Survival probability of an immobile target surrounded by mobile traps

We study analytically, in one dimension, the survival probability $P_{s}(t)$ up to time $t$ of an immobile target surrounded by mutually noninteracting traps each performing a continuous-time random walk (CTRW) in continuous space. We consider a general CTRW with symmetric and continuous (but otherwise arbitrary) jump length distribution $f(\eta)$ and arbitrary waiting time distribution $\psi(\tau)$. The traps are initially distributed uniformly in space with density $\rho$. We prove an exact relation, valid for all time $t$, between $P_s(t)$ and the expected maximum $E[M(t)]$ of the trap process up to time $t$, for rather general stochastic motion $x_{\rm trap}(t)$ of each trap. When $x_{\rm trap}(t)$ represents a general CTRW with arbitrary $f(\eta)$ and $\psi(\tau)$, we are able to compute exactly the first two leading terms in the asymptotic behavior of $E[M(t)]$ for large $t$. This allows us subsequently to compute the precise asymptotic behavior, $P_s(t)\sim a\, \exp[-b\, t^{\theta}]$, for large $t$, with exact expressions for the stretching exponent $\theta$ and the constants $a$ and $b$ for arbitrary CTRW. By choosing appropriate $f(\eta)$ and $\psi(\tau)$, we recover the previously known results for diffusive and subdiffusive traps. However, our result is more general and includes, in particular, the superdiffusive traps as well as totally anomalous traps

Tight focal spots using azimuthally polarised light from a Fresnel cone

When focusing a light beam at high numerical aperture, the resulting electric field profile in the focal plane depends on the transverse polarisation profile, as interference between different parts of the beam needs to be taken into account. It is well known that radial polarised light produces a longitudinal polarisation component and can be focused below the conventional diffraction limit for homogeneously polarised light, and azimuthally polarised light that carries one unit of angular momentum can achieve even tighter focal spots. This is of interest for example for enhancing resolution in scanning microscopy. There are numerous ways to generate such polarisation structures, however, setups can be expensive and usually rely on birefringent components, hence prohibiting broadband operation. We have recently demonstrated a passive, low-cost technique using a simple glass cone (Fresnel cone) to generate beams with structured polarisation. We show here that the polarisation structure generated by Fresnel cones focuses better than radial polarised light at all numerical apertures. Furthermore, we investigate in detail the application of polarised light structures for two-photon microscopy. Specifically we demonstrate a method that allows us to generate the desired polarisation structure at the back aperture of the microscope by pre-compensating any detrimental phase shifts using a combination of waveplates

La didactique du francais dans les écoles primaires sénégalaises

Die vorliegende Arbeit bietet im ersten Teil einen Überblick über allgemeine Forschungsergebnisse aus der Fremdspracherwerbsforschung (vor allem zu den Aspekten: Eingangsvoraussetzungen von Schülern, Qualität von Lehrbüchern und Effektivität von Lehrmethoden). Der zweite Teil setzt sich intensiv mit der aktuellen Situation des Französischunterrichts an senegalesischen Primarschulen auseinander. Eine Analyse typischer Fehler wolof-phoner Schüler im mündlichen und schriftlichen Gebrau des Französischen zeigt die Relevanz des Einflussfaktors Herkunftssprache. Eine kritische Auseinandersetzung mit aktuell in Gebrauch befindlichen Lehrbüchern verdeutlicht die konzeptionellen Schwächen des Sprachunterrichts. Diese wiederum werden bestätigt durch Analysen der methodischen Unterrichtsgestaltung durch die Lehrer. Im dritten und letzten Teil werden Ansätze zur Verbesserung der aufgezeigten Schwächen des derzeitigen Systems diskutiert

Different canonical formulations of Einstein's theory of gravity

We describe the four most famous versions of the classical canonical formalism in the Einstein theory of gravity: the Arnovitt-Deser-Misner formalism, the Faddeev-Popov formalism, the tetrad formalism in the usual form, and the tetrad formalism in the form best suited for constructing the loop theory of gravity, which is now being developed. We present the canonical transformations relating these formalisms. The paper is written mainly for pedagogical purposes.Comment: LaTeX, 18 pages, some misprints in formulas (131)-(134) are correcte

Formation of dispersive hybrid bands at an organic-metal interface

An electronic band with quasi-one dimensional dispersion is found at the interface between a monolayer of a charge-transfer complex (TTF-TCNQ) and a Au(111) surface. Combined local spectroscopy and numerical calculations show that the band results from a complex mixing of metal and molecular states. The molecular layer folds the underlying metal states and mixes with them selectively, through the TTF component, giving rise to anisotropic hybrid bands. Our results suggest that, by tuning the components of such molecular layers, the dimensionality and dispersion of organic-metal interface states can be engineered

A functional non-central limit theorem for jump-diffusions with periodic coefficients driven by stable Levy-noise

We prove a functional non-central limit theorem for jump-diffusions with periodic coefficients driven by strictly stable Levy-processes with stability index bigger than one. The limit process turns out to be a strictly stable Levy process with an averaged jump-measure. Unlike in the situation where the diffusion is driven by Brownian motion, there is no drift related enhancement of diffusivity.Comment: Accepted to Journal of Theoretical Probabilit

Comparison of quantum field perturbation theory for the light front with the theory in lorentz coordinates

The relationship between the perturbation theory in light-front coordinates and Lorentz-covariant perturbation theory is investigated. A method for finding the difference between separate terms of the corresponding series without their explicit evaluation is proposed. A procedure of constructing additional counter-terms to the canonical Hamiltonian that compensate this difference at any finite order is proposed. For the Yukawa model, the light-front Hamiltonian with all of these counter-terms is obtained in a closed form. Possible application of this approach to gauge theories is discussed.Comment: LaTex 2.09, 20 pages, 5 figure