411 research outputs found
Conformal scattering for a nonlinear wave equation on a curved background
The purpose of this paper is to establish a geometric scattering result for a
conformally invariant nonlinear wave equation on an asymptotically simple
spacetime. The scattering operator is obtained via trace operators at null
infinities. The proof is achieved in three steps. A priori linear estimates are
obtained via an adaptation of the Morawetz vector field in the Schwarzschild
spacetime and a method used by H\"ormander for the Goursat problem. A
well-posedness result for the characteristic Cauchy problem on a light cone at
infinity is then obtained. This requires a control of the nonlinearity uniform
in time which comes from an estimates of the Sobolev constant and a decay
assumption on the nonlinearity of the equation. Finally, the trace operators on
conformal infinities are built and used to define the conformal scattering
operator
Recovering the mass and the charge of a Reissner-Nordstr\"om black hole by an inverse scattering experiment
In this paper, we study inverse scattering of massless Dirac fields that
propagate in the exterior region of a Reissner-Nordstr\"om black hole. Using a
stationary approach we determine precisely the leading terms of the high-energy
asymptotic expansion of the scattering matrix that, in turn, permit us to
recover uniquely the mass of the black hole and its charge up to a sign
Universal Bound on Dynamical Relaxation Times and Black-Hole Quasinormal Ringing
From information theory and thermodynamic considerations a universal bound on
the relaxation time of a perturbed system is inferred, , where is the system's temperature. We prove that black holes
comply with the bound; in fact they actually {\it saturate} it. Thus, when
judged by their relaxation properties, black holes are the most extreme objects
in nature, having the maximum relaxation rate which is allowed by quantum
theory.Comment: 4 page
Local energy decay of massive Dirac fields in the 5D Myers-Perry metric
We consider massive Dirac fields evolving in the exterior region of a
5-dimensional Myers-Perry black hole and study their propagation properties.
Our main result states that the local energy of such fields decays in a weak
sense at late times. We obtain this result in two steps: first, using the
separability of the Dirac equation, we prove the absence of a pure point
spectrum for the corresponding Dirac operator; second, using a new form of the
equation adapted to the local rotations of the black hole, we show by a Mourre
theory argument that the spectrum is absolutely continuous. This leads directly
to our main result.Comment: 40 page
The role of bevacizumab in solid tumours: A literature based meta-analysis of randomised trials
BACKGROUND:
Bevacizumab is a humanised monoclonal antibody which blocks the binding of circulating vascular endothelial growth factor to its receptors. To date, the Food and Drug Administration has approved bevacizumab for the treatment of several solid tumours. To assess the impact of bevacizumab-based regimens on outcome in these advanced solid tumour types, we performed a meta-analysis. We included all of the randomised trials (phase II or III) where bevacizumab was tested in the first line setting compared with a control arm, including chemotherapy, placebo or other anti-neoplastic agents.
METHODS:
A literature-based meta-analysis of randomised controlled trials (RCTs) in accordance with the preferences for reported items in systematic reviews and meta-analyses guidelines were undertaken. The primary end-point considered was overall survival (OS). The secondary end-points were progression-free survival (PFS) time, response rate and safety. A subgroup analysis was performed to highlight any differences between studies in different tumour types for all end-points.
RESULTS:
The pooled analysis from RCTs on bevacizumab-based regimens revealed significantly increased OS (hazard ratio [HR] for death 0.92, 95% confidence interval [CI]: 0.88-0.95; P < 0.0001), PFS (HR: 0.72, 95% CI: 0.67-0.78; P < 0.00001) and response rate (risk ratio: 1.38, 95% CI: 1.27-1.50; P < 0.00001) compared to control arm in solid tumours overall and in colorectal, lung, ovarian and renal cancer as single indications. However, notably, no effect on survival was seen in breast cancer.
CONCLUSION:
This study confirmed that bevacizumab-based regimens result in a significant effect on survival and response in advanced colorectal, lung, ovarian and kidney cancer. In cancers where bevacizumab failed overall as in breast cancer, a dedicated biomarkers analysis is warranted to select the proper subgroup of patient that might have the adequate clinical benefi
Mapping the Electromagnetic Near-Field Enhancements of Gold Nanocubes
International audienceWe imaged and quantitatively characterized electromagnetic hot spots near the surfaces of plasmon resonant gold nanocubes. The strongest fields are localized at the nanocube corners as compared to those on the sides. The near-field enhancement on the surface of the cube was imaged as a function of incident polarization, leading to information on the localization of fields on specific regions on the surface. We found that the field intensity drops dramatically when the nanocube corner is slightly tilted with respect to the incident laser polarization. This dramatic dependence on angle was verified by electrodynamics simulations. These results will enable the use of gold nanocubes in field enhancement applications and refractive-index sensing
Quantum Effects for the Dirac Field in Reissner-Nordstrom-AdS Black Hole Background
The behavior of a charged massive Dirac field on a Reissner-Nordstrom-AdS
black hole background is investigated. The essential self-adjointness of the
Dirac Hamiltonian is studied. Then, an analysis of the discharge problem is
carried out in analogy with the standard Reissner-Nordstrom black hole case.Comment: 18 pages, 5 figures, Iop styl
Quasinormal Spectrum and Quantization of Charged Black Holes
Black-hole quasinormal modes have been the subject of much recent attention,
with the hope that these oscillation frequencies may shed some light on the
elusive theory of quantum gravity. We study {\it analytically} the asymptotic
quasinormal spectrum of a {\it charged} scalar field in the (charged)
Reissner-Nordstr\"om spacetime. We find an analytic expression for these
black-hole resonances in terms of the black-hole physical parameters: its
Bekenstein-Hawking temperature , and its electric potential . We
discuss the applicability of the results in the context of black-hole
quantization. In particular, we show that according to Bohr's correspondence
principle, the asymptotic resonance corresponds to a fundamental area unit
.Comment: 4 page
Time-Translation Invariance of Scattering Maps and Blue-Shift Instabilities on Kerr Black Hole Spacetimes
In this paper, we provide an elementary, unified treatment of two distinct
blue-shift instabilities for the scalar wave equation on a fixed Kerr black
hole background: the celebrated blue-shift at the Cauchy horizon (familiar from
the strong cosmic censorship conjecture) and the time-reversed red-shift at the
event horizon (relevant in classical scattering theory).
Our first theorem concerns the latter and constructs solutions to the wave
equation on Kerr spacetimes such that the radiation field along the future
event horizon vanishes and the radiation field along future null infinity
decays at an arbitrarily fast polynomial rate, yet, the local energy of the
solution is infinite near any point on the future event horizon. Our second
theorem constructs solutions to the wave equation on rotating Kerr spacetimes
such that the radiation field along the past event horizon (extended into the
black hole) vanishes and the radiation field along past null infinity decays at
an arbitrarily fast polynomial rate, yet, the local energy of the solution is
infinite near any point on the Cauchy horizon.
The results make essential use of the scattering theory developed in [M.
Dafermos, I. Rodnianski and Y. Shlapentokh-Rothman, A scattering theory for the
wave equation on Kerr black hole exteriors, preprint (2014) available at
\url{http://arxiv.org/abs/1412.8379}] and exploit directly the time-translation
invariance of the scattering map and the non-triviality of the transmission
map.Comment: 26 pages, 12 figure
Plasmon-based photopolymerization: near-field probing, advanced photonic nanostructures and nanophotochemistry
Cataloged from PDF version of article.Hybrid nanomaterials are targeted by a rapidly growing group of nanooptics researchers, due to the promise of optical behavior that is difficult or even impossible to create with nanostructures of homogeneous composition. Examples of important areas of interest include coherent coupling, Fano resonances, optical gain, solar energy conversion, photocatalysis, and nonlinear optical interactions. In addition to the coupling interactions, the strong dependence of optical resonances and damping on the size, shape, and composition of the building blocks provides promise that the coupling interactions of hybrid nanomaterials can be controlled and manipulated for a desired outcome. Great challenges remain in reliably synthesizing and characterizing hybrid nanomaterials for nanooptics. In this review, we describe the synthesis, characterization, and applications of hybrid nanomaterials created through plasmon-induced photopolymerization. The work is placed within the broader context of hybrid nanomaterials involving plasmonic metal nanoparticles and molecular materials placed within the length scale of the evanescent field from the metal surface. We specifically review three important applications of free radical photopolymerization to create hybrid nanoparticles: local field probing, photoinduced synthesis of advanced hybrid nanoparticles, and nanophotochemistry
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