Exact temporal evolution for some non-linear diffusion process

Exact solutions to FokkerPlanck equations with nonlinear drift are considered. Applications of these exact solutions for concrete models are studied. We arrive at the conclusion that for certain drifts we obtain divergent moments (and infinite relaxation time) if the diffusion process can be extended without any obstacle to the whole space. But if we introduce a potential barrier that limits the diffusion process, moments converge with a finite relaxation time.

Petrou types D and II perfect-fluid solutions in generalized Kerr-Schild form.

Petrov types D and II perfect-fluid solutions are obtained starting from conformally flat perfect-fluid metrics and by using a generalized KerrSchild ansatz. Most of the Petrov type D metrics obtained have the property that the velocity of the fluid does not lie in the two-space defined by the principal null directions of the Weyl tensor. The properties of the perfect-fluid sources are studied. Finally, a detailed analysis of a new class of spherically symmetric static perfect-fluid metrics is given.

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.

Coherence and anticoherence resonance tunned by noise

We present numerical evidence and a theoretical analysis of the appearance of anticoherence resonance induced by noise, not predicted in former analysis of coherence resonance. We have found that this phenomenon occurs for very small values of the intensity of the noise acting on an excitable system, and we claim that this is a universal signature of a nonmonotonous relaxational behavior near its oscillatory regime. Moreover, we demonstrate that this new phenomenon is totally compatible with the standard situation of coherence resonance appearing at intermediate values of noise intensity.

Stochastic generation of homogeneous isotropic turbulence with well-defined-spectra

A precise and simple computational model to generate well-behaved two-dimensional turbulent flows is presented. The whole approach rests on the use of stochastic differential equations and is general enough to reproduce a variety of energy spectra and spatiotemporal correlation functions. Analytical expressions for both the continuous and the discrete versions, together with simulation algorithms, are derived. Results for two relevant spectra, covering distinct ranges of wave numbers, are given.

Enhanced pulse propagation in non-linear arrays of oscillators

The propagation of a pulse in a nonlinear array of oscillators is influenced by the nature of the array and by its coupling to a thermal environment. For example, in some arrays a pulse can be speeded up while in others a pulse can be slowed down by raising the temperature. We begin by showing that an energy pulse (one dimension) or energy front (two dimensions) travels more rapidly and remains more localized over greater distances in an isolated array (microcanonical) of hard springs than in a harmonic array or in a soft-springed array. Increasing the pulse amplitude causes it to speed up in a hard chain, leaves the pulse speed unchanged in a harmonic system, and slows down the pulse in a soft chain. Connection of each site to a thermal environment (canonical) affects these results very differently in each type of array. In a hard chain the dissipative forces slow down the pulse while raising the temperature speeds it up. In a soft chain the opposite occurs: the dissipative forces actually speed up the pulse, while raising the temperature slows it down. In a harmonic chain neither dissipation nor temperature changes affect the pulse speed. These and other results are explained on the basis of the frequency vs energy relations in the various arrays

Breathers and thermal relaxation in Fermi-Pasta-Ulam arrays

Breather stability and longevity in thermally relaxing nonlinear arrays depend sensitively on their interactions with other excitations. We review numerical results for the relaxation of breathers in Fermi¿Pasta¿Ulam arrays, with a specific focus on the different relaxation channels and their dependence on the interparticle interactions, dimensionality, initial condition, and system parameters

Travelling-stripe forcing generates hexagonal patterns

We study the response of Turing stripe patterns to a simple spatiotemporal forcing. This forcing has the form of a traveling wave and is spatially resonant with the characteristic Turing wavelength. Experiments conducted with the photosensitive chlorine dioxide-iodine-malonic acid reaction reveal a striking symmetry-breaking phenomenon of the intrinsic striped patterns giving rise to hexagonal lattices for intermediate values of the forcing velocity. The phenomenon is understood in the framework of the corresponding amplitude equations, which unveils a complex scenario of dynamical behaviors.

SIMSAFADIM-CLASTIC: A new approach to mathematical 3D forward simulation modelling for terrigenous and carbonate marine sedimentation

Most sedimentary modelling programs developed in recent years focus on either terrigenous or carbonate marine sedimentation. Nevertheless, only a few programs have attempted to consider mixed terrigenous-carbonate sedimentation, and most of these are two-dimensional, which is a major restriction since geological processes take place in 3D. This paper presents the basic concepts of a new 3D mathematical forward simulation model for clastic sediments, which was developed from SIMSAFADIM, a previous 3D carbonate sedimentation model. The new extended model, SIMSAFADIM-CLASTIC, simulates processes of autochthonous marine carbonate production and accumulation, together with clastic transport and sedimentation in three dimensions of both carbonate and terrigenous sediments. Other models and modelling strategies may also provide realistic and efficient tools for prediction of stratigraphic architecture and facies distribution of sedimentary deposits. However, SIMSAFADIM-CLASTIC becomes an innovative model that attempts to simulate different sediment types using a process-based approach, therefore being a useful tool for 3D prediction of stratigraphic architecture and facies distribution in sedimentary basins. This model is applied to the neogene Vallès-Penedès half-graben (western Mediterranean, NE Spain) to show the capacity of the program when applied to a realistic geologic situation involving interactions between terrigenous clastics and carbonate sediments.

Progress in front propagation research

We review the progress in the field of front propagation in recent years. We survey many physical, biophysical and cross-disciplinary applications, including reduced-variable models of combustion flames, Reid's paradox of rapid forest range expansions, the European colonization of North America during the 19th century, the Neolithic transition in Europe from 13 000 to 5000 years ago, the description of subsistence boundaries, the formation of cultural boundaries, the spread of genetic mutations, theory and experiments on virus infections, models of cancer tumors, etc. Recent theoretical advances are unified in a single framework, encompassing very diverse systems such as those with biased random walks, distributed delays, sequential reaction and dispersion, cohabitation models, age structure and systems with several interacting species. Directions for future progress are outlined

First-passage and escape problems in the Feller process

The Feller process is an one-dimensional diffusion process with linear drift and state-dependent diffusion coefficient vanishing at the origin. The process is positive definite and it is this property along with its linear character that have made Feller process a convenient candidate for the modeling of a number of phenomena ranging from single-neuron firing to volatility of financial assets. While general properties of the process have long been well known, less known are properties related to level crossing such as the first-passage and the escape problems. In this work we thoroughly address these questions.

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.

Progress in front propagation research

We review the progress in the field of front propagation in recent years. We survey many physical, biophysical and cross-disciplinary applications, including reduced-variable models of combustion flames, Reid's paradox of rapid forest range expansions, the European colonization of North America during the 19th century, the Neolithic transition in Europe from 13 000 to 5000 years ago, the description of subsistence boundaries, the formation of cultural boundaries, the spread of genetic mutations, theory and experiments on virus infections, models of cancer tumors, etc. Recent theoretical advances are unified in a single framework, encompassing very diverse systems such as those with biased random walks, distributed delays, sequential reaction and dispersion, cohabitation models, age structure and systems with several interacting species. Directions for future progress are outlined

Integro-difference equations for interacting species and the Neolithic transition

We introduce a set of sequential integro-difference equations to analyze the dynamics of two interacting species. Firstly, we derive the speed of the fronts when a species invades a space previously occupied by a second species, and check its validity by means of numerical random-walk simulations. As an example, we consider the Neolithic transition: the predictions of the model are consistent with the archaeological data for the front speed, provided that the interaction parameter is low enough. Secondly, an equation for the coexistence time between the invasive and the invaded populations is obtained for the first time. It agrees well with the simulations, is consistent with observations of the Neolithic transition, and makes it possible to estimate the value of the interaction parameter between the incoming and the indigenous populations

Fronts from integrodifference equations and persistence effects on the Neolithic transition

We extend a previous model of the Neolithic transition in Europe [J. Fort and V. Méndez, Phys. Rev. Lett. 82, 867 (1999)] by taking two effects into account: (i) we do not use the diffusion approximation (which corresponds to second-order Taylor expansions), and (ii) we take proper care of the fact that parents do not migrate away from their children (we refer to this as a time-order effect, in the sense that it implies that children grow up with their parents, before they become adults and can survive and migrate). We also derive a time-ordered, second-order equation, which we call the sequential reaction-diffusion equation, and use it to show that effect (ii) is the most important one, and that both of them should in general be taken into account to derive accurate results. As an example, we consider the Neolithic transition: the model predictions agree with the observed front speed, and the corrections relative to previous models are important (up to 70%)