Reaction-diffusion scheme for the clock and wavefront mechanism of pattern formation

We present a model of pattern formation in reaction-diffusion systems that is based on coupling between a propagating wave front and temporal oscillations. To study effects of internal fluctuations on the spatial structure development we use a chemical master equation for our reaction-diffusion model. First, a model with local, uncoupled oscillators is studied. Based on it we show that synchronization of oscillations in neighboring cells is necessary for the formation of regular patterns. We introduce synchronization through diffusion, but then, to get a stable pattern, it is necessary to add an additional species that represents the local state of the system. Numerical simulations of the master equation show that this extended model is resistant to fluctuations

Scaling of submicrometric Turing patterns in concentrated growing systems

The wavelength of a periodic spatial structure of Turing type is an intrinsic property of the considered reaction-diffusion dynamics and we address the question of its control at the microscopic scale for given dynamical parameters. The direct simulation Monte Carlo method, initially introduced to simulate particle dynamics in rarefied gases, is adapted to the simulation of concentrated solutions. We perform simulations of a submicrometric Turing pattern with appropriate boundary conditions and show that taking into account the role of the solvent in the chemical mechanism allows us to control the wavelength of the structure. Typically, doubling the concentration of the solution leads to decreasing the wavelength by two. The results could be used to design materials with controled submicrometric properties in chemical engineering. They could also be considered as a possible interpretation of proportion preservation of embryos in morphogenesis.Comment: 23 pages, 5 figure

DSMC simulations of Turing patterns in concentrated growing systems

International audienc

The FKPP wave front as a sensor of perturbed diffusion in concentrated systems

The sensitivity to perturbations of the Fisher and Kolmogorov, Petrovskii, Piskunov front is used to find a quantity revealing perturbations of diffusion in a concentrated solution of two chemical species with different diffusivities. The deterministic dynamics includes cross-diffusion terms due to the deviation from the dilution limit. The behaviors of the front speed, the shift between the concentration profiles of the two species, and the width of the reactive zone are investigated, both analytically and numerically. The shift between the two profiles turns out to be a well-adapted criterion presenting noticeable variations with the deviation from the dilution limit in a wide range of parameter values.Comment: 22 pages, 5 figure

Termination Mechanisms of Turing Patterns in Growing Systems

International audienceThe question of the termination of a periodic spatial structure of Turing type in a growing system is addressed in a chemical engineering perspective and a biomimetic approach. The effects of the dynamical parameters on the stability and the wavelength of the structure are analytically studied and used to propose experimental conditions for which a Turing pattern stops by itself with a decreasing wavelength. The proposed mechanism is successfully checked by the numerical integration of the equations governing the dynamics of the activator and the inhibitor. We conclude that a local increase of the concentration of the reservoir which controls the injection rate of the inhibitor into the system can be used to achieve the appropriate termination of a Turing pattern

The impact of the financial situation on the operative effectiveness of Polish families

The modern Polish family has been subject to many changes – not only cultural and social but also economic. The society, after a period of economic transformation ever since 1989, has noted an increase in the diversification of earnings and the level of affluence of Poles. In addition to people who earn very well, there is still a large percentage of the poor who have problems with satisfying the essential needs of their existence. The economic status of the family is a mean that significantly affects the way of people’s life, both their social and cultural activity, but it also participates in many important decisions which have to be taken in their lives. The article outlines the conversion of the material situation of Polish families over the last few years as well as the relevance of the material status for the choice of a future model for the family, including the fact that the material situation affects fertility decisions and investments for the family’s offspring.Współczesna rodzina polska podlega wielu przemianom – nie tylko kulturowym i społecznym, ale również ekonomicznym. Po okresie transformacji gospodarczej rozpoczętej w 1989 roku, obserwuje się w społeczeństwie wzrost zróżnicowania zarobków i poziomu zamożności Polaków. Oprócz osób, które zarabiają bardzo dobrze, wciąż jest duży odsetek tych, którzy mają problemy z zaspokojeniem niezbędnych potrzeb związanych z ich egzystencją. Status materialny rodziny w sposób istotny wpływa sposób życia człowieka, jego aktywność społeczną i kulturową, jak też na podejmowanie ważnych decyzji dotyczących jego życia. W artykule omówiono przemiany sytuacji materialnej polskich rodzin w ostatnich kilku latach, a także znaczenie statusu materialnego w wyborze przyszłego modelu rodziny oraz sposób, w jaki sytuacja materialna wpływa na decyzje prokreacyjne i inwestowanie we własne dziecko

Stochastic approach to Fisher and Kolmogorov, Petrovskii, and Piskunov wave fronts for species with different diffusivities in dilute and concentrated solutions

A wave front of Fisher and Kolmogorov, Petrovskii, and Piskunov type involving two species A and B with different diffusion coefficients and is studied using a master equation approach in dilute and concentrated solutions. Species A and B are supposed to be engaged in the autocatalytic reaction A+B 2A. Contrary to the results of a deterministic description, the front speed deduced from the master equation in the dilute case sensitively depends on the diffusion coefficient of species B. A linear analysis of the deterministic equations with a cutoff in the reactive term cannot explain the decrease of the front speed observed for . In the case of a concentrated solution, the transition rates associated with cross-diffusion are derived from the corresponding diffusion fluxes. The properties of the wave front obtained in the dilute case remain valid but are mitigated by cross-diffusion which reduces the impact of different diffusion coefficients