Excitability transitions and wave dynamics under spatiotemporal structured noise

We present an analytic and numerical study of the effects of external fluctuations in active media. Our analytical methodology transforms the initial stochastic partial differential equations into an effective set of deterministic reaction-diffusion equations. As a result we are able to explain and make quantitative predictions on the systematic and constructive effects of the noise, for example, target patterns created out of noise and traveling or spiral waves sustained by noise. Our study includes the case of realistic noises with temporal and spatial structures.

Ballistic and diffusive corrections to front propagation in the presence of multiplicative noise

We study the dynamics of reaction-diffusion fronts under the influence of multiplicative noise. An approximate theoretical scheme is introduced to compute the velocity of the front and its diffusive wandering due to the presence of noise. The theoretical approach is based on a multiple scale analysis rather than on a small noise expansion and is confirmed with numerical simulations for a wide range of the noise intensity. We report on the possibility of noise sustained solutions with a continuum of possible velocities, in situations where only a single velocity is allowed without noise.

Front propagation in spatially modulated media

A two-dimensional reaction-diffusion front which propagates in a modulated medium is studied. The modulation consists of a spatial variation of the local front velocity in the transverse direction to that of the front propagation. We study analytically and numerically the final steady-state velocity and shape of the front, resulting from a nontrivial interplay between the local curvature effects and the global competition process between different maxima of the control parameter. The transient dynamics of the process is also studied numerically and analytically by means of singular perturbation techniques.

Excitability transitions and wave dynamics under spatiotemporal structured noise

We present an analytic and numerical study of the effects of external fluctuations in active media. Our analytical methodology transforms the initial stochastic partial differential equations into an effective set of deterministic reaction-diffusion equations. As a result we are able to explain and make quantitative predictions on the systematic and constructive effects of the noise, for example, target patterns created out of noise and traveling or spiral waves sustained by noise. Our study includes the case of realistic noises with temporal and spatial structures.

Regular wave propagation out of noise in chemical active media

A pacemaker, regularly emitting chemical waves, is created out of noise when an excitable photosensitive Belousov-Zhabotinsky medium, strictly unable to autonomously initiate autowaves, is forced with a spatiotemporal patterned random illumination. These experimental observations are also reproduced numerically by using a set of reaction-diffusion equations for an activator-inhibitor model, and further analytically interpreted in terms of genuine coupling effects arising from parametric fluctuations. Within the same framework we also address situations of noise-sustained propagation in subexcitable media.

Space Competition and Time Delays in Human Range Expansions. Application to the Neolithic Transition

Space competition effects are well-known in many microbiological and ecological systems. Here we analyze such an effectin human populations. The Neolithic transition (change from foraging to farming) was mainly the outcome of a demographic process that spread gradually throughout Europe from the Near East. In Northern Europe, archaeological data show a slowdown on the Neolithic rate of spread that can be related to a high indigenous (Mesolithic) population density hindering the advance as a result of the space competition between the two populations. We measure this slowdown from a database of 902 Early Neolithic sites and develop a time-delayed reaction-diffusion model with space competition between Neolithic and Mesolithic populations, to predict the observed speeds. The comparison of the predicted speed with the observations and with a previous non-delayed model show that both effects, the time delay effect due to the generation lag and the space competition between populations, are crucial in order to understand the observations

The estimation of PMP and PMF on alpine basins in Switzerland

This paper presents a very fine grid hydrological model based on the spatiotemporal repartition of precipitation and on the topography. The goal is to estimate the flood on a catchment area, using a Probable Maximum Precipitation (PMP) leading to a Probable Maximum Flood (PMF). The spatiotemporal distribution of the precipitation was realized using six clouds modeled by the advection-diffusion equation. The equation shows the movement of the clouds over the terrain and also gives the evolution of the rain intensity in time. This hydrological modeling is followed by a hydraulic modeling of the surface and subterranean flows, done considering the factors that contribute to the hydrological cycle, such as the infiltration, the exfiltration and the snowmelt. This model was applied to several Swiss basins using measured rain, with results showing a good correlation between the simulated and observed flows. This good correlation proves that the model is valid and gives us the confidence that the results can be extrapolated to phenomena of extreme rainfall of PMP type. In this article we present some results obtained using a PMP rainfall and the developed model.

Time-delayed fronts from biased random walks

We generalize a previous model of time-delayed reaction–diffusion fronts (Fort and Méndez 1999 Phys. Rev. Lett. 82 867) to allow for a bias in the microscopic random walk of particles or individuals. We also present a second model which takes the time order of events (diffusion and reproduction) into account. As an example, we apply them to the human invasion front across the USA in the 19th century. The corrections relative to the previous model are substantial. Our results are relevant to physical and biological systems with anisotropic fronts, including particle diffusion in disordered lattices, population invasions, the spread of epidemics, etc

An active strain electromechanical model for cardiac tissue

We propose a finite element approximation of a system of partial differential equations describing the coupling between the propagation of electrical potential and large deformations of the cardiac tissue. The underlying mathematical model is based on the active strain assumption, in which it is assumed that a multiplicative decomposition of the deformation tensor into a passive and active part holds, the latter carrying the information of the electrical potential propagation and anisotropy of the cardiac tissue into the equations of either incompressible or compressible nonlinear elasticity, governing the mechanical response of the biological material. In addition, by changing from an Eulerian to a Lagrangian configuration, the bidomain or monodomain equations modeling the evolution of the electrical propagation exhibit a nonlinear diffusion term. Piecewise quadratic finite elements are employed to approximate the displacements field, whereas for pressure, electrical potentials and ionic variables are approximated by piecewise linear elements. Various numerical tests performed with a parallel finite element code illustrate that the proposed model can capture some important features of the electromechanical coupling, and show that our numerical scheme is efficient and accurate.

When cholesterol is not cholesterol: a note on the enzymatic determination of its concentration in model systems containing vegetable extracts

Background: Experimental evidences demonstrate that vegetable derived extracts inhibit cholesterol absorption in the gastrointestinal tract. To further explore the mechanisms behind, we modeled duodenal contents with several vegetable extracts. Results: By employing a widely used cholesterol quantification method based on a cholesterol oxidase-peroxidase coupled reaction we analyzed the effects on cholesterol partition. Evidenced interferences were analyzed by studying specific and unspecific inhibitors of cholesterol oxidase-peroxidase coupled reaction. Cholesterol was also quantified by LC/MS. We found a significant interference of diverse (cocoa and tea-derived) extracts over this method. The interference was strongly dependent on model matrix: while as in phosphate buffered saline, the development of unspecific fluorescence was inhibitable by catalase (but not by heat denaturation), suggesting vegetable extract derived H2O2 production, in bile-containing model systems, this interference also comprised cholesterol-oxidase inhibition. Several strategies, such as cholesterol standard addition and use of suitable blanks containing vegetable extracts were tested. When those failed, the use of a mass-spectrometry based chromatographic assay allowed quantification of cholesterol in models of duodenal contents in the presence of vegetable extracts. Conclusions: We propose that the use of cholesterol-oxidase and/or peroxidase based systems for cholesterol analyses in foodstuffs should be accurately monitored, as important interferences in all the components of the enzymatic chain were evident. The use of adequate controls, standard addition and finally, chromatographic analyses solve these issues.

Diverse set of Turing nanopatterns coat corneae across insect lineages.

Nipple-like nanostructures covering the corneal surfaces of moths, butterflies, and Drosophila have been studied by electron and atomic force microscopy, and their antireflective properties have been described. In contrast, corneal nanostructures of the majority of other insect orders have either been unexamined or examined by methods that did not allow precise morphological characterization. Here we provide a comprehensive analysis of corneal surfaces in 23 insect orders, revealing a rich diversity of insect corneal nanocoatings. These nanocoatings are categorized into four major morphological patterns and various transitions between them, many, to our knowledge, never described before. Remarkably, this unexpectedly diverse range of the corneal nanostructures replicates the complete set of Turing patterns, thus likely being a result of processes similar to those modeled by Alan Turing in his famous reaction-diffusion system. These findings reveal a beautiful diversity of insect corneal nanostructures and shed light on their molecular origin and evolutionary diversification. They may also be the first-ever biological example of Turing nanopatterns.

Language extinction and linguistic fronts

Language diversity has become greatly endangered in the past centuries owing to processes of language shift from indigenous languages to other languages that are seen as socially and economically more advantageous, resulting in the death or doom of minority languages. In this paper, we define a new language competition model that can describe the historical decline of minority languages in competition with more advantageous languages. We then implement this non-spatial model as an interaction term in a reactiondiffusion system to model the evolution of the two competing languages. We use the results to estimate the speed at which the more advantageous language spreads geographically, resulting in the shrinkage of the area of dominance of the minority language. We compare the results from our model with the observed retreat in the area of influence of the Welsh language in the UK, obtaining a good agreement between the model and the observed data

Critical behavior in nonequilibrium phase transitions

The nonequilibrium phase transitions occurring in a fast-ionic-conductor model and in a reaction-diffusion Ising model are studied by Monte Carlo finite-size scaling to reveal nonclassical critical behavior; our results are compared with those in related models.

The Role of the Delay Time in the Modeling of Biological Range Expansions

The time interval between successive migrations of biological species causes a delay time in the reaction-diffusion equations describing their space-time dynamics. This lowers the predicted speed of the waves of advance, as compared to classical models. It has been shown that this delay-time effect improves the modeling of human range expansions. Here, we demonstrate that it can also be important for other species. We present two new examples where the predictions of the time-delayed and the classical (Fisher) approaches are compared to experimental data. No free or adjustable parameters are used. We show that the importance of the delay effect depends on the dimensionless product of the initial growth rate and the delay time. We argue that the delay effect should be taken into account in the modeling of range expansions for biological species

Speed of travelling fronts: Two-dimensional and ballistic dispersal probability distributions

The speed of traveling fronts for a two-dimensional model of a delayed reactiondispersal process is derived analytically and from simulations of molecular dynamics. We show that the one-dimensional (1D) and two-dimensional (2D) versions of a given kernel do not yield always the same speed. It is also shown that the speeds of time-delayed fronts may be higher than those predicted by the corresponding non-delayed models. This result is shown for systems with peaked dispersal kernels which lead to ballistic transport