Fermat Principle in Finsler Spacetimes

It is shown that, on a manifold with a Finsler metric of Lorentzian signature, the lightlike geodesics satisfy the following variational principle. Among all lightlike curves from a point (emission event) to a timelike curve (worldline of receiver), the lightlike geodesics make the arrival time stationary. Here ``arrival time'' refers to a parametrization of the timelike curve. This variational principle can be applied (i) to the vacuum light rays in an alternative spacetime theory, based on Finsler geometry, and (ii) to light rays in an anisotropic non-dispersive medium with a general-relativistic spacetime as background.Comment: 18 pages, submitted to Gen. Rel. Gra

Electrostatic Patch Effect in Cylindrical Geometry. I. Potential and Energy between Slightly Non-Coaxial Cylinders

We study the effect of any uneven voltage distribution on two close cylindrical conductors with parallel axes that are slightly shifted in the radial and by any length in the axial direction. The investigation is especially motivated by certain precision measurements, such as the Satellite Test of the Equivalence Principle (STEP). By energy conservation, the force can be found as the energy gradient in the vector of the shift, which requires determining potential distribution and energy in the gap. The boundary value problem for the potential is solved, and energy is thus found to the second order in the small transverse shift, and to lowest order in the gap to cylinder radius ratio. The energy consists of three parts: the usual capacitor part due to the uniform potential difference, the one coming from the interaction between the voltage patches and the uniform voltage difference, and the energy of patch interaction, entirely independent of the uniform voltage. Patch effect forces and torques in the cylindrical configuration are derived and analyzed in the next two parts of this work.Comment: 26 pages, 1 Figure. Submitted to Classical and Quantum Gravit

Detection of the 2010 Chilean Tsunami Using Satellite Altimetry

Tsunamis are difficult to detect and measure in the open ocean because the wave amplitude is much smaller than it is closer to shore. An effective early warning system, however, must be able to observe an impending tsunami threat far away from the shore in order to provide the necessary lead-time for coastal inhabitants to find safety. Given the expansiveness of the ocean, sensors capable of detecting the tsunami must also have very broad areal coverage. The 2004 Sumatra-Andaman tsunami was definitively detected in the open ocean from both sea surface height and sea surface roughness measurements provided by satellite altimeters. This tsunami, however, was exceptionally strong and questions remain about the ability to use such measurements for the detection of weaker tsunamis. Here we study the 2010 Chilean tsunami and demonstrate the ability to detect the tsunami in the open ocean. Specifically, we analyze the utility of filtering in extracting the tsunami signal from sea surface height measurements, and, through the use of statistical analyses of satellite altimeter observations, we demonstrate that the 2010 Chilean tsunami induced distinct and detectable changes in sea surface roughness. While satellite altimeters do not provide the temporal and spatial coverage necessary to form the basis of an effective early warning system, tsunami-induced changes in sea surface roughness can be detected using orbiting microwave radars and radiometers, which have a broad surface coverage across the satellite ground track

Poly(4-vinyl pyridine) radiografted PVDF track etched membranes as sensors for monitoring trace mercury in water

International audiencePoly-4-vinyl pyridine chains were radiografted inside the etched-tracks of PVDF nanoporous membrane. P4VP grafting was found to be localized on the solid PVDF surface. Coating of these PVDF-g-P4VP membranes with a very thin layer of gold results in an ASV electrochemical sensor. Functionalized ion track-etched PVDF-g-P4VP sensors were found very selective and highly sensitive for mercury LOD 5 ng/L. a b s t r a c t By a radiation-induced grafting technique, we have functionalized track-etched nanoporous polymer membranes with mercury sensitive poly-4-vinyl pyridine (P4VP). Coating of these membranes with a very thin layer of gold results in an electrochemical sensor that is very selective and highly sensitive for mercury LOD 5 ng/L – well below the norms for water (0.015 mg/L potable water and 0.5 mg/L residual waters-French water norms of 27 October 2011). E-beam irradiation permitted optimization of the radiografting synthesis on PVDF thin films prior to ion-track grafting. Synthesis and characterization by EPR, FESEM and FTIR are described in detail. A comparison between FTIR in ATR and transmission modes enabled us to localize the grafting on the surface of the e-beam irradiated PVDF films allowing us to extrapolate what happens on the etched tracks. Using Square Wave Anodic Stripping Voltammetry (SW-ASV), mercury concentrations of 1 mg/L are detected in 2 h and low ng/L concentrations are detected after 24 h of adsorption. The adsorption is passive so sensors do not require instrumentation and the analysis takes only 3–4 min. Also, the P4VP functionalized sensor appears insensitive to pH variations (pHs 3–9), high salt concentrations (up to 1 g/ L) and the presence of other heavy metals in the same solution.

The Effect of the Environment on alpha-Al_2O_3 (0001) Surface Structures

We report that calculating the Gibbs free energy of the alpha-Al_2O_3 (0001) surfaces in equilibrium with a realistic environment containing both oxygen and hydrogen species is essential for obtaining theoretical predictions consistent with experimental observations. Using density-functional theory we find that even under conditions of high oxygen partial pressure, the metal terminated surface is surprisingly stable. An oxygen terminated alpha-Al_2O_3 (0001) surface becomes stable only if hydrogen is present on the surface. In addition, including hydrogen on the surface resolves discrepancies between previous theoretical work and experimental results with respect to the magnitude and direction of surface relaxations.Comment: 4 pages including 2 figures. Submitted to Phys. Rev. Lett. Related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Could Satellite Altimetry Have Improved Early Detection and Warning of the 2011 Tohoku Tsunami?

The 2011 Tohoku tsunami devastated Japan and affected coastal populations all around the Pacific Ocean. Accurate early warning of an impending tsunami requires the detection of the tsunami in the open ocean. While the lead-time was not sufficient for use in warning coastal populations in Japan, satellite altimetry observations of the tsunami could have been used to improve predictions and warnings for other affected areas. By comparing to both model results and historical satellite altimeter data, we use near-real-time satellite altimeter measurements to demonstrate the potential for detecting the 2011 Tohoku tsunami within a few hours of the tsunami being generated. We show how satellite altimeter data could be used to both directly detect tsunamis in the open ocean and also improve predictions made by models

Extended states in 1D lattices: application to quasiperiodic copper-mean chain

The question of the conditions under which 1D systems support extended electronic eigenstates is addressed in a very general context. Using real space renormalisation group arguments we discuss the precise criteria for determining the entire spertrum of extended eigenstates and the corresponding eigenfunctions in disordered as well as quasiperiodic systems. For purposes of illustration we calculate a few selected eigenvalues and the corresponding extended eigenfunctions for the quasiperiodic copper-mean chain. So far, for the infinite copper-mean chain, only a single energy has been numerically shown to support an extended eigenstate [ You et al. (1991)] : we show analytically that there is in fact an infinite number of extended eigenstates in this lattice which form fragmented minibands.Comment: 10 pages + 2 figures available on request; LaTeX version 2.0

Anomalous transparency of water-air interface for low-frequency sound

Sound transmission through water-air interface is normally weak because of a strong mass density contrast. Here we show that the transparency of the interface increases dramatically at low frequencies. Rather counterintuitively, almost all acoustic energy emitted by a sufficiently shallow monopole source under water is predicted to be radiated into atmosphere. Physically, increased transparency at lower frequencies is due to the increasing role of inhomogeneous waves and a destructive interference of direct and surface-reflected waves under water. The phenomenon of anomalous transparency has significant implications for acoustic communication across the water-air interface, generation of ambient noise, and detection of underwater explosions.Comment: 29 pages, including 4 figure

Ray-based description of normal mode amplitudes in a range-dependent waveguide

An analogue of the geometrical optics for description of the modal structure of a wave field in a range-dependent waveguide is considered. In the scope of this approach the mode amplitude is expressed through solutions of the ray equations. This analytical description accounts for mode coupling and remains valid in a nonadiabatic environment. It has been used to investigate the applicability condition of the adiabatic approximation. An applicability criterion is formulated as a restriction on variations of the action variable of the ray.Comment: 11 pages, 5 figure