On the orthogonality of natural modes of vibration

The natural modes of a discrete linear system are orthogonal with respect to the mass and stiffness matrices in a generalized sense. However, these modes are usually not orthogonal to each other in the ordinary sense. The purpose of this paper is to document a number of conditions under which the modes are also orthogonal in an ordinary fashion.     

Structural and vibrational properties of dilute GaNxAs1−x(P1−x)

We report a comprehensive analyzes of the Fourier transform infrared (FTIR) absorption and Raman scattering data on the structural and vibrational properties of dilute ternary GaAs_1−xN_x,[GaP_1−xN_x] (x<0.03) alloys grown on GaAs [GaP] by metal organic chemical vapor deposition (MOCVD) and solid source molecular beam epitaxy (MBE). By using realistic total energy and lattice dynamical calculations, the origin of experimentally observed N-induced vibrational features are characterized. Useful information is obtained about the structural stability, vibrational frequencies, lattice relaxations and compositional disorder in GaNAs (GaNP) alloys. At lower composition (x<0.015) most of the N atoms occupy the As [P] sublattice {N_As[N_P]}—they prefer moving out of their substitutional sites to more energetically favorable locations at higher x. Our results for the N-isotopic shifts of local mode frequencies compare favorably well with the existing FTIR data.     

随机环境中双移民生灭过程的极限性质

引入了随机环境中双移民生灭过程的概念，定义了过程的模态指示函数，在此基础上研究了其转移矩阵的平稳分布，给出了平稳分布众数的位置与模态指示函数之间的关系．研究了平稳分布的众数与边界关系．     

Interface Optical Phonon Modes and Frohlich Electron-Phonon Interaction Hamiltonian in a Multi-shell Spherical Nanoheterosystem

Under dielectric continuum approximation, interface optical (IO) phonon modes and the Frohlich electron-IO phonon interaction Hamiltonian in a multi-shell spherical nanoheterosystem were derived and studied. Numericalcalculations on three-layer and four-layer CdS/HgS spherical nanoheterosystems have been performed. Results revealthat there are four IO phonon modes for the three-layer system and six IO phonon modes for the four-layer system.On each interface, there are two IO phonon modes, the frequency of one is between WTO,CdS and WLO,CdS, and that ofthe other is between WTO,HgS and WLO,HgS. With the increasing of quantum number l, the frequency of each IO modeapproaches one of the two frequency values of the single CdS/HgS heterostructure, and the potential for each IO modeis more and more localized at a certain interface, furthermore, the coupling between the electron-lO phonons becomes weaker.     

Light scattering by groups of spherical particles

Light scattering by groups of spherical particles is considered. It is shown that the structure of the groups and their orientational distribution can be judged from the spectrum and polarization of the scattered light. Syktyvkar State University, 55, Oktyabr'skii Ave., Syktyvkar, 167001, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 2, pp. 228–231, March–April, 1997.     

Parking Capacity and Pricing in Park'n Ride Trips: A Continuous Equilibrium Network Design Problem

In this paper we consider the problem of designing parking facilities for park'n ride trips. We present a new continuous equilibrium network design problem to decide the capacity and fare of these parking lots at a tactical level. We assume that the parking facilities have already been located and other topological decisions have already been taken.The modeling approach proposed is mathematical programming with equilibrium constraints. In the outer optimization problem, a central Authority evaluates the performance of the transport network for each network design decision. In the inner problem a multimodal traffic assignment with combined modes, formulated as a variational inequality problem, generates the share demand for modes of transportation, and for parking facilities as a function of the design variables of the parking lots. The objective is to make optimal parking investment and pricing decisions in order to minimize the total travel cost in a subnetwork of the multimodal transportation system.We present a new development in model formulation based on the use of generalized parking link cost as a design variable.The bilevel model is solved by a simulated annealing algorithm applied to the continuous and non-negative design decision variables. Numerical tests are reported in order to illustrate the use of the model, and the ability of the approach to solve applications of moderate size.     

Analysis of Radiation Phenomena in a Wedge Ended Dielectric Slab Waveguide

Radiation phenomena observed in a wedge shape ended dielectric slab waveguide are analyzed using mode matching technique. The case of transverse electric polarization (TE) being parallel to dielectric slab waveguide is assumed. In order to describe the fields in the wedge region, a stack of dielectric plates is assumed and in each layer the fields are expanded in terms of the mixed spectrum of guided and radiated modes. A similar expansion is used in the constant thickness slab waveguide while in free space medium a continuous-radiation mode expansion is used. Then a mode matching approach is applied, incorporating the orthogonality properties of mixed spectrum modes, in order to compute the wave fields inside the dielectric slab waveguide and wedge medium. Mode matching is achieved by discretizing the continuous radiation mode spectrum leading into a numerically stable solution provided a sufficient large number of points are used to convert integrals into finite summations. Numerical computations are carried out for various wedge geometries and shapes including linear and exponential profiles.     

Modification of Spatial Coherence by Means of Low-Order Zernike-Mode Adaptive Optics

Spatial coherence of the field modified by low-order adaptive optics is analyzed to establish a theoretical basis for the recent idea of using adaptive optics as a spatial coherence modifier. In this context low-order adaptive optics has the ability to correct some of the low-order aberrations specified by Zernike polynomials. The initial field to be modified is assumed to be a spatially partially coherent one resulting from phase disturbance. It is demonstrated, as in the previous study, that low-order adaptive optics serves to enhance the spatial coherence of the resultant field and that the effect of the enhancement becomes stronger as the spatial coherence of the initially partially coherent field increases. Potential applications of low-order adaptive optics as a spatial coherence modifier are briefly discussed.     

Demonstration of the stability or instability of multibreathers at low coupling

Whereas there exists a mathematical proof for one-site breathers stability, and an unpublished one for two-site breathers, the methods for determining the stability properties of multibreathers rely on numerical computation of the Floquet multipliers or on the weak nonlinearity approximation leading to discrete nonlinear Schrödinger equations. Here we present a set of multibreather stability theorems (MST) that provides a simple method to determine multibreathers stability in Klein–Gordon systems. These theorems are based in the application of degenerate perturbation theory to Aubry’s band theory. We illustrate them with several examples.     

One‐Dimensional,Cofacial Porphyrin Polymers Formed by Self‐Assembly of meso‐Tetrakis(ERE Donor) Zinc(II) Porphyrins

A series of meso‐tetrakis‐(ERE donor) zinc(II) porphyrins n Zn (ERE donor=4‐R‐3,5‐bis[(E)‐methyl]phenyl; 1 Zn: E=NMe₂, R=Br; 2 Zn: E=NMe₂, R=H; 3 Zn: E=OMe, R=Br; 4 Zn: E=OMe, R=H) have been synthesized in excellent yields. As a result of the combination of a Lewis acidic site and eight Lewis basic sites within one molecule, monomeric molecules of n Zn self‐assemble to form one‐dimensional porphyrin polymers [ n Zn]_∞ in the solid state, as confirmed for 1 Zn and 3 Zn by X‐ray crystallography. The coordination environment around the zinc(II) ions in these polymers is octahedral. They are ligated by four equatorial nitrogen atoms of the porphyrin and two apical E atoms (E=N, O) provided by the EBrE donor groups of adjacent n Zn molecules. Complexes 2 Zn and 4 Zn did not form single crystals, but solid‐state UV/Vis analysis points to the formation of similar structures. Solution UV/Vis and ¹H NMR spectroscopy indicated that interactions between 1 Zn and 2 Zn monomers in the polymers are stronger than between 3 Zn and 4 Zn monomers. Interestingly, they also revealed that the presence of a neighboring bromine atom in the EBrE donor groups has a considerable influence on the coordination properties of the benzylic N or O atoms. The zinc(II) ions of the porphyrins most likely adopt only hexacoordination in the solid state, owing to the unique predisposition of Lewis acidic and basic sites in the n Zn molecules. Several parameters of the aggregates, for example, the interplanar separation between porphyrins and the zinc–zinc distances, change as a function of the coordinating E groups. The high degree of modularity in their synthesis makes these zinc(II) porphyrins an interesting new entry in noncovalent multiporphyrin assemblies.