Simultaneous Identification of the Diffusion Coefficient and the Potential for the Schr\"odinger Operator with only one Observation

This article is devoted to prove a stability result for two independent coefficients for a Schr\"odinger operator in an unbounded strip. The result is obtained with only one observation on an unbounded subset of the boundary and the data of the solution at a fixed time on the whole domain

Rotation of an immersed cylinder sliding near a thin elastic coating

It is known that an object translating parallel to a soft wall in a viscous fluid produces hydro- dynamic stresses that deform the wall, which, in turn, results in a lift force on the object. Recent experiments with cylinders sliding under gravity near a soft incline, which confirmed theoretical arguments for the lift force, also reported an unexplained steady-state rotation of the cylinders [Saintyves et al. PNAS 113(21), 2016]. Motivated by these observations, we show, in the lubrication limit, that an infinite cylinder that translates in a viscous fluid parallel to a soft wall at constant speed and separation distance must also rotate in order to remain free of torque. Using the Lorentz reciprocal theorem, we show analytically that for small deformations of the elastic layer, the angular velocity of the cylinder scales with the cube of the sliding speed. These predictions are confirmed numerically. We then apply the theory to the gravity-driven motion of a cylinder near a soft incline and find qualitative agreement with the experimental observations, namely that a softer elastic layer results in a greater angular speed of the cylinder.Comment: 16 pages, 4 figure

The Bright Side of Coulomb Blockade

We explore the photonic (bright) side of dynamical Coulomb blockade (DCB) by measuring the radiation emitted by a dc voltage-biased Josephson junction embedded in a microwave resonator. In this regime Cooper pair tunneling is inelastic and associated to the transfer of an energy 2eV into the resonator modes. We have measured simultaneously the Cooper pair current and the photon emission rate at the resonance frequency of the resonator. Our results show two regimes, in which each tunneling Cooper pair emits either one or two photons into the resonator. The spectral properties of the emitted radiation are accounted for by an extension to DCB theory.Comment: 4 pages, 4 figures + 3 pages, 1 figure supplementary materia

Population structures of Brazilian tall coconut ( Cocos nuciferaL.) by microsatellite markers.

In this study we investigated the genetic diversity of 10 populations of Brazilian Tall coconut trees, employing 13 SSR loci to characterize their genetic variability, population structure, and reproductive system

Independent Origins of Cultivated Coconut (Cocos nucifera L.) in the Old World Tropics

As a portable source of food, water, fuel, and construction materials, the coconut (Cocos nucifera L.) played a fundamental role in human migrations and the development of civilization across the humid tropics. Here we investigated the coconut's domestication history and its population genetic structure as it relates to human dispersal patterns. A sample of 1,322 coconut accessions, representing the geographical and phenotypic diversity of the species, was examined using ten microsatellite loci. Bayesian analyses reveal two highly genetically differentiated subpopulations that correspond to the Pacific and Indo-Atlantic oceanic basins. This pattern suggests independent origins of coconut cultivation in these two world regions, with persistent population structure on a global scale despite long-term human cultivation and dispersal. Pacific coconuts show additional genetic substructure corresponding to phenotypic and geographical subgroups; moreover, the traits that are most clearly associated with selection under human cultivation (dwarf habit, self-pollination, and “niu vai” fruit morphology) arose only in the Pacific. Coconuts that show evidence of genetic admixture between the Pacific and Indo-Atlantic groups occur primarily in the southwestern Indian Ocean. This pattern is consistent with human introductions of Pacific coconuts along the ancient Austronesian trade route connecting Madagascar to Southeast Asia. Admixture in coastal east Africa may also reflect later historic Arab trading along the Indian Ocean coastline. We propose two geographical origins of coconut cultivation: island Southeast Asia and southern margins of the Indian subcontinent

A global Carleman estimate in a transmission wave equation and application to a one-measurement inverse problem

We consider a transmission wave equation in two embedded domains in $R^2$, where the speed is $a1 > 0$ in the inner domain and $a2 > 0$ in the outer domain. We prove a global Carleman inequality for this problem under the hypothesis that the inner domain is strictly convex and $a1 > a2$ . As a consequence of this inequality, uniqueness and Lip- schitz stability are obtained for the inverse problem of retrieving a stationary potential for the wave equation with Dirichlet data and discontinuous principal coefficient from a single time-dependent Neumann boundary measurement