Locally strong endomorphisms of paths

We determine the number of locally strong endomorphisms of directed and undirected paths—direction here is in the sense of a bipartite graph from one partition set to the other. This is done by the investigation of congruence classes, leading to the concept of a complete folding, which is used to characterize locally strong endomorphisms of paths. A congruence belongs to a locally strong endomorphism if and only if the number l of congruence classes divides the length of the original path and the points of the path are folded completely into the l classes, starting from 0 to l and then back to 0, then again back to l and so on. It turns out that for paths locally strong endomorphisms form a monoid if and only if the length of the path is prime or equal to 4 in the undirected case and in the directed case also if the length is 8. Finally some algebraic properties of these monoids are described.     

Adaptive finite element methods for Cahn–Hilliard equations

We develop a method for adaptive mesh refinement for steady state problems that arise in the numerical solution of Cahn–Hilliard equations with an obstacle free energy. The problem is discretized in time by the backward-Euler method and in space by linear finite elements. The adaptive mesh refinement is performed using residual based a posteriori estimates; the time step is adapted using a heuristic criterion. We describe the space–time adaptive algorithm and present numerical experiments in two and three space dimensions that demonstrate the usefulness of our approach.     

Separation of lignosulfonate from its aqueous solution using supported liquid membrane

This paper presents an experimental and theoretical study on facilitated transport of lignosulfonate (LS) through a flat sheet supported liquid membrane using trioctylamine (TOA) as carrier and dichloroethane as diluent. The studies were carried out with various support materials and operating conditions (viz. carrier concentration, strip phase concentration, salt concentration, etc.) and their effects on the transport of LS. The results were analyzed to identify a suitable combination of support and operating condition that would yield best performance of the supported liquid membrane (SLM) in terms of fast and efficient transport of LS. The stability of the SLM was assessed in terms of loss of liquid from the pores of membrane support. The SLM is found to be stable till 10 h. Co-transport mechanism has been adopted in this work by using NaOH as the strip phase. It was observed that extraction of LS is increased with increase in concentration of NaOH up to a limiting value of 0.5 M NaOH. Difference of salt concentration between feed and strip phase considerably affect the separation process. The diffusional resistances of organic membrane (Δorg) and aqueous solution (Δaq) calculated from the permeation model, which is again a combination of three unique mechanisms viz., diffusion through a feed aqueous layer, a fast interfacial chemical reaction, and diffusion of carrier–complex through the organic membrane, are found to be 609.9 and 176.6 s cm⁻¹, respectively. The values of the diffusion coefficient in the membrane (D_org) and in the bulk organic phase (D_complex) are 1.67×10⁻⁹ and 6.68 × 10⁻⁸ m²s⁻¹, respectively. The extraction of LS is about 90%. Nearly 43% of LS can be recovered at optimum condition.     

Gradient bounds for minimizers of free discontinuity problems related to cohesive zone models in fracture mechanics

In this note we consider a free discontinuity problem for a scalar function, whose energy depends also on the size of the jump. We prove that the gradient of every smooth local minimizer never exceeds a constant, determined only by the data of the problem.     

Four applications of majorization to convexity in the calculus of variations

The resemblance between the Horn-Thompson theorem and a recent theorem by Dacorogna-Marcellini-Tanteri indicates that Schur-convexity and the majorization relation are relevant for applications in the calculus of variations and its related notions of convexity, such as rank one convexity or quasiconvexity. In Theorem 6.6, we give simple necessary and sufficient conditions for an isotropic objective function to be rank one convex on the set of matrices with positive determinant.Majorization is used in order to give a very short proof of a theorem of Thompson and Freede [R.C. Thompson, L.J. Freede, Eigenvalues of sums of Hermitian matrices III, J. Res. Nat. Bur. Standards B 75B (1971) 115-120], Ball [J.M. Ball, Constitutive inequalities and existence theorems in nonlinear elastostatics, in: R.J. Knops (Ed.), Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, vol. 1, Res. Notes Math., 17, Pitman, 1977, pp. 187-241], or Le Dret [H. Le Dret, Sur les fonctions de matrices convexes et isotropes, CR Acad. Sci. Paris, Série I 310 (1990) 617-620], concerning the convexity of a class of isotropic functions which appear in nonlinear elasticity.Next we prove (Theorem 7.3) a lower semicontinuity result for functionals with the form _∫Ωw(D?(x))dx, with w(F)=h(lnV_F). Here F=R_FU_F=V_FR_F is the usual polar decomposition of F∈gl(n,R), and lnV_F is Hencky’s logarithmic strain.We close this paper with a compact proof of Dacorogna-Marcellini-Tanteri theorem, based only on classical results about majorization. The mentioned resemblance of this theorem with the Horn-Thompson theorem is thus explained.     

A vanishing viscosity approach to a quasistatic evolution problem with nonconvex energy

We study a quasistatic evolution problem for a nonconvex elastic energy functional. Due to lack of convexity, the natural energetic formulation can be obtained only in the framework of Young measures. Since the energy functional may present multiple wells, an evolution driven by global minimizers may exhibit unnatural jumps from one well to another one, which overcome large potential barriers. To avoid this phenomenon, we study a notion of solution based on a viscous regularization. Finally we compare this solution with the one obtained with global minimization.     

Concentrators of deformations and fracture of plastic bodies

An approach to the investigation of shape discontinuity regions as strain concentrators is proposed. The near-concentrator strain fields are determined on the basis of the theory of ideal rigid-plastic body; under the condition of plane deformation, their determination is reduced to integration of ordinary differential equations. The deformation as a function of the location of the plastic region and its shape evolution in the process of plastic flow is studied. The plastic flow is demonstrated to be not unique (within the framework of solution completeness). A deformation criterion for the choice of the preferred plastic flow is suggested. The fracture of a V-notched strip is considered. On the basis of the solutions obtained, an approach to the investigation of the fracture processes for more complicated models is formulated.     

Fem for Schrödinger equation with Rashba effect

A finite element method for treating two-dimensional electron systems with Rashba spin–orbit interaction is developed. The Rashba spin–orbit interaction removes spin degeneracy, so that each spin contributes to the conductance differently. By accounting for the connection between a system and leads, this method yields the conductance of a nanoscale quantum device for each spin state. As an example, this calculation method is applied to a model of a quantum point contact. The results of this calculation indicate conductance quantization and a large spin polarization. We discuss the estimated accuracies of this calculation.     

An evolutionary game based particle swarm optimization algorithm

Particle swarm optimization (PSO) is an evolutionary algorithm used extensively. This paper presented a new particle swarm optimizer based on evolutionary game (EGPSO). We map particles’ finding optimal solution in PSO algorithm to players’ pursuing maximum utility by choosing strategies in evolutionary games, using replicator dynamics to model the behavior of particles. And in order to overcome premature convergence a multi-start technique was introduced. Experimental results show that EGPSO can overcome premature convergence and has great performance of convergence property over traditional PSO.     

XRAOO射频识别(RFID)芯片的原理及应用

XRA00是意法半导体公司推出的一个甚高频(UHF)RFID存储器芯片，可用于设计感应式射频识别系统。文中介绍了XRA00射频识别芯片的基本工作原理，给出了它作为电子标签在消费品零售和行李搬运领域的典型应用。