4,900 research outputs found

    A Variational Principle for the Asymptotic Speed of Fronts of the Density Dependent Diffusion--Reaction Equation

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    We show that the minimal speed for the existence of monotonic fronts of the equation ut=(um)xx+f(u)u_t = (u^m)_{xx} + f(u) with f(0)=f(1)=0f(0) = f(1) = 0, m>1m >1 and f>0f>0 in (0,1)(0,1) derives from a variational principle. The variational principle allows to calculate, in principle, the exact speed for arbitrary ff. The case m=1m=1 when f′(0)=0f'(0)=0 is included as an extension of the results.Comment: Latex, postcript figure availabl

    The ILR School at Fifty: Voices of the Faculty, Alumni & Friends (Full Text)

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    A collection of reflections on the first fifty years of the School of Industrial and Labor Relations at Cornell University. Compiled by Robert B. McKersie, J. Gormly Miller, Robert L. Aronson, and Robert R. Julian. Edited by Elaine Gruenfeld Goldberg. It was the hope of the compilers that the reflections contained in this book would both kindle memories of the school and stimulate interest on the part of future generations of ILRies who have not yet shared in its special history. Dedicated to the Memory of J. Gormly Miller, 1914-1995. Copyright 1996 by Cornell University. All rights reserved

    Erosion waves: transverse instabilities and fingering

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    Two laboratory scale experiments of dry and under-water avalanches of non-cohesive granular materials are investigated. We trigger solitary waves and study the conditions under which the front is transversally stable. We show the existence of a linear instability followed by a coarsening dynamics and finally the onset of a fingering pattern. Due to the different operating conditions, both experiments strongly differ by the spatial and time scales involved. Nevertheless, the quantitative agreement between the stability diagram, the wavelengths selected and the avalanche morphology reveals a common scenario for an erosion/deposition process.Comment: 4 pages, 6 figures, submitted to PR

    Development of a theory of the spectral reflectance of minerals, part 2

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    Theory of diffuse reflectance of particulate media including garnet, glass, corundum powders, and mixture

    Test of Special Relativity and Equivalence principle from K Physics

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    A violation of Local Lorentz Invariance (VLI) and hence the special theory of relativity or a violation of equivalence principle (VEP) in the Kaon system can, in principle, induce oscillations between K0K^0 and Kˉ0\bar{K}^0. We construct a general formulation in which simultaneous pairwise diagonalization of mass, momemtum, weak or gravitational eigenstates is not assumed. %and the maximum attainable %velocities of the velocity eigenstates are different. We discuss this problem in a general way and point out that, as expected, the VEP and VLI contributions are indistinguishable. We then insist on the fact that VEP or VLI can occur even when CPT is conserved. A possible CP violation of the superweak type induced by VEP or VLI is introduced and discussed. We show that the general VEP mechanism (or the VLI mechanism, but not both simultaneously), with or without conserved CPT, could be clearly tested experimentally through the energy dependence of the KL−KSK_L-K_S mass difference and of η+−\eta_{+-}, η00\eta_{00}, δ\delta. Constraints imposed by present experiments are calculated.Comment: Latex, 15 pages, 1 figure, version to appear in Phys. Rev.

    Shift in the velocity of a front due to a cut-off

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    We consider the effect of a small cut-off epsilon on the velocity of a traveling wave in one dimension. Simulations done over more than ten orders of magnitude as well as a simple theoretical argument indicate that the effect of the cut-off epsilon is to select a single velocity which converges when epsilon tends to 0 to the one predicted by the marginal stability argument. For small epsilon, the shift in velocity has the form K(log epsilon)^(-2) and our prediction for the constant K agrees very well with the results of our simulations. A very similar logarithmic shift appears in more complicated situations, in particular in finite size effects of some microscopic stochastic systems. Our theoretical approach can also be extended to give a simple way of deriving the shift in position due to initial conditions in the Fisher-Kolmogorov or similar equations.Comment: 12 pages, 3 figure

    Neutron, electron and X-ray scattering investigation of Cr1-xVx near Quantum Criticality

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    The weakness of electron-electron correlations in the itinerant antiferromagnet Cr doped with V has long been considered the reason that neither new collective electronic states or even non Fermi liquid behaviour are observed when antiferromagnetism in Cr1−x_{1-x}Vx_{x} is suppressed to zero temperature. We present the results of neutron and electron diffraction measurements of several lightly doped single crystals of Cr1−x_{1-x}Vx_{x} in which the archtypal spin density wave instability is progressively suppressed as the V content increases, freeing the nesting-prone Fermi surface for a new striped charge instability that occurs at xc_{c}=0.037. This novel nesting driven instability relieves the entropy accumulation associated with the suppression of the spin density wave and avoids the formation of a quantum critical point by stabilising a new type of charge order at temperatures in excess of 400 K. Restructuring of the Fermi surface near quantum critical points is a feature found in materials as diverse as heavy fermions, high temperature copper oxide superconductors and now even elemental metals such as Cr.Comment: 6 pages, 6 figures. Accepted to Physical Review
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