Showing papers on "Antisymmetric relation published in 1976"
TL;DR: In this article, an approximate perturbation method is developed which gives simple expressions for the threshold gains, and external Q's of some tapered distributed feedback structures, tested against two exact solutions, the uniform and the stepped-k DFB laser.
Abstract: In a distributed feedback (DFB) laser with spatial index modulation, an antisymmetric taper of the feedback parameter, k , removes the threshold degeneracy, which is characteristic of uniform structures, and leads to one mode of particularly low threshold. Exact solutions are presented for the special case of an antisymmetric step of k . An approximate perturbation method is developed which gives simple expressions for the threshold gains, and external Q 's of some tapered distributed feedback structures. The method is tested against two exact solutions, the uniform, and the stepped- k DFB laser. It is shown that the threshold of the stepped- k DFB laser is the lowest of any structure with an antisymmetric taper and a prescribed maximum value of |k| .
315 citations
TL;DR: In this article, an atom-diatomic molecule collision is simulated by considering an idealized potential energy surface which is a two-dimensional duct with an adjustable potential in the corner region.
Abstract: An atom–diatomic molecule collision is simulated by considering an idealized potential energy surface which is a two‐dimensional duct with an adjustable potential in the corner region. This potential is symmetric with respect to an interchange of the x and y Cartesian coordinates. Explicit expressions for the wavefunctions are obtained which make use of this symmetry. Also analytical relations are obtained between the transmission and reflection coefficients and their phases. Quantum mechanical streamlines are computer graphed for a large number of energies and positive, negative, and zero values of the potential energy in the corner region. Special attention is given to the quantized vortices (surrounding wavefunction nodes) which appear in the streamlines. When only one energy channel is open, the streamlines are symmetric and the flux is antisymmetric. This occurs because the wavefunction is a linear combination (with complex coefficients) of two real solutions, one symmetric, the other antisymmetric. ...
91 citations
TL;DR: In this article, the first symmetric and antisymmetric free vibration modes of a cantilever plate for a wide range of aspect ratios were analyzed using the method of superposition.
64 citations
TL;DR: In this paper, a vibronic theory of the Raman effect is developed within a semiclassical framework which provides explicit expressions for the symmetric and antisymmetric components of both the real and imaginary parts of the vibrational Raman transition tensor.
Abstract: A vibronic theory of the Raman effect is developed within a semiclassical framework which provides explicit expressions for the symmetric and antisymmetric components of both the real and imaginary parts of the vibrational Raman transition tensor. The antisymmetric component of the real part is shown to originate in vibronic coupling and to vanish completely at transparent frequencies. Dispersion and absorption lineshape functions are introduced, and by allowing for interference between the α and β electronic absorption bands in ferrocytochrome c, excitation profiles are derived for symmetric and antisymmetric resonance Raman scattering in this region which agree well with observation.
36 citations
TL;DR: In this paper, a finite element technique was introduced into an integro-differential equation formulation of a shallow arch to investigate two forms of instability when subjected to a symmetric dynamic load.
Abstract: When a shallow arch is subjected to a symmetric dynamic load, this load becomes “critical” if a slight increase in the load magnitude leads to a sudden snap-through. Another form of instability occurs when a slight antisymmetric component in the load produces a sharply increasing antisymmetric response. Both forms of instability are investigated by means of a numerical procedure which introduces a finite element technique into an integro-differential equation formulation. Where applicable the results generally confirm previous results obtained elsewhere, but cover a broader range of problems and are believed to be more accurate.
31 citations
TL;DR: In this article, a new method based upon the Zwanzig-mori projection operator technique has been introduced to treat the spin-lattice relaxation problem of coupled nuclear spin systems in liquids, with emphasis on high-resolution NMR spectroscopy.
Abstract: A new method based upon the Zwanzig–Mori projection operator technique has been introduced to treat the spin–lattice relaxation problem of coupled nuclear spin systems in liquids, with emphasis on high resolution NMR spectroscopy. The important quantities required for the use of the method are a set of orthogonal operators which can readily be constructed and given physical meaning in the eigenstate representation for any particular spin system. Some of the expectation values of these orthogonal operators may be related to the measurable quantity in high resolution NMR experiments. The time rate of change of each observable may then be formulated in terms of the trace of various operator functions, allowing the calculation to be carried out in any representation. The computational advantage of using simple spin‐product functions is obvious. The prescription for constructing irreducible orthogonal tensor operators is given, and a variety of such tensor operators are explicitly given for several common spin systems. In the present method each orthogonal operator has a definite symmetry property under spin inversion which can be used to separate the coupled equations into a symmetric and an antisymmetric set. The problem of multiexponential decay in the time evaluation of the longitudinal magnetization, owing to effects of interferences between pairwise dipolar interactions, becomes clear in the present formalism. The present paper is a generalization of earlier work on the relaxation behavior of multiplet spectral structure in high resolution NMR.A new method based upon the Zwanzig–Mori projection operator technique has been introduced to treat the spin–lattice relaxation problem of coupled nuclear spin systems in liquids, with emphasis on high resolution NMR spectroscopy. The important quantities required for the use of the method are a set of orthogonal operators which can readily be constructed and given physical meaning in the eigenstate representation for any particular spin system. Some of the expectation values of these orthogonal operators may be related to the measurable quantity in high resolution NMR experiments. The time rate of change of each observable may then be formulated in terms of the trace of various operator functions, allowing the calculation to be carried out in any representation. The computational advantage of using simple spin‐product functions is obvious. The prescription for constructing irreducible orthogonal tensor operators is given, and a variety of such tensor operators are explicitly given for several common spin...
29 citations
TL;DR: In this paper, a solution of the balance equations over a sphere is presented and compared with the Laplace's tidal equations results obtained by Longuet-Higgins, and a partial answer concerning the accuracy of balance system for describing slow, large-scale motions in the atmosphere is given.
Abstract: Solutions of the linearized balance equations over a sphere are presented and compared with the Laplace's tidal equations results obtained by Longuet-Higgins. On these lines, this study searches for a partial answer concerning the accuracy of the balance system for describing slow, large-scale motions in the atmosphere. The solutions corresponding to Hough's second class waves [small values of ϵ = (2 Ωa)2/c2] are well described by the balance system. At large values of ϵ there are apparent discrepancies for the Rossby symmetric modes as compared to Longuet-Higgins type 2 solutions. Nevertheless, for the antisymmetric modes the agreement is good. The linearized version of the motions studied by Burger is also a solution of the balance equations, corresponding to small frequencies and negative values of ϵ. There are also unrealistic solutions (in the light of the balance approximation) with high frequencies and ϵ 0 only westward propagating waves are solu...
23 citations
TL;DR: In this article, the zero-energy positronium-hydrogen scattering length using the Kohn variational method was calculated using the trial wave function up to 35 terms to describe short range effects.
Abstract: A calculation of the zero-energy positronium-hydrogen scattering lengths using the Kohn variational method is presented. Including, in the trial wavefunction up to 35 terms to describe short range effects, the scattering lengths are found to be a+=5.844a0 (the space symmetric case) and a-=2.319a0 (the space antisymmetric case).
16 citations
TL;DR: Very simple approximate frequency equations are derived in this article for the case of a vibrating circular plate which executes antisymmetric modes. But the authors assume that the plate has no edge deflection but is elastically restrained against rotation along the edge.
10 citations
PARC1
TL;DR: In this paper, a perturbation technique was used to determine the response of periodic structures to Bragg reflectors or filters, and the results obtained by evaluating the formula were presented graphically.
Abstract: Periodic structures that vary spatially in coupling strength, period, and gain/loss are analyzed using a perturbation technique to determine their response as Bragg reflectors or filters. A formula for the response, accurate to first order in the perturbation, is given. Results obtained by evaluating the formula are presented graphically. It is also shown analytically that antisymmetric variations in coupling and/or periodicity have a negligible effect on response (to first order) when neither gain nor loss is present.
6 citations
TL;DR: In this article, a theoretical basis is given based upon a Lagrange formulation in which the strength of ships may be analyzed for antisymmetric distortions caused by waves in a seaway.
Abstract: A theoretical basis is given based upon a Lagrange formulation in which the strength of ships may be analysed for antisymmetric distortions caused by waves. This present study relates to conventional, ‘box-like’, vessels such as tankers. It is shown that analysis of antisymmetric motions in a seaway is merely a special case of the structural analysis.
TL;DR: In this article, a method to construct an asymptotic process to find the axisymmetric vibration frequencies of a circular plate is proposed, which can be considered as a model on which the practical convergence of the method proposed is analyzed and the accuracy of finding the frequencies at each step of the process is estimated.
TL;DR: In this paper, the root locus technique is used to analyse a system with antisymmetric coupling. And the normal gain K may be augmented to include antisymmetric coupling γ and rules for sketching the loci for each value of γ are given.
Abstract: Similar systems with antisymmetric coupling may be analysed by a root locus technique which is a more general version of the standard method. The normal gain K may be augmented to include antisymmetric coupling γ. and rules for sketching the loci for each value of γ are given. Filters may be used to add complex poles/zeros without their complex conjugates. An important class of systems to which the method is relevant is the body having similar pitch/yaw characteristics, and which is spinning at constant rate about its axis of symmetry.
TL;DR: In this paper, a solution for the problem of N-completeness is given for practical calculations for many electron systems because of the necessity of employing a finite basis set of antisymmetric two-particle functions.
Abstract: A solution is given for the problem of N-completeness which arises in practical calculations for many electron systems because of the necessity of employing a finite basis set of antisymmetric two-particle functions.
TL;DR: In this paper, a theoretical technique is outlined upon which the strength of container ships, and other vessels with large deck openings, might be based, and it is demonstrated that analysis of transverse strength in waves can be made to provide the information that is normally sought in independent studies of'seakeeping'.
Abstract: A theoretical technique is outlined upon which the strength of container ships, and other vessels with large deck openings, might be based. Such ships require special consideration because the warping of cross sections cannot be neglected when they suffer antisymmetric distortions. In the development of the theory, a number of new results are given relating to antisymmetric vibration of a thin-walled beam of open section; these relate to the modes and to the orthogonality conditions that they satisfy. It is demonstrated that analysis of transverse strength in waves can be made to provide the information that is normally sought in independent studies of 'seakeeping'.
TL;DR: In this paper, the authors deal with the determination of very simple approximate frequency equations which allow prediction of natural frequencies in the case of a vibrating circular plate which executes antisymmetric modes.
Abstract: The analysis of flexural vibrations of plates with edges elastically restrained against rotation is of interest to the design engineer since ideal supports or clamps are difficult to obtain in practice. A survey of the literature reveals that several investigations have been performed in the past on (a) vibrating circular edges (without in‐plane loading) and (b) vibrating simply supported and clamped circular plates subjected to hydrostatic in‐plane loading. The present paper deals with the determination of very simple, approximate frequency equations which allow prediction of natural frequencies in the case of a vibrating circular plate which executes antisymmetric modes. It is shown that use of simple polynomial expression and a variational approach leads, in some cases, to numerical values which are more accurate than those available in the technical literature. The approach followed in the present investigation can be extended in a straightforward fashion to the case where the edge has translational flexibility.
TL;DR: In this paper, a method for direct obtainment of SC bond orders for π even systems with a twofold symmetry axis not crossing a π center is presented. But the method is not suitable for the 4-electron case.
Abstract: A method for direct obtainment of SC bond orders is shown for π even systems with a twofold symmetry axis not crossing a π center. Two sets of equations are stated, one referring to symmetric and the other to antisymmetric basis functions. Pauli matrices are used for solving the 4-electron case.
TL;DR: In this article, the influence of antisymmetric Dzialoshinsky-Moriya exchange interaction and a symmetric anisotropy in the exchange parameters on the paramagnetic-spin-spin relaxation and resonance process was investigated.
Abstract: We investigate the influence of antisymmetric Dzialoshinsky-Moriya exchange interaction and a symmetric anisotropy in the exchange parameters on the paramagnetic-spin-spin relaxation and resonance process. The investigation is restricted to the high-temperature dynamical behaviour of three-dimensional S = 1 2 systems with mainly isotropic (secular) interactions. The introduction of the antisymmetric interaction in CuCl 2 ·2H 2 O and LiCuCl 3 ·2H 2 O totally removes the discrepancy between the theoretical values, calculated using an interaction hamiltonian which only contains dipolar and isotropic Heisenberg interactions, and the experimental values for the relaxation times and the resonance linewidths.
TL;DR: In this article, a study of the linear theory of free vibrations of membranes in which, owing to the self-weight of the membrane, some sag is present in the static profile is made.
Abstract: A study is made of the linear theory of free vibrations of membranes in which, owing to the self-weight of the membrane, some sag is present in the static profile. The theory applies only to those membranes with relatively shallow profiles. However, because a major application of the theory relates to the use of certain types of cable networks to support the roofs of buildings of large span, and because such networks must be relatively flat if structural efficiency is to be achieved, the theory is of some practical importance. A detailed examination is made of the circular membrane and the rectangular membrane. It is found that the symmetric modes of vibration are heavily dependent on the value of a characteristic geometric and elastic parameter - a parameter which can vary by several orders of magnitude in the suspended membranes typical of those under consideration. In particular, when the parameter is very large the membrane may be considered inextensible. In a practical sense, this corresponds to a membrane of shallow, although appreciable, curvature. For certain intermediate values of the parameter, situations arise in which the natural frequency of a symmetric mode is identical to that of an antisymmetric mode. And when it is very small, the symmetric modes of the classical circular and rectangular membranes are recovered, although, in the case of the classical square membrane, the theory points to conclusions which could not have been drawn from classical membrane theory alone.
TL;DR: The most general covariant spinor derivative compatible with the Minkowski line element leads in a unique way to an antisymmetric torsion tensor, expressed by means of a pseudovector potential, counterpart of the usual vector potential of electrodynamics as mentioned in this paper.
Abstract: The most general covariant spinor derivative compatible with the Minkowski line element leads in a unique way to an antisymmetric torsion tensor It turns out that this can be expressed by means of a pseudovector potential, counterpart of the usual vector potential of electrodynamics In this way some of the models for a symmetrized theory of the electromagnetic interaction with spin-1/2 particles are rederived
TL;DR: In this paper, the coherent potential approximation is used to compute the antisymmetric part (which depends linearly on the spin-orbital interaction) of the optical conductivity tensor of a disordered ferromagnetic alloy.
Abstract: The coherent potential approximation is used to compute the antisymmetric part (which depends linearly on the spin-orbital interaction) of the optical conductivity tensor of a disordered ferromagnetic alloy. The scattering of magnetized conduction electrons on the “impurity” potential of the alloy and on thermal vibrations of the lattice is considered.