Analytical layer-element solutions of Biot’s consolidation with anisotropic permeability and incompressible fluid and solid constituents

Based on the governing equations of 2D plane-strain Biot’s consolidation, the relationship between generalized displacements and stresses of a single soil layer with anisotropic permeability and incompressible fluid and solid constituents is described by an analytical layer-element, which is deduced in the Laplace–Fourier transform domain by using the eigenvalue approach. Taking the boundary conditions and the continuity of the soil layers into consideration, a global stiffness matrix is subsequently assembled and solved. As to the 3D case, the same derivation is employed after the application of a decoupling transformation. The actual solutions in the physical domain can further be acquired by inverting the Laplace–Fourier transform. Finally, numerical examples are carried out to verify the presented theory and discuss the influence of the anisotropic permeability on the consolidation behavior.     

Monitoring of the stability of cocaine and some metabolites in water and oral fluid by a newly developed CE method

A new CE method was here developed, in order to study the stability of cocaine and some of its metabolites in water and in oral fluid. At first, standard mixtures of cocaine (COC), benzoylecgonine (BE) and cocaethylene (COET) in water were used to study the optimal CE parameters to separate the three compounds. Voltage, sample temperature and pH were investigated, and 25 kV, 25°C and a pH of 4.7 were selected to achieve the best separation. The stability of the three compounds in water and oral fluid was then monitored by applying the previously developed method. Three different storage temperatures (8, 25 and 37°C) were selected and analyses during a week were performed. A decrease of COC and COET peak areas and an increase of BE peak area were observed over time at 25 and 37°C. In addition, in oral fluid, the presence of enzymes and other proteins, and the differences in the molecular structures between COC and COET, caused a stronger degradation of the first compound. Instead, when samples were stored at a low temperature (8°C), the peak areas of the compounds did not vary. Thus, the use of this storage temperature is recommended, above all when sample must be analyzed after a relatively long time.     

Dynamical mean‐field theory for correlated electrons

Electronic correlations strongly influence the properties of matter. For example, they can induce a discontinuous transition from conducting to insulating behavior. In this paper basic terms of the physics of correlated electrons are explained. In particular, I describe some of the steps that led to the formulation of a comprehensive, non‐perturbative many‐body approach to correlated quantum many‐body systems, the dynamical mean‐field theory (DMFT). The DMFT becomes exact in the limit of high lattice dimensions (d → ∞) and allows one to go beyond the investigation of simple correlation models and thereby better understand, and even predict, the properties of electronically correlated materials.     

Unsteady hydromagnetic flow of a reactive variable viscosity third‐grade fluid in a channel with convective cooling

This paper examines the combined effects of a transverse magnetic field and variable viscosity on unsteady flow of a reactive third‐grade electrically conducting fluid and heat transfer in a channel with convective cooling at the surface. It is assumed that the fluid has small electrical conductivity and the electromagnetic force produced is very small. The coupled nonlinear partial differential equations governing the problem are derived and solved numerically using a semi‐implicit finite‐difference scheme. Both numerical and graphical results are presented and physical aspects of the problem are discussed with respect to various parameters embedded in the system. It is in general noted that those parameters that increase/decrase one flow quantity (velocity or temperature) also lead to the increase/decrease respectively of the other quantity. Copyright © 2011 John Wiley & Sons, Ltd.     

Application of topological degree theory to semi-definite complementarity problem

The topological degree theory is applied to study the problem of existence of solutions to the semi-definite complementarity problem (SDCP). A notion of an exceptional family of matrices is introduced, and assertions of a non-strict alternative type are obtained. Namely, for a continuous mapping, there exists at least one of the following two items: either a solution to the SDCP, or an exceptional family of matrices. Hence, if there is no exceptional family, then at least one solution exists     

First-principles study of structural stability and elastic property of pre-perovskite PbTiO3

The structural stability and the elastic properties of a novel structure of lead titanate,which is named preperovskite PbTiO₃ （PP-PTO） and is constructed with TiO₆ octahedral columns arranged in a one-dimensional manner,are investigated by using first-principles calculations.PP-PTO is energetically unstable compared with conventional perovskite phases,however it is mechanically stable.The equilibrium transition pressures for changing from preperovskite to cubic and tetragonal phases are 0.5 GPa and 1.4 GPa,respectively,with first-order characteristics.Further,the differences in elastic properties between pre-perovskite and conventional perovskite phases are discussed for the covalent bonding network,which shows a highly anisotropic character in PP-PTO.This study provides a crucial insight into the structural stabilities of PP-PTO and conventional perovskite.     

Steady-state and Hopf bifurcations in the Langford ODE and PDE systems

This paper is concerned with the Langford ODE and PDE systems. For the Langford ODE system, the existence of steady-state solutions is firstly obtained by Lyapunov–Schmidt method, and the stability and bifurcation direction of periodic solutions are established. Then for the Langford PDE system, the steady-state bifurcations from simple and double eigenvalues are intensively studied. The techniques of space decomposition and implicit function theorem are adopted to deal with the case of double eigenvalue. Finally, by the center manifold theory and the normal form method, the direction of Hopf bifurcation and the stability of spatially homogeneous and inhomogeneous periodic solutions for the PDE system are investigated.     

Flow of a micropolar fluid due to a porous stretching sheet and heat transfer

The present work investigates the micropolar fluid flow due to a permeable stretching sheet and the resulting heat transfer. Unlike the existing numerical works on the flow phenomenon in the literature, the prime interest here is to analytically work out shape of the solutions and identify whether they are unique. Indeed, unique solutions are detected and presented in the exact formulas for the associated boundary layer equations. Temperature field influenced by the microrotation is also mathematically resolved in the cases of constant wall temperature, constant heat flux and Newtonian heating. To discover the salient physical features of many mechanisms acting on the considered problem, it is adequate to have the analytical velocity and temperature fields and also closed-form skin friction/couple stress/heat transfer coefficients, all as given in the current paper. For instance, the practically significant rate of heat transfer is represented by a single formula valid for all three temperature cases.