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 $\tau$ of a perturbed system is inferred, $\tau \geq \hbar/\pi T$, where $T$ 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 $T_{BH}$, and its electric potential $\Phi$. 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 $\Delta A=4\hbar\ln2$.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