5,982 research outputs found
Energy propagation in dissipative systems Part II: Centrovelocity for nonlinear wave equations
We consider nonlinear wave equations, first order in time, of a specific form. In the absence of dissipation, these equations are given by a Poisson system, with a Hamiltonian that is the integral of some density. The functional I, defined to be the integral of the square of the waveform, is a constant of motion of the unperturbed system. It will be shown that Z, the center of gravity of this density, is canonically conjugate to I and can be used as a measure to locate the position of the waveform. By introducing new coordinates based on Z, we get expressions for the centrovelocity, Image, and the decay of I, which compare to the ones of part I, in both the conservative and the dissipative case. With the derived expressions, we investigate the decay of solitary waves of the Korteweg-de Vries equation, when different kinds of dissipation are added
Perturbations of embedded eigenvalues for the planar bilaplacian
Operators on unbounded domains may acquire eigenvalues that are embedded in
the essential spectrum. Determining the fate of these embedded eigenvalues
under small perturbations of the underlying operator is a challenging task, and
the persistence properties of such eigenvalues is linked intimately to the
multiplicity of the essential spectrum. In this paper, we consider the planar
bilaplacian with potential and show that the set of potentials for which an
embedded eigenvalue persists is locally an infinite-dimensional manifold with
infinite codimension in an appropriate space of potentials
Inferring telescope polarization properties through spectral lines without linear polarization
We present a technique to determine the polarization properties of a
telescope through observations of spectral lines that have no intrinsic linear
polarization signals. For such spectral lines, any observed linear polarization
must be induced by the telescope optics. We apply the technique to observations
taken with the SPINOR at the DST and demonstrate that we can retrieve the
characteristic polarization properties of the DST at three wavelengths of 459,
526, and 615 nm. We determine the amount of crosstalk between the intensity
Stokes I and the linear and circular polarization states Stokes Q, U, and V,
and between Stokes V and Stokes Q and U. We fit a set of parameters that
describe the polarization properties of the DST to the observed crosstalk
values. The values for the ratio of reflectivities X and the retardance tau
match those derived with the telescope calibration unit within the error bars.
Residual crosstalk after applying a correction for the telescope polarization
stays at a level of 3-10%. We find that it is possible to derive the parameters
that describe the polarization properties of a telescope from observations of
spectral lines without intrinsic linear polarization signal. Such spectral
lines have a dense coverage (about 50 nm separation) in the visible part of the
spectrum (400-615 nm), but none were found at longer wavelengths. Using
spectral lines without intrinsic linear polarization is a promising tool for
the polarimetric calibration of current or future solar telescopes such as
DKIST.Comment: 22 pages, 24 figures, accepted for publication in A&
Mathematical models for sleep-wake dynamics: comparison of the two-process model and a mutual inhibition neuronal model
Sleep is essential for the maintenance of the brain and the body, yet many
features of sleep are poorly understood and mathematical models are an
important tool for probing proposed biological mechanisms. The most well-known
mathematical model of sleep regulation, the two-process model, models the
sleep-wake cycle by two oscillators: a circadian oscillator and a homeostatic
oscillator. An alternative, more recent, model considers the mutual inhibition
of sleep promoting neurons and the ascending arousal system regulated by
homeostatic and circadian processes. Here we show there are fundamental
similarities between these two models. The implications are illustrated with
two important sleep-wake phenomena. Firstly, we show that in the two-process
model, transitions between different numbers of daily sleep episodes occur at
grazing bifurcations.This provides the theoretical underpinning for numerical
results showing that the sleep patterns of many mammals can be explained by the
mutual inhibition model. Secondly, we show that when sleep deprivation disrupts
the sleep-wake cycle, ostensibly different measures of sleepiness in the two
models are closely related. The demonstration of the mathematical similarities
of the two models is valuable because not only does it allow some features of
the two-process model to be interpreted physiologically but it also means that
knowledge gained from study of the two-process model can be used to inform
understanding of the mutual inhibition model. This is important because the
mutual inhibition model and its extensions are increasingly being used as a
tool to understand a diverse range of sleep-wake phenomena such as the design
of optimal shift-patterns, yet the values it uses for parameters associated
with the circadian and homeostatic processes are very different from those that
have been experimentally measured in the context of the two-process model
On extensions of the core and the anticore of transferable utility games
We consider several related set extensions of the core and the anticore of games with transferable utility. An efficient allocation is undominated if it cannot be improved, in a specific way, by sidepayments changing the allocation or the game. The set of all such allocations is called the undominated set, and we show that it consists of finitely many polytopes with a core-like structure. One of these polytopes is the L1-center, consisting of all efficient allocations that minimize the sum of the absolute values of the excesses. The excess Pareto optimal set contains the allocations that are Pareto optimal in the set obtained by ordering the sums of the absolute values of the excesses of coalitions and the absolute values of the excesses of their complements. The L1-center is contained in the excess Pareto optimal set, which in turn is contained in the undominated set. For three-person games all these sets coincide. These three sets also coincide with the core for balanced games and with the anticore for antibalanced games. We study properties of these sets and provide characterizations in terms of balanced collections of coalitions. We also propose a single-valued selection from the excess Pareto optimal set, the min-prenucleolus, which is defined as the prenucleolus of the minimum of a game and its dual.Transferable utility game; core; anticore; core extension; min-prenucleolus
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