一类具有非齐次项对称双曲系统整体弱解的存在性

研究一类具有非齐次项的对称双曲系统Cauchy问题,用补偿紧性方法和最大值原理,得到其有界弱解的整体存在性结果.这一结果推广文献[7]中对称双曲系统到非齐次对称双曲系统.这样一类问题产生于弹性理论、磁流体动力学和石油再开采领域中,具有一定理论和应用价值.     

Petrov-Galerkin Spectral Element Method for Mixed Inhomogeneous Boundary Value Problems on Polygons

The authors investigate Petrov-Galerkin spectral element method. Some results on Legendre irrational quasi-orthogonal approximations are established, which play important roles in Petrov-Galerkin spectral element method for mixed inhomogeneous boundary value problems of partial differential equations defined on polygons. As examples of applications, spectral element methods for two model problems, with the spectral accuracy in certain Jacobi weighted Sobolev spaces, are proposed. The techniques developed in this paper are also applicable to other higher order methods.     

EXISTENCE AND NONEXISTENCE OF GLOBAL POSITIVE SOLUTIONS FOR DEGENERATE PARABOLIC EQUATIONS IN EXTERIOR DOMAINS

This article deals with the degenerate parabolic equations in exterior domains and with inhomogeneous Dirichlet boundary conditions. We obtain that pc = (σ+m)n/(n-σ-2) is its critical exponent provided max{-1, [(1-m)n-2]/(n+1)} σ n-2. This critical exponent is not the same as that for the corresponding equations with the boundary value 0, but is more closely tied to the critical exponent of the elliptic type degenerate equations. Furthermore, we demonstrate that if max{1, σ + m} p ≤ pc, then every positive solution of the equations blows up in finite time; whereas for ppc, the equations admit global positive solutions for some boundary values and initial data. Meantime, we also demonstrate that its positive solutions blow up in finite time provided n ≤σ+2.     

Selective Deflection of Polarized Light Via Coherently Driven Four-Level Atoms in a Double-A Configuration

We study the interaction of a weak probe field, having two circular polarized components, i.e., cr- and a＋ polarization, with an optically dense medium of four-level atoms in a double-A configuration, which is mediated by the electromagnetically induced transparency with a polarized control light with spatially inhomogeneous profile. We analyse the deflection of the polarized probe light and we find that we can selectively determine which circular component will be deflected after the polarized probe light enters the atom medium via adjusting the polarization and detuning of the control field.     

A New Method for High-Resolution NMR Spectra in Inhomogeneous Fields with Efficient Solvent Suppression

High-resolution nuclear magnetic resonance （NMR） is one of the most powerful tools for analyzing molecular structures and dynamics. Magnetic field homogeneity is required for conventional high-resolution spectra. However, there are many chemical and/or biological circumstances where the spatial homogeneities of the magnetic fields are degraded. Intense solvent signal is another obstacle for obtaining high-resolution spectra, especially in in vivo and in situ NMR spectroscopy. In this paper, a new pulse sequence based on intermolecular multiple quantum coherence （iMQC） was reported. This sequence can effectively remove the effect of magnetic field inhomogeneity and suppress the solvent signal. It can recover the spectral information such as chemical shifts, coupling constants, multiplet patterns, and relative peak areas in inhomogeneous fields. Theoretical analyses and experimental verifications are presented to demonstrate the feasibility of this method.     

Investigations of hard elastic polypropylene with respect to the coil-strand-transition model

Hard elastic polypropylene was investigated by x-ray scattering using synchrotron radiation and by performing stress strain measurements in different liquids. It was found that the long period increases with elongation up to 1.3–1.4. Beyond this extension a change in the deformation behavior takes place. In the range from 1.1 to 1.3–1.4 the deformation measurements in the different liquids are in good agreement with the coil-strand-transition model. The proposed linear relationship between the deformation work and the elongation could be confirmed. The same holds for the surface energy. Moreover, the calculated ratio between the surface energy and the deformation work agrees with the measurements.     

Characterization of inhomogeneous polyacrylamide hydrogels

The physical and structural properties of acrylamide gels have been characterized by osmotic deswelling, mechanical compression, and x-ray scattering. These properties vary considerably with the concentration of the crosslinking agent bisacrylamide, at fixed total monomers concentration (10% wt/wt water). In particular, changes in the properties appear more prominent at a crosslinking level of about 5-6% (wt bisacrylamide/wt monomers). The compression modulus of as-prepared and swollen gels passes through a maximum at this level of crosslinking. The swelling pressure curves can be separated into osmotic and elastic contributions of the gel network. The elastic part exhibits similar behavior to the compression modulus. The scaling of the osmotic part with the gel concentration varies with the degree of crosslinking, changing from 2.33 to 3.09. This indicates that the solvent power of water decreases with increasing crosslinking level, towards Φ conditions. The scattering patterns from the gels have been analyzed as arising from additive contributions from a homogeneous gel matrix, and embedded heterogeneities having a higher crosslinking density. These heterogeneities become much more prominent at the same level of crosslinking about 5-6%. Hysteresis observed in the sorption/desorption behavior of polyacrylamide gel suggests that further irreversible structural changes may occur at water activities lower than probed by osmotic deswelling. © 1992 John Wiley & Sons, Inc.     

Roe linearization for the Euler equations augmented by the convective terms from the k–ω turbulence model

This paper describes the method of calculation of the eigenvalues, eigenvectors of the Jacobian matrix of the Euler equations augmented by the convective part of k–ω turbulence model. The equations are 3D and values are expressed in terms of cell normals of a finite volume. The expressions for wave strengths are also found, which are also necessary to calculate the inter‐cell fluxes for Roe's scheme. Copyright © 2007 John Wiley & Sons, Ltd.     

Modeling of Microwave Images of Buried Cylindrical Objects

Tomographic methods of image reconstruction of two-dimensional cross-sections of volumetric objects in millimeter wavelengths band are suggested and considered.It is shown that in the frequency band under consideration, the images of investigated objects may be obtained by first-order diffraction tomography method (Born, Rytov or high frequency approximation of the first-order for scattered electromagnetic field).