On the propagation of an optical wave in a photorefractive medium

The aim of this paper is first to review the derivation of a model describing the propagation of an optical wave in a photorefractive medium and to present various mathematical results on this model: Cauchy problem, solitary waves

Predictable hydrodynamic conditions explain temporal variations in the density of benthic foraging seabirds in a tidal stream environment

VC International Council for the Exploration of the Sea 2016. James J. Waggitt was funded by a NERC Case studentship supported by OpenHydro Ltd and Marine Scotland Science (NE/J500148/1). Shore-based surveys were funded by a NERC (NE/J004340/1) and a Scottish National Heritage (SNH) grant. FVCOM was funded by a NERC grant (NE/J004316/1). The bathymetry data used in hydrodynamic models (HI 1122 Sanday Sound to Westray Firth) was collected by the Maritime and Coastguard Agency (MCA) as part of the UK Civil Hydrography Programme. We wish to thank Christina Bristow, Matthew Finn and Jennifer Norris at the European Marine Energy Centre (EMEC); Ian Davies at Marine Scotland Science; Gail Davoren, Shaun Fraser, Pauline Goulet, Alex Robbins and Helen Wade for invaluable discussions; Thomas Cornulier, Alex Douglas, James Grecian and Samantha Patrick for their help with statistical analysis; and Jenny Campbell and the Cockram family for assistance during fieldwork.Peer reviewedPublisher PD

ESD Ideas: A 6-year oscillation in the whole Earth system?

An oscillation of about 6 years has been reported in Earth&rsquo;s fluid core motions, magnetic field, rotation, and crustal deformations. Recently, a 6-year cycle has also been detected in several climatic parameters (e.g., sea level, surface temperature, precipitation, land ice, land hydrology, and atmospheric angular momentum). Here we suggest that the 6-year oscillations detected in the Earth&rsquo;s deep interior, mantle rotation, and atmosphere are linked together, and that the core processes previously proposed as drivers of the 6-year cycle in the Earth&rsquo;s rotation, cause in addition the atmosphere to oscillate together with the mantle, inducing fluctuations in the climate system with similar periodicities.</p

Well-Posedness for Semi-Relativistic Hartree Equations of Critical Type

We prove local and global well-posedness for semi-relativistic, nonlinear Schr\"odinger equations $i \partial_t u = \sqrt{-\Delta + m^2} u + F(u)$ with initial data in $H^s(\mathbb{R}^3)$, $s \geq 1/2$. Here $F(u)$ is a critical Hartree nonlinearity that corresponds to Coulomb or Yukawa type self-interactions. For focusing $F(u)$, which arise in the quantum theory of boson stars, we derive a sufficient condition for global-in-time existence in terms of a solitary wave ground state. Our proof of well-posedness does not rely on Strichartz type estimates, and it enables us to add external potentials of a general class.Comment: 18 pages; replaced with revised version; remark and reference on blow up adde

(Semi)classical limit of the Hartree equation with harmonic potential

Nonlinear Schrodinger Equations (NLS) of the Hartree type occur in the modeling of quantum semiconductor devices. Their "semiclassical" limit of vanishing (scaled) Planck constant is both a mathematical challenge and practically relevant when coupling quantum models to classical models. With the aim of describing the semi-classical limit of the 3D Schrodinger--Poisson system with an additional harmonic potential, we study some semi-classical limits of the Hartree equation with harmonic potential in space dimension n>1. The harmonic potential is confining, and causes focusing periodically in time. We prove asymptotics in several cases, showing different possible nonlinear phenomena according to the interplay of the size of the initial data and the power of the Hartree potential. In the case of the 3D Schrodinger-Poisson system with harmonic potential, we can only give a formal computation since the need of modified scattering operators for this long range scattering case goes beyond current theory. We also deal with the case of an additional "local" nonlinearity given by a power of the local density - a model that is relevant when incorporating the Pauli principle in the simplest model given by the "Schrodinger-Poisson-X$\alpha$ equation". Further we discuss the connection of our WKB based analysis to the Wigner function approach to semiclassical limits.Comment: 26 page

Orbital stability of periodic waves for the nonlinear Schroedinger equation

The nonlinear Schroedinger equation has several families of quasi-periodic travelling waves, each of which can be parametrized up to symmetries by two real numbers: the period of the modulus of the wave profile, and the variation of its phase over a period (Floquet exponent). In the defocusing case, we show that these travelling waves are orbitally stable within the class of solutions having the same period and the same Floquet exponent. This generalizes a previous work where only small amplitude solutions were considered. A similar result is obtained in the focusing case, under a non-degeneracy condition which can be checked numerically. The proof relies on the general approach to orbital stability as developed by Grillakis, Shatah, and Strauss, and requires a detailed analysis of the Hamiltonian system satisfied by the wave profile.Comment: 34 pages, 7 figure

Gene induction during differentiation of human monocytes into dendritic cells: an integrated study at the RNA and protein levels

Changes in gene expression occurring during differentiation of human monocytes into dendritic cells were studied at the RNA and protein levels. These studies showed the induction of several gene classes corresponding to various biological functions. These functions encompass antigen processing and presentation, cytoskeleton, cell signalling and signal transduction, but also an increase in mitochondrial function and in the protein synthesis machinery, including some, but not all, chaperones. These changes put in perspective the events occurring during this differentiation process. On a more technical point, it appears that the studies carried out at the RNA and protein levels are highly complementary.Comment: website publisher: http://www.springerlink.com/content/ha0d2c351qhjhjdm

On the density-potential mapping in time-dependent density functional theory

The key questions of uniqueness and existence in time-dependent density functional theory are usually formulated only for potentials and densities that are analytic in time. Simple examples, standard in quantum mechanics, lead however to non-analyticities. We reformulate these questions in terms of a non-linear Schr\"odinger equation with a potential that depends non-locally on the wavefunction.Comment: 8 pages, 2 figure