Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential

We address a two-dimensional nonlinear elliptic problem with a finite-amplitude periodic potential. For a class of separable symmetric potentials, we study the bifurcation of the first band gap in the spectrum of the linear Schr\"{o}dinger operator and the relevant coupled-mode equations to describe this bifurcation. The coupled-mode equations are derived by the rigorous analysis based on the Fourier--Bloch decomposition and the Implicit Function Theorem in the space of bounded continuous functions vanishing at infinity. Persistence of reversible localized solutions, called gap solitons, beyond the coupled-mode equations is proved under a non-degeneracy assumption on the kernel of the linearization operator. Various branches of reversible localized solutions are classified numerically in the framework of the coupled-mode equations and convergence of the approximation error is verified. Error estimates on the time-dependent solutions of the Gross--Pitaevskii equation and the coupled-mode equations are obtained for a finite-time interval.Comment: 32 pages, 16 figure

The Rayleigh-Schr\"odinger perturbation series of quasi-degenerate systems

We present the first representation of the general term of the Rayleigh-Schr\"odinger series for quasidegenerate systems. Each term of the series is represented by a tree and there is a straightforward relation between the tree and the analytical expression of the corresponding term. The combinatorial and graphical techniques used in the proof of the series expansion allow us to derive various resummation formulas of the series. The relation with several combinatorial objects used for special cases (degenerate or non-degenerate systems) is established.Comment: 16 pages, 3 figure

Crystal properties of eigenstates for quantum cat maps

Using the Bargmann-Husimi representation of quantum mechanics on a torus phase space, we study analytically eigenstates of quantized cat maps. The linearity of these maps implies a close relationship between classically invariant sublattices on the one hand, and the patterns (or `constellations') of Husimi zeros of certain quantum eigenstates on the other hand. For these states, the zero patterns are crystals on the torus. As a consequence, we can compute explicit families of eigenstates for which the zero patterns become uniformly distributed on the torus phase space in the limit $\hbar\to 0$. This result constitutes a first rigorous example of semi-classical equidistribution for Husimi zeros of eigenstates in quantized one-dimensional chaotic systems.Comment: 43 pages, LaTeX, including 7 eps figures Some amendments were made in order to clarify the text, mainly in the 4 first sections. Figures are unchanged. To be published in: Nonlinearit

Single-grain TT-OSL bleaching characteristics: Insights from modern analogues and OSL dating comparisons

Previous assessments of thermally transferred optically stimulated luminescence (TT-OSL) signal resetting in natural sedimentary settings have been based on relatively limited numbers of observations, and have been conducted primarily at the multi-grain scale of equivalent dose (De) analysis. In this study, we undertake a series of single-grain TT-OSL bleaching assessments on nineteen modern and geological dating samples from different sedimentary environments. Daylight bleaching experiments performed over several weeks confirm that single-grain TT-OSL signals are optically reset at relatively slow, and potentially variable, rates. Single-grain TT-OSL residual doses range between 0 and 24 Gy for thirteen modern samples, with >50% of these samples yielding weighted mean De values of 0 Gy at 2σ. Single-grain OSL and TT-OSL dating comparisons performed on well-bleached and heterogeneously bleached late Pleistocene samples from Kangaroo Island, South Australia, yield consistent replicate age estimates. Our results reveal that (i) single-grain TT-OSL residuals can potentially be reduced down to insignificant levels when compared with the natural dose range of interest for most TT-OSL dating applications; (ii) the slow bleaching properties of TT-OSL signals may not necessarily limit their dating applicability to certain depositional environments; and (iii) non-trivial differences may be observed between single-grain and multi-grain TT-OSL bleaching residuals in some modern samples. Collectively, these findings suggest that single-grain TT-OSL dating may offer advantages over multi-grain TT-OSL dating in certain complex depositional environments

Quantum Mechanics on the cylinder

A new approach to deformation quantization on the cylinder considered as phase space is presented. The method is based on the standard Moyal formalism for R^2 adapted to (S^1 x R) by the Weil--Brezin--Zak transformation. The results are compared with other solutions of this problem presented by Kasperkovitz and Peev (Ann. Phys. vol. 230, 21 (1994)0 and by Plebanski and collaborators (Acta Phys. Pol. vol. B 31}, 561 (2000)). The equivalence of these three methods is proved.Comment: 21 pages, LaTe

Kirchhoff's Rule for Quantum Wires

In this article we formulate and discuss one particle quantum scattering theory on an arbitrary finite graph with $n$ open ends and where we define the Hamiltonian to be (minus) the Laplace operator with general boundary conditions at the vertices. This results in a scattering theory with $n$ channels. The corresponding on-shell S-matrix formed by the reflection and transmission amplitudes for incoming plane waves of energy $E>0$ is explicitly given in terms of the boundary conditions and the lengths of the internal lines. It is shown to be unitary, which may be viewed as the quantum version of Kirchhoff's law. We exhibit covariance and symmetry properties. It is symmetric if the boundary conditions are real. Also there is a duality transformation on the set of boundary conditions and the lengths of the internal lines such that the low energy behaviour of one theory gives the high energy behaviour of the transformed theory. Finally we provide a composition rule by which the on-shell S-matrix of a graph is factorizable in terms of the S-matrices of its subgraphs. All proofs only use known facts from the theory of self-adjoint extensions, standard linear algebra, complex function theory and elementary arguments from the theory of Hermitean symplectic forms.Comment: 40 page

Hybridization in parasites: consequences for adaptive evolution, pathogenesis and public health in a changing world

[No abstract available

Losartan Slows Pancreatic Tumor Progression and Extends Survival of SPARC-Null Mice by Abrogating Aberrant TGFβ Activation

Pancreatic adenocarcinoma, a desmoplastic disease, is the fourth leading cause of cancer-related death in the Western world due, in large part, to locally invasive primary tumor growth and ensuing metastasis. SPARC is a matricellular protein that governs extracellular matrix (ECM) deposition and maturation during tissue remodeling, particularly, during wound healing and tumorigenesis. In the present study, we sought to determine the mechanism by which lack of host SPARC alters the tumor microenvironment and enhances invasion and metastasis of an orthotopic model of pancreatic cancer. We identified that levels of active TGFβ1 were increased significantly in tumors grown in SPARC-null mice. TGFβ1 contributes to many aspects of tumor development including metastasis, endothelial cell permeability, inflammation and fibrosis, all of which are altered in the absence of stromal-derived SPARC. Given these results, we performed a survival study to assess the contribution of increased TGFβ1 activity to tumor progression in SPARC-null mice using losartan, an angiotensin II type 1 receptor antagonist that diminishes TGFβ1 expression and activation in vivo. Tumors grown in SPARC-null mice progressed more quickly than those grown in wild-type littermates leading to a significant reduction in median survival. However, median survival of SPARC-null animals treated with losartan was extended to that of losartan-treated wild-type controls. In addition, losartan abrogated TGFβ induced gene expression, reduced local invasion and metastasis, decreased vascular permeability and altered the immune profile of tumors grown in SPARC-null mice. These data support the concept that aberrant TGFβ1-activation in the absence of host SPARC contributes significantly to tumor progression and suggests that SPARC, by controlling ECM deposition and maturation, can regulate TGFβ availability and activation