1,556 research outputs found

    Clarke subgradients of stratifiable functions

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    We establish the following result: if the graph of a (nonsmooth) real-extended-valued function f:Rn→RâˆȘ{+∞}f:\mathbb{R}^{n}\to \mathbb{R}\cup\{+\infty\} is closed and admits a Whitney stratification, then the norm of the gradient of ff at x∈domfx\in{dom}f relative to the stratum containing xx bounds from below all norms of Clarke subgradients of ff at xx. As a consequence, we obtain some Morse-Sard type theorems as well as a nonsmooth Kurdyka-\L ojasiewicz inequality for functions definable in an arbitrary o-minimal structure

    Mechanical properties of Pt monatomic chains

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    The mechanical properties of platinum monatomic chains were investigated by simultaneous measurement of an effective stiffness and the conductance using our newly developed mechanically controllable break junction (MCBJ) technique with a tuning fork as a force sensor. When stretching a monatomic contact (two-atom chain), the stiffness and conductance increases at the early stage of stretching and then decreases just before breaking, which is attributed to a transition of the chain configuration and bond weakening. A statistical analysis was made to investigate the mechanical properties of monatomic chains. The average stiffness shows minima at the peak positions of the length-histogram. From this result we conclude that the peaks in the length-histogram are a measure of the number of atoms in the chains, and that the chains break from a strained state. Additionally, we find that the smaller the initial stiffness of the chain is, the longer the chain becomes. This shows that softer chains can be stretched longer.Comment: 6 pages, 5 figure

    The effect of thermal annealing on the properties of Al-AlOx-Al single electron tunneling transistors

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    The effect of thermal annealing on the properties of Al-AlOx-Al single electron tunneling transistors is reported. After treatment of the devices by annealing processes in forming gas atmosphere at different temperatures and for different times, distinct and reproducible changes of their resistance and capacitance values were found. According to the temperature regime, we observed different behaviors as regards the resistance changes, namely the tendency to decrease the resistance by annealing at T = 200 degree C, but to increase the resistance by annealing at T = 400 degree C. We attribute this behavior to changes in the aluminum oxide barriers of the tunnel junctions. The good reproducibility of these effects with respect to the changes observed allows the proper annealing treatment to be used for post-process tuning of tunnel junction parameters. Also, the influence of the annealing treatment on the noise properties of the transistors at low frequency was investigated. In no case did the noise figures in the 1/f-regime show significant changes.Comment: 6 pages, 7 eps-figure

    Lectures on the Asymptotic Expansion of a Hermitian Matrix Integral

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    In these lectures three different methods of computing the asymptotic expansion of a Hermitian matrix integral is presented. The first one is a combinatorial method using Feynman diagrams. This leads us to the generating function of the reciprocal of the order of the automorphism group of a tiling of a Riemann surface. The second method is based on the classical analysis of orthogonal polynomials. A rigorous asymptotic method is established, and a special case of the matrix integral is computed in terms of the Riemann ζ\zeta-function. The third method is derived from a formula for the τ\tau-function solution to the KP equations. This method leads us to a new class of solutions of the KP equations that are \emph{transcendental}, in the sense that they cannot be obtained by the celebrated Krichever construction and its generalizations based on algebraic geometry of vector bundles on Riemann surfaces. In each case a mathematically rigorous way of dealing with asymptotic series in an infinite number of variables is established

    Three Dimensional Structure and Energy Balance of a Coronal Mass Ejection

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    The Ultraviolet Coronagraph Spectrometer (UVCS) observed Doppler shifted material of a partial Halo Coronal Mass Ejection (CME) on December 13 2001. The observed ratio of [O V]/O V] is a reliable density diagnostic important for assessing the state of the plasma. Earlier UVCS observations of CMEs found evidence that the ejected plasma is heated long after the eruption. We have investigated the heating rates, which represent a significant fraction of the CME energy budget. The parameterized heating and radiative and adiabatic cooling have been used to evaluate the temperature evolution of the CME material with a time dependent ionization state model. The functional form of a flux rope model for interplanetary magnetic clouds was also used to parameterize the heating. We find that continuous heating is required to match the UVCS observations. To match the O VI-bright knots, a higher heating rate is required such that the heating energy is greater than the kinetic energy. The temperatures for the knots bright in Lyα\alpha and C III emission indicate that smaller heating rates are required for those regions. In the context of the flux rope model, about 75% of the magnetic energy must go into heat in order to match the O VI observations. We derive tighter constraints on the heating than earlier analyses, and we show that thermal conduction with the Spitzer conductivity is not sufficient to account for the heating at large heights.Comment: 40 pages, 16 figures, accepted for publication in ApJ For associated mpeg file, please see https://www.cora.nwra.com/~jylee/mpg/f5.mp

    Bispectral KP Solutions and Linearization of Calogero-Moser Particle Systems

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    A new construction using finite dimensional dual grassmannians is developed to study rational and soliton solutions of the KP hierarchy. In the rational case, properties of the tau function which are equivalent to bispectrality of the associated wave function are identified. In particular, it is shown that there exists a bound on the degree of all time variables in tau if and only if the wave function is rank one and bispectral. The action of the bispectral involution, beta, in the generic rational case is determined explicitly in terms of dual grassmannian parameters. Using the correspondence between rational solutions and particle systems, it is demonstrated that beta is a linearizing map of the Calogero-Moser particle system and is essentially the map sigma introduced by Airault, McKean and Moser in 1977.Comment: LaTeX, 24 page
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