Deformed Harry Dym and Hunter-Zheng Equations

We study the deformed Harry Dym and Hunter-Zheng equations with two arbitrary deformation parameters. These reduce to various other known models in appropriate limits. We show that both these systems are bi-Hamiltonian with the same Hamiltonian structures. They are integrable and belong to the same hierarchy corresponding to positive and negative flows. We present the Lax pair description for both the systems and construct the conserved charges of negative order from the Lax operator. For the deformed Harry Dym equation, we construct the non-standard Lax representation for two special classes of values of the deformation parameters. In general, we argue that a non-standard description will involve a pseudo-differential operator of infinite order.Comment: Latex file, 15 page

Catalogue des habitats forestiers de Guyane

Grâce à de nombreux efforts de prospections et d'inventaires naturalistes, la biodiversité guyanaise est de mieux en mieux connue et les listes d'espèces nouvelles ne cessent de s'allonger années après années. Cependant l'écosystème forestier ne se résume pas à une juxtaposition d'individus et d'espèces : de complexes relations interspécifiques régissent le fonctionnement des communautés qui sont elles-mêmes influencées par les conditions environnementales. dans lesquelles elles se développent. Gérer et conserver la biodiversité guyanaise implique de mieux cerner ces interactions entre faune, flore et environnement ; interactions qui façonnent toute une diversité d'habitats forestiers avec des dynamiques propres et des compositions originales. Plusieurs programmes de recherche se sont attelés à démêler cet écheveau écologique en se concentrant tout d'abord sur quelques plateformes scientifiques (Paracou, Nouragues, Piste de Saint-Elie) puis en élargissant la focale à l'ensemble de notre territoire sous l'impulsion des gestionnaires publics et des associations naturalistes guyanaises (programmes de recherche DIME, ECOTROP, HABITATS, etc.). Ce catalogue des habitats forestiers présente une synthèse de ces résultats sous la forme de fiches descriptives dressant un portrait précis des différents habitats naturels rencontrés en forêt guyanaise et des mécanismes qui les ont peu à peu façonnés. Un travail collectif important a été accompli pour fournir des éléments précis concernant les cortèges de grande faune, les peuplements d'arbres qui les abritent et la qualité des sols qui les supportent

Use of specific Green's functions for solving direct problems involving a heterogeneous rigid frame porous medium slab solicited by acoustic waves

A domain integral method employing a specific Green's function (i.e., incorporating some features of the global problem of wave propagation in an inhomogeneous medium) is developed for solving direct and inverse scattering problems relative to slab-like macroscopically inhomogeneous porous obstacles. It is shown how to numerically solve such problems, involving both spatially-varying density and compressibility, by means of an iterative scheme initialized with a Born approximation. A numerical solution is obtained for a canonical problem involving a two-layer slab.Comment: submitted to Math.Meth.Appl.Sc

Initial-boundary value problems for discrete evolution equations: discrete linear Schrodinger and integrable discrete nonlinear Schrodinger equations

We present a method to solve initial-boundary value problems for linear and integrable nonlinear differential-difference evolution equations. The method is the discrete version of the one developed by A. S. Fokas to solve initial-boundary value problems for linear and integrable nonlinear partial differential equations via an extension of the inverse scattering transform. The method takes advantage of the Lax pair formulation for both linear and nonlinear equations, and is based on the simultaneous spectral analysis of both parts of the Lax pair. A key role is also played by the global algebraic relation that couples all known and unknown boundary values. Even though additional technical complications arise in discrete problems compared to continuum ones, we show that a similar approach can also solve initial-boundary value problems for linear and integrable nonlinear differential-difference equations. We demonstrate the method by solving initial-boundary value problems for the discrete analogue of both the linear and the nonlinear Schrodinger equations, comparing the solution to those of the corresponding continuum problems. In the linear case we also explicitly discuss Robin-type boundary conditions not solvable by Fourier series. In the nonlinear case we also identify the linearizable boundary conditions, we discuss the elimination of the unknown boundary datum, we obtain explicitly the linear and continuum limit of the solution, and we write down the soliton solutions.Comment: 41 pages, 3 figures, to appear in Inverse Problem

Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux-Crum Transformations

Simple derivation is presented of the four families of infinitely many shape invariant Hamiltonians corresponding to the exceptional Laguerre and Jacobi polynomials. Darboux-Crum transformations are applied to connect the well-known shape invariant Hamiltonians of the radial oscillator and the Darboux-P\"oschl-Teller potential to the shape invariant potentials of Odake-Sasaki. Dutta and Roy derived the two lowest members of the exceptional Laguerre polynomials by this method. The method is expanded to its full generality and many other ramifications, including the aspects of generalised Bochner problem and the bispectral property of the exceptional orthogonal polynomials, are discussed.Comment: LaTeX2e with amsmath, amssymb, amscd 26 pages, no figure

Local and non-local equivalent potentials for p-12C scattering

A Newton-Sabatier fixed energy inversion scheme has been used to equate inherently non-local p-${}^{12}$C potentials at a variety of energies to pion threshold, with exactly phase equivalent local ones. Those energy dependent local potentials then have been recast in the form of non-local Frahn-Lemmer interactions.Comment: 15 pages plus 9 figures submitted to Phys. Rev.

Polarization of coalitions in an agent-based model of political discourse

Political discourse is the verbal interaction between political actors in a policy domain. This article explains the formation of polarized advocacy or discourse coalitions in this complex phenomenon by presenting a dynamic, stochastic, and discrete agent-based model based on graph theory and local optimization. In a series of thought experiments, actors compute their utility of contributing a specific statement to the discourse by following ideological criteria, preferential attachment, agenda-setting strategies, governmental coherence, or other mechanisms. The evolving macro-level discourse is represented as a dynamic network and evaluated against arguments from the literature on the policy process. A simple combination of four theoretical mechanisms is already able to produce artificial policy debates with theoretically plausible properties. Any sufficiently realistic configuration must entail innovative and path-dependent elements as well as a blend of exogenous preferences and endogenous opinion formation mechanisms

Exploring the role of materials in policy change: innovation in low energy housing in the UK

There remains uncertainty in models of the policy process about how and when radical change takes place. Most policy authors focus on explaining incremental change, and yet in practice a pattern of change described as punctuated equilibrium has been observed, with periods of stability interspersed with periods of rapid, abrupt change. It is argued here that the influence of materials and technologies—the substance of policy—must be incorporated into models of the policy process in order to help further our understanding of radical change. Concepts from science and technology studies concerning the inseparability of social and technical spheres are used to explore how people and materials interact to create opportunities for radical change. These ideas are particularly relevant to policy sectors comprising durable, capital-intensive infrastructure, such as housing. Drawing on examples from the UK housing sector, ideas about policy networks and large technical systems are synthesised to develop a more holistic, interdisciplinary account of policy change