A priori error estimates for numerical methods for scalar conservation laws. Part I: The general approach

In this paper, we construct a general theory of a priori error estimates for scalar conservation laws by suitably modifying the original Kuznetsov approximation theory. As a first application of this general technique, we show that error estimates for conservation laws can be obtained without having to use explicitly any regularity properties of the approximate solution. Thus, we obtain optimal error estimates for the Engquist-Osher scheme without using the fact (i) that the solution is uniformly bounded, (ii) that the scheme is total variation diminishing, and (iii) that the discrete semigroup associated with the scheme has the -contraction property, which guarantees an upper bound for the modulus of continuity in time of the approximate solution.

     

An energy-transport model for semiconductors derived from the Boltzmann equation

An energy-transport model is rigorously derived from the Boltzmann transport equation of semiconductors under the hypothesis that the energy gain or loss of the electrons by the phonon collisions is weak. Retaining at leading order electron-electron collisions and elastic collisions (i.e., impurity scattering and the elastic part of phonon collisions), a rigorous diffusion limit of the Boltzmann equation can be carried over, which leads to a set of diffusion equations for the electron density and temperature. The derivation is given in both the degenerate and nondegenerate cases.     

Morphology and crystallization of blends of linear low density polyethylene with a semiflexible liquid crystalline polymer

The morphology and the crystallization behavior of blends of linear low density polyethylene (LLDPE) with an experimental sample of a semiflexible liquid crystalline polymer (SBH 112 by Eniricerche, Italy) have been studied by differential scanning calorimetry (DSC), polarized optical microscopy (POM) and scanning electron microscopy (SEM). The blends possess a two-phase morphology, due to immiscibility of the two components. SEM observations show that dispersion of the minor SBH phase is favored at low (相似文献   

Degenerate polynomial patches of degree 11 for almostGC 2 interpolation over triangles

We consider the problem of interpolating scattered data in ³ by analmost geometrically smoothGC ² surface, where almostGC ² meansGC ² except in a finite number of points (the vertices), where the surface isGC ¹. A local method is proposed, based on employing so-called degenerate triangular Bernstein-Bézier patches. We give an analysis of quintic patches forGC ¹ and patches of degree eleven for almostGC ² interpolation.     

Alternating Sign Matrices and Some Deformations of Weyl's Denominator Formulas

An alternating sign matrix is a square matrix whose entries are 1, 0, or –1, and which satisfies certain conditions. Permutation matrices are alternating sign matrices. In this paper, we use the (generalized) Littlewood's formulas to expand the products and 2 as sums indexed by sets of alternating sign matrices invariant under a 180° rotation. If we put t = 1, these expansion formulas reduce to the Weyl's denominator formulas for the root systems of type B _n and C _n. A similar deformation of the denominator formula for type D _n is also given.     

Crosslinking of vinyl‐terminated biphenyl and naphthalene side‐chain liquid‐crystalline poly(epichlorohydrin) derivatives

We performed the crosslinking of vinyl‐terminated biphenyl and naphthalene side‐chain liquid‐crystalline polyethers using peroxide‐type initiators with and without the addition of tertiary amine promoters. The crosslinking temperatures were chosen in the range of mesophase stability to allow the mesophase order to be frozen. The biphenyl derivatives, with a high isotropization temperature, were crosslinked to a large extent. This led to anisotropic thermosets. To crosslink naphthalene derivatives, amine promoters were needed, but degrees of crosslinking were lower, and anisotropic elastomers were obtained. Crosslinking processes were studied by differential scanning calorimetry, polarized optical microscopy, and Fourier transform infrared spectroscopy. The nature of the frozen mesophase was confirmed by X‐ray diffraction studies on mechanically oriented samples. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2237–2244, 2002     

Dielectric behaviour of a side-chain-bearing liquid-crystalline polysiloxane

The relaxation of electric field-induced polar orientation in a side-chain-bearing liquid-crystalline polysiloxane was measured by means of thermally stimulated depolarization currents. Different relaxation mechanisms were identified and characterized: the glass transition cooperative relaxation exhibits compensation behaviour. On the other hand, lowerT _g and upperT _g discharges were observed and their molecular nature is discussed.     

Fractional occupation numbers and spin density functional calculations of degenerate systems

We implemented ab initio self‐consistent field (SCF) fractional occupation numbers (FON) calculation with Dunlap's interpolation scheme for the twisted ethylene, which is a prototype molecule of a σ–π biradical system. The calculational results are compared with those of complete‐active‐space (CAS) SCF and spin‐unrestricted Kohn–Sham (UKS) calculations on potential surfaces, occupation numbers of natural orbitals, and correlation entropies. It was found that the UKS methods gave similar results to CASSCF, while the FON solutions appeared in only the nearly complete degenerate region. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 317–323, 2003     

A New Chemo‐Enzymatic Route to Side‐Chain Liquid‐Crystalline Polymers: The Synthesis and Polymerization of 6‐(4‐Methoxybiphenyl‐4′‐oxy)hexyl Vinyl Hexanedioate

A novel synthetic method combining chemo and enzymatic synthesis strategies was employed to prepare a vinyl acetate type monomer, 6‐(4‐methoxybiphenyl‐4′‐oxy)hexyl vinyl hexanedioate (VA‐LC). Homo‐ and copolymers of VA‐LC with maleic anhydride (MAn) were prepared by conventional free radical polymerization using 2,2′‐azobisisobutyronitrile (AIBN) and 1,1′‐azobis (cyclohexane carbonitrile) (AHCN) as an initiator at 95 and 60 °C, respectively. The thermal properties of the generated polymeric material were investigated by differential scanning calorimetry (DSC), and the optical texture was inspected by polarizing optical microscopy (POM). While the monomer VA‐LC does not exhibit liquid‐crystalline properties, poly(VA‐LC), and the alternating copolymer of VA‐LC with maleic anhydride both displayed such properties.

     

A convergence result for a sequence of distributed-parameter optimal control problems

In this paper, we consider a sequence of abstract optimal control problems by allowing the cost integrand, the partial differential operator, and the control constraint set all to vary simultaneously. Using the notions of -convergence of functions,G-convergence of operators, and Kuratowski-Mosco convergence of sets, we show that the values of the approximating problems converge to that of the limit problem. Also we show that a convergent sequence of optimal pairs for the approximating problems has a limit which is optimal for the limit problem. A concrete example of parabolic optimal control problems is worked out in detail.This research was supported by NSF Grant No. DMS-88-02688.