35,436 research outputs found
A parabolic free boundary problem with Bernoulli type condition on the free boundary
Consider the parabolic free boundary problem For a
realistic class of solutions, containing for example {\em all} limits of the
singular perturbation problem we prove that one-sided
flatness of the free boundary implies regularity.
In particular, we show that the topological free boundary
can be decomposed into an {\em open} regular set (relative to
) which is locally a surface with H\"older-continuous space
normal, and a closed singular set.
Our result extends the main theorem in the paper by H.W. Alt-L.A. Caffarelli
(1981) to more general solutions as well as the time-dependent case. Our proof
uses methods developed in H.W. Alt-L.A. Caffarelli (1981), however we replace
the core of that paper, which relies on non-positive mean curvature at singular
points, by an argument based on scaling discrepancies, which promises to be
applicable to more general free boundary or free discontinuity problems
A performance comparison of fullband and different subband adaptive equalisers
We present two different fractionally spaced (FS) equalisers based on subband methods, with the aim of reducing the computational complexity and increasing the convergence rate of a standard fullband FS equaliser. This is achieved by operating in decimated subbands; at a considerably lower update rate and by exploiting the prewhitening effect that a filter bank has on the considerable spectral dynamics of a signal received through a severely distorting channel. The two presented subband structures differ in their level of realising the feedforward and feedback part of the equaliser in the subband domain, with distinct impacts on the updating. Simulation results pinpoint the faster convergence at lower cost for the proposed subband equalisers
Optical Properties of Quantum-Dot-Doped Liquid Scintillators
Semiconductor nanoparticles (quantum dots) were studied in the context of
liquid scintillator development for upcoming neutrino experiments. The unique
optical and chemical properties of quantum dots are particularly promising for
the use in neutrinoless double beta decay experiments. Liquid scintillators for
large scale neutrino detectors have to meet specific requirements which are
reviewed, highlighting the peculiarities of quantum-dot-doping. In this paper,
we report results on laboratory-scale measurements of the attenuation length
and the fluorescence properties of three commercial quantum dot samples. The
results include absorbance and emission stability measurements, improvement in
transparency due to filtering of the quantum dot samples, precipitation tests
to isolate the quantum dots from solution and energy transfer studies with
quantum dots and the fluorophore PPO.Comment: version 2, minor text update
On integrability of the differential constraints arising from the singularity analysis
Integrability of the differential constraints arising from the singularity
analysis of two (1+1)-dimensional second-order evolution equations is studied.
Two nonlinear ordinary differential equations are obtained in this way, which
are integrable by quadratures in spite of very complicated branching of their
solutions.Comment: arxiv version is already offcia
Modeling quasar accretion disc temperature profiles
Microlensing observations indicate that quasar accretion discs have
half-light radii larger than expected from standard theoretical predictions
based on quasar fluxes or black hole masses. Blackburne and colleagues have
also found a very weak wavelength dependence of these half-light radii. We
consider disc temperature profile models that might match these observations.
Nixon and colleagues have suggested that misaligned accretion discs around
spinning black holes will be disrupted at radii small enough for the
Lense-Thirring torque to overcome the disc's viscous torque. Gas in precessing
annuli torn off a disc will spread radially and intersect with the remaining
disc, heating the disc at potentially large radii. However, if the intersection
occurs at an angle of more than a degree or so, highly supersonic collisions
will shock-heat the gas to a Compton temperature of T~10^7 K, and the spectral
energy distributions (SEDs) of discs with such shock-heated regions are poor
fits to observations of quasar SEDs. Torn discs where heating occurs in
intermittent weak shocks that occur whenever the intersection angle reaches a
tenth of a degree pose less of a conflict with observations, but do not have
significantly larger half-light radii than standard discs. We also study two
phenomenological disc temperature profile models. We find that discs with a
temperature spike at relatively large radii and lowered temperatures at radii
inside the spike yield improved and acceptable fits to microlensing sizes in
most cases. Such temperature profiles could in principle occur in sub-Keplerian
discs partially supported by magnetic pressure. However, such discs overpredict
the fluxes from quasars studied with microlensing except in the limit of
negligible continuum emission from radii inside the temperature spike.Comment: Submitted to MNRAS. Comments welcome. 20 pages, 5 figure
Tangential Touch between the Free and the Fixed Boundary in a Semilinear Free Boundary Problem in Two Dimensions
The main result of this paper concerns the behavior of a free boundary
arising from a minimization problem, close to the fixed boundary in two
dimensions
Cancer therapeutic potential of combinatorial immuno- and vaso-modulatory interventions
Currently, most of the basic mechanisms governing tumor-immune system
interactions, in combination with modulations of tumor-associated vasculature,
are far from being completely understood. Here, we propose a mathematical model
of vascularized tumor growth, where the main novelty is the modeling of the
interplay between functional tumor vasculature and effector cell recruitment
dynamics. Parameters are calibrated on the basis of different in vivo
immunocompromised Rag1-/- and wild-type (WT) BALB/c murine tumor growth
experiments. The model analysis supports that tumor vasculature normalization
can be a plausible and effective strategy to treat cancer when combined with
appropriate immuno-stimulations. We find that improved levels of functional
tumor vasculature, potentially mediated by normalization or stress alleviation
strategies, can provide beneficial outcomes in terms of tumor burden reduction
and growth control. Normalization of tumor blood vessels opens a therapeutic
window of opportunity to augment the antitumor immune responses, as well as to
reduce the intratumoral immunosuppression and induced-hypoxia due to vascular
abnormalities. The potential success of normalizing tumor-associated
vasculature closely depends on the effector cell recruitment dynamics and tumor
sizes. Furthermore, an arbitrary increase of initial effector cell
concentration does not necessarily imply a better tumor control. We evidence
the existence of an optimal concentration range of effector cells for tumor
shrinkage. Based on these findings, we suggest a theory-driven therapeutic
proposal that optimally combines immuno- and vaso-modulatory interventions
Combined Error Correction Techniques for Quantum Computing Architectures
Proposals for quantum computing devices are many and varied. They each have
unique noise processes that make none of them fully reliable at this time.
There are several error correction/avoidance techniques which are valuable for
reducing or eliminating errors, but not one, alone, will serve as a panacea.
One must therefore take advantage of the strength of each of these techniques
so that we may extend the coherence times of the quantum systems and create
more reliable computing devices. To this end we give a general strategy for
using dynamical decoupling operations on encoded subspaces. These encodings may
be of any form; of particular importance are decoherence-free subspaces and
quantum error correction codes. We then give means for empirically determining
an appropriate set of dynamical decoupling operations for a given experiment.
Using these techniques, we then propose a comprehensive encoding solution to
many of the problems of quantum computing proposals which use exchange-type
interactions. This uses a decoherence-free subspace and an efficient set of
dynamical decoupling operations. It also addresses the problems of
controllability in solid state quantum dot devices.Comment: Contribution to Proceedings of the 2002 Physics of Quantum
Electronics Conference", to be published in J. Mod. Optics. This paper
provides a summary and review of quant-ph/0205156 and quant-ph/0112054, and
some new result
Stability of quantum breathers
Using two methods we show that a quantized discrete breather in a 1-D lattice
is stable. One method uses path integrals and compares correlations for a
(linear) local mode with those of the quantum breather. The other takes a local
mode as the zeroth order system relative to which numerical, cutoff-insensitive
diagonalization of the Hamiltonian is performed.Comment: 4 pages, 3 figure
Reaction-Diffusion Process Driven by a Localized Source: First Passage Properties
We study a reaction-diffusion process that involves two species of atoms,
immobile and diffusing. We assume that initially only immobile atoms, uniformly
distributed throughout the entire space, are present. Diffusing atoms are
injected at the origin by a source which is turned on at time t=0. When a
diffusing atom collides with an immobile atom, the two atoms form an immobile
stable molecule. The region occupied by molecules is asymptotically spherical
with radius growing as t^{1/d} in d>=2 dimensions. We investigate the survival
probability that a diffusing atom has not become a part of a molecule during
the time interval t after its injection and the probability density of such a
particle. We show that asymptotically the survival probability (i) saturates in
one dimension, (ii) vanishes algebraically with time in two dimensions (with
exponent being a function of the dimensionless flux and determined as a zero of
a confluent hypergeometric function), and (iii) exhibits a stretched
exponential decay in three dimensions.Comment: 7 pages; version 2: section IV is re-written, references added, 8
pages (final version
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