7,157 research outputs found

    Mode-coupling theory of the glass transition for confined fluids

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    We present a detailed derivation of a microscopic theory for the glass transition of a liquid enclosed between two parallel walls relying on a mode-coupling approximation. This geometry lacks translational invariance perpendicular to the walls, which implies that the density profile and the density-density correlation function depends explicitly on the distances to the walls. We discuss the residual symmetry properties in slab geometry and introduce a symmetry adapted complete set of two-point correlation functions. Since the currents naturally split into components parallel and perpendicular to the walls the mathematical structure of the theory differs from the established mode-coupling equations in bulk. We prove that the equations for the nonergodicity parameters still display a covariance property similar to bulk liquids.Comment: 16 pages; to be published in PR

    Exact renormalization group equation in presence of rescaling anomaly II - The local potential approximation

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    Exact renormalization group techniques are applied to mass deformed N=4 supersymmetric Yang-Mills theory, viewed as a regularised N=2 model. The solution of the flow equation, in the local potential approximation, reproduces the one-loop (perturbatively exact) expression for the effective action of N=2 supersymmetric Yang-Mills theory, when the regularising mass, M, reaches the value of the dynamical cutoff. One speculates about the way in which further non-perturbative contributions (instanton effects) may be accounted for.Comment: 13 pages, no figures, uses JHEP3.cl

    Technical Report: Compressive Temporal Higher Order Cyclostationary Statistics

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    The application of nonlinear transformations to a cyclostationary signal for the purpose of revealing hidden periodicities has proven to be useful for applications requiring signal selectivity and noise tolerance. The fact that the hidden periodicities, referred to as cyclic moments, are often compressible in the Fourier domain motivates the use of compressive sensing (CS) as an efficient acquisition protocol for capturing such signals. In this work, we consider the class of Temporal Higher Order Cyclostationary Statistics (THOCS) estimators when CS is used to acquire the cyclostationary signal assuming compressible cyclic moments in the Fourier domain. We develop a theoretical framework for estimating THOCS using the low-rate nonuniform sampling protocol from CS and illustrate the performance of this framework using simulated data

    Tracking p-adic precision

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    We present a new method to propagate pp-adic precision in computations, which also applies to other ultrametric fields. We illustrate it with many examples and give a toy application to the stable computation of the SOMOS 4 sequence
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