Time of ruin in a risk model with generalized Erlang (n) interclaim times and a constant dividend barrier

In this paper we analyze the time of ruin in a risk process with the interclaim times being Erlang(n) distributed and a constant dividend barrier. We obtain an integro-differential equation for the Laplace Transform of the time of ruin. Explicit solutions for the moments of the time of ruin are presented when the individual claim amounts have a distribution with rational Laplace transform. Finally, some numerical results and a compare son with the classical risk model, with interclaim times following an exponential distribution, are given.

Mean first-passage time of continuous non-Markovian processes driven by colored noise

An equation for mean first-passage times of non-Markovian processes driven by colored noise is derived through an appropriate backward integro-differential equation. The equation is solved in a Bourret-like approximation. In a weak-noise bistable situation, non-Markovian effects are taken into account by an effective diffusion coefficient. In this situation, our results compare satisfactorily with other approaches and experimental data.

Diffusion in spatially and temporarily inhomogeneous media: Effects of turbulent mixing

We consider diffusion of a passive substance C in a phase-separating nonmiscible binary alloy under turbulent mixing. The substance is assumed to have different diffusion coefficients in the pure phases A and B, leading to a spatially and temporarily dependent diffusion ¿coefficient¿ in the diffusion equation plus convective term. In this paper we consider especially the effects of a turbulent flow field coupled to both the Cahn-Hilliard type evolution equation of the medium and the diffusion equation (both, therefore, supplemented by a convective term). It is shown that the formerly observed prolonged anomalous diffusion [H. Lehr, F. Sagués, and J.M. Sancho, Phys. Rev. E 54, 5028 (1996)] is no longer seen if a flow of sufficient intensity is supplied.

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.

Morphological changes in convection-diffusion-limited deposition

The effect of hydrodynamic flow upon diffusion-limited deposition on a line is investigated using a Monte Carlo model. The growth process is governed by the convection and diffusion field. The convective diffusion field is simulated by the biased-random walker resulting from a superimposed drift that represents the convective flow. The development of distinct morphologies is found with varying direction and strength of drift. By introducing a horizontal drift parallel to the deposition plate, the diffusion-limited deposit changes into a single needle inclined to the plate. The width of the needle decreases with increasing strength of drift. The angle between the needle and the plate is about 45° at high flow rate. In the presence of an inclined drift to the plate, the convection-diffusion-limited deposit leads to the formation of a characteristic columnar morphology. In the limiting case where the convection dominates, the deposition process is equivalent to ballistic deposition onto an inclined surface.

Diffusion of passive scalars under stochastic convection

The diffusion of passive scalars convected by turbulent flows is addressed here. A practical procedure to obtain stochastic velocity fields with well¿defined energy spectrum functions is also presented. Analytical results are derived, based on the use of stochastic differential equations, where the basic hypothesis involved refers to a rapidly decaying turbulence. These predictions are favorable compared with direct computer simulations of stochastic differential equations containing multiplicative space¿time correlated noise.

Morphology and segregation in two-component diffusion-limited aggregation

A diffusion-limited-aggregation (DLA) model with two components (A and B species) is presented to investigate the structure of the composite deposits. The sticking probability PAB (=PBA) between the different species is introduced into the original DLA model. By using computer simulation it is shown that various patterns are produced with varying the sticking probabilities PAB (=PBA) and PAA (= PBB), where PAA (=PBB) is the sticking probability between the same species. Segregated patterns can be analyzed under the condition PAB < PAA, assumed throughout the paper. With decreasing sticking probability PAB, a clustering of the same species occurs. With sufficiently small values of both sticking probabilities PAB and PAA, the deposit becomes dense and the segregated patterns of the composite deposit show a striped structure. The effect of the concentration on the pattern morphology is also shown.

Inter-firm labor mobility and knowledge diffusion: a theoretical approach

[cat] Analitzem una economia amb dues característiques principals: la mobilitat dels treballadors implica transferència de coneixement i la productivitat de l’empresa augmenta amb l’intercanvi de coneixement. Cada empresa desenvolupa un tipus de coneixement que serà trasmès a la resta de la indústria mitjançant la mobilitat de treballadors. Estudiem dues estructures de mercat laboral i utilitzant un anàlisi comparatiu derivem les implicacions del model. Els resultats revelen com la mobilitat de treballadors depèn en la varietat i nivell del coneixement, la presència de costos de mobilitat, les institucions, la capacitat d’absorvir coneixement per part de les empreses i la mida de la indústria. Els resultats no depenen de l’estructura del mercat laboral.

Molecular hydrogen diffusion in nanostructured amorphous silicon thin films

We study hydrogen stability and its evolution during thermal annealing in nanostructured amorphous silicon thin films. From the simultaneous measurement of heat and hydrogen desorption, we obtain the experimental evidence of molecular diffusion in these materials. In addition, we introduce a simple diffusion model which shows good agreement with the experimental data

Effect of drift on segregation in two-component diffusion-limited aggregation

An effect of drift is investigated on the segregation pattern in diffusion-limited aggregation (DLA) with two components (A and B species). The sticking probability PAB (=PBA) between the different species is introduced into the DLA model with drift, where the sticking probability PAA (=PBB) between the same species equals 1. By using computer simulation it is found that the drift has an important effect on not only the morphology but also the segregation pattern. Under the drift and the small sticking probability, a characteristic pattern appears where elongated clusters of A species and of B species are periodically dispersed. The period decreases with increasing drift. The periodic structure of the deposits is characterized by an autocorrelation function. The shape of the cluster consisting of only A species (or B species) shows a vertically elongated filamentlike structure. Each cluster becomes vertically longer with decreasing sticking probability PAB. The segregation pattern is distinctly different from that with no drift and a small sticking probability PAA. The effect of the concentration on the segregation pattern is also shown.

Microstructural evolution of primary crystallization in diffusion-controlled grain growth

A model has been developed for evaluating grain size distributions in primary crystallizations where the grain growth is diffusion controlled. The body of the model is grounded in a recently presented mean-field integration of the nucleation and growth kinetic equations, modified conveniently in order to take into account a radius-dependent growth rate, as occurs in diffusion-controlled growth. The classical diffusion theory is considered, and a modification of this is proposed to take into account interference of the diffusion profiles between neighbor grains. The potentiality of the mean-field model to give detailed information on the grain size distribution and transformed volume fraction for transformations driven by nucleation and either interface- or diffusion-controlled growth processes is demonstrated. The model is evaluated for the primary crystallization of an amorphous alloy, giving an excellent agreement with experimental data. Grain size distributions are computed, and their properties are discussed.

El marmor de Tarraco. Explotació, utilització i comercialització de la pedra de Santa Tecla en època romana Tarraco marmor. The Quarrying, Use and Trade of Santa Tecla Stone in Roman Times

Aquest és el llibre més complet que hi ha sobre la pedra de Santa Tecla i el llisós, dos materials procedents de Tarragona i molt utilitzats en època romana. Els autors, arqueòlegs i geòlegs, caracteritzen aquestes dues varietats i presenten el panorama de les seves aplicacions, i també donen pautes per identificar-les i diferenciar-les d’altres pedres que s’hi podrien confondre, com la “portasanta” o la pedra de Buixcarró.

Diffusion in stationary flow from mesoscopic nonequilibrium thermodynamics

We analyze the diffusion of a Brownian particle in a fluid under stationary flow. By using the scheme of nonequilibrium thermodynamics in phase space, we obtain the Fokker-Planck equation that is compared with others derived from the kinetic theory and projector operator techniques. This equation exhibits violation of the fluctuation-dissipation theorem. By implementing the hydrodynamic regime described by the first moments of the nonequilibrium distribution, we find relaxation equations for the diffusion current and pressure tensor, allowing us to arrive at a complete description of the system in the inertial and diffusion regimes. The simplicity and generality of the method we propose makes it applicable to more complex situations, often encountered in problems of soft-condensed matter, in which not only one but more degrees of freedom are coupled to a nonequilibrium bath.

Biased diffusion in confined media: Test of the Fick-Jacobs approximation and validity criteria

We study biased, diffusive transport of Brownian particles through narrow, spatially periodic structures in which the motion is constrained in lateral directions. The problem is analyzed under the perspective of the Fick-Jacobs equation, which accounts for the effect of the lateral confinement by introducing an entropic barrier in a one-dimensional diffusion. The validity of this approximation, based on the assumption of an instantaneous equilibration of the particle distribution in the cross section of the structure, is analyzed by comparing the different time scales that characterize the problem. A validity criterion is established in terms of the shape of the structure and of the applied force. It is analytically corroborated and verified by numerical simulations that the critical value of the force up to which this description holds true scales as the square of the periodicity of the structure. The criterion can be visualized by means of a diagram representing the regions where the Fick-Jacobs description becomes inaccurate in terms of the scaled force versus the periodicity of the structure.