910 research outputs found
Transient currents in a molecular photo-diode
Light-induced charge transmission through a molecular junction (molecular
diode) is studied in the framework of a HOMO-LUMO model and in using a kinetic
description. Expressions are presented for the sequential (hopping) and direct
(tunneling) transient current components together with kinetic equations
governing the time-dependent populations of the neutral and charged molecular
states which participate in the current formation. Resonant and off-resonant
charge transmission processes are analyzed in detail. It is demonstrated that
the transient currents are associated with a molecular charging process which
is initiated by photo excitation of the molecule. If the coupling of the
molecule to the electrodes is strongly asymmetric the transient currents can
significantly exceed the steady state current.Comment: 17 pages, 12 figures, accepted for publication in Chemical Physic
A short survey on nonlinear models of the classic Costas loop: rigorous derivation and limitations of the classic analysis
Rigorous nonlinear analysis of the physical model of Costas loop --- a
classic phase-locked loop (PLL) based circuit for carrier recovery, is a
challenging task. Thus for its analysis, simplified mathematical models and
numerical simulation are widely used. In this work a short survey on nonlinear
models of the BPSK Costas loop, used for pre-design and post-design analysis,
is presented. Their rigorous derivation and limitations of classic analysis are
discussed. It is shown that the use of simplified mathematical models, and the
application of non rigorous methods of analysis (e.g., simulation and
linearization) may lead to wrong conclusions concerning the performance of the
Costas loop physical model.Comment: Accepted to American Control Conference (ACC) 2015 (Chicago, USA
Mod-Gaussian convergence and its applications for models of statistical mechanics
In this paper we complete our understanding of the role played by the
limiting (or residue) function in the context of mod-Gaussian convergence. The
question about the probabilistic interpretation of such functions was initially
raised by Marc Yor. After recalling our recent result which interprets the
limiting function as a measure of "breaking of symmetry" in the Gaussian
approximation in the framework of general central limit theorems type results,
we introduce the framework of -mod-Gaussian convergence in which the
residue function is obtained as (up to a normalizing factor) the probability
density of some sequences of random variables converging in law after a change
of probability measure. In particular we recover some celebrated results due to
Ellis and Newman on the convergence in law of dependent random variables
arising in statistical mechanics. We complete our results by giving an
alternative approach to the Stein method to obtain the rate of convergence in
the Ellis-Newman convergence theorem and by proving a new local limit theorem.
More generally we illustrate our results with simple models from statistical
mechanics.Comment: 49 pages, 21 figure
Statistical properties of Lorenz like flows, recent developments and perspectives
We comment on mathematical results about the statistical behavior of Lorenz
equations an its attractor, and more generally to the class of singular
hyperbolic systems. The mathematical theory of such kind of systems turned out
to be surprisingly difficult. It is remarkable that a rigorous proof of the
existence of the Lorenz attractor was presented only around the year 2000 with
a computer assisted proof together with an extension of the hyperbolic theory
developed to encompass attractors robustly containing equilibria. We present
some of the main results on the statisitcal behavior of such systems. We show
that for attractors of three-dimensional flows, robust chaotic behavior is
equivalent to the existence of certain hyperbolic structures, known as
singular-hyperbolicity. These structures, in turn, are associated to the
existence of physical measures: \emph{in low dimensions, robust chaotic
behavior for flows ensures the existence of a physical measure}. We then give
more details on recent results on the dynamics of singular-hyperbolic
(Lorenz-like) attractors.Comment: 40 pages; 10 figures; Keywords: sensitive dependence on initial
conditions, physical measure, singular-hyperbolicity, expansiveness, robust
attractor, robust chaotic flow, positive Lyapunov exponent, large deviations,
hitting and recurrence times. Minor typos corrected and precise
acknowledgments of financial support added. To appear in Int J of Bif and
Chaos in App Sciences and Engineerin
Image preprocessing for artistic robotic painting
Artistic robotic painting implies creating a picture on canvas according to a brushstroke map preliminarily computed from a source image. To make the painting look closer to the human artwork, the source image should be preprocessed to render the effects usually created by artists. In this paper, we consider three preprocessing effects: aerial perspective, gamut compression and brushstroke coherence. We propose an algorithm for aerial perspective amplification based on principles of light scattering using a depth map, an algorithm for gamut compression using nonlinear hue transformation and an algorithm for image gradient filtering for obtaining a well-coherent brushstroke map with a reduced number of brushstrokes, required for practical robotic painting. The described algorithms allow interactive image correction and make the final rendering look closer to a manually painted artwork. To illustrate our proposals, we render several test images on a computer and paint a monochromatic image on canvas with a painting robot
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