8,467 research outputs found
Survival probability of an immobile target surrounded by mobile traps
We study analytically, in one dimension, the survival probability
up to time 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 and arbitrary waiting time
distribution . The traps are initially distributed uniformly in
space with density . We prove an exact relation, valid for all time ,
between and the expected maximum of the trap process up to
time , for rather general stochastic motion of each trap.
When represents a general CTRW with arbitrary and
, we are able to compute exactly the first two leading terms in the
asymptotic behavior of for large . This allows us subsequently to
compute the precise asymptotic behavior, , for large , with exact expressions for the stretching exponent
and the constants and for arbitrary CTRW. By choosing
appropriate and , 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
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