Nonturnpike Optimal Solutions and Their Approximations in Infinite Horizon

Recently, the authors have proposed a new necessary and sufficient condition for turnpike optimality in calculus of variations with singular Euler equation. The method is based on a characterization of the value function and generalizes the well known method based on the Green theorem. Furthermore, it allows the optimality of a competition between several turnpikes to be characterized. For a class of such problems not enjoying the turnpike property, we give an explicit formula for the value function and show how to characterize the optimal solution as the limiting solution of a family of perturbed problems satisfying the turnpike property. The considered problems are scalar with infinite horizon.     

New solitons and kink solutions for the Gardner equation

The Gardner equation, also called combined KdV–mKdV equation, is studied. New hyperbolic ansatze are proposed to derive solitons solutions. The tanh method is used as well to obtain kink solutions.     

Study of local lattice relaxation of substitutional impurities in silicon and germanium

Local lattice relaxation of substitutional donors in silicon investigated using self‐consistent multiple scattering Xα (MSXα) method within the framework of the standard muffin‐tin potential approximation is extended to substitutional donors in germanium and substitutional acceptors in both silicon and germanium. Incorporating the effect of lattice relaxation surrounding the impurity makes the model suitable for both shallow and deep levels. Chemical trends of some aspects of impurity states, such as local lattice relaxation and charge transfer, of the impurities both in silicon and germanium are inferred. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

The concentration effect on the ‘hydrophobic’ and ‘hydrophilic’ behaviour around DMSO in dilute aqueous DMSO solutions. A computer simulation study

We have carried out a molecular dynamics study of dimethyl sulfoxide (DMSO) in water at 298 K at two different densities by simulating two different concentrations: 0.055 and 0.19 mole fraction. We have found an enhancement in the structure of water, an effect that becomes more pronounced as the concentration of DMSO increases. At both concentrations there is a well-defined hydration structure around the oxygen atom of DMSO, which is able to establish strong hydrogen bonds with surrounding water molecules. An increase in the concentration of DMSO depletes the solution of bulk water molecules, reducing the number of hydrogen bonds that water can have in the immediate vicinity of DMSO but increasing the strength of the hydrogen bonds made between the oxygen atom of DMSO and water. There is clear evidence of ‘hydrophobic’ hydration around the methyl groups of DMSO, which is enhanced as the concentration of DMSO increases.     

Ab-initio simulation of elastic constants for some ceramic materials

Athermal elasticity for some ceramic materials (α-Al₂O₃, SiC (α and β phases), TiO₂ (rutile and anatase), hexagonal AlN and TiB₂, cubic BN and CaF₂, and monoclinic ZrO₂) have been investigated via density functional theory. Energy-volume equation-of-state computations to obtain the zero pressure equilibrium volume and bulk modulus as well as computations of the full elastic constant tensor of these ceramics at the experimental zero pressure volume have been performed. The present results for the single crystal elasticity are in good agreement with experiments both for the aggregate properties (bulk and shear modulus) and the elastic anisotropy. In contrast, a considerable discrepancy for the zero pressure bulk modulus of some ceramics evaluated from the energy-volume fit to the computational zero pressure volume has been observed.     

Global and exploding solutions in a model of self-gravitating systems

We study asymptotic properties of solutions to an extension to arbitrary dimensions of the astrophysical model proposed by Chavanis et al. to explain phenomena of gravitational collapse in clouds of self-gravitating particles. In particular, we show that in the two-dimensional case the solutions can be continued to global ones, while in three space dimensions large data of negative energy blow up in a finite time. Relations between isothermal, Streater's energy-transport and the present models are also studied.     

环上半线性椭圆型方程正解的存在性和唯一性

本文讨论了半线性椭圆方程△u+f(u)=0在三种边界条件下正解的存在性和唯一性,给出了正解存在和唯一的一些条件.     

Two classes of piecewise-linear difference equations with eventual periodicity three

In this paper, we will study two classes of difference equations which are piecewise-linear and of similar forms. We will show that all nontrivial solutions of one equation are eventually periodic with prime period three. We will show this result for one case of the second equation.     

A Nonlinear Drift - Diffusion System with Electric Convection Arising in Electrophoretic and Semiconductor Modeling

A multi-dimensional transient drift-diffusion model for (at most) three charged particles, consisting of the continuity equations for the concentrations of the species and the Poisson equation for the electric potential, is considered. The diffusion terms depend on the concentrations. Such a system arises in electrophoretic modeling of three species (neutrally, positively and negatively charged) and in semiconductor theory for two species (positively charged holes and negatively charged electrons). Diffusion terms of degenerate type are also possible in semiconductor modeling. For the initial boundary value problem with mixed Dirichlet - Neumann boundary conditions and general reaction rates, a global existence result is proved. Uniqueness of solutions follows in the Dirichlet boundary case if the diffusion terms are uniformly parabolic or if the initial and boundary densities are strictly positive. Finally, we prove that solutions exist which are positive uniformly in time and globally bounded if the reaction rates satisfy appropriate growth conditions.     

Activity coefficients for NaBr in aqueous ternary solutions with sodium propionate and butyrate from EMF measurements

The activity coefficients of NaBr in the NaBr–NaPropionate–H₂O and NaBr–NaButyrate–H₂O systems were determined from EMF measurements at constant total ionic strength of 0.1 0.5 1.0 1.5 2.0 and 2.5 mol-kg^–1 and at 25° C. The activity coefficients were fitted using Scatchard, Pitzer and Lim equations. Finally the excess Gibbs free energy of these mixtures were also calculated.