12,845 research outputs found
Emergence of steady and oscillatory localized structures in a phytoplankton-nutrient model
Co-limitation of marine phytoplankton growth by light and nutrient, both of
which are essential for phytoplankton, leads to complex dynamic behavior and a
wide array of coherent patterns. The building blocks of this array can be
considered to be deep chlorophyll maxima, or DCMs, which are structures
localized in a finite depth interior to the water column. From an ecological
point of view, DCMs are evocative of a balance between the inflow of light from
the water surface and of nutrients from the sediment. From a (linear)
bifurcational point of view, they appear through a transcritical bifurcation in
which the trivial, no-plankton steady state is destabilized. This article is
devoted to the analytic investigation of the weakly nonlinear dynamics of these
DCM patterns, and it has two overarching themes. The first of these concerns
the fate of the destabilizing stationary DCM mode beyond the center manifold
regime. Exploiting the natural singularly perturbed nature of the model, we
derive an explicit reduced model of asymptotically high dimension which fully
captures these dynamics. Our subsequent and fully detailed study of this model
- which involves a subtle asymptotic analysis necessarily transgressing the
boundaries of a local center manifold reduction - establishes that a stable DCM
pattern indeed appears from a transcritical bifurcation. However, we also
deduce that asymptotically close to the original destabilization, the DCM
looses its stability in a secondary bifurcation of Hopf type. This is in
agreement with indications from numerical simulations available in the
literature. Employing the same methods, we also identify a much larger DCM
pattern. The development of the method underpinning this work - which, we
expect, shall prove useful for a larger class of models - forms the second
theme of this article
Signatures of superconducting gap inhomogeneities in optical properties
Scanning tunneling spectroscopy applied to the high- cuprates has
revealed significant spatial inhomogeneity on the nanoscale. Regions on the
order of a coherence length in size show variations of the magnitude of the
superconducting gap of order or more. An important unresolved question
is whether or not these variations are also present in the bulk, and how they
influence superconducting properties. As many theories and data analyses for
high- superconductivity assume spatial homogeneity of the gap magnitude,
this is a pressing question. We consider the far-infrared optical conductivity
and evaluate, within an effective medium approximation, what signatures of
spatial variations in gap magnitude are present in various optical quantities.
In addition to the case of d-wave superconductivity, relevant to the high-
cuprates, we have also considered s-wave gap symmetry in order to provide
expected signatures of inhomogeneities for superconductors in general. While
signatures of gap inhomogeneities can be strongly manifested in s-wave
superconductors, we find that the far-infrared optical conductivity in d-wave
is robust against such inhomogeneity.Comment: 8 pages, 7 figure
Bose-Einstein condensates in standing waves: The cubic nonlinear Schroedinger equation with a periodic potential
We present a new family of stationary solutions to the cubic nonlinear
Schroedinger equation with a Jacobian elliptic function potential. In the limit
of a sinusoidal potential our solutions model a dilute gas Bose-Einstein
condensate trapped in a standing light wave. Provided the ratio of the height
of the variations of the condensate to its DC offset is small enough, both
trivial phase and nontrivial phase solutions are shown to be stable. Numerical
simulations suggest such stationary states are experimentally observable.Comment: 4 pages, 4 figure
Vacuum Breakdown near a Black Hole Charged by Hypercritical Accretion
We consider a black hole accreting spherically from the surrounding medium.
If accretion produces a luminosity close to the Eddington limit the hole
acquires a net charge so that electrons and ions can fall with the same
velocity. The condition for the electrostatic field to be large enough to break
the vacuum near the hole horizon translates into an upper limit for the hole
mass, The astrophysical conditions under
which this phaenomenon can take place are rather extreme, but in principle they
could be met by a mini black hole residing at the center of a star.Comment: 6 pages, accepted for publication in the Astrophysical Journa
Functional co-monotony of processes with applications to peacocks and barrier options
We show that several general classes of stochastic processes satisfy a
functional co-monotony principle, including processes with independent
increments, Brownian diffusions, Liouville processes. As a first application,
we recover some recent results about peacock processes obtained by Hirsch et
al. which were themselves motivated by a former work of Carr et al. about the
sensitivity of Asian Call options with respect to their volatility and residual
maturity (seniority). We also derive semi-universal bounds for various barrier
options.Comment: 27 page
Tunable tunneling: An application of stationary states of Bose-Einstein condensates in traps of finite depth
The fundamental question of how Bose-Einstein condensates tunnel into a
barrier is addressed. The cubic nonlinear Schrodinger equation with a finite
square well potential, which models a Bose-Einstein condensate in a
quasi-one-dimensional trap of finite depth, is solved for the complete set of
localized and partially localized stationary states, which the former evolve
into when the nonlinearity is increased. An immediate application of these
different solution types is tunable tunneling. Magnetically tunable Feshbach
resonances can change the scattering length of certain Bose-condensed atoms,
such as Rb, by several orders of magnitude, including the sign, and
thereby also change the mean field nonlinearity term of the equation and the
tunneling of the wavefunction. We find both linear-type localized solutions and
uniquely nonlinear partially localized solutions where the tails of the
wavefunction become nonzero at infinity when the nonlinearity increases. The
tunneling of the wavefunction into the non-classical regime and thus its
localization therefore becomes an external experimentally controllable
parameter.Comment: 11 pages, 5 figure
Gravitationally Lensed Gamma-Ray Bursts as Probes of Dark Compact Objects
If dark matter in the form of compact objects comprises a large fraction of
the mass of the universe, then gravitational lensing effects on gamma-ray
bursts are expected. We utilize BATSE and Ulysses data to search for lenses of
different mass ranges, which cause lensing in the milli, pico, and femto
regimes. Null results are used to set weak limits on the cosmological abundance
of compact objects in mass ranges from 10 to 10 . A
stronger limit is found for a much discussed universe dominated
by black holes of masses , which is ruled out at the
90% confidence level.Comment: 14 pages, 4 figures, fixed minor corrections. Accepted for
publication in ApJ(L
The unusual thickness dependence of superconductivity in -MoGe thin films
Thin films of -MoGe show progressively reduced 's as the
thickness is decreased below 30 nm and the sheet resistance exceeds 100
. We have performed far-infrared transmission and reflection
measurements for a set of -MoGe films to characterize this weakened
superconducting state. Our results show the presence of an energy gap with
ratio in all films studied, slightly higher
than the BCS value, even though the transition temperatures decrease
significantly as film thickness is reduced. The material properties follow
BCS-Eliashberg theory with a large residual scattering rate except that the
coherence peak seen in the optical scattering rate is found to be strongly
smeared out in the thinner superconducting samples. A peak in the optical mass
renormalization at is predicted and observed for the first time
The evolution of pebble size and shape in space and time
We propose a mathematical model which suggests that the two main geological
observations about shingle beaches, i.e. the emergence of predominant pebble
size ratios and strong segregation by size are interrelated. Our model is a
based on a system of ODEs called the box equations, describing the evolution of
pebble ratios. We derive these ODEs as a heuristic approximation of Bloore's
PDE describing collisional abrasion. While representing a radical
simplification of the latter, our system admits the inclusion of additional
terms related to frictional abrasion. We show that nontrivial attractors
(corresponding to predominant pebble size ratios) only exist in the presence of
friction. By interpreting our equations as a Markov process, we illustrate by
direct simulation that these attractors may only stabilized by the ongoing
segregation process.Comment: 22 pages, 8 figure
Millimeter Wave Localization: Slow Light and Enhanced Absorption
We exploit millimeter wave technology to measure the reflection and
transmission response of random dielectric media. Our samples are easily
constructed from random stacks of identical, sub-wavelength quartz and Teflon
wafers. The measurement allows us to observe the characteristic transmission
resonances associated with localization. We show that these resonances give
rise to enhanced attenuation even though the attenuation of homogeneous quartz
and Teflon is quite low. We provide experimental evidence of disorder-induced
slow light and superluminal group velocities, which, in contrast to photonic
crystals, are not associated with any periodicity in the system. Furthermore,
we observe localization even though the sample is only about four times the
localization length, interpreting our data in terms of an effective cavity
model. An algorithm for the retrieval of the internal parameters of random
samples (localization length and average absorption rate) from the external
measurements of the reflection and transmission coefficients is presented and
applied to a particular random sample. The retrieved value of the absorption is
in agreement with the directly measured value within the accuracy of the
experiment.Comment: revised and expande
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