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At least 343 records · Page 19

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NASA NTRS1989

Ground-state coding in partially connected neural networks

Patterns over (-1,0,1) define, by their outer products, partially connected neural networks, consisting of internally strongly connected, externally weakly connected subnetworks. The connectivity patterns may have highly organized structures, such as lattices and fractal trees or nests. Subpatterns over (-1,1) define the subcodes stored in the subnetwork, that agree in their common bits. It is first shown that the code words are locally stable stares of the network, provided that each of the subcodes consists of mutually orthogonal words or of, at most, two words. Then it is shown that if each of the subcodes consists of two orthogonal words, the code words are the unique ground states (absolute minima) of the Hamiltonian associated with the network. The regions of attraction associated with the code words are shown to grow with the number of subnetworks sharing each of the neurons. Depending on the particular network architecture, the code sizes of partially connected networks can be vastly greater than those of fully connected ones and their error correction capabilities can be significantly greater than those of the disconnected subnetworks. The codes associated with lattice-structured and hierarchical networks are discussed in some detail.

Baram, Yoram↗

NASA NTRS1989

Spin-lattice relaxation and the calculation of gain, pump power, and noise temperature in ruby

The use of a quantitative analysis of the dominant source of relaxation in ruby spin systems to make predictions of key maser amplifier parameters is described. The spin-lattice Hamiltonian which describes the interaction of the electron spins with the thermal vibrations of the surrounding lattice is obtained from the literature. Taking into account the vibrational anisotropy of ruby, Fermi's rule is used to calculate the spin transition rates between the maser energy levels. The spin population rate equations are solved for the spin transition relaxation times, and a comparison with previous calculations is made. Predictions of ruby gain, inversion ratio, and noise temperature as a function of physical temperature are made for 8.4-GHz and 32-GHz maser pumping schemes. The theory predicts that ruby oriented at 90 deg will have approximately 50 percent higher gain in dB and slightly lower noise temperature than a 54.7-deg ruby at 32 GHz (assuming pump saturation). A specific calculation relating pump power to inversion ratio is given for a single channel of the 32-GHz reflected wave maser.

Lyons, J. R.↗

NASA NTRS1989

A finite element based method for solution of optimal control problems

A temporal finite element based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables that are expanded in terms of elemental values and simple shape functions. Unlike other variational approaches to optimal control problems, however, time derivatives of the states and costates do not appear in the governing variational equation. Instead, the only quantities whose time derivatives appear therein are virtual states and virtual costates. Also noteworthy among characteristics of the finite element formulation is the fact that in the algebraic equations which contain costates, they appear linearly. Thus, the remaining equations can be solved iteratively without initial guesses for the costates; this reduces the size of the problem by about a factor of two. Numerical results are presented herein for an elementary trajectory optimization problem which show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The goal is to evaluate the feasibility of this approach for real-time guidance applications. To this end, a simplified two-stage, four-state model for an advanced launch vehicle application is presented which is suitable for finite element solution.

Bless, Robert R.↗

NASA NTRS1990

Charge transfer polarisation wave and carrier pairing in the high T(sub c) copper oxides

The High T(sub c) oxides are highly polarizable materials and are charge transfer insulators. The charge transfer polarization wave formalism is developed in these oxides. The dispersion relationships due to long range dipole-dipole interaction of a charge transfer dipole lattice are obtained in 3-D and 2-D. These are high frequency bosons and their coupling with carriers is weak and antiadiabatic in nature. As a result, the mass renormalization of the carriers is negligible in complete contrast to conventional electron-phonon interaction, that give polarons and bipolarons. Both bound and superconducting pairing is discussed for a model Hamiltonian valid in the antiadiabatic regime, both in 3-D and 2-D. The stability of the charge transfer dipole lattice has interesting consequences that are discussed.

Chakraverty, B. K.↗

NASA NTRS1990

Coupled bipolarons and optical phonons as a model for high-T(sub c) superconductors

The coherence length of the new high-temperature superconductors reaches very small value which is comparable to the dimensions of unit cell of these compounds. This means that a pair consists of two holes occupying the same site or two adjacent sites. Such a situation seems to be described by a model of the local-pairs (bipolarons). The origin of local-pairs may come not only from strong enough electron or hole-phonon interaction but also from other interactions. Independent of the specific nature of such local-pairs, they can undergo a Bose-like condensation to the superconducting state at a critical temperature which is usually much lower than the temperature of the pair formation. An interplay of ferroelectric and superconducting properties is considered within the model of hole-like local-pairs interacting with optical phonons. Therefore, researchers extend the usual local-pair Hamiltonian by including a direct interaction between the local-pairs and the optical phonons. These optical phonons are known to play an important role in the ferroelectric transition, if any, and they transform into an additional pseudo-acoustic branch at the ferroelectric critical temperature. (This is associated with nonzero electric polarization due to the existence of two separate lattices composed of negative and positive ions, respectively.)

Kasperczyk, J.↗

NASA NTRS1990

Spin bipolaron in the framework of emery model for high-T(sub c) copper oxide superconductors

The high-T(sub c) oxide compounds discovered recently exhibit a number of interesting physical properties. Two-dimensional antiferromagnetic spin order has been observed in these materials at the oxygen deficiency. This fact can be explained by strong correlation of the spins, situated on Cu sites in the conducting planes of the oxide superconductors. The doping or the oxygen deficiency lead to the occurrence of holes, occupying the oxygen p-orbitals according to the Emery model. At the small hole concentration they can move along the antiferromagnetic lattice of spins, localized on Cu sites. Researchers consider the two holes situation and describe in what way their behavior depends on the antiferromagnetic exchange interation J. It is known that in the framework of Hubbard model with strong on-site Coulomb repulsion, a single hole can form a spin polaron of the large radius. It is reasonable to admit that two holes with parallel spins (triplet) form the spin bipolaron complex owing to the hole excitations' capability to polarize Cu spin surroundings. Such an excitation was considered in the phenomenological way. Here the problem is discussed on the basis of the microscopic approach in the framework of the variational principle. A special kind of wave function is used for such a purpose. The wave function is constructed by generalizing the trial functions proposed in over two holes excitation situation (triplet) and then the region of spin bipolaron existance in the framework of Emery model is studied. In this model the Hamiltonian can be easily rewritten by forming the oxygen states transforming as the irreducible representations of the group D(sub 4).

Golub, A. A.↗

NASA NTRS1990

Electron energy spectrum and magnetic interactions in high-T(sub c) superconductors

The character of magnetic interactions in La-Sr-Cu-O and Y-Ba-Cu-O systems is of primary importance for analysis of high-T(sub c) superconductivity in these compounds. Neutron diffraction experiments showed the antiferromagnetic ground state for nonsuperconducting La2CuO4 and YBa2Cu3O6 with the strongest antiferromagnetic superexchange being in the ab plane. The nonsuperconducting '1-2-3' system has two Neel temperatures T sub N1 and T sub N2. The first one corresponds to the ordering of Cu atoms in the CuO2 planes; T sub N2 reflects the antiferromagnetic ordering of magnetic moments in CuO chains relatively to the moments in the planes T sub N1 and T sub N2 depend strongly on the oxygen content. Researchers describe magnetic interactions in high-T superconductors based on the Linear Muffin-Tin Orbitals (LMTO) band structure calculations. Exchange interaction parameters can be defined from the effective Heisenberg hamiltonian. When the magnetic moments are not too large, as copper magnetic moments in superconducting oxides, J sub ij parameters can be defined through the non-local magnetic susceptibility of spin restricted solution for the crystal. The results of nonlocal magnetic susceptibility calculations and the values of exchange interaction parameters for La CuO and YBa2Cu3O7 systems are given in tabular form. Strong anisotropy of exchange interactions in the ab plane and along the c axis in La2CuO4 is obviously seen. The value of Neel temperature found agrees well with the experimental data available. In the planes of '1-2-3' system there are quite strong antiferromagnetic Cu-O and O-O interaction which appear due to holes in oxygen subbands. These results are in line with the magnetic model of oxygen holes pairing in high-T(sub c) superconductors.

Turshevski, S. A.↗

NASA NTRS1989

Semiclassical approximations in the coherent-state representation

The semiclassical limit of the stationary Schroedinger equation in the coherent-state representation is analyzed simultaneously for the groups W1, SU(2), and SU(1,1). A simple expression for the first two orders for the wave function and the associated semiclassical quantization rule is obtained if a definite choice for the classical Hamiltonian and expansion parameter is made. The behavior of the modulus of the wave function, which is a distribution function in a curved phase space, is studied for the three groups. The results are applied to the quantum triaxial rotor.

Kurchan, J.↗

NASA NTRS1990

Particle acceleration by a wave in a strong magnetic field - Regular and stochastic motion

A general theory for the acceleration of a charged particle by a coherent wave of arbitrary polarization, propagation angle, and phase velocity in the presence of a uniform and strong magnetic field is presented. It is shown that the Hamiltonian surfaces are topologically open for waves with parallel phase velocity, equal to or larger than the speed of light. The trapping width is found to be a strong function of the index of refraction (N), and for N = 1 the trapping width increases as a function of the harmonic number. A novel mechanism for coherently accelerating particles to unlimited energies is presented.

Karimabadi, H.↗

NASA NTRS1990

The rotational spectrum of the CH radical in its a 4Sigma(-) state, studied by far-infrared laser magnetic resonance

The CH radical has been detected in its a 4Sigma(-) state by the technique of laser magnetic resonance at far-infrared wavelengths. Spectra relating to different spin components of the first three rotational transitions have been recorded. The molecule was generated either by the reaction of F atoms with CH4, with a trace of added oxygen or by the reaction of O atoms with C2H2. The observed resonances have been analyzed and fitted to determine the parameters of an effective Hamiltonian for a molecule in a 4Sigma state. The principal quantities determined are the rotational constant B0 = 451 138.434(94) MHz and the spin-spin parameter lambda(0) = 2785.83(18) MHz. Proton hyperfine parameters have also been determined.

Nelis, Thomas↗

NASA NTRS1990

Fractal boundaries in magnetotail particle dynamics

It has been recently established that particle dynamics in the magnetotail geometry can be described as a nonintegrable Hamiltonian system with well-defined entry and exit regions through which stochastic orbits can enter and exit the system after repeatedly crossing the equatorial plane. It is shown that the phase space regions occupied by orbits of different numbers of equatorial crossings or different exit modes are separated by fractal boundaries. The fractal boundaries in an entry region for stochastic orbits are examined and the capacity dimension is determined.

Chen, J.↗

NASA NTRS1990

A computational procedure for the dynamics of flexible beams within multibody systems

The dynamic analysis of three dimensional elastic beams which experience large rotational and large deformational motions are examined. The beam motion is modeled using an inertial reference for the translational displacements and a body-fixed reference for the rotational quantities. Finite strain rod theories are then defined in conjunction with the beam kinematic description which accounts for the effects of stretching, bending, torsion, and transverse shear deformations. A convected coordinate representation of the Cauchy stress tensor and a conjugate strain definition is introduced to model the beam deformation. To treat the beam dynamics, a two-stage modification of the central difference algorithm is presented to integrate the translational coordinates and the angular velocity vector. The angular orientation is then obtained from the application of an implicit integration algorithm to the Euler parameter/angular velocity kinematical relation. The combined developments of the objective internal force computation with the dynamic solution procedures result in the computational preservation of total energy for undamped systems. The present methodology is also extended to model the dynamics of deployment/retrieval of the flexible members. A moving spatial grid corresponding to the configuration of a deployed rigid beam is employed as a reference for the dynamic variables. A transient integration scheme which accurately accounts for the deforming spatial grid is derived from a space-time finite element discretization of a Hamiltonian variational statement. The computational results of this general deforming finite element beam formulation are compared to reported results for a planar inverse-spaghetti problem.

Downer, Janice Diane↗

NASA NTRS1990

Optimal guidance law development for an advanced launch system

A regular perturbation analysis is presented. Closed-loop simulations were performed with a first order correction including all of the atmospheric terms. In addition, a method was developed for independently checking the accuracy of the analysis and the rather extensive programming required to implement the complete first order correction with all of the aerodynamic effects included. This amounted to developing an equivalent Hamiltonian computed from the first order analysis. A second order correction was also completed for the neglected spherical Earth and back-pressure effects. Finally, an analysis was begun on a method for dealing with control inequality constraints. The results on including higher order corrections do show some improvement for this application; however, it is not known at this stage if significant improvement will result when the aerodynamic forces are included. The weak formulation for solving optimal problems was extended in order to account for state inequality constraints. The formulation was tested on three example problems and numerical results were compared to the exact solutions. Development of a general purpose computational environment for the solution of a large class of optimal control problems is under way. An example, along with the necessary input and the output, is given.

Calise, Anthony J.↗

NASA NTRS1990

Chaos in driven Alfven systems

The chaos in a one-dimensional system, which would be nonlinear stationary Alfven waves in the absence of an external driver, is characterized. The evolution equations are numerically integrated for the transverse wave magnetic field amplitude and phase using the derivative nonlinear Schroedinger equation (DNLS), including resistive wave damping and a long-wavelength monochromatic, circularly polarized driver. A Poincare map analysis shows that, for the nondissipative (Hamiltonian) case, the solutions near the phase space (soliton) separatrices of this system become chaotic as the driver amplitude increases, and 'strong' chaos appears when the driver amplitude is large. The dissipative system exhibits a wealth of dynamical behavior, including quasiperiodic orbits, period-doubling bifurcations leading to chaos, sudden transitions to chaos, and several types of strange attractors.

Hada, T.↗

NASA NTRS1990

Two-photon transitions in hydrogen - A test of pseudostate summation

A technique in which the intermediate states of conventional second-order perturbation theory are replaced by a finite set of psudostates, while the energy denominators are supplanted by the expectation values of the unperturbed Hamiltonian with respect to those pseudostates, is presently used to investigate the 2S-1S transition rate on the bases of both the E-x and A-p forms of the interaction. The results thus obtained are noted to closely reflect those conventionally derived, even in cases where only a small number of terms are used; these results are also found not to be strongly dependent on the exact form of the basis functions employed.

Drachman, Richard J.↗

NASA NTRS1989

Distributed structural control using multilayered piezoelectric actuators. I - Analysis

Timoshenko beam theory is applied to beams with multiple layers of piezoelectric material attached. The model is developed using a Hamiltonian approach, and includes a model of the external electrical circuits to which the piezoelectric layers are attached, as well as a complete set of boundary conditions. The resulting model is then formulated in state space, and compared to a state space model of the standard Timoshenko beam.

Cudney, H. H.↗

NASA NTRS1991

The nonconvex multi-dimensional Riemann problem for Hamilton-Jacobi equations

Simple inequalities are presented for the viscosity solution of a Hamilton-Jacobi equation in N space dimensions when neither the initial data nor the Hamiltonian need be convex (or concave). The initial data are uniformly Lipschitz and can be written as the sum of a convex function in a group of variables and a concave function in the remaining variables, therefore including the nonconvex Riemann problem. The inequalities become equalities wherever a 'maxmin' equals a 'minmax', and thus a representation formula for this problem is obtained, generalizing the classical Hopi formulas.

Bardi, Martino↗

NASA NTRS1990

Finite element solution of optimal control problems with inequality constraints

A finite-element method based on a weak Hamiltonian form of the necessary conditions is summarized for optimal control problems. Very crude shape functions (so simple that element numerical quadrature is not necessary) can be used to develop an efficient procedure for obtaining candidate solutions (i.e., those which satisfy all the necessary conditions) even for highly nonlinear problems. An extension of the formulation allowing for discontinuities in the states and derivatives of the states is given. A theory that includes control inequality constraints is fully developed. An advanced launch vehicle (ALV) model is presented. The model involves staging and control constraints, thus demonstrating the full power of the weak formulation to date. Numerical results are presented along with total elapsed computer time required to obtain the results. The speed and accuracy in obtaining the results make this method a strong candidate for a real-time guidance algorithm.

Bless, Robert R.↗