Positivity of Lyapunov exponents for a continuous matrix-valued Anderson model

We study a continuous matrix-valued Anderson-type model. Both leading Lyapunov exponents of this model are proved to be positive and distinct for all ernergies in $(2,+\infty)$ except those in a discrete set, which leads to absence of absolutely continuous spectrum in $(2,+\infty)$. This result is an improvement of a previous result with Stolz. The methods, based upon a result by Breuillard and Gelander on dense subgroups in semisimple Lie groups, and a criterion by Goldsheid and Margulis, allow for singular Bernoulli distributions

Inverse Scattering for Gratings and Wave Guides

We consider the problem of unique identification of dielectric coefficients for gratings and sound speeds for wave guides from scattering data. We prove that the "propagating modes" given for all frequencies uniquely determine these coefficients. The gratings may contain conductors as well as dielectrics and the boundaries of the conductors are also determined by the propagating modes.Comment: 12 page

Targeted ablation of NrCAM or ankyrin-B results in disorganized lens fibers leading to cataract formation

The NgCAM-related cell adhesion molecule (NrCAM) is an immunoglobulin superfamily member of the L1 subgroup that interacts intracellularly with ankyrins. We reveal that the absence of NrCAM causes the formation of mature cataracts in the mouse, whereas significant pathfinding errors of commissural axons at the midline of the spinal cord or of proprioceptive axon collaterals are not detected. Cataracts, the most common cause of visual impairment, are generated in NrCAM-deficient mice by a disorganization of lens fibers, followed by cellular disintegration and accumulation of cellular debris. The disorganization of fiber cells becomes histologically distinct during late embryonic development and includes abnormalities of the cytoskeleton and of connexin50-containing gap junctions. Furthermore, analysis of lenses of ankyrin-B mutant mice also reveals a disorganization of lens fibers at postnatal day 1, indistinguishable from that generated by the absence of NrCAM, indicating that NrCAM and ankyrin-B are required to maintain contact between lens fiber cells. Also, these studies provide genetic evidence of an interaction between NrCAM and ankyrin-B

Global Bounds for the Lyapunov Exponent and the Integrated Density of States of Random Schr\"odinger Operators in One Dimension

In this article we prove an upper bound for the Lyapunov exponent $\gamma(E)$ and a two-sided bound for the integrated density of states $N(E)$ at an arbitrary energy $E>0$ of random Schr\"odinger operators in one dimension. These Schr\"odinger operators are given by potentials of identical shape centered at every lattice site but with non-overlapping supports and with randomly varying coupling constants. Both types of bounds only involve scattering data for the single-site potential. They show in particular that both $\gamma(E)$ and $N(E)-\sqrt{E}/\pi$ decay at infinity at least like $1/\sqrt{E}$. As an example we consider the random Kronig-Penney model.Comment: 9 page

Physics Analysis Expert PAX: First Applications

PAX (Physics Analysis Expert) is a novel, C++ based toolkit designed to assist teams in particle physics data analysis issues. The core of PAX are event interpretation containers, holding relevant information about and possible interpretations of a physics event. Providing this new level of abstraction beyond the results of the detector reconstruction programs, PAX facilitates the buildup and use of modern analysis factories. Class structure and user command syntax of PAX are set up to support expert teams as well as newcomers in preparing for the challenges expected to arise in the data analysis at future hadron colliders.Comment: Talk from the 2003 Computing in High Energy and Nuclear Physics (CHEP03), La Jolla, Ca, USA, March 2003, 7 pages, LaTeX, 10 eps figures. PSN THLT00

Structure and Reactivity of α-Al₂O₃(0001) Surfaces: How Do Al-I and Gibbsite-like Terminations Interconvert?

The α-Al2O3(0001) surface has been extensively studied because of its significance in both fundamental research and application. Prior work suggests that in ultra-high-vacuum (UHV), in the absence of water, the so-called Al–I termination is thermodynamically favored, while in ambient, in contact with liquid water, a Gibbsite-like layer is created. While the view of the α-Al2O3(0001)/H2O(l) interface appears relatively clear in theory, experimental characterization of this system has resulted in estimates of surface acidity, i.e., isoelectric points, that differ by 4 pH units and surface structure that in some reports has non-hydrogen-bonded surface aluminol (Al–OH) groups and in others does not. In this study, we employed vibrational sum frequency spectroscopy (VSFS) and density functional theory (DFT) simulation to study the surface phonon modes of the differently terminated α-Al2O3(0001) surfaces in both UHV and ambient. We find that, on either water dosing of the Al–I in UHV or heat-induced dehydroxylation of the Gibbsite-like in ambient, the surfaces do not interconvert. This observation offers a new explanation for disagreements in prior work on the α-Al2O3(0001)/liquid water interface─different preparation methods may create surfaces that do not interconvert─and shows that the surface phonon spectral response offers a novel probe of interfacial hydrogen bonding structure

Analysis of effective mobility and hall effect mobility in high-k based In0.75Ga0.25As metal-oxide-semiconductor high-electron-mobility transistors

We report an In0.75Ga0.25As metal-oxide-semiconductor high-electron-mobility transistor with a peak Hall mobility of 8300 cm(2)/Vs at a carrier density of 2 x 10(12) cm(-2). Comparison of split capacitance-voltage (CV) and Hall Effect measurements for the extracted electron mobility have shown that the split-CV can lead to an overestimation of the channel carrier concentration and a corresponding underestimation of electron mobility. An analysis of the electron density dependence versus gate voltage allows quantifying the inaccuracy of the split-CV technique. Finally, the analysis supported by multi-channel conduction simulations indicates presence of carriers spill over into the top InP barrier layer at high gate voltages. (C) 2011 American Institute of Physics. (doi: 10.1063/1.3665033

Low lying spectrum of weak-disorder quantum waveguides

We study the low-lying spectrum of the Dirichlet Laplace operator on a randomly wiggled strip. More precisely, our results are formulated in terms of the eigenvalues of finite segment approximations of the infinite waveguide. Under appropriate weak-disorder assumptions we obtain deterministic and probabilistic bounds on the position of the lowest eigenvalue. A Combes-Thomas argument allows us to obtain so-called 'initial length scale decay estimates' at they are used in the proof of spectral localization using the multiscale analysis.Comment: Accepted for publication in Journal of Statistical Physics http://www.springerlink.com/content/0022-471

Determining the shape of defects in non-absorbing inhomogeneous media from far-field measurements

International audienceWe consider non-absorbing inhomogeneous media represented by some refraction index. We have developed a method to reconstruct, from far-field measurements, the shape of the areas where the actual index differs from a reference index. Following the principle of the Factorization Method, we present a fast reconstruction algorithm relying on far field measurements and near field values, easily computed from the reference index. Our reconstruction result is illustrated by several numerical test cases