Entanglement and bifurcations in Jahn-Teller models

We compare and contrast the entanglement in the ground state of two Jahn-Teller models. The Exbeta system models the coupling of a two-level electronic system, or qubit, to a single-oscillator mode, while the Exepsilon models the qubit coupled to two independent, degenerate oscillator modes. In the absence of a transverse magnetic field applied to the qubit, both systems exhibit a degenerate ground state. Whereas there always exists a completely separable ground state in the Exbeta system, the ground states of the Exepsilon model always exhibit entanglement. For the Exbeta case we aim to clarify results from previous work, alluding to a link between the ground-state entanglement characteristics and a bifurcation of a fixed point in the classical analog. In the Exepsilon case we make use of an ansatz for the ground state. We compare this ansatz to exact numerical calculations and use it to investigate how the entanglement is shared between the three system degrees of freedom.

A note on bifurcation from an interval

We study the global bifurcation of nonlinear Sturm-Liouville problems of the form -(pu')' + qu = lambda a(x)f(u), b(0)u(0) - c(0)u' (0) = 0, b(1)u(1) + c(1)u'(1) = 0 which are not linearizable in any neighborhood of the origin. (c) 2005 Published by Elsevier Ltd.

Asymptotic bifurcation results for quasilinear elliptic operators

We develop results for bifurcation from the principal eigenvalue for certain operators based on the p-Laplacian and containing a superlinear nonlinearity with a critical Sobolev exponent. The main result concerns an asymptotic estimate of the rate at which the solution branch departs from the eigenspace. The method can also be applied for nonpotential operators.

An exceptionally rich complex of Sanguinicolidae von Graff, 1907 (Platyhelminthes : Trematoda) from Siganidae, Labridae and Mullidae (Teleostei : Perciformes) from the Indo-West Pacific Region

We describe an unprecedented radiation of sanguinicolid blood flukes ( Digenea: Sanguinicolidae) from two species of Labridae (Choerodon venustus and C. cauteroma), seven species of Mullidae (Mulloidichthys vanicolensis, Parupeneus barberinoides, P. barberinus, P. bifasciatus, P. cyclostomus, P. indicus and P. multifasciatus) and ten species of Siganidae (Siganus argenteus, S. corallinus, S. doliatus, S. fuscescens, S. lineatus, S. margaritiferus, S. puellus, S. punctatus, S. virgatus and S. vulpinus) from sites off Australia and Palau. The flukes were morphologically similar in having the combination of a long thread-like body, tegumental spines in lateral transverse rows, a vestigial oral sucker bearing concentric rows of fine spines, an H-shaped intestine, a cirrussac, a notch level with the male genital pore, a lateral or post-ovarian uterus, a uterine chamber and separate genital pores. These species are divided into two genera on the basis of testis number. Sanguinicolids from Siganus fuscescens have a single large testis between the intestinal bifurcation and the ovary and are placed in Ankistromeces Nolan & Cribb, 2004. Species from the remaining nine species of Siganidae, Labridae and Mullidae are placed in Phthinomita n. g.; these species have two testes, the anterior testis being large and between the intestinal bifurcation and the ovary whereas the small posterior testis is at the posterior end of the body and appears rudimentary or degenerate and probably non-functional. The second internal transcribed spacer (ITS2) of ribosomal DNA ( rDNA) from 29 host/parasite/location combinations (h/p/l) was sequenced together with that of Ankistromeces mariae Nolan & Cribb, 2004 for comparison. From 135 samples we found 19 distinct genotypes which were interpreted as representing at least that many species. Replicate sequences were obtained for 25 of 30 h/p/l combinations ( including A. mariae); there was no intraspecific variation between replicates sequences for any of these. Interspecific variation ranged from 1 - 41 base differences (0.3 - 12.7% sequence divergence). The 19 putative species were difficult to recognise by morphological examination. We describe 13 new species; we do not describe (= name) six species characterised solely by molecular sequences and three putative species for which morphological data is available but for which molecular data is not. We have neither morphological nor molecular data for sanguinicolids harboured in five hosts species ( Siganus margaritiferus, S. puellus, Choerodon cauteroma, Parupeneus indicus and P. multifasciatus) in which we have seen infections. Where host species were infected in different localities they almost always harboured distinct species. Some host species ( for example, S. argenteus and S. lineatus from Lizard Island) harboured two or three species in a single geographical location. This suggests that, for parts of this system, parasite speciation has outstripped host speciation. Distance analysis of ITS2 showed species from each host family ( Siganidae, Mullidae and Labridae) did not form monophyletic clades to the exclusion of species from other host families. However, a host defined clade was formed by the sequences from sanguinicolids from S. fuscescens.

Degenerate dentition of the dugong (Dugong dugon), or why a grazer does not need teeth: morphology, occlusion and wear of mouthparts

The morphology and functional occlusion of the cheekteeth of 57 dugongs Dugong dugon of both sexes were examined using reflected light and scanning electron microscopy, radiography, hardness testing and skull manipulation. The functional morphology of the horny oral pads was also described. Mouthparts and body size allometry was examined for ontogenetic and gender-related trends. We found that the worn erupted cheekteeth of the dugong are simple flat pegs composed of soft degenerative dentine. During occlusion, the mandible moves in a mainly antero-lingual direction, with the possibility of mandibular retraction in some individuals. Anterior parts of the cheektooth row may become non-functional as a dugong ages. As a function of body size, dugong cheekteeth are extremely small compared with those of other mammalian herbivores, and with other hindgut fermenters in particular. The morphology, small size and occlusal variability of the cheekteeth suggest that there has not been strong selective pressure acting to maintain an effective dentition. In contrast, great development of the horny pads and associated skull parameters and their lower size variability suggest that the horny pads may have assumed the major role in food comminution.

Bifurcation analysis of a dynamic power system with SVC devices

Bifurcation analysis is a very useful tool for power system stability assessment. In this paper, detailed investigation of power system bifurcation behaviour is presented. One and two parameter bifurcation analysis are conducted on a 3-bus power system. We also examined the impact of FACTS devices on power system stability through Hopf bifurcation analysis by taking static Var compensator (SVC) as an example. A simplified first-order model of the SVC device is included in the 3-bus sample system. Real and reactive powers are used as bifurcation parameter in the analysis to compare the system oscillatory properties with and without SVC. The simulation results indicate that the linearized system model with SVC enlarge the voltage stability boundary by moving Hopf bifurcation point to higher level of loading conditions. The installation of SVC increases the dynamic stability range of the system, however complicates the Hopf bifurcation behavior of the system