679 research outputs found
The Nights of Our Lives: Why We Sleep & Dream
Explore the most recent theories and evidence of why we sleep, and what happens in the brain during sleep and the consequences of sleep loss and sleep disorders
On a differential inclusion related to the Born-Infeld equations
We study a partial differential relation that arises in the context of the
Born-Infeld equations (an extension of the Maxwell's equations) by using
Gromov's method of convex integration in the setting of divergence free fields
Zero Entropy Interval Maps And MMLS-MMA Property
We prove that the flow generated by any interval map with zero topological
entropy is minimally mean-attractable (MMA) and minimally mean-L-stable (MMLS).
One of the consequences is that any oscillating sequence is linearly disjoint
with all flows generated by interval maps with zero topological entropy. In
particular, the M\"obius function is orthogonal to all flows generated by
interval maps with zero topological entropy (Sarnak's conjecture for interval
maps). Another consequence is a non-trivial example of a flow having the
discrete spectrum.Comment: 12 page
Rank-(n – 1) convexity and quasiconvexity for divergence free fields
No description supplie
Homogenization of Maxwell's equations in periodic composites
We consider the problem of homogenizing the Maxwell equations for periodic
composites. The analysis is based on Bloch-Floquet theory. We calculate
explicitly the reflection coefficient for a half-space, and derive and
implement a computationally-efficient continued-fraction expansion for the
effective permittivity. Our results are illustrated by numerical computations
for the case of two-dimensional systems. The homogenization theory of this
paper is designed to predict various physically-measurable quantities rather
than to simply approximate certain coefficients in a PDE.Comment: Significantly expanded compared to v1. Accepted to Phys.Rev.E. Some
color figures in this preprint may be easier to read because here we utilize
solid color lines, which are indistinguishable in black-and-white printin
Mechanisms of Spontaneous Current Generation in an Inhomogeneous d-Wave Superconductor
A boundary between two d-wave superconductors or an s-wave and a d-wave
superconductor generally breaks time-reversal symmetry and can generate
spontaneous currents due to proximity effect. On the other hand, surfaces and
interfaces in d-wave superconductors can produce localized current-carrying
states by supporting the T-breaking combination of dominant and subdominant
order parameters. We investigate spontaneous currents in the presence of both
mechanisms and show that at low temperature, counter-intuitively, the
subdominant coupling decreases the amplitude of the spontaneous current due to
proximity effect. Superscreening of spontaneous currents is demonstrated to be
present in any d-d (but not s-d) junction and surface with d+id' order
parameter symmetry. We show that this supercreening is the result of
contributions from the local magnetic moment of the condensate to the
spontaneous current.Comment: 4 pages, 5 figures, RevTe
The nonlinear diffusion limit for generalized Carleman models: the initial-boundary value problem
Consider the initial-boundary value problem for the 2-speed Carleman model of
the Boltzmann equation of the kinetic theory of gases set in some bounded
interval with boundary conditions prescribing the density of particles entering
the interval. Under the usual parabolic scaling, a nonlinear diffusion limit is
established for this problem. In fact, the techniques presented here allow
treating generalizations of the Carleman system where the collision frequency
is proportional to some power of the macroscopic density, with exponent in
[-1,1]
A C0 interior penalty discontinuous Galerkin method for fourth‐order total variation flow I: Derivation of the method and numerical results
We consider the numerical solution of a fourth‐order total variation flow problem representing surface relaxation below the roughening temperature. Based on a regularization and scaling of the nonlinear fourth‐order parabolic equation, we perform an implicit discretization in time and a C0 Interior Penalty Discontinuous Galerkin (C0IPDG) discretization in space. The C0IPDG approximation can be derived from a mixed formulation involving numerical flux functions where an appropriate choice of the flux functions allows to eliminate the discrete dual variable. The fully discrete problem can be interpreted as a parameter dependent nonlinear system with the discrete time as a parameter. It is solved by a predictor corrector continuation strategy featuring an adaptive choice of the time step sizes. A documentation of numerical results is provided illustrating the performance of the C0IPDG method and the predictor corrector continuation strategy. The existence and uniqueness of a solution of the C0IPDG method will be shown in the second part of this paper
Bounds on strong field magneto-transport in three-dimensional composites
This paper deals with bounds satisfied by the effective non-symmetric
conductivity of three-dimensional composites in the presence of a strong
magnetic field. On the one hand, it is shown that for general composites the
antisymmetric part of the effective conductivity cannot be bounded solely in
terms of the antisymmetric part of the local conductivity, contrary to the
columnar case. So, a suitable rank-two laminate the conductivity of which has a
bounded antisymmetric part together with a high-contrast symmetric part, may
generate an arbitrarily large antisymmetric part of the effective conductivity.
On the other hand, bounds are provided which show that the antisymmetric part
of the effective conductivity must go to zero if the upper bound on the
antisymmetric part of the local conductivity goes to zero, and the symmetric
part of the local conductivity remains bounded below and above. Elementary
bounds on the effective moduli are derived assuming the local conductivity and
effective conductivity have transverse isotropy in the plane orthogonal to the
magnetic field. New Hashin-Shtrikman type bounds for two-phase
three-dimensional composites with a non-symmetric conductivity are provided
under geometric isotropy of the microstructure. The derivation of the bounds is
based on a particular variational principle symmetrizing the problem, and the
use of Y-tensors involving the averages of the fields in each phase.Comment: 21 page
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