Diffusion of moisture in deformable porous media. Anisotropic fibrous materials

This paper presents a study on the deformation of anisotropic fibrous porous media subjected to moistening by water in the liquid phase. The deformation of the medium is studied by applying the concept of effective stress. Given the structure of the medium, the displacement of the solid matrix is not taken into account with respect to the displacement of the liquid phase. The transport equations are derived from the model proposed by Narasimhan. The transport coefficients and the relation between the variation in apparent density and effective stress are obtained by test measurements. A numerical model has been established and applied for studying drip moistening of mineral wool samples capable or incapable of deformation.Nomenclature D mass diffusion coefficient [L²t^–1] - e void fraction - g gravity acceleration [Lt^–2] - J mass transfer density [ML^–2t^–1] - K hydraulic conductivity [Lt^–1] - K _s hydraulic conductivity of the solid phase [Lt^–1] - K ^* hydraulic conductivity of the deformable porous medium [Lt^–1] - P pressure of moistening liquid [ML^–1 t^–2] - S degree of saturation - t time [t] - V speed [Lt^–1] - X horizontal coordinate [L] - Z vertical coordinate measured from the bottom of porous medium [L] - z z-coordinate [L] Greek Letters porosity - ₁ total hydric potential [L] - _g gas density [ML^–3] - ₁ liquid density [ML^–3] - ₀ apparent density [ML^–3] - _s density of the solid phase [ML^–3] - density of the moist porous medium [ML^–3] - external load [ML^–1t^–2] - effective stress [ML^–1t^–2] - bishop's parameter - matrix potential or capillary suction [L] Indices g gas - 1 moistening liquid - p direction perpendicular to fiber planes - s solid matrix - t direction parallel to fiber planes - v pore Exponent * movement of solid particles taken into account     

Analysis of viscoelastic contact with normal compliance,friction and wear diffusionAnalyse d'un problème viscoélastique avec compliance normale,frottement et diffusion d'usure

We consider a quasistatic problem of frictional contact between a viscoelastic body and a moving foundation. The contact is with wear and is modeled by normal compliance and a law of dry friction. The novelty in the model is that it allows for the diffusion of the wear debris over the potential contact surface. Such kind of phenomena arise in orthopaedic biomechanics and influence the properties of joint prosthesis. We derive a weak formulation of the problem and state that, under a smallness assumption on the problem data, there exists a unique weak solution for the model. To cite this article: M. Shillor et al., C. R. Mecanique 331 (2003).     

Delay-independent exponential stability of stochastic Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion terms

Different from the approaches used in the earlier papers, in this paper, the Halanay inequality technique, in combination with the Lyapunov method, is exploited to establish a delay-independent sufficient condition for the exponential stability of stochastic Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion terms. Moreover, for the deterministic delayed Cohen–Grossberg neural networks, with or without reaction–diffusion terms, sufficient criteria for their global exponential stability are also obtained. The proposed results improve and extend those in the earlier literature and are easier to verify. An example is also given to illustrate the correctness of our results.     

The Effects of Blowing and Suction on Double Diffusion by Mixed Convection over Inclined Permeable Surfaces

A boundary layer analysis is used to investigate the effect of lateral mass flux on mixed convection heat and mass transfer over inclined permeable surfaces in porous media. The conservation equations that govern the problem are reduced to a system of non-linear ordinary differential equations and then the resulting equations is solved by numerical method. The numerical results for heat and mass transfer in terms of Nusselt and Sherwood number are presented in x-y plots for the buoyancy ratio (N) and Lewis number (Le) with mass flux pammeter (Fw). The obtained results are validated against previously published results with on special case of the problem.     

Nonfickian effect in time and space for diffusion processes

Diffusion processes are usually simulated using the classical diffusion equation. In certain scenarios, such equation induces anomalous behavior and consequently several improvements were introduced in the literature to overcome them. One of the most popular was the replacement of the diffusion equation by an integro‐differential equation. Such equation can be established considering a modification of Fick's mass flux where a delay in time is introduced. In this article, we consider mathematical models for diffusion processes that take into account a memory effect in time and space. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1589–1602, 2015     

Global bifurcation of solutions for a predator–prey model with prey‐taxis

We study pattern formations in a predator–prey model with prey‐taxis. It is proved that a branch of nonconstant solutions can bifurcate from the positive equilibrium only when the chemotactic is repulsive. Furthermore, we find the stable bifurcating solutions near the bifurcation point under suitable conditions. Copyright © 2014 John Wiley & Sons, Ltd.     

Automated in-syringe single-drop head-space micro-extraction applied to the determination of ethanol in wine samples

A novel approach of head-space single-drop micro-extraction applied to the determination of ethanol in wine is presented. For the first time, the syringe of an automated syringe pump was used as an extraction chamber of adaptable size for a volatile analyte. This approach enabled to apply negative pressure during the enrichment step, which favored the evaporation of the analyte. Placing a slowly spinning magnetic stirring bar inside the syringe, effective syringe cleaning as well as mixing of the sample with buffer solution to suppress the interference of acetic acid was achieved.     

Synthesis and Electronic/ionic Transport Properties of MoO2/rGO Anode for Lithium Ion Batteries

MoO₂/rGO (reduced graphite oxide) composites have been synthesized by hydrothermal method followed by anneal and characterized by X‐ray diffraction (XRD) and scanning electron microscope (SEM). Galvanostatic charge/discharge testing and electrochemical impedance spectroscopy (EIS) techniques are employed to evaluate the kinetic behaviors of the MoO₂/rGO during lithiation/delithiation. The obtained MoO₂‐based materials have monoclinic crystal structure, and worm like shape with average dimensions of 100‐200 nm width and 500 nm‐1 μm length. There are two steps of lithium ion intercalation/de‐intercalation for the MoO₂/rGO anode at the potential ranging from 1.0 to 3.5 V, locating at E_Li/Li⁺ = 1.60/1.75 V, 1.25/1.40 V, and the first discharge and charge capacities are, respectively, 221.0 and 185.4 mAh g^?1. The resistances of R_SEI and R_CT for the MoO₂/rGO anode are 2‐4 Ω and below 5 Ω. Moreover, the lithium diffusion coefficient calculated from the EIS measurement is about 3.6×10^?9 cm² s^?1.     

Particle methods for PDEs arising in financial modeling

We numerically study convection–diffusion equations arising in financial modeling. We focus on the convection-dominated cases, in which the diffusion coefficients are relatively small. Both finite-difference and Monte-Carlo methods which are widely used in the problems of this kind might be inefficient due to severe restrictions on the meshsize and the number of realizations needed to achieve high resolution.We propose an alternative approach based on particle methods which have extremely low numerical diffusion and thus do not have the aforementioned restrictions. Our approach is based on the operator splitting: The hyperbolic steps are made using the method of characteristics, while the parabolic steps are performed using either a special discretization of the integral representation of the solution (which leads to a deterministic particle method) or a stochastic random walk approach.We apply the designed particle methods to a variety of test problems and the numerical results indicate high accuracy, efficiency and robustness of both the deterministic and stochastic methods. In addition, our numerical experiments clearly demonstrate that the deterministic particle method outperforms its stochastic counterpart.