On convergence towards a self-similar solution for a nonlinear wave equation - a case study

We consider the problem of asymptotic stability of a self-similar attractor for a simple semilinear radial wave equation which arises in the study of the Yang-Mills equations in 5+1 dimensions. Our analysis consists of two steps. In the first step we determine the spectrum of linearized perturbations about the attractor using a method of continued fractions. In the second step we demonstrate numerically that the resulting eigensystem provides an accurate description of the dynamics of convergence towards the attractor.Comment: 9 pages, 5 figure

On approximate solutions of semilinear evolution equations II. Generalizations, and applications to Navier-Stokes equations

In our previous paper [12] (Rev. Math. Phys. 16, 383-420 (2004)), a general framework was outlined to treat the approximate solutions of semilinear evolution equations; more precisely, a scheme was presented to infer from an approximate solution the existence (local or global in time) of an exact solution, and to estimate their distance. In the first half of the present work the abstract framework of \cite{uno} is extended, so as to be applicable to evolutionary PDEs whose nonlinearities contain derivatives in the space variables. In the second half of the paper this extended framework is applied to theincompressible Navier-Stokes equations, on a torus T^d of any dimension. In this way a number of results are obtained in the setting of the Sobolev spaces H^n(T^d), choosing the approximate solutions in a number of different ways. With the simplest choices we recover local existence of the exact solution for arbitrary data and external forces, as well as global existence for small data and forces. With the supplementary assumption of exponential decay in time for the forces, the same decay law is derived for the exact solution with small (zero mean) data and forces. The interval of existence for arbitrary data, the upper bounds on data and forces for global existence, and all estimates on the exponential decay of the exact solution are derived in a fully quantitative way (i.e., giving the values of all the necessary constants; this makes a difference with most of the previous literature). Nextly, the Galerkin approximate solutions are considered and precise, still quantitative estimates are derived for their H^n distance from the exact solution; these are global in time for small data and forces (with exponential time decay of the above distance, if the forces decay similarly).Comment: LaTeX, 84 pages. The final version published in Reviews in Mathematical Physic

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

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

Tidal stream turbines could have several direct impacts upon pursuit-diving seabirds foraging within tidal stream environments (mean horizontal current speeds > 2 ms−1), including collisions and displacement. Understanding how foraging seabirds respond to temporally variable but predictable hydrodynamic conditions immediately around devices could identify when interactions between seabirds and devices are most likely to occur; information which would quantify the magnitude of potential impacts, and also facilitate the development of suitable mitigation measures. This study uses shore-based observational surveys and Finite Volume Community Ocean Model outputs to test whether temporally predictable hydrodynamic conditions (horizontal current speeds, water elevation, turbulence) influenced the density of foraging black guillemots Cepphus grylle and European shags Phalacrocorax aristotelis in a tidal stream environment in Orkney, United Kingdom, during the breeding season. These species are particularly vulnerable to interactions with devices due to their tendency to exploit benthic and epi-benthic prey on or near the seabed. The density of both species decreased as a function of horizontal current speeds, whereas the density of black guillemots also decreased as a function of water elevation. These relationships could be linked to higher energetic costs of dives in particularly fast horizontal current speeds (>3 ms−1) and deeper water. Therefore, interactions between these species and moving components seem unlikely at particularly high horizontal current speeds. Combining this information, with that on the rotation rates of moving components at lower horizontal current speeds, could be used to assess collision risk in this site during breeding seasons. It is also likely that moderating any device operation during both lowest water elevation and lowest horizontal current speeds could reduce the risk of collisions for these species in this site during this season. The approaches used in this study could have useful applications within Environmental Impact Assessments, and should be considered when assessing and mitigating negative impacts from specific devices within development sites

Higher order Schrodinger and Hartree-Fock equations

The domain of validity of the higher-order Schrodinger equations is analyzed for harmonic-oscillator and Coulomb potentials as typical examples. Then the Cauchy theory for higher-order Hartree-Fock equations with bounded and Coulomb potentials is developed. Finally, the existence of associated ground states for the odd-order equations is proved. This renders these quantum equations relevant for physics.Comment: 19 pages, to appear in J. Math. Phy

Nonlinear Quantum Mechanics and Locality

It is shown that, in order to avoid unacceptable nonlocal effects, the free parameters of the general Doebner-Goldin equation have to be chosen such that this nonlinear Schr\"odinger equation becomes Galilean covariant.Comment: 10 pages, no figures, also available on http://www.pt.tu-clausthal.de/preprints/asi-tpa/012-97.htm

Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system

We describe the asymptotic behavior as time goes to infinity of solutions of the 2 dimensional corotational wave map system and of solutions to the 4 dimensional, radially symmetric Yang-Mills equation, in the critical energy space, with data of energy smaller than or equal to a harmonic map of minimal energy. An alternative holds: either the data is the harmonic map and the soltuion is constant in time, or the solution scatters in infinite time

Phototesting and photoprotection in LE

Photosensitivity and induction of skin lesions following UV radiation is a common problem of patients with cutaneous and systemic forms of lupus erythematosus. The detrimental effect of UV radiation to patients with lupus erythematosus was already recognized in the last century. Skin lesions can now be provoked under standardized conditions allowing the diagnosis and classification of patients with photosensitive disorders. The aim of this review is to give an overview on the history, test procedure and test results in patients with lupus erythematosus

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