Numerical analysis of reversible A + B <-> C reaction-diffusion systems

We develop an effective numerical method of studying large-time properties of reversible reaction-diffusion systems of type A + B C with initially separated reactants. Using it we find that there are three types of asymptotic reaction zones. In particular we show that the reaction rate can be locally negative and concentrations of species A and B can be nonmonotonic functions of the space coordinate x, locally significantly exceeding their initial values.Comment: To appear in EPJ B, 5 pages + 6 figure

How to Calculate Tortuosity Easily?

Tortuosity is one of the key parameters describing the geometry and transport properties of porous media. It is defined either as an average elongation of fluid paths or as a retardation factor that measures the resistance of a porous medium to the flow. However, in contrast to a retardation factor, an average fluid path elongation is difficult to compute numerically and, in general, is not measurable directly in experiments. We review some recent achievements in bridging the gap between the two formulations of tortuosity and discuss possible method of numerical and an experimental measurements of the tortuosity directly from the fluid velocity field.Comment: 6 pages, 8 figure

Grammar-based Representation and Identification of Dynamical Systems

In this paper we propose a novel approach to identify dynamical systems. The method estimates the model structure and the parameters of the model simultaneously, automating the critical decisions involved in identification such as model structure and complexity selection. In order to solve the combined model structure and model parameter estimation problem, a new representation of dynamical systems is proposed. The proposed representation is based on Tree Adjoining Grammar, a formalism that was developed from linguistic considerations. Using the proposed representation, the identification problem can be interpreted as a multi-objective optimization problem and we propose a Evolutionary Algorithm-based approach to solve the problem. A benchmark example is used to demonstrate the proposed approach. The results were found to be comparable to that obtained by state-of-the-art non-linear system identification methods, without making use of knowledge of the system description.Comment: Submitted to European Control Conference (ECC) 201

Link between the diversity, heterogeneity and kinetic properties of amorphous ice structures

Based on neutron wide-angle diffraction and small-angle neutron scattering experiments, we show that there is a correlation between the preparational conditions of amorphous ice structures, their microscopic structural properties, the extent of heterogeneities on a mesoscopic spatial scale and the transformation kinetics. There are only two modifications that can be identified as homogeneous disordered structures, namely the very high-density vHDA and the low-density amorphous LDA ice. Structures showing an intermediate static structure factor with respect to vHDA and LDA are heterogeneous phases. This holds independently from their preparation procedure, i.e. either obtained by pressure amorphisation of ice I_h or by heating of vHDA. The degree of heterogeneity can be progressively suppressed when higher pressures and temperatures are applied for the sample preparation. In accordance with the suppressed heterogeneity the maximum of the static structure factor displays a pronounced narrowing of the first strong peak, shifting towards higher Q-numbers. Moreover, the less heterogeneous the obtained structures are the slower is the transformation kinetics from the high--density modifications into LDA. The well known high-density amorphous structure HDA does not constitute any particular state of the amorphous water network. It is formed due to the preparational procedure working in liquid nitrogen as thermal bath, i.e. at about 77 K