A half-moment model for radiative transfer in a 3D gray medium and its reduction to a moment model for hot, opaque sources

We present in this paper a new 3D half-moment model for radiative transfer in a gray medium, called the model, which uses maximum entropy closure. This model is a generalization to 3D of the 1D version recently proposed in (J. Comp. Phys. 180 (2002) 584). The direction space Ω is divided into two pieces, Ω⁺ and Ω^-, in a dynamical way by the plane perpendicular to the total radiative flux, and the half moments are defined from these subspaces. The model closure and the integrations of the radiative transfer equation performed on the moving Ω^± spaces are detailed. 1D planar results, which have motivated the extension of the model of (J. Comp. Phys. 180 (2002) 584) to multi-dimensions, are shown. These results are very good. The model is thereafter derived for 3D spherically symmetric geometry, where the correctness of the non-trivial border terms can be checked. Two 3D spherically symmetric problems are numerically solved in order to show the accuracy of the closure and the role of the border terms. Once again, compared to the solution obtained with a ray tracing solver, results are very good. From the 3D half-moment model, a new moment model, called , is derived for the particular case of a 3D hot and opaque source radiating into a cold medium, for applications such as simulations of stellar atmospheres and fires. Two-dimensional numerical results are presented and compared to those obtained solving the RTE and with other moment models. They demonstrate the very good accuracy of the model, its good convergence properties, and better prediction compared to all other existing moment models in its domain of applicability.     

On the Existence of Strong Solutions to a Coupled Fluid-Structure Evolution Problem

We consider here a model of fluid-structure evolution problem which, in particular, has been largely studied from the numerical point of view. We prove the existence of a strong solution to this problem.     

Wave front shape for a constrained cylindrically anisotropic elastic solid

The two-dimensional wave front shape caused by a point impulse excitation in a cylindrically anisotropic elastic solid is considered. The elastic parameters of the solid are constrained such that E = G This constraint allows the parametric equations of the wave front to be expressed exactly in terms of elementary transcendental functions. The precise location of double and cusp points on the front is treated in detail. Time histories of several wave front patterns are presented and an interesting feature of the front is generalized to the unconstrained solid.     

Classification of Material <Emphasis Type="Italic">G</Emphasis>-Structures

A geometrical interpretation of the G-structures associated to elastic material bodies is given. In addition, characterizations of their integrability are obtained. Since the lack of integrability is a geometrical measure of the lack of homogeneity, the corresponding inhomogeneity conditions are obtained.     

Stability and linear oscillations of liquid bridges with varied boundary conditions under zero gravity

This article deals with stability and small linear oscillations of liquid bridges between fixed solid surfaces (parallel plates, spheres, ...) under zero gravity. A general investigation method for any kind of axisymmetric liquid bridge is exposed but the author focus his work on the spherical liquid bridge cases. In particular, he exposes a full theoretical study of spherical liquid bridges between two spheres, plates and cones.     

Improved taylor-series location algorithm for cooperation networks

This article presents an iterative algorithm for estimating the location of the destination mobile station (DS) when some extra mobile stations around the DS are involved in and assist the base stations to complete the localization process. The proposed method is based on the taylor-series (TS) method and jointly estimates both the DS and the extra mobile stations, named reference mobile station (RS) in this article, positions simultaneously. Moreover, the time-differential-of-arrival (TDOA) measurements between DS and pairs of RSs are obtained by ultra-wide-band (UWB) signal, which is adept in accurate ranging application. According to the theoretic analysis, the Cramér-Rao lower bound (CRLB) of the modified TS algorithm reduces significantly. The actual performance, under a given simulation scenario, is enhanced by 25% at best.     

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.