6,646 research outputs found
Reaction rate calculation with time-dependent invariant manifolds
The identification of trajectories that contribute to the reaction rate is
the crucial dynamical ingredient in any classical chemical reactivity
calculation. This problem often requires a full scale numerical simulation of
the dynamics, in particular if the reactive system is exposed to the influence
of a heat bath. As an efficient alternative, we propose here to compute
invariant surfaces in the phase space of the reactive system that separate
reactive from nonreactive trajectories. The location of these invariant
manifolds depends both on time and on the realization of the driving force
exerted by the bath. These manifolds allow the identification of reactive
trajectories simply from their initial conditions, without the need of any
further simulation. In this paper, we show how these invariant manifolds can be
calculated, and used in a formally exact reaction rate calculation based on
perturbation theory for any multidimensional potential coupled to a noisy
environment
Projet de conversion et d'unification des titres des Series B. C. & D. de la Dette Ottomane
Taha Toros Arşivi, Dosya No: 71-Duyun-u Umumiyeİstanbul Kalkınma Ajansı (TR10/14/YEN/0033) İstanbul Development Agency (TR10/14/YEN/0033
Bubble concentration on spheres for supercritical elliptic problems
We consider the supercritical Lane-Emden problem (P_\eps)\qquad
-\Delta v= |v|^{p_\eps-1} v \ \hbox{in}\ \mathcal{A} ,\quad u=0\ \hbox{on}\
\partial\mathcal{A}
where is an annulus in \rr^{2m}, and
p_\eps={(m+1)+2\over(m+1)-2}-\eps, \eps>0.
We prove the existence of positive and sign changing solutions of (P_\eps)
concentrating and blowing-up, as \eps\to0, on dimensional spheres.
Using a reduction method (see Ruf-Srikanth (2010) J. Eur. Math. Soc. and
Pacella-Srikanth (2012) arXiv:1210.0782)we transform problem (P_\eps) into a
nonhomogeneous problem in an annulus \mathcal D\subset \rr^{m+1} which can be
solved by a Ljapunov-Schmidt finite dimensional reduction
A Concept for Using Combined Multimodal Queries in Digital Music Libraries
Περιέχει το πλήρες κείμενοIn this paper, we propose a concept for using combined
multimodal queries in the context of digital music libraries. Whereas
usual mechanisms for content-based music retrieval only consider a single
query mode, such as query-by-humming, full-text lyrics-search or
query-by-example using short audio snippets, our proposed concept allows
to combine those different modalities into one integrated query.
Our particular contributions consist of concepts for query formulation,
combined content-based retrieval and presentation of a suitably ranked
result list. The proposed concepts have been realized within the context
of the PROBADO Music Repository and allow for music retrieval based
on combining full-text lyrics search and score-based query-by-example
search
Finite-barrier corrections for multidimensional barriers in colored noise
The usual identification of reactive trajectories for the calculation of reaction rates requires very timeconsuming simulations, particularly if the environment presents memory effects. In this paper, we develop a
method that permits the identification of reactive trajectories in a system under the action of a stochastic colored
driving. This method is based on the perturbative computation of the invariant structures that act as separatrices
for reactivity. Furthermore, using this perturbative scheme, we have obtained a formally exact expression for the
reaction rate in multidimensional systems coupled to colored noisy environments
An algorithm for calculating the Lorentz angle in silicon detectors
Future experiments will use silicon sensors in the harsh radiation
environment of the LHC (Large Hadron Collider) and high magnetic fields. The
drift direction of the charge carriers is affected by the Lorentz force due to
the high magnetic field. Also the resulting radiation damage changes the
properties of the drift.
In this paper measurements of the Lorentz angle of electrons and holes before
and after irradiation are reviewed and compared with a simple algorithm to
compute the Lorentz angle.Comment: 13 pages, 7 figures, final version accepted by NIMA. Mainly
clarifications included and slightly shortene
Reaction rate calculation with time-dependent invariant manifolds
The identification of trajectories that contribute to the reaction rate is the crucial dynamical ingredient
in any classical chemical reactivity calculation. This problem often requires a full scale numerical
simulation of the dynamics, in particular if the reactive system is exposed to the influence of a heat
bath. As an efficient alternative, we propose here to compute invariant surfaces in the phase space of
the reactive system that separate reactive from nonreactive trajectories. The location of these invariant
manifolds depends both on time and on the realization of the driving force exerted by the bath.
These manifolds allow the identification of reactive trajectories simply from their initial conditions,
without the need of any further simulation. In this paper, we show how these invariant manifolds
can be calculated, and used in a formally exact reaction rate calculation based on perturbation theory
for any multidimensional potential coupled to a noisy environment
The geometry of transition states: How invariant manifolds determine reaction rates
Over the last years, a new geometrical perspective on transition state theory has been developed that provides a deeper insight on the reaction mechanisms of chemical systems. This new methodology is based on the identification of the invariant structures that organize the dynamics at the top of the energetic barrier that separates reactants and products. Moreover, it has allowed to solve, or at least circumvent, the recrossing-free problem in rate calculations. In this paper, we will discuss which kind of objects determine the reaction dynamics in the presence of dilute, dense and condensed phase baths
Finite size effects on transport coefficients for models of atomic wires coupled to phonons
We consider models of quasi-1-d, planar atomic wires consisting of several,
laterally coupled rows of atoms, with mutually non-interacting electrons. This
electronic wire system is coupled to phonons, corresponding, e.g., to some
substrate. We aim at computing diffusion coefficients in dependence on the wire
widths and the lateral coupling. To this end we firstly construct a numerically
manageable linear collision term for the dynamics of the electronic occupation
numbers by following a certain projection operator approach. By means of this
collision term we set up a linear Boltzmann equation. A formula for extracting
diffusion coefficients from such Boltzmann equations is given. We find in the
regime of a few atomic rows and intermediate lateral coupling a significant and
non-trivial dependence of the diffusion coefficient on both, the width and the
lateral coupling. These results, in principle, suggest the possible
applicability of such atomic wires as electronic devices, such as, e.g.,
switches.Comment: 9 pages, 5 figures, accepted for publication in Eur. Phys. J.
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