1,592 research outputs found
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 . 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 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 channels. The
corresponding on-shell S-matrix formed by the reflection and transmission
amplitudes for incoming plane waves of energy 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
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