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The rapid change in direction and magnitude of the magnetic field vector in crossing the quasi-neutral sheet in the geomagnetic tail leads to deterministic Hamiltonian chaos. The finite correlation times in the single particle orbits due to the continuum of orbital frequencies leads to well-defined collisionless transport coefficients. The transport coefficients are derived for plasma trapped in the quasi-neutral sheet.
Phase space structure and chaos near a neutral line are studied with numerical surface-of-section (SOS) techniques and analytic methods. Results are presented for a linear neutral line model with zero crosstail electric field. It was found that particle motion can be divided into three regimes dependening on the value of the conserved canonical momentum, Py, and the conserved Hamiltonian, h. The phase space structure, using Poincare SOS plots, is highly sensitive to bn = Bn/B0 variations, but not to h variations. It is verified that the slow motion preserves the action, Jz, as evaluated by Sonnerup (1971), when the period of the fast motion is smaller than the time scale of the slow motion. Results show that the phase space structure and particle chaos depend sensitively upon Py and bn, but are independent of h.
Nested neural networks are constructed from outer products of patterns over (-1,0,1)N, whose nonzero bits define subnetworks and the subcodes stored in them. The set of permissible words, which are network-size binary patterns composed of subcode words that agree in their common bits, is characterized, and their number is derived. It is shown that if the bitwise products of the subcode words are linearly independent, the permissible words are the unique global minima of the Hamiltonian associated with the network.
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) which 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.
The coherence length of the new high-temperature superconductors reaches a small value which is comparable to the dimensions of the unit cell of the compound. This means that a pair consists of two holes occupying the same site or two adjacent sites. Such a situation is 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 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.)
A new field of multi-particle interferometry is introduced using a nonlinear optical spontaneous parametric down conversion (SPDC) of a photon into more than two photons. The study of SPDC using a realistic Hamiltonian in a multi-mode shows that at least a low conversion rate limit is possible. The down converted field exhibits many stronger nonclassical phenomena than the usual two photon parametric down conversion. Application of the multi-particle interferometry to a recently proposed many particle Bell's theorem on the Einstein-Podolsky-Rosen problem is given.
The photon number-amplification and number-duplication mechanism are analyzed in the ideal case. The search for unitary evolutions leads to consider also a number-deamplification mechanism, the symmetry between amplification and deamplification being broken by the integer-value nature of the number operator. Both transformations, amplification and duplication, need an auxiliary field which, in the case of amplification, turns out to be amplified in the inverse way. Input-output energy conservation is accounted for using a classical pump or through frequency-conversion of the fields. Ignoring one of the fields is equivalent to considering the amplifier as an open system involving entropy production. The Hamiltonians of the ideal devices are given and compared with those of realistic systems.
A procedure to calculate all second-order polarizability tensor elements in static fields has been developed. The calculations are based on semiempirical Hamiltonians (MNDO) that include shaped electric fields. The technique has been applied to mono-, di-, and trisubstituted benzenes incorporating nitro, methyl, and primary and secondary amino groups.
The Generalized Newton Variational Principle for 3D quantum mechanical reactive scattering is briefly reviewed. Then three techniques are described which improve the efficiency of the computations. First, the fact that the Hamiltonian is Hermitian is used to reduce the number of integrals computed, and then the properties of localized basis functions are exploited in order to eliminate redundant work in the integral evaluation. A new type of localized basis function with desirable properties is suggested. It is shown how partitioned matrices can be used with localized basis functions to reduce the amount of work required to handle the complex boundary conditions. The new techniques do not introduce any approximations into the calculations, so they may be used to obtain converged solutions of the Schroedinger equation.
A computational formulation for the dynamic analysis of spacecraft with deploying appendages is presented. The appendage model is based on a geometrically nonlinear beam formulation which accurately accounts for large rotational and large deformation motions. A moving finite element reference grid is incorporated within the nonlinear beam formulation to model the deployment motion. Hamilton's Law is used to formulate the general equations of motion, and a transient integration solution procedure is derived from a space-time finite element discretization of the Hamiltonian variational statement. Computational results of the methodology are presented for a classical gravity gradient stabilized satellite configuration.
A temporal finite element based on a mixed form of Hamilton's weak principle is summarized for optimal control problems. The resulting weak Hamiltonian finite element method is extended to allow for discontinuities in the states and/or discontinuities in the system equations. An extension of the formulation to allow for control inequality constraints is also presented. The formulation does not require element quadrature, and it produces a sparse system of nonlinear algebraic equations. To evaluate its feasibility for real-time guidance applications, this approach is applied to the trajectory optimization of a four-state, two-stage model with inequality constraints for an advanced launch vehicle. Numerical results for this model are presented and compared to results from a multiple-shooting code. The results show the accuracy and computational efficiency of the finite element method.
Second-order sums are computed for the two-electron positive ions Li(+), Be(2+), and B(3+) by representing the intermediate states as discrete pseudostates. The Hamiltonian for the system is given and translated to semi-Jacobi variables for its derivation in reduced Rydberg units. The interaction potential is developed in its multipole form and employed in second-order perturbation theory. The perturbation is always a multipole-potential term, and the initial and intermediate states are constructed from two-particle Hylleraas basis sets. The resulting pseudostates are shown to represent the continuum with good convergence, and the asymptotic-optical-potential method is applied to the two-body quantities to determine the energy levels of three-electron systems in high Rydberg states. The method is shown to give accurate values for the polarizabilities of the two-electron isoelectronic systems.
A semianalytic method to predict the orbit of a spacecraft orbiting a planet and perturbed by oblateness and a gravity anomaly (mascon) is presented. The Hamiltonian is first expressed in closed form in terms of the nonsingular canonical set of Poincare elements where the mascon is represented by a point-mass. The planet global potential is limited to the second and third harmonics. The mascon potential in harmonics is limited to second degree and first order. The original Lie-Hori method is then applied to transform the canonical equations of motion from the osculating element space to the mean element space. Numerical integration of the new equations is used.
It is demonstrated that the weak Hamiltonian finite-element formulation is amenable to the solution of optimal control problems with inequality constraints which are functions of both state and control variables. Difficult problems can be treated on account of the ease with which algebraic equations can be generated before having to specify the problem. These equations yield very accurate solutions. Owing to the sparse structure of the resulting Jacobian, computer solutions can be obtained quickly when the sparsity is exploited.
This paper addresses the motion and force control problem of multiple robot arms manipulating a cooperatively held object. A general control paradigm is introduced which decouples the motion and force control problems. For motion control, different control strategies are constructed based on the variables used as the control input in the controller design. There are three natural choices; acceleration of a generalized coordinate, arm tip force vectors, and the joint torques. The first two choices require full model information but produce simple models for the control design problem. The last choice results in a class of relatively model independent control laws by exploiting the Hamiltonian structure of the open loop system. The motion control only determines the joint torque to within a manifold, due to the multiple-arm kinematic constraint. To resolve the nonuniqueness of the joint torques, two methods are introduced. If the arm and object models are available, an optimization can be performed to best allocate the desired and effector control force to the joint actuators. The other possibility is to control the internal force about some set point. It is shown that effective force regulation can be achieved even if little model information is available.
The high-resolution laboratory millimeter- and submillimeter-wave spectra of C-12H(3)OH and C-13H(3)OH have been extended to include transitions involving significantly higher angular momentum quantum numbers than studied previously. For C-12H(3)OH, the data set now includes 549 A torsional substate transitions and 524 E torsional substate transitions through J is not greater than 24, exclusive of blends. For C-13H(3)OH the data set now includes 453 A torsional substate transitions and 440 E torsional substate transitions through J is not greater than 24, exclusive of blends. The extended internal axis method Hamiltonian has been used to analyze the transitions to experimental accuracy. The molecular constants determined by this approach have been used to predict accurately the frequencies of many transitions through J = 25 not measured in the laboratory.
The proposed investigation on a Matched Asymptotic Expansion (MAE) method was carried out. It was concluded that the method of MAE is not applicable to launch vehicle ascent trajectory optimization due to a lack of a suitable stretched variable. More work was done on the earlier regular perturbation approach using a piecewise analytic zeroth order solution to generate a more accurate approximation. In the meantime, a singular perturbation approach using manifold theory is also under current investigation. Work on a general computational environment based on the use of MACSYMA and the weak Hamiltonian finite element method continued during this period. This methodology is capable of the solution of a large class of optimal control problems.
A general family of asymptotically stabilizing control laws is introduced for a class of nonlinear Hamiltonian systems. The inherent passivity property of this class of systems and the Passivity Theorem are used to show the closed-loop input/output stability which is then related to the internal state space stability through the stabilizability and detectability condition. Applications of these results include fully actuated robots, flexible joint robots, and robots with link flexibility.