Diffusion coefficients and MSD measurements on curved membranes and porous media.

We study some geometric aspects that influence the transport properties of particles that diffuse on curved surfaces. We compare different approaches to surface diffusion based on the Laplace-Beltrami operator adapted to predict concentration along entire membranes, confined subdomains along surfaces, or within porous media. Our goal is to summarize, firstly, how diffusion in these systems results in different types of diffusion coefficients and mean square displacement measurements, and secondly, how these two factors are affected by the concavity of the surface, the shape of the possible barriers or obstacles that form the available domains, the sinuosity, tortuosity, and constrictions of the trajectories and even how the observation plane affects the measurements of the diffusion.

Adiabatic limit collapse and local interaction effects in non-linear active microrheology molecular simulations of two-dimensional fluids.

Nonlinear active microrheology molecular dynamics simulations of high-density two-dimensional fluids show that the presence of strong confining forces and an external pulling force induces a correlation between the velocity and position dynamics of the tracer particle. This correlation manifests in the form of an effective temperature and an effective mobility of the tracer particle, which is responsible for the breaking of the equilibrium fluctuation-dissipation theorem. This fact is shown by measuring the tracer particle's temperature and mobility directly from the first two moments of the velocity distribution of a tracer particle and by formulating a diffusion theory in which effective thermal and transport properties are decoupled from the velocity dynamics.

Surface diffusion in narrow channels on curved domains.

We study the transport properties of diffusing particles restricted to confined regions on curved surfaces. We relate particle mobility to the curvature of the surface where they diffuse and the constraint due to confinement. Applying the Fick-Jacobs procedure to diffusion in curved manifolds shows that the local diffusion coefficient is related to average geometric quantities such as constriction and tortuosity.

Eckhaus selection: The mechanism of pattern persistence in a reaction-diffusion system.

In this work, we show theoretically and numerically that a one-dimensional reaction-diffusion system, near the Turing bifurcation, produces different number of stripes when, in addition to random noise, the Fourier mode of a prepattern used to initialize the system changes. We also show that the Fourier modes that persist are inside the Eckhaus stability regions, while those outside this region follow a wave number selection process not predicted by the linear analysis. To test our results, we use the Brusselator reaction-diffusion system obtaining an excellent agreement between the weakly nonlinear predictions of the real Ginzburg-Landau equations and the numerical solutions near the bifurcation.

Entropic restrictions control the electric conductance of superprotonic ionic solids.

The crystallographic structure of solid electrolytes and other materials determines the protonic conductivity in devices such as fuel cells, ionic-conductors, and supercapacitors. Experiments show that a rise of the temperature in a narrow interval may lead to a sudden increase of several orders of magnitude of the conductivity of some materials, a process called a superprotonic transition. Here, we use a novel macro-transport theory for irregular domains to show that the change of entropic restrictions associated with solid-solid phase or structural transitions controls the sudden change of the ionic conductivity when the superprotonic transition takes place.

Spatio-temporal secondary instabilities near the Turing-Hopf bifurcation.

In this work, we provide a framework to understand and quantify the spatiotemporal structures near the codimension-two Turing-Hopf point, resulting from secondary instabilities of Mixed Mode solutions of the Turing-Hopf amplitude equations. These instabilities are responsible for solutions such as (1) patterns which change their effective wavenumber while they oscillate as well as (2) phase instability combined with a spatial pattern. The quantification of these instabilities is based on the solution of the fourth order polynomial for the dispersion relation, which is solved using perturbation techniques.

Patchy spread patterns in three-species bistable systems with facultative mutualism.

A three-species population system under a facultative mutualistic relationship of one of the species is studied. The considered interactions are as follows: facultative between the first species and the second species, obligatory mutualism between the second species and the first one, and the third species is a predator of the first species. For this purpose, we extend the model proposed by Morozov et al.

Relation between the porosity and tortuosity of a membrane formed by disconnected irregular pores and the spatial diffusion coefficient of the Fick-Jacobs model.

In this work, we provide a theoretical relationship between the spatial-dependent diffusion coefficient derived in the Fick-Jacobs (FJ) approximation and the macroscopic diffusion coefficient of a membrane that depends on the porosity, tortuosity, and the constriction factors. Based on simple mass conservation arguments under equilibrium as well as in nonequilibrium conditions, we generalize previous expressions for the effective diffusion coefficient of an irregular pore, originally obtained by Festa and d'Agliano for horizontal and periodic pores, and then extended by Bradley for tortuous periodic pores, to the case of pores with arbitrary geometry. Through a formal definition of the constrictivity factor in terms of the geometry of the pore, our results provide very clear physical interpretation of experimental measurements since they link the local properties of the flow with macroscopic quantities of experimental relevance in the design and optimization of porous materials.

The interplay between phenotypic and ontogenetic plasticities can be assessed using reaction-diffusion models : The case of Pseudoplatystoma fishes.

Every morphological, behavioral, or even developmental character expression of living beings is coded in its genotype and is expressed in its phenotype. Nevertheless, the interplay between phenotypic and ontogenetic plasticities, that is, the capability to manifest trait variations, is a current field of research that needs morphometric, numerical, or even mathematical modeling investigations. In the present work, we are searching for a phenotypic index able to identify the underlying correlation among phenotypic, ontogenetic, and geographic distribution of the evolutionary development of species of the same genus.