6,337 research outputs found
Characterisation and representation of non-dissipative electromagnetic medium with a double light cone
We study Maxwell's equations on a 4-manifold N with a medium that is
non-dissipative and has a linear and pointwise response. In this setting, the
medium can be represented by a suitable (2,2)-tensor on the 4-manifold N.
Moreover, in each cotangent space on N, the medium defines a Fresnel surface.
Essentially, the Fresnel surface is a tensorial analogue of the dispersion
equation that describes the response of the medium for signals in the geometric
optics limit. For example, in isotropic medium the Fresnel surface is at each
point a Lorentz light cone. In a recent paper, I. Lindell, A. Favaro and L.
Bergamin introduced a condition that constrains the polarisation for plane
waves. In this paper we show (under suitable assumptions) that a slight
strengthening of this condition gives a pointwise characterisation of all
medium tensors for which the Fresnel surface is the union of two distinct
Lorentz null cones. This is for example the behaviour of uniaxial medium like
calcite. Moreover, using the representation formulas from Lindell et al. we
obtain a closed form representation formula that pointwise parameterises all
medium tensors for which the Fresnel surface is the union of two distinct
Lorentz null cones. Both the characterisation and the representation formula
are tensorial and do not depend on local coordinates
Extreme points of the set of density matrices with positive partial transpose
We present a necessary and sufficient condition for a finite dimensional
density matrix to be an extreme point of the convex set of density matrices
with positive partial transpose with respect to a subsystem. We also give an
algorithm for finding such extreme points and illustrate this by some examples.Comment: 4 pages, 2 figure
Determination of electromagnetic medium from the Fresnel surface
We study Maxwell's equations on a 4-manifold where the electromagnetic medium
is described by an antisymmetric -tensor . In this setting,
the Tamm-Rubilar tensor density determines a polynomial surface of fourth order
in each cotangent space. This surface is called the Fresnel surface and acts as
a generalisation of the light-cone determined by a Lorentz metric; the Fresnel
surface parameterises electromagnetic wave-speed as a function of direction.
Favaro and Bergamin have recently proven that if has only a principal
part and if the Fresnel surface of coincides with the light cone for a
Lorentz metric , then is proportional to the Hodge star operator of
. That is, under additional assumptions, the Fresnel surface of
determines the conformal class of . The purpose of this paper is
twofold. First, we provide a new proof of this result using Gr\"obner bases.
Second, we describe a number of cases where the Fresnel surface does not
determine the conformal class of the original -tensor . For
example, if is invertible we show that and have
the same Fresnel surfaces.Comment: 23 pages, 1 figur
Statistical properties of Klauder-Perelomov coherent states for the Morse potential
We present in this paper a realistic construction of the coherent states for
the Morse potential using the Klauder-Perelomov approach . We discuss the
statistical properties of these states, by deducing the Q- and P-distribution
functions. The thermal expectations for the quantum canonical ideal gas of the
Morse oscillators are also calculated
Correction: Ocean acidification at a coastal CO2 vent induces expression of stress-related transcripts and transposable elements in the sea anemone Anemonia viridis.
[This corrects the article DOI: 10.1371/journal.pone.0210358.]
Switching dynamics of surface stabilized ferroelectric liquid crystal cells: effects of anchoring energy asymmetry
We study both theoretically and experimentally switching dynamics in surface
stabilized ferroelectric liquid crystal cells with asymmetric boundary
conditions. In these cells the bounding surfaces are treated differently to
produce asymmetry in their anchoring properties. Our electro-optic measurements
of the switching voltage thresholds that are determined by the peaks of the
reversal polarization current reveal the frequency dependent shift of the
hysteresis loop. We examine the predictions of the uniform dynamical model with
the anchoring energy taken into account. It is found that the asymmetry effects
are dominated by the polar contribution to the anchoring energy. Frequency
dependence of the voltage thresholds is studied by analyzing the properties of
time-periodic solutions to the dynamical equation (cycles). For this purpose,
we apply the method that uses the parameterized half-period mappings for the
approximate model and relate the cycles to the fixed points of the composition
of two half-period mappings. The cycles are found to be unstable and can only
be formed when the driving frequency is lower than its critical value. The
polar anchoring parameter is estimated by making a comparison between the
results of modelling and the experimental data for the shift vs frequency
curve. For a double-well potential considered as a deformation of the
Rapini-Papoular potential, the branch of stable cycles emerges in the low
frequency region separated by the gap from the high frequency interval for
unstable cycles.Comment: 35 pages, 15 figure
Embryogenesis and Larval Biology of the Cold-WaterCoral Lophelia pertusa
Cold-water coral reefs form spectacular and highly diverse ecosystems in the deep sea but little is known about
reproduction, and virtually nothing about the larval biology in these corals. This study is based on data from two locations
of the North East Atlantic and documents the first observations of embryogenesis and larval development in Lophelia
pertusa, the most common framework-building cold-water scleractinian. Embryos developed in a more or less organized
radial cleavage pattern from ,160 mm large neutral or negatively buoyant eggs, to 120â270 mm long ciliated planulae.
Embryogenesis was slow with cleavage occurring at intervals of 6â8 hours up to the 64-cell stage. Genetically characterized
larvae were sexually derived, with maternal and paternal alleles present. Larvae were active swimmers (0.5 mm s21) initially
residing in the upper part of the water column, with bottom probing behavior starting 3â5 weeks after fertilization.
Nematocysts had developed by day 30, coinciding with peak bottom-probing behavior, and possibly an indication that
larvae are fully competent to settle at this time. Planulae survived for eight weeks under laboratory conditions, and
preliminary results indicate that these planulae are planktotrophic. The late onset of competency and larval longevity
suggests a high dispersal potential. Understanding larval biology and behavior is of paramount importance for biophysical
modeling of larval dispersal, which forms the basis for predictions of connectivity among populations
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