Strong coupling solution to Schrödinger Equation: the mixing of states

In this paper we give some ideas that can be useful to solve Schrödinger equations in the case when the Hamiltonian contains a large term. We obtain an expansion of the solution in reciprocal powers of the large coupling constant. The procedure followed consists in considering that the small part of the Hamiltonian engenders a motion adiabatic to the motion generated by the large part of the same.

Particle dispersion in synthetic turbulent flows

We study particle dispersion advected by a synthetic turbulent flow from a Lagrangian perspective and focus on the two-particle and cluster dispersion by the flow. It has been recently reported that Richardson¿s law for the two-particle dispersion can stem from different dispersion mechanisms, and can be dominated by either diffusive or ballistic events. The nature of the Richardson dispersion depends on the parameters of our flow and is discussed in terms of the values of a persistence parameter expressing the relative importance of the two above-mentioned mechanisms. We support this analysis by studying the distribution of interparticle distances, the relative velocity correlation functions, as well as the relative trajectories.

Reaction-diffusion fronts under stochastic advection

We study front propagation in stirred media using a simplified modelization of the turbulent flow. Computer simulations reveal the existence of the two limiting propagation modes observed in recent experiments with liquid phase isothermal reactions. These two modes respectively correspond to a wrinkled although sharp propagating interface and to a broadened one. Specific laws relative to the enhancement of the front velocity in each regime are confirmed by our simulations.

Dispersion of passive particles by a quasi-two-dimensional turbulent flow

Using the experimental data of Paret and Tabeling [Phys. Rev. Lett. 79, 4162 (1997)] we consider in detail the dispersion of particle pairs by a two-dimensional turbulent flow and its relation to the kinematic properties of the velocity field. We show that the mean square separation of a pair of particles is governed by rather rare, extreme events and that the majority of initially close pairs are not dispersed by the flow. Another manifestation of the same effect is the fact that the dispersion of an initially dense cluster is not the result of homogeneously spreading the particles within the whole system. Instead it proceeds through a splitting into smaller but also dense clusters. The statistical nature of this effect is discussed.

Sobre el area de dispersion de Artemisia tournefortiana Reich. en la Peninsula Iberica

Al consultar los pliegos de Artemisia L. contenidos en el Herbario BCF, con motivo de la revisión de dicho género en la Península Ibérica, que estamos realizando como tesis doctoral, hemos hallado dos de ellos (BCF n.° 7473 y n.° 7475) recolectados por don Salvador Rivas Goday, el 17 de septiembre de 1948, en Titulcia (MADRID) y determinados como Artemisia variabilis Ten.

A proposito de la dispersion de Verbascum boerhavii L. var. bicolor (Bad.) Arcang. en Catalunya

A propósito de la dispersión de Verbascum boerhavii var. bicolor (Bad.) Arcang. en Catalunya. Verbascum boerhavii L. var. bicolor (Bad.) Arcang., Comp. Fl. Ital. 505 (1882). = V. bicolor Bad., Osserv., 3 (1824) = V. boerhavii L. fma. bicolor (Bad.) Murb., Lunds. Univ. Arssk, 29 (2): 159 (1933). = V. maiale DC. var. bicolor (Bad.) Rouy, Fl. Fr. 9:9 (1909).

Power variation of some integral fractional processes

We consider the asymptotic behaviour of the realized power variation of processes of the form ¿t0usdBHs, where BH is a fractional Brownian motion with Hurst parameter H E(0,1), and u is a process with finite q-variation, q<1/(1¿H). We establish the stable convergence of the corresponding fluctuations. These results provide new statistical tools to study and detect the long-memory effect and the Hurst parameter.

Stochastic delay equations with non-negativity constraints driven by fractional Brownian motion

In this note we prove an existence and uniqueness result for the solution of multidimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter H > 1/2. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann¿Stieltjes integral.

Approximation and support theorem for a wave equation in two space dimensions

We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an approximation theorem, in the convergence of probability, for equations obtained by smoothing the random noise. For some particular classes of coefficients, approximation in the Lp-norm for p¿1 is also proved.

Experimental investigation of the initial regime in fingering electrodeposition: Dispersion relation and velocity measurements.

Recently a fingering morphology, resembling the hydrodynamic Saffman-Taylor instability, was identified in the quasi-two-dimensional electrodeposition of copper. We present here measurements of the dispersion relation of the growing front. The instability is accompanied by gravity-driven convection rolls at the electrodes, which are examined using particle image velocimetry. While at the anode the theory presented by Chazalviel et al. [J. Electroanal. Chem. 407, 61 (1996)] describes the convection roll, the flow field at the cathode is more complicated because of the growing deposit. In particular, the analysis of the orientation of the velocity vectors reveals some lag of the development of the convection roll compared to the finger envelope.

Interaction of Spiral Waves in the Complex Ginzburg-Landau Equation

Solutions of the general cubic complex Ginzburg-Landau equation comprising multiple spiral waves are considered, and laws of motion for the centers are derived. The direction of the motion changes from along the line of centers to perpendicular to the line of centers as the separation increases, with the strength of the interaction algebraic at small separations and exponentially small at large separations. The corresponding asymptotic wave number and frequency are also determined, which evolve slowly as the spirals move

Rapid and sudden advection of warm and dry air in the Mediterranean Basin

Rapid advection of extremely warm and dry air is studied during two events in the Mediterranean Basin. On 27 August 2010 a rapid advection of extremely warm and dry air affected the northeast Iberian Peninsula during a few hours. At the Barcelona city center, the temperature reached 39.3 ° C, which is the maximum temperature value recorded during 230 yr of daily data series. On 23 March 2008 a rapid increase of temperature and drop of relative humidity were recorded for a few hours in Heraklion (Crete). During the morning on that day, the recorded temperature reached 34 °C for several hours on the northern coastline of this island.According to the World Meteorological Organization none of these events can be classified as a heat wave, which requires at least two days of abnormally high temperatures; neither are they a heat burst as defined by the American Meteorological Society, where abnormal temperatures take place during a few minutes. For this reason, we suggest naming this type of event flash heat. By using data from automatic weather stations in the Barcelona and Heraklion area and WRF mesoscale numerical simulations, these events are analyzed. Additionally, the primary risks and possible impacts on several fields are presented.

Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schr odinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schrödinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.