with experimental data. The idea behind and motivation for the GCDW-EIS model is to improve the theory with respect to experiment by including contributions from nonzero magnetic quantum numbers. We also therefore incidentally provide a new derivation of the theory of continuum distorted waves for zero magnetic quantum numbers while simultaneously generalizing it. (C) 2004 Wiley Periodicals, Inc.

Electro-thermal theory of intermodulation distortion in lossy microwave components

An analytic formulation of dynamic electro-thermally induced nonlinearity is developed for a general resistive element, yielding a self-heating circuit model based on a fractional derivative. The model explains the 10 dB/decade slope of the intermodulation products observed in two-tone testing. Two-tone testing at 400 MHz of attenuators, microwave chip terminations, and coaxial terminations is reported with tone spacing ranging from 1 to 100 Hz.

Density-potential mapping in time-dependent density-functional theory

The key questions of uniqueness and existence in time-dependent density-functional theory are usually formulated only for potentials and densities that are analytic in time. Simple examples, standard in quantum mechanics, lead, however, to nonanalyticities. We reformulate these questions in terms of a nonlinear Schroedinger equation with a potential that depends nonlocally on the wave function.

Nonlinear theory of solitary waves associated with longitudinal particle motion in lattices - Application to longitudinal grain oscillations in a dust crystal

The nonlinear aspects of longitudinal motion of interacting point masses in a lattice are revisited, with emphasis on the paradigm of charged dust grains in a dusty plasma (DP) crystal. Different types of localized excitations, predicted by nonlinear wave theories, are reviewed and conditions for their occurrence (and characteristics) in DP crystals are discussed. Making use of a general formulation, allowing for an arbitrary (e.g. the Debye electrostatic or else) analytic potential form phi(r) and arbitrarily long site-to-site range of interactions, it is shown that dust-crystals support nonlinear kink-shaped localized excitations propagating at velocities above the characteristic DP lattice sound speed v(0). Both compressive and rarefactive kink-type excitations are predicted, depending on the physical parameter values, which represent pulse- (shock-)like coherent structures for the dust grain relative displacement. Furthermore, the existence of breather-type localized oscillations, envelope-modulated wavepackets and shocks is established. The relation to previous results on atomic chains as well as to experimental results on strongly-coupled dust layers in gas discharge plasmas is discussed.