Showing papers on "Antisymmetric relation published in 1977"

On the theory of identical particles

Abstract: The classical configuration space of a system of identical particles is examined. Due to the identification of points which are related by permutations of particle indices, it is essentially different, globally, from the Cartesian product of the one-particle spaces. This fact is explicity taken into account in a quantization of the theory. As a consequence, no symmetry constraints on the wave functions and the observables need to be postulated. The two possibilities, corresponding to symmetric and antisymmetric wave functions, appear in a natural way in the formalism. But this is only the case in which the particles move in three- or higher-dimensional space. In one and two dimensions a continuum of possible intermediate cases connects the boson and fermion cases. The effect of particle spin in the present formalism is discussed.

An analytical and experimental stress analysis of a practical mode II fracture test specimen

Abstract: A boundary-collocation method has been employed to determine the Mode II stress-intensity factors for a pair of through-the-thickness edge cracks in a finite isotropic plate. An elastostatic analysis has been carried out in terms of the complete Williams stress function employing both even and old components. The results of the numerical analysis were verified by a two-step procedure whereby the symmetric (Mode I) and antisymmetric (Mode II) portions of the solution were independently compared with existing solutions. Since no previous analytical solutions existed for the asymmetric loading of an edge-cracked plate, the complete solution was verified by comparison with a photoelastic analysis.

On the Branching Structure of Diffusive Climatological Models

Abstract: We consider the general structure of the equilibrium solutions of simple, zonally averaged, energy-balance climatological models with diffusive heat transport and a nonlinear ice albedo feedback The relation between the appearance of unstable modes and the bifurcation of equilibrium solutions is elucidated, in particular the relation between antisymmetric modes and bifurcation of asymmetric equilibrium solutions Numerical solution of a specific model, which has been shown by others to possess an equilibrium solution similar to the present climate of the earth, shows that as well as the several previously known symmetric equilibrium solutions, it possesses asymmetric solutions, including ones with an ice cap at only one pole One of these types of asymmetric solutions is shown to be stable for values of parameters which represent present conditions on earth

Square-root algorithms for the continuous-time linear least squares estimation problem

Abstract: We present a simple differential equation for the triangular square root of the state error variance of the continuous-time Kalman filter. Unlike earlier methods of Andrews, and Tapley and Choe, this algorithm does not explicitly involve any antisymmetric matrix in the differential equation for the square roots. The role of antisymmetric matrices is clarified: it is shown that they are just the generators of the orthogonal transformations that connect the various square roots; in the constant model case, a similar set of antisymmetric matrices appears inside the Chandrasekhar-type equations for the square roots of the derivative of the error variance. Several square-root algorithms for the smoothing problem are also presented and are related to some well-known smoothing approaches.

Generalised antisymmetric fluid forces applied to a ship in a seaway

Abstract: Using a structural theory for antisymmetric motions and distortions of a hull, equations of response to oblique sinusoidal waves are set up. The fluid actions are found as generalised forces at the principal coordinates of the dry hull. A form of strip theory is employed for this purpose. A complete set of linear equations governing antisymmetric ship response to waves is presented.

Prediction of Elastic-Airplane Lateral Dynamics from Rigid-Body Aerodynamics

Abstract: Control-configured vehicle technology has increased the demand for detailed analysis of dynamic stability and control, handling and ride qualities, and control system dynamics at the early stages of preliminary design and development. For these early analyses an approximate, but reasonably accurate, set of equations of motion for elastic airplanes is needed. Such a formulation is developed for the lateral dynamics of elastic airplanes. It makes use of rigid-body aerodynamic stability derivatives and the antisymmetric elastic mode shapes and frequencies in formulating the forces and moments due to elastic motion. Verification of accuracy was made by comparison with B-1 airplane dynamics obtained by other methods. Frequencies and damping ratios of the coupled modes agree acceptably well with four antisymmetric elastic modes included.

The measurement of the antisymmetric components of nonlinear optical susceptibilities of TeO2 crystal

Abstract: The antisymmetric components of the second‐order nonlinear optical susceptibility of TeO2 crystal have been measured by the process of sum‐frequency mixing between the laser beams at the wavelengths of 1.064 and 0.532 μm. The experimental results were χ123/ (χ123+χ132) =0.59, χ132/(χ123 +χ132) =0.41, and χ312/(χ123+χ132) =−χ321/(χ123+χ132) =−0.18, which imply that χ123 and χ132 are slightly asymmetric and χ312 and χ321 are antisymmetric in the second and third suffices. It is thus concluded that the contribution of the antisymmetric component to the signal at the sum frequency may be comparable with that of the symmetric one forbidden by the Kleinman symmetry relation. Moreover, the symmetric and antisymmetric components of the nonlinear optical polarizabilities of the bond Te‐O have been estimated in terms of the scheme of bond additivity by assuming a bond symmetry ∞.

Non-linear oscillations using antisymmetric transfer characteristics of a differential pair

Abstract: A comprehensive analysis has been presented for a regenerative system with an associated non-linearity given by the antisymmetric self-saturating characteristics of an emittcr-couplcd differential pair. Tho asymptotic rise and fall of the saturation characteristics has been approximated by a transcendental function of hyperbolic tangent type, which gives a two-parameter (e,β) oscillator equation rather than a single (e) Van der Pol equation. It has been shown that the theoretically (computerized solution) obtained amplitude, frequency and wave shape are more conformable with the experimental results in both harmonic and relaxation mode of oscillation than for Van der POI'S equation. Particularly in the relaxation mode. Van der Pol's equation fails to account for the sharp rise and semi-exponential decay in the wave shape which is accounted for in this analysis.

Voltage-controlled oscillator using an emitter-coupled differential pair

Abstract: A voltage-controlled oscillator using the antisymmetric transfer characteristics of an emitter-coupled differential pair of transistors is presented. Variation of the differential bias condition of this pair changes the average slope of Its transconductance parameter, thereby changing the frequency of the near harmonic mode of oscillation in a system which has been shown to produce van-der-Pol-type oscillations with passive parameter control only. Over a sufficiently wide range of frequency the distortion of this oscillation is reasonably low. A simple slope/differential-voltage relation is proposed to calculate the frequencies by computer solution of the general relation, as well as by approximate solution by using the method of small parameters. Experimental results are also presented for comparison.

Buckling of cylindrical shells with smeared-out and discrete orthogonal stiffeners

Abstract: The buckling equations for the orthogonally stiffened cylindrical shells under uniform axial compression and external pressure and with classical simply supported boundary conditions are formulated by treating the stiffeners as discrete elements. By assuming identical and equally spaced stringers and identical and equally spaced rings, the buckling equations can be uncoupled into several sets of simpler and manageable equations for the symmetric and antisymmetric longitudinal modes and symmetric and antisymmetric circumferential modes. The uncoupled submatrices are further reduced by partitioning and substitution. Effort is made to preserve the sparseness of the matrices in order to use a special compact storage scheme. A method to compute the minimum eigenvalue for a large general eigenvalue problem, the Ritz iteration method combined with Chebyshev procedure, is developed and its accuracies are evaluated. Examples are performed and results are compared to other computational and experimental results available. A a},a2

Minimum Weight Design of Cylindrical Shell with Multiple Stiffener Sizes Under Buckling Constraint

Abstract: : The buckling equations for the orthogonally stiffened cylindrical shells under uniform axial compression and external pressure and with classical simply supported boundary conditions are formulated by treating the stiffeners as discrete elements. By assuming identical and equally spaced stringers and identical and equally spaced rings, the buckling equations can be uncoupled into several sets of simpler and manageable equations for the symmetric and antisymmetric longitudinal modes and symmetric and antisymmetric circumferential modes. The uncoupled submatrices are further reduced by partitioning and substitution. Effort is made to preserve the sparseness of the matrices in order to use a special compact storage scheme. A method to compute the minimum eigenvalue for a large general eigenvalue problem, the Ritz iteration method combined with Chebyshev procedure, is developed and its accuracies are evaluated. Examples are performed and results are compared to other computational and experimental results available.

Resonating group model for few-nucleon problems

Abstract: A simplified procedure based on the Resonating Group Approximation is proposed to obtain the integral equations for three- and four-nucleon problems.Faddeev three-nucleon approach has been extended to obtain theFaddeev-Yakubovsky (FY) model of four nucleons taking into account of their spin and isospin in two-channel resonating group approximation. In this approximation we consider a completely antisymmetric wave function which can be written as the clustering of d+d and n+He3 (or p+H3) systems with antisymmetric spin-isospin states. The two nucleon interaction is assumed to be of the separableYamaguchi form in3s1 and1s0 states. The equations for the states with quantum numbersS=2, 1, 0;T=0 are obtained. It is shown that the FY equations reduce to a set of one-dimensional coupled integral equations with the kernels containing the functions of two- and three-nucleon problems. By this conjecture one can treat few-body problems involving any number of bound subsystems.