Dynamics of a classical Hall system driven by a time-dependent Aharonov--Bohm flux

We study the dynamics of a classical particle moving in a punctured plane under the influence of a strong homogeneous magnetic field, an electrical background, and driven by a time-dependent singular flux tube through the hole. We exhibit a striking classical (de)localization effect: in the far past the trajectories are spirals around a bound center; the particle moves inward towards the flux tube loosing kinetic energy. After hitting the puncture it becomes ``conducting'': the motion is a cycloid around a center whose drift is outgoing, orthogonal to the electric field, diffusive, and without energy loss

Correlated Markov Quantum Walks

We consider the discrete time unitary dynamics given by a quantum walk on $\Z^d$ performed by a particle with internal degree of freedom, called coin state, according to the following iterated rule: a unitary update of the coin state takes place, followed by a shift on the lattice, conditioned on the coin state of the particle. We study the large time behavior of the quantum mechanical probability distribution of the position observable in $\Z^d$ for random updates of the coin states of the following form. The random sequences of unitary updates are given by a site dependent function of a Markov chain in time, with the following properties: on each site, they share the same stationnary Markovian distribution and, for each fixed time, they form a deterministic periodic pattern on the lattice. We prove a Feynman-Kac formula to express the characteristic function of the averaged distribution over the randomness at time $n$ in terms of the nth power of an operator $M$. By analyzing the spectrum of $M$, we show that this distribution posesses a drift proportional to the time and its centered counterpart displays a diffusive behavior with a diffusion matrix we compute. Moderate and large deviations principles are also proven to hold for the averaged distribution and the limit of the suitably rescaled corresponding characteristic function is shown to satisfy a diffusion equation. An example of random updates for which the analysis of the distribution can be performed without averaging is worked out. The random distribution displays a deterministic drift proportional to time and its centered counterpart gives rise to a random diffusion matrix whose law we compute. We complete the picture by presenting an uncorrelated example.Comment: 37 pages. arXiv admin note: substantial text overlap with arXiv:1010.400

Unanimity Rule on networks

We introduce a model for innovation-, evolution- and opinion dynamics whose spreading is dictated by unanimity rules, i.e. a node will change its (binary) state only if all of its neighbours have the same corresponding state. It is shown that a transition takes place depending on the initial condition of the problem. In particular, a critical number of initially activated nodes is needed so that the whole system gets activated in the long-time limit. The influence of the degree distribution of the nodes is naturally taken into account. For simple network topologies we solve the model analytically, the cases of random, small-world and scale-free are studied in detail.Comment: 7 pages 4 fig

An axisymmetric time-domain spectral-element method for full-wave simulations: Application to ocean acoustics

The numerical simulation of acoustic waves in complex 3D media is a key topic in many branches of science, from exploration geophysics to non-destructive testing and medical imaging. With the drastic increase in computing capabilities this field has dramatically grown in the last twenty years. However many 3D computations, especially at high frequency and/or long range, are still far beyond current reach and force researchers to resort to approximations, for example by working in 2D (plane strain) or by using a paraxial approximation. This article presents and validates a numerical technique based on an axisymmetric formulation of a spectral finite-element method in the time domain for heterogeneous fluid-solid media. Taking advantage of axisymmetry enables the study of relevant 3D configurations at a very moderate computational cost. The axisymmetric spectral-element formulation is first introduced, and validation tests are then performed. A typical application of interest in ocean acoustics showing upslope propagation above a dipping viscoelastic ocean bottom is then presented. The method correctly models backscattered waves and explains the transmission losses discrepancies pointed out in Jensen et al. (2007). Finally, a realistic application to a double seamount problem is considered.Comment: Added a reference, and fixed a typo (cylindrical versus spherical

Random Time-Dependent Quantum Walks

We consider the discrete time unitary dynamics given by a quantum walk on the lattice $\Z^d$ performed by a quantum particle with internal degree of freedom, called coin state, according to the following iterated rule: a unitary update of the coin state takes place, followed by a shift on the lattice, conditioned on the coin state of the particle. We study the large time behavior of the quantum mechanical probability distribution of the position observable in $\Z^d$ when the sequence of unitary updates is given by an i.i.d. sequence of random matrices. When averaged over the randomness, this distribution is shown to display a drift proportional to the time and its centered counterpart is shown to display a diffusive behavior with a diffusion matrix we compute. A moderate deviation principle is also proven to hold for the averaged distribution and the limit of the suitably rescaled corresponding characteristic function is shown to satisfy a diffusion equation. A generalization to unitary updates distributed according to a Markov process is also provided. An example of i.i.d. random updates for which the analysis of the distribution can be performed without averaging is worked out. The distribution also displays a deterministic drift proportional to time and its centered counterpart gives rise to a random diffusion matrix whose law we compute. A large deviation principle is shown to hold for this example. We finally show that, in general, the expectation of the random diffusion matrix equals the diffusion matrix of the averaged distribution.Comment: Typos and minor errors corrected. To appear In Communications in Mathematical Physic

Réponses phénologiques du riz irrigué dans le Sahel

Dans le Sahel, les périodes froides causent des pertes de rendement dues à la stérilité des épillets chez le riz cultivé tardivement. Les systèmes de riziculture au Sahel pourront donc bénéficier des hausses de températures. Des températures plus élevées pendant la phase végétative entraîneront des cycles de culture raccourcis, tandis que pendant les périodes froides de la phase reproductive, des températures plus élevées pourront réduire la stérilité. Pour les périodes chaudes, ont attend des effets négatifs sur la production de la biomasse et l'augmentation de la stérilité causée par la chaleur. Sur la base des données phénologiques d'une vaste gamme de matériel génétique collectées au début des années 1990 au Sénégal, un modèle (RIDEV) a été développé pour estimer la durée et la stérilité de multiples variétés de riz dans le Sahel comme une fonction de la date de semis. Cependant, des différences observées entre les cycles observés dans les champs des paysans et ceux évalués par RIDEV ont été rapportées. Cela pourrait s'expliquer soit par des défaillances du modèle, l'évolution variétale et/ ou par le changement climatique. Actuellement, à Ndiaye (zone côtière semi-aride) et Fanaye (zone continentale semi-aride), 10 variétés de riz très différentes sont cultivées toute l'année avec des dates de semis décalées d'un mois en vue de déterminer la durée, le taux d'apparition des feuilles et la stérilité dans les conditions climatiques actuelles. Ces variétés incluent certains des génotypes précédemment observés de même que certaines variétés de référence tolérantes à la chaleur et au froid. Les résultats seront utilisés pour améliorer RIDEV en vue des prédictions des réponses des cultures au changement climatique. Les résultats préliminaires avec une attention particulière sur la dérivation des constantes photothermiques seront présentés pour l'ensemble de la première année et comparés aux résultats issus des années précédentes.(Texte intégral

New method for the time calibration of an interferometric radio antenna array

Digital radio antenna arrays, like LOPES (LOFAR PrototypE Station), detect high-energy cosmic rays via the radio emission from atmospheric extensive air showers. LOPES is an array of dipole antennas placed within and triggered by the KASCADE-Grande experiment on site of the Karlsruhe Institute of Technology, Germany. The antennas are digitally combined to build a radio interferometer by forming a beam into the air shower arrival direction which allows measurements even at low signal-to-noise ratios in individual antennas. This technique requires a precise time calibration. A combination of several calibration steps is used to achieve the necessary timing accuracy of about 1 ns. The group delays of the setup are measured, the frequency dependence of these delays (dispersion) is corrected in the subsequent data analysis, and variations of the delays with time are monitored. We use a transmitting reference antenna, a beacon, which continuously emits sine waves at known frequencies. Variations of the relative delays between the antennas can be detected and corrected for at each recorded event by measuring the phases at the beacon frequencies.Comment: 9 pages, 9 figures, 1 table, pre-print of article published in Nuclear Inst. and Methods in Physics Research, A, available at: http://www.sciencedirect.com/science/article/B6TJM-4Y9CF4B-4/2/37bfcb899a0f387d9875a5a0729593a

Ballistic transport in random magnetic fields with anisotropic long-ranged correlations

We present exact theoretical results about energetic and dynamic properties of a spinless charged quantum particle on the Euclidean plane subjected to a perpendicular random magnetic field of Gaussian type with non-zero mean. Our results refer to the simplifying but remarkably illuminating limiting case of an infinite correlation length along one direction and a finite but strictly positive correlation length along the perpendicular direction in the plane. They are therefore ``random analogs'' of results first obtained by A. Iwatsuka in 1985 and by J. E. M\"uller in 1992, which are greatly esteemed, in particular for providing a basic understanding of transport properties in certain quasi-two-dimensional semiconductor heterostructures subjected to non-random inhomogeneous magnetic fields