关于非线性Pochhammer-Chree方程的解

本文研究了弹性杆纵向形变方程:u_(tt)—u_(ttxx)—u_(xx)—(1/3)(u~3)xx=0的椭圆余弦波解,并用Adomian分解法,求出了其初边值问题解.     

激光拉曼光谱在高分子中的应用

论述了激光拉曼光谱对高分子结构、结晶形态和表征,反应动力学过程和取向的研究,还介绍了纵向声学模、共振、高温高压、光波导和付里叶拉曼光谱在高分子研究中的最新进展。     

Optical vs. direct sorption and swelling measurements for the study of stiff-chain polymer-penetrant interactions

This work involves interferometric ‘optical thickness’ and refractive index measurements performed in an optical thickness meter (OTM), on supported cellulose acetate (CA) films equilibrated with various activities of methylene chloride (MC) vapor. The relevant equilibrium sorption and volume swelling isotherms were determined by application of the Claussius-Mossotti equation on the assumption that these films swell unidimensionally along the thickness direction, and were compared with corresponding direct equilibrium sorption (weight gain), elongation and thickness dilation measurements on similar free films performed in a vacuum sorption/swelling apparatus (VSA) and complemented with refractive index data. Combined elongation and thickness dilation data from the VSA showed that free glass-cast CA films exhibit pronounced swelling anisotropy. The said anisotropy, although it cannot be completely eliminated, by conditioning at high degrees of swelling, does not appear to affect the extent of volume swelling significantly, thus permitting quantitative comparison of sorption and swelling isotherms determined by the VSA and the OTM. Such comparison showed satisfactory agreement between these two sets of results up to an MC uptake of ca. 0.4 gMC/cm³ of dry CA corresponding to a degree of swelling of ca. 0.2. Increasing discrepancies are observed at higher MC concentrations, which are attributable to breakdown of the assumption used that the supported films swell unidimensionally along the thickness direction. The present CA-MC volume swelling data exhibit the negative deviation from volume additivity on mixing typical glassy polymers.     

Magneto-optical visualization of three spatial components of inhomogeneous stray fields

The article deals with the physical principles of magneto-optical visualization (MO) of three spatial components of inhomogeneous stray fields with the help of FeCo metal indicator films in the longitudinal Kerr effect geometry. The inhomogeneous field is created by permanent magnets. Both p- and s-polarization light is used for obtaining MO images with their subsequent summing, subtracting and digitizing. As a result, the MO images and corresponding intensity coordinate dependences reflecting the distributions of the horizontal and vertical magnetization components in pure form have been obtained. Modeling of both the magnetization distribution in the indicator film and the corresponding MO images shows that corresponding to polar sensitivity the intensity is proportional to the normal field component, which permits normal field component mapping. Corresponding to longitudinal sensitivity, the intensity of the MO images reflects the angular distribution of the planar field component. MO images have singular points in which the planar component is zero and their movement under an externally homogeneous planar field permits obtaining of additional information on the two planar components of the field under study. The intensity distribution character in the vicinity of sources and sinks (singular points) remains the same under different orientations of the light incidence plane. The change of incident plane orientation by π/2 alters the distribution pattern in the vicinity of the saddle points.     

The localized longitudinal index theorem for Lie groupoids and the van Est map

We define the “localized index” of longitudinal elliptic operators on Lie groupoids associated with Lie algebroid cohomology classes. We derive a topological expression for these numbers using the algebraic index theorem for Poisson manifolds on the dual of the Lie algebroid. Underlying the definition and computation of the localized index, is an action of the Hopf algebroid of jets around the unit space, and the characteristic map it induces on Lie algebroid cohomology. This map can be globalized to differentiable groupoid cohomology, giving a definition of the “global index”, that can be computed by localization. This correspondence between the “global” and “localized” index is given by the van Est map for Lie groupoids.     

Longitudinal wave propagation in a piezoelectric nanoplate considering surface effects and nonlocal elasticity theory

The propagation characteristics of the longitudinal wave in a piezoelectric nanoplate were investigated in this study. The nonlocal elasticity theory was used and the surface effects were taken into account. In addition, the group velocity and phase velocity were derived and investigated, respectively. The dispersion relation was analyzed with different scale coefficients, wavenumbers, and voltages. The results showed that the dispersion degree can be strengthened by increasing the wavenumber and scale coefficient.     

Analysis of longitudinal multispin orders in strongly coupled spin systems

Longitudinal multispin orders provide an effective way for measurement of scalar couplings and also to probe molecular interactions and dynamics. Analysis of longitudinal orders has been made in strongly coupled AB and ABX spin systems to determine the dependence of strong coupling parameter on these orders. Experimental and simulated spectra of various longitudinal orders are illustrated for these spin systems. This general procedure can be extended to broad range of spin systems to understand the influence of strong coupling on longitudinal orders.     

Determination of T1-spin-lattice relaxation time in a two-level system by continuous wave multiquantum electron paramagnetic resonance spectroscopy in a presence of tetrachromatic microwave irradiation

Applicability of continuous wave multiquantum EPR methods to study relaxation times at X-band is examined. Multiquantum transitions excited in a two-level system by tetrachromatic irradiation are used for these studies. The Bloch equation model is applied to simulate lineshapes of the three quantum transitions as a function of frequency difference between exciting fields. The dependence of multiquantum transition signals on relaxation times and microwave amplitude is shown. On this basis a method of deducing relaxation times from these signals is formulated. The case of a homogeneously and inhomogeneously broadened resonance line is considered. Two experimental methods are used to verify the proposed hypothesis: the X-band continuous wave multiquantum EPR with four frequencies microwave field and saturation recovery EPR. The values of T₁ obtained from CW MQ EPR and SR EPR are compared.     

Effect of magnon–phonon interaction on transverse acoustic phonon excitation at finite temperature

A magnon–phonon interaction model is developed on the basis of two-dimensional square Heisenberg ferromagnetic system. By using Matsubara Green function theory transverse acoustic phonon excitation is studied and transverse acoustic phonon excitation dispersion curves is calculated on the main symmetric point and line in the first Brillouin zone. On line Σ it is found that there is hardening for transverse acoustic phonon on small wave vector zone (nearby point Γ), there is softening for transverse acoustic phonon on the softening zone and there is hardening for transverse acoustic phonon near point M. On line Δ it is found there is no softening and hardening for transverse acoustic phonon. On line Z it is found that there is softening for transverse acoustic phonon on small wave vector zone (nearby point X) and there is hardening for transverse acoustic phonon nearby point M. The influences of various parameters on transverse acoustic phonon excitation are also explored and it is found that the coupling of the magnon–phonon and the spin wave stiffness constant play an important role for the softening of transverse acoustic phonon.     

Biclustering Three-Dimensional Data Arrays With Plaid Models

Three-dimensional data arrays (collections of individual data matrices) are increasingly prevalent in modern data and pose unique challenges to pattern extraction and visualization. This article introduces a biclustering technique for exploration and pattern detection in such complex structured data. The proposed framework couples the popular plaid model together with tools from functional data analysis to guide the estimation of bicluster responses over the array. We present an efficient algorithm that first detects biclusters that exhibit strong deviations for some data matrices, and then estimates their responses over the entire data array. Altogether, the framework is useful to home in on and display underlying structure and its evolution over conditions/time. The methods are scalable to large datasets, and can accommodate a variety of dynamic patterns. The proposed techniques are illustrated on gene expression data and bilateral trade networks. Supplementary materials are available online.