95 research outputs found

    The band spectrum of the periodic airy-schrodinger operator on the real line

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    We introduce the periodic Airy-Schr\"odinger operator and we study its band spectrum. This is an example of an explicitly solvable model with a periodic potential which is not differentiable at its minima and maxima. We define a semiclassical regime in which the results are stated for a fixed value of the semiclassical parameter and are thus estimates instead of asymptotic results. We prove that there exists a sequence of explicit constants, which are zeroes of classical functions, giving upper bounds of the semiclassical parameter for which the spectral bands are in the semiclassical regime. We completely determine the behaviour of the edges of the first spectral band with respect to the semiclassical parameter. Then, we investigate the spectral bands and gaps situated in the range of the potential. We prove precise estimates on the widths of these spectral bands and these spectral gaps and we determine an upper bound on the integrated spectral density in this range. Finally, in the semiclassical regime, we get estimates of the edges of every spectral bands and thus of the widths of every spectral bands and spectral gaps

    A matrix-valued point interactions model

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    We study a matrix-valued Schr\"odinger operator with random point interactions. We prove the absence of absolutely continuous spectrum for this operator by proving that away from a discrete set its Lyapunov exponents do not vanish. For this we use a criterion by Gol'dsheid and Margulis and we prove the Zariski denseness, in the symplectic group, of the group generated by the transfer matrices. Then we prove estimates on the transfer matrices which lead to the H\"older continuity of the Lyapunov exponents. After proving the existence of the integrated density of states of the operator, we also prove its H\"older continuity by proving a Thouless formula which links the integrated density of states to the sum of the positive Lyapunov exponents

    Localization for a matrix-valued Anderson model

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    We study localization properties for a class of one-dimensional, matrix-valued, continuous, random Schr\"odinger operators, acting on L^2(\R)\otimes \C^N, for arbitrary N1N\geq 1. We prove that, under suitable assumptions on the F\"urstenberg group of these operators, valid on an interval IRI\subset \R, they exhibit localization properties on II, both in the spectral and dynamical sense. After looking at the regularity properties of the Lyapunov exponents and of the integrated density of states, we prove a Wegner estimate and apply a multiscale analysis scheme to prove localization for these operators. We also study an example in this class of operators, for which we can prove the required assumptions on the F\"urstenberg group. This group being the one generated by the transfer matrices, we can use, to prove these assumptions, an algebraic result on generating dense Lie subgroups in semisimple real connected Lie groups, due to Breuillard and Gelander. The algebraic methods used here allow us to handle with singular distributions of the random parameters

    H\"older continuity of the IDS for matrix-valued Anderson models

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    We study a class of continuous matrix-valued Anderson models acting on L^{2}(\R^{d})\otimes \C^{N}. We prove the existence of their Integrated Density of States for any d1d\geq 1 and N1N\geq 1. Then for d=1d=1 and for arbitrary NN, we prove the H\"older continuity of the Integrated Density of States under some assumption on the group GμEG_{\mu_{E}} generated by the transfer matrices associated to our models. This regularity result is based upon the analoguous regularity of the Lyapounov exponents associated to our model, and a new Thouless formula which relates the sum of the positive Lyapounov exponents to the Integrated Density of States. In the final section, we present an example of matrix-valued Anderson model for which we have already proved, in a previous article, that the assumption on the group GμEG_{\mu_{E}} is verified. Therefore the general results developed here can be applied to this model

    Localization Properties of the Chalker-Coddington Model

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    The Chalker Coddington quantum network percolation model is numerically pertinent to the understanding of the delocalization transition of the quantum Hall effect. We study the model restricted to a cylinder of perimeter 2M. We prove firstly that the Lyapunov exponents are simple and in particular that the localization length is finite; secondly that this implies spectral localization. Thirdly we prove a Thouless formula and compute the mean Lyapunov exponent which is independent of M.Comment: 29 pages, 1 figure. New section added in which simplicity of the Lyapunov spectrum and finiteness of the localization length are proven. To appear in Annales Henri Poincar

    Fatigue Life Prediction of Welded Box Structures

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    The objective of this study is to predict fatigue life of metal welded boxes. Experimental results of fatigue life are satisfactory predicted using an analytical scheme based on the volumetric approach.Проведено прогнозирование усталостной долговечности сварных коробчатых конструкций. Результаты расчета усталостной долговечности с использованием аналитической схемы, базирующейся на объемном методе, хорошо согласуются с соответствующими экспериментальными данными.Проведено прогнозування довговічності зварних коробчастих конструкцій від утомленості. Результати розрахунку довговічності від утомленості з використанням аналітичної схеми, що базується на об’ємному методі, добре узгоджуються з відповідними експериментальними даними

    Cystatin C: A Candidate Biomarker for Amyotrophic Lateral Sclerosis

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    Amyotrophic lateral sclerosis (ALS) is a fatal neurologic disease characterized by progressive motor neuron degeneration. Clinical disease management is hindered by both a lengthy diagnostic process and the absence of effective treatments. Reliable panels of diagnostic, surrogate, and prognostic biomarkers are needed to accelerate disease diagnosis and expedite drug development. The cysteine protease inhibitor cystatin C has recently gained interest as a candidate diagnostic biomarker for ALS, but further studies are required to fully characterize its biomarker utility. We used quantitative enzyme-linked immunosorbent assay (ELISA) to assess initial and longitudinal cerebrospinal fluid (CSF) and plasma cystatin C levels in 104 ALS patients and controls. Cystatin C levels in ALS patients were significantly elevated in plasma and reduced in CSF compared to healthy controls, but did not differ significantly from neurologic disease controls. In addition, the direction of longitudinal change in CSF cystatin C levels correlated to the rate of ALS disease progression, and initial CSF cystatin C levels were predictive of patient survival, suggesting that cystatin C may function as a surrogate marker of disease progression and survival. These data verify prior results for reduced cystatin C levels in the CSF of ALS patients, identify increased cystatin C levels in the plasma of ALS patients, and reveal correlations between CSF cystatin C levels to both ALS disease progression and patient survival

    Congenic Mesenchymal Stem Cell Therapy Reverses Hyperglycemia in Experimental Type 1 Diabetes

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    OBJECTIVE - A number of clinical trials are underway to test whether mesenchymal stem cells (MSCs) are effective in treating various diseases, including type 1 diabetes. Although this cell therapy holds great promise, the optimal source of MSCs has yet to be determined with respect to major histocompatibility complex matching. Here, we examine this question by testing the ability of congenic MSCs, obtained from the NOR mouse strain, to reverse recent-onset type 1 diabetes in NOD mice, as well as determine the immunomodulatory effects of NOR MSCs in vivo. RESEARCH DESIGN AND METHODS - NOR MSCs were evaluated with regard to their in vitro immunomodulatory function in the context of autoreactive T-cell proliferation and dendritic cell (DC) generation. The in vivo effect of NOR MSC therapy on reversal of recent-onset hyperglycemia and on immunogenic cell subsets in NOD mice was also examined. RESULTS - NOR MSCs were shown to suppress diabetogenic T-cell proliferation via PD-L1 and to suppress generation of myeloid/inflammatory DCs predominantly through an IL-6-dependent mechanism. NOR MSC treatment of experimental type 1 diabetes resulted in long-term reversal of hyperglycemia, and therapy was shown to alter diabetogenic cytokine profile, to diminish T-cell effector frequency in the pancreatic lymph nodes, to alter antigen-presenting cell frequencies, and to augment the frequency of the plasmacytoid subset of DCs. CONCLUSIONS - These studies demonstrate the inimitable benefit of congenic MSC therapy in reversing experimental type 1 diabetes. These data should benefit future clinical trials using MSCs as treatment for type 1 diabetes
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