Modelling of chloride transport in non-saturated concrete : from microscale to macroscale

A model for chloride transport in concrete is proposed. The model accounts for transport several transport mechanisms such as diffusion, advection, migration, etc. This work shows the chloride transport equations at the macroscopic scale in non-saturated concrete. The equations involve diffusion, migration, capillary suction, chloride combination and precipitation mechanisms. The material is assumed to be infinitely rigid, though the porosity can change under influence of chloride binding and precipitation. The involved microscopic and macroscopic properties of the materials are measured by standardized methods. The variables which must be imposed on the boundaries are temperature, relative humidity and chloride concentration. The output data of the model are the free, bound, precipitated and total chloride ion concentrations, as well as the pore solution content and the porosity. The proposed equations are solved by means of the finite element method (FEM) implemented in MATLAB (classical Galerkin formulation and the streamline upwind Petrov-Galerkin (SUPG) method to avoid spatial instabilities for advection dominated flows).

Nonlinear Time-Fractional Differential Equations in Combustion Science

MSC 2010: 34A08 (main), 34G20, 80A25

A FEM procedure based on positions and unconstrained vectors applied to non-linear dynamic of 3D frames

This study presents an alternative three-dimensional geometric non-linear frame formulation based on generalized unconstrained vector and positions to solve structures and mechanisms subjected to dynamic loading. The formulation is classified as total Lagrangian with exact kinematics description. The resulting element presents warping and non-constant transverse strain modes, which guarantees locking-free behavior for the adopted three-dimensional constitutive relation, Saint-Venant-Kirchhoff, for instance. The application of generalized vectors is an alternative to the use of finite rotations and rigid triad`s formulae. Spherical and revolute joints are considered and selected dynamic and static examples are presented to demonstrate the accuracy and generality of the proposed technique. (C) 2010 Elsevier B.V. All rights reserved.

Application of Petrov-Galerkin methods to transient boundary value problems in chemical engineering: adsorption with steep gradients in bidisperse solids

Petrov-Galerkin methods are known to be versatile techniques for the solution of a wide variety of convection-dispersion transport problems, including those involving steep gradients. but have hitherto received little attention by chemical engineers. We illustrate the technique by means of the well-known problem of simultaneous diffusion and adsorption in a spherical sorbent pellet comprised of spherical, non-overlapping microparticles of uniform size and investigate the uptake dynamics. Solutions to adsorption problems exhibit steep gradients when macropore diffusion controls or micropore diffusion controls, and the application of classical numerical methods to such problems can present difficulties. In this paper, a semi-discrete Petrov-Galerkin finite element method for numerically solving adsorption problems with steep gradients in bidisperse solids is presented. The numerical solution was found to match the analytical solution when the adsorption isotherm is linear and the diffusivities are constant. Computed results for the Langmuir isotherm and non-constant diffusivity in microparticle are numerically evaluated for comparison with results of a fitted-mesh collocation method, which was proposed by Liu and Bhatia (Comput. Chem. Engng. 23 (1999) 933-943). The new method is simple, highly efficient, and well-suited to a variety of adsorption and desorption problems involving steep gradients. (C) 2001 Elsevier Science Ltd. All rights reserved.

Dynamical features of reaction-diffusion fronts in fractals

The speed of front propagation in fractals is studied by using (i) the reduction of the reaction-transport equation into a Hamilton-Jacobi equation and (ii) the local-equilibrium approach. Different equations proposed for describing transport in fractal media, together with logistic reaction kinetics, are considered. Finally, we analyze the main features of wave fronts resulting from this dynamic process, i.e., why they are accelerated and what is the exact form of this acceleration

Effect of initial conditions on the speed of reaction-diffusion fronts

The effect of initial conditions on the speed of propagating fronts in reaction-diffusion equations is examined in the framework of the Hamilton-Jacobi theory. We study the transition between quenched and nonquenched fronts both analytically and numerically for parabolic and hyperbolic reaction diffusion. Nonhomogeneous media are also analyzed and the effect of algebraic initial conditions is also discussed

Reaction-diffusion wave fronts: Multigeneration biological species under climate change

A generalization of reaction-diffusion models to multigeneration biological species is presented. It is based on more complex random walks than those in previous approaches. The new model is developed analytically up to infinite order. Our predictions for the speed agree to experimental data for several butterfly species better than existing models. The predicted dependence for the speed on the number of generations per year allows us to explain the change in speed observed for a specific invasion

Time-delayed reaction-diffusion fronts

A time-delayed second-order approximation for the front speed in reaction-dispersion systems was obtained by Fort and Méndez [Phys. Rev. Lett. 82, 867 (1999)]. Here we show that taking proper care of the effect of the time delay on the reactive process yields a different evolution equation and, therefore, an alternate equation for the front speed. We apply the new equation to the Neolithic transition. For this application the new equation yields speeds about 10% slower than the previous one

Reaction-diffusion waves of advance in the transition to agricultural economics

In a previous paper [J.Fort and V.Méndez, Phys. Rev. Lett. 82, 867 (1999)], the possible importance of higher-order terms in a human population wave of advance has been studied. However, only a few such terms were considered. Here we develop a theory including all higher-order terms. Results are in good agreement with the experimental evidence involving the expansion of agriculture in Europe

Kinetics of K release from soils of Brazilian coffee regions: effect of organic acids

Kinetic studies on soil potassium release can contribute to a better understanding of K availability to plants. This study was conducted to evaluate K release rates from the whole soil, clay, silt, and sand fractions of B-horizon samples of a basalt-derived Oxisol and a sienite-derived Ultisol, both representative soils from coffee regions of Minas Gerais State, Brazil. Potassium was extracted from each fraction after eight different shaking time periods (0-665 h) with either 0.001 mol L-1 citrate or oxalate at a 1:10 solid:solution ratio. First-order, Elovich, zero-order, and parabolic diffusion equations were used to parameterize the time dependence of K release. For the Oxisol, the first-order equation fitted best to the experimental data of K release, with similar rates for all fractions and independent of the presence of citrate or oxalate in the extractant solution. For all studied Ultisol fractions, in which K release rates increased when extractions were performed with citrate solution, the Elovich model described K release kinetics most adequately. The highest potassium release rate of the Ultisol silt fraction was probably due to the transference of "non-exchangeable" K to the extractant solution, whereas in the Oxisol exchangeable potassium represented the main K source in all studied fractions.

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

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%)

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

Front Speed of Language Replacement

We use two coupled equations to analyze the space-time dynamics of two interacting languages. Firstly, we introduce a cohabitation model, which is more appropriate for human populations than classical (non-cohabitation) models. Secondly, using numerical simulations we nd the front speed of a new language spreading into a region where another language was previously used. Thirdly, for a special case we derive an analytical formula that makes it possible to check the validity of our numerical simulations. Finally, as an example, we nd that the observed front speed for the spread of the English language into Wales in the period 1961-1981 is consistent with the model predictions. We also nd that the e¤ects of linguistic parameters are much more important than those of parameters related to population dispersal and reproduction. If the initial population densities of both languages are similar, they have no e¤ect on the front speed. We outline the potential of the new model to analyze relationships between language replacement and genetic replacement

Cultural Diffusion Was the Main Driving Mechanism of the Neolithic Transition in Southern Africa

It is well known that the Neolithic transition spread across Europe at a speed of about 1 km/yr. This result has been previously interpreted as a range expansion of the Neolithic driven mainly by demic diffusion (whereas cultural diffusion played a secondary role). However, a long-standing problem is whether this value (1 km/yr) and its interpretation (mainly demic diffusion) are characteristic only of Europe or universal (i.e. intrinsic features of Neolithic transitions all over the world). So far Neolithic spread rates outside Europe have been barely measured, and Neolithic spread rates substantially faster than 1 km/yr have not been previously reported. Here we show that the transition from hunting and gathering into herding in southern Africa spread at a rate of about 2.4 km/yr, i.e. about twice faster than the European Neolithic transition. Thus the value 1 km/yr is not a universal feature of Neolithic transitions in the world. Resorting to a recent demic-cultural wave-of-advance model, we also find that the main mechanism at work in the southern African Neolithic spread was cultural diffusion (whereas demic diffusion played a secondary role). This is in sharp contrast to the European Neolithic. Our results further suggest that Neolithic spread rates could be mainly driven by cultural diffusion in cases where the final state of this transition is herding/pastoralism (such as in southern Africa) rather than farming and stockbreeding (as in Europe)