7,157 research outputs found
Mode-coupling theory of the glass transition for confined fluids
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
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
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
We present a new method to propagate -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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