Order Parameters of the Dilute A Models

The free energy and local height probabilities of the dilute A models with broken \Integer_2 symmetry are calculated analytically using inversion and corner transfer matrix methods. These models possess four critical branches. The first two branches provide new realisations of the unitary minimal series and the other two branches give a direct product of this series with an Ising model. We identify the integrable perturbations which move the dilute A models away from the critical limit. Generalised order parameters are defined and their critical exponents extracted. The associated conformal weights are found to occur on the diagonal of the relevant Kac table. In an appropriate regime the dilute A$_3$ model lies in the universality class of the Ising model in a magnetic field. In this case we obtain the magnetic exponent $\delta=15$ directly, without the use of scaling relations.Comment: 53 pages, LaTex, ITFA 93-1

Reconstruction of Bandlimited Functions from Unsigned Samples

We consider the recovery of real-valued bandlimited functions from the absolute values of their samples, possibly spaced nonuniformly. We show that such a reconstruction is always possible if the function is sampled at more than twice its Nyquist rate, and may not necessarily be possible if the samples are taken at less than twice the Nyquist rate. In the case of uniform samples, we also describe an FFT-based algorithm to perform the reconstruction. We prove that it converges exponentially rapidly in the number of samples used and examine its numerical behavior on some test cases

Diagonalization of the XXZ Hamiltonian by Vertex Operators

We diagonalize the anti-ferroelectric XXZ-Hamiltonian directly in the thermodynamic limit, where the model becomes invariant under the action of affine U_q( sl(2) ). Our method is based on the representation theory of quantum affine algebras, the related vertex operators and KZ equation, and thereby bypasses the usual process of starting from a finite lattice, taking the thermodynamic limit and filling the Dirac sea. From recent results on the algebraic structure of the corner transfer matrix of the model, we obtain the vacuum vector of the Hamiltonian. The rest of the eigenvectors are obtained by applying the vertex operators, which act as particle creation operators in the space of eigenvectors. We check the agreement of our results with those obtained using the Bethe Ansatz in a number of cases, and with others obtained in the scaling limit --- the $su(2)$-invariant Thirring model.Comment: 65 page

Micro-evolutionary diversification among Indian Ocean parrots: temporal and spatial changes in phylogenetic diversity as a consequence of extinction and invasion

Almost 90% of global bird extinctions have occurred on islands. The loss of endemic spe- cies from island systems can dramatically alter evolutionary trajectories of insular species biodiversity, resulting in a loss of evolutionary diversity important for species adaptation to changing environments. The Western Indian Ocean islands have been the scene of evolution for a large number of endemic parrots. Since their discovery in the 16th cen- tury, many of these parrots have become extinct or have declined in numbers. Alongside the extinction of species, a number of the Indian Ocean islands have experienced coloni- zation by highly invasive parrots, such as the Ring-necked Parakeet Psittacula krameri. Such extinctions and invasions can, on an evolutionary timescale, drive changes in spe- cies composition, genetic diversity and turnover in phylogenetic diversity, all of which can have important impacts on species potential for adaptation to changing environmen- tal and climatic conditions. Using mtDNA cytochrome b data, we resolve the taxonomic placement of three extinct Indian Ocean parrots: the Rodrigues Psittacula exsul, Sey- chelles Psittacula wardi and Reunion Parakeets Psittacula eques. This case study quantifies how the extinction of these species has resulted in lost historical endemic phylogenetic diversity and reduced levels of species richness, and illustrates how it is being replaced by non-endemic invasive forms such as the Ring-necked Parakeet. Finally, we use our phylogenetic framework to identify and recommend a number of phylogenetically appro- priate ecological replacements for the extinct parrots. Such replacements may be intro- duced once invasive forms have been cleared, to rejuvenate ecosystem function and restore lost phylogenetic diversity

PP-Wave Light-Cone Free String Field Theory at Finite Temperature

In this paper, a real-time formulation of light-cone pp-wave string field theory at finite temperature is presented. This is achieved by developing the thermo field dynamics (TFD) formalism in a second quantized string scenario. The equilibrirum thermodynamic quantities for a pp-wave ideal string gas are derived directly from expectation values on the second quantized string thermal vacuum. Also, we derive the real-time thermal pp-wave closed string propagator. In the flat space limit it is shown that this propagator can be written in terms of Theta functions, exactly as the zero temperature one. At the end, we show how supestrings interactions can be introduced, making this approach suitable to study the BMN dictionary at finite temperature.Comment: 27 pages, revtex

Nonlinear flexural waves in fluid–filled elastic channels

Nonlinear waves on liquid sheets between thin infinite elastic plates are studied analytically and numerically. Linear and nonlinear models are used for the elastic plates coupled to the Euler equations for the fluid. One-dimensional time dependent equations are derived based on a long-wavelength approximation. Inertia of the elastic plates is neglected, so linear perturbations are stable. Symmetric and mixed-mode travelling waves are found with the linear plate model and symmetric travelling waves are found for the nonlinear case. Numerical simulations are employed to study the evolution in time of initial disturbances and to compare the different models used. Nonlinear effects are found to decrease the travelling wave speed compared with linear models. At sufficiently large amplitude of initial disturbances, higher order temporal oscillations induced by non-linearity can lead to thickness of the liquid sheet approaching zero

Towards a glacial-sensitive model of island biogeography

Although the role that Pleistocene glacial cycles have played in shaping the present biota of oceanic islands world-wide has long been recognized, their geographical, biogeographical and ecological implications have not yet been fully incorporated within existing biogeographical models. Here we summarize the different types of impacts that glacial cycles may have had on oceanic islands, including cyclic changes in climate, shifts in marine currents and wind regimes and, especially, cycles of sea level change. The latter have affected geographical parameters such as island area, isolation and elevation. They have also influenced the configurations of archipelagos via island fusion and fission, and cycles of seamount emergence and submergence. We hypothesize that these sea level cycles have had significant impacts on the biogeographical processes shaping oceanic island biotas, influencing the rates and patterns of immigration and extinction and hence species richness. Here we provide a first step toward the development of a glacial-sensitive model of island biogeography, representing the tentative temporal evolution of those biogeographical parameters during the last glacial cycle. From this reasoning we attempt to derive predictions regarding the imprint of sea level cycles on genetic, demographic or biogeographical patterns within remote island biotas

New directions in island biogeography

Aim: Much of our current understanding of ecological and evolutionary processes comes from island research. With the increasing availability of data on distributions and phylogenetic relationships and new analytical approaches to understanding the processes that shape species distributions and interactions, a re-evaluation of this ever-interesting topic is timely. Location: Islands globally. Methods: We start by arguing that the reasons why island research has achieved so much in the past also apply to the future. We then critically assess the current state of island biogeography, focusing on recent changes in emphasis, including research featured in this special issue of Global Ecology and Biogeography. Finally, we suggest promising themes for the future. We cover both ecological and evolutionary topics, although the greater emphasis on island ecology reflects our own backgrounds and interests. Results: Much ecological theory has been directly or indirectly influenced by research on island biotas. Currently, island biogeography is renascent, with research focusing on, among other things, patterns and processes underlying species interaction networks, species coexistence and the assembly of island communities through ecological and evolutionary time. Continuing island research should provide additional insight into biological invasions and other impacts of human activities, functional diversity and ecosystem functioning, extinction and diversification, species pools and more. Deeper understanding of the similarities and differences between island and mainland systems will aid transferability of island theory to continental regions. Main conclusions: As research in biogeography and related fields expands in new directions, islands continue to provide opportunities for developing insights, both as natural laboratories for ecology and evolution and because of the exceptions islands often present to the usual ‘rules’ of ecology. New data collection initiatives are needed on islands world-wide and should be directed towards filling gaps in our knowledge of within-island distributions of species, as well as the functional traits and phylogenetic relationships of island species

Drinfeld twist and symmetric Bethe vectors of the open XYZ chain with non-diagonal boundary terms

With the help of the Drinfeld twist or factorizing F-matrix for the eight-vertex solid-on-solid (SOS) model, we find that in the F-basis provided by the twist the two sets of pseudo-particle creation operators simultaneously take completely symmetric and polarization free form. This allows us to obtain the explicit and completely symmetric expressions of the two sets of Bethe states of the model.Comment: Latex file, 25 page