Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins

In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the-energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As examples we apply the theory to several models of current interest in the study of Bose-Einstein condensates, which have been successfully created using ultracold dilute atomic gases. The first model we introduce describes Josephson tunnelling between two coupled Bose-Einstein condensates. It can be used not only for the study of tunnelling between condensates of atomic gases, but for solid state Josephson junctions and coupled Cooper pair boxes. The theory is also applicable to models of atomic-molecular Bose-Einstein condensates, with two examples given and analysed. Additionally, these same two models are relevant to studies in quantum optics; Finally, we discuss the model of Bardeen, Cooper and Schrieffer in this framework, which is appropriate for systems of ultracold fermionic atomic gases, as well as being applicable for the description of superconducting correlations in metallic grains with nanoscale dimensions.; In applying all the above models to. physical situations, the need for an exact analysis of small-scale systems is established due to large quantum fluctuations which render mean-field approaches inaccurate.

Superconducting Correlations in Metallic Nanoparticles: Exact Solution of the BCS Model by the Algebraic Bethe Ansatz

Superconducting pairing of electrons in nanoscale metallic particles with discrete energy levels and a fixed number of electrons is described by the reduced Bardeen, Cooper, and Schrieffer model Hamiltonian. We show that this model is integrable by the algebraic Bethe ansatz. The eigenstates, spectrum, conserved operators, integrals of motion, and norms of wave functions are obtained. Furthermore, the quantum inverse problem is solved, meaning that form factors and correlation functions can be explicitly evaluated. Closed form expressions are given for the form factors and correlation functions that describe superconducting pairing.

Modelling fungal growth on surfaces

Fungal growth in time and space at the substrate surface was modelled for a simple system mimicking solid-state fermentation, using a polycarbonate Nucleopore membrane laid over a glucose solution. Biomass production depends on both tip density and the diffusion of glucose within the fungal hyphae. The model predicts early increases in both height and concentration, followed by a period in which the biomass profile moves with a constant wavefront. The rate of increase in height increases as tip diffusivity increases or as the Monod saturation constant for glucose decreases.

Algebraic Bethe ansatz for integrable Kondo impurities in the one-dimensional supersymmetric t-J model

An integrable Kondo problem in the one-dimensional supersymmetric t-J model is studied by means of the boundary supersymmetric quantum inverse scattering method. The boundary K matrices depending on the local moments of the impurities are presented as a nontrivial realization of the graded reflection equation algebras in a two-dimensional impurity Hilbert space. Further, the model is solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained. (C) 1999 Elsevier Science B.V.

A comparative study of the fluidized-bed coating of cylindrical metal surfaces with various thermoplastic polymer powders

This paper reports the results of an experimental investigation into the fluidized-bed coating of cylindrical metal specimens using two types of thermoplastic powders, Rilsan(R) PA11, a nylon-11 powder produced by Elf Atochem, France and Cotene(TM) 4612, a linear low density polyethylene powder produced by J.R Courtenay (New Zealand). The effects of dipping time, preheat temperature and particle size distribution on coating thickness and surface finish were investigated. Consistent trends in coating thickness growth with dipping time were obtained for both nylon-11 and polyethylene powders with increases in coating thickness with preheat temperature. For the same preheat temperature, the lower melting point of polyethylene results in thicker coatings compared to those of nylon-11. There is a negligible change in the coating thickness for sieved powders compared to that for unsieved powders. A pre-heat temperatures of between 240 degrees C and 300 degrees C is necessary to achieve an acceptable surface finish with both nylon-11 and polyethylene powders. To minimize errors in achieving the desired coating thickness, dipping times shorter than 2 s are not recommended. The use of graphs of coating thickness versus dipping time in combination with the coating surface roughness plots presented in this paper enable the optimal choice of pre-heat temperature and dipping time to achieve acceptable surface finish. (C) 1999 Elsevier Science S.A. All rights reserved.

Heat flow for Yang-Mills-Higgs fields, part I

The Yang-Mills-Higgs field generalizes the Yang-Mills field. The authors establish the local existence and uniqueness of the weak solution to the heat flow for the Yang-Mills-Higgs field in a vector bundle over a compact Riemannian 4-manifold, and show that the weak solution is gauge-equivalent to a smooth solution and there are at most finite singularities at the maximum existing time.

Algebraic Bethe ansatz for integrable one-dimensional extended Hubbard models with open boundary conditions

Nine classes of integrable open boundary conditions, further extending the one-dimensional U-q (gl (212)) extended Hubbard model, have been constructed previously by means of the boundary Z(2)-graded quantum inverse scattering method. The boundary systems are now solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained for all nine cases.

Algebraic Bethe ansatz for the anisotropic supersymmetric U model

We present an algebraic Bethe ansatz for the anisotropic supersymmetric U model for correlated electrons on the unrestricted 4(L)-dimensional electronic Hilbert space x(n=l)(L)C(4)(where L is the lattice length). The supersymmetry algebra of the local Hamiltonian is the quantum superalgebra U-q[gl(2\1)] and the model contains two symmetry-preserving free real parameters; the quantization parameter q and the Hubbard interaction parameter U. The parameter U arises from the one-parameter family of inequivalent typical four-dimensional irreps of U-q[gl(2\1)]. Eigenstates of the model are determined by the algebraic Bethe ansatz on a one-dimensional periodic lattice.

Myelin proteolipid protein expressed in COS-1 cells is targeted to actin-associated surfaces

The compact myelin sheath represents one of the largest expanses of membrane-membrane contact in the body and, in the central nervous system, requires the myelin proteolipid protein (PLP) for assembly, To determine whether the molecular properties of PLP promote membrane adhesion and direct its subcellular localization in the absence of oligodendrocyte-specific targeting mechanisms, PLP was expressed in COS-I fibroblasts, Immunofluorescence staining indicated that PUP was translated effectively, transited the rough endoplasmic reticulum and Golgi apparatus, was delivered to the cell surface, and was endocytosed, In the plasma membrane, the PLP distribution was patchy and only sporadically coincided with sites of membrane-membrane contact between PLP-expressing cells, PLP was not randomly distributed, however, but correlated closely with microfilament locations in leading edge membranes and microvilli, as demonstrated by phalloidin double labeling, Our results indicate that even in non-myelinating cells, PLP can be concentrated in membranes associated with movement and growth, and suggest possible roles for the actin cytoskeleton in PLP localization, As PLP, DM20, and the DM20-like M6 protein all associate with actin-enriched membranes, this may be a common feature of PLP/DM20 gene family members. (C) 1997 Wiley-Liss, Inc.

Algebraic Bethe ansatz for integrable extended Hubbard models arising from supersymmetric group solutions

Integrable extended Hubbard models arising from symmetric group solutions are examined in the framework of the graded quantum inverse scattering method. The Bethe ansatz equations for all these models are derived by using the algebraic Bethe ansatz method.

Receptor for Fc on the surfaces of schistosomes

Schistosoma mansoni masks its surface with adsorbed host proteins including erythrocyte antigens, immunoglobulins, major histocompatibility complex class I, and beta (2)-microglobulin (beta (2)m), presumably as a means of avoiding host immune responses, How this is accomplished has not been explained. To identify surface receptors for host proteins, we biotinylated the tegument of live S, mansoni adults and mechanically transformed schistosomula and then removed the parasite surface with detergent, Incubation of biotinylated schistosome surface extracts witt l human immunoglobulin G (IgG) Fc-Sepharose resulted in purification of a 97-kDa protein that was subsequently identified as paramyosin (Pmy), using antiserum specific for recombinant Pmy, Fc also bound recombinant S. mansoni Pmy and native S. japonicum Pmy, Antiserum to Pmy decreased the binding of Pmy to Fc-Sepharose, and no proteins bound after removal of Pmy from extracts. Fluoresceinated human Fe bound to the surface, vestigial penetration glands, and nascent oral cavity of mechanically transformed schistosomula, and rabbit anti-Pmy Fab fragments ablated the binding of Fc to the schistosome surface, Pmy coprecipitated with host IgG from parasite surface extracts, indicating that complexes formed on the parasite surface as well as in vitro. Binding of Pmy to Fe was not inhibited by soluble protein A, suggesting that Pmy does not bind to the region between the CH2 and CH3 domains used by many other Fc-binding proteins. beta (2)m did not bind to the schistosome Fc receptor (Pmy), a finding that contradicts reports from earlier workers but did bind to a heteromultimer of labeled schistosomula surface proteins, This is the first report of the molecular identity of a schistosome Fc receptor; moreover it demonstrates an additional aspect of the unusual and multifunctional properties of Pmy from schistosomes and other parasitic flatworms.

Empirical evidence for ultrametric structure in multi-layer perceptron error surfaces

Combinatorial optimization problems share an interesting property with spin glass systems in that their state spaces can exhibit ultrametric structure. We use sampling methods to analyse the error surfaces of feedforward multi-layer perceptron neural networks learning encoder problems. The third order statistics of these points of attraction are examined and found to be arranged in a highly ultrametric way. This is a unique result for a finite, continuous parameter space. The implications of this result are discussed.

Exploring complex fitness surfaces: Multiple ornamentation and polymorphism in male guppies

The sexual ornamentation used by male guppies to attract females comprises many components, each of which varies considerably among males. Although natural and sexual selection have been shown to contribute to divergence among populations in male sexual ornaments, the role of sexual selection in maintaining polymorphism within populations is less clear. We used both parametric quadratic regression and nonparametric projection pursuit regression techniques to reveal the major axes of non-linear sexual selection on male ornaments. We visualized the fitness surfaces defined by these axes using thin-plate splines to allow a direct comparison of the two methodologies. Identification of the major axes of selection and their visualization was critical in determining the form and strength of nonlinear selection. Both types of analysis revealed fitness surfaces comprising three peaks, suggesting that there is more than one way to make an attractive guppy. Disruptive selection may be an important process underlying the presence of multiple sexual ornaments and may contribute to the maintenance of the high levels of polymorphism in male sexual ornaments found in guppy populations.