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 $L^1$-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