3,073 research outputs found
A Nonliearly Dispersive Fifth Order Integrable Equation and its Hierarchy
In this paper, we study the properties of a nonlinearly dispersive integrable
system of fifth order and its associated hierarchy. We describe a Lax
representation for such a system which leads to two infinite series of
conserved charges and two hierarchies of equations that share the same
conserved charges. We construct two compatible Hamiltonian structures as well
as their Casimir functionals. One of the structures has a single Casimir
functional while the other has two. This allows us to extend the flows into
negative order and clarifies the meaning of two different hierarchies of
positive flows. We study the behavior of these systems under a hodograph
transformation and show that they are related to the Kaup-Kupershmidt and the
Sawada-Kotera equations under appropriate Miura transformations. We also
discuss briefly some properties associated with the generalization of second,
third and fourth order Lax operators.Comment: 11 pages, LaTex, version to be published in Journal of Nonlinear
Mathematical Physics, has expanded discussio
Individual variation in EEG spectral power enhancement and intelligence
This study tested the relationship between short-term neuroplasticity and individual differences in intelligence. Twenty-two participants completed cognitive testing and a visual EEG experiment involving exposures to repeated and novel stimuli. Time-frequency analyses of phase-locked (evoked) and non-phase-locked (induced) power showed a small effect of decreasing evoked/induced theta (4-8 Hz) ratios over stimulus exposures, irrespective of condition. Hypotheses that intelligence would relate to an increase in this ratio over exposures were not supported. However, the magnitude of the ratio positively correlated with intelligence; while the amount of induced gamma (30-50Hz) activation pre- to post-stimulus was highly inversely related to g. Results suggest that transient changes in neural network phase strongly relate to intelligence in physiological measurements acquired over brief intervals
Photon-Photon Interaction in a Photon Gas
Using the effective Lagrangian for the low energy photon-photon interaction
the lowest order photon self energy at finite temperature and in
non-equilibrium is calculated within the real time formalism. The Debye mass,
the dispersion relation, the dielectric tensor, and the velocity of light
following from the photon self energy are discussed. As an application we
consider the interaction of photons with the cosmic microwave background
radiation.Comment: REVTEX, 7 pages, 1 PostSrcipt figur
Robotic control of the seven-degree-of-freedom NASA laboratory telerobotic manipulator
A computationally efficient robotic control scheme for the NASA Laboratory Telerobotic Manipulator (LTM) is presented. This scheme utilizes the redundancy of the seven-degree-of-freedom LTM to avoid joint limits and singularities. An analysis to determine singular configurations is presented. Performance criteria are determined based on the joint limits and singularity analysis. The control scheme is developed in the framework of resolved rate control using the gradient projection method, and it does not require the generalized inverse of the Jacobian. An efficient formulation for determining the joint velocities of the LTM is obtained. This control scheme is well suited for real-time implementation, which is essential if the end-effector trajectory is continuously modified based on sensory feedback. Implementation of this scheme on a Motorola 68020 VME bus-based controller of the LTM is in progress. Simulation results demonstrating the redundancy utilization in the robotic mode are presented
About the connection between vacuum birefringence and the light-light scattering amplitude
Birefringence phenomena stemming from vacuum polarization are revisited in
the framework of coherent scattering. Based on photon-photon scattering, our
analysis brings out the direct connection between this process and vacuum
birefringence. We show how this procedure can be extended to the Kerr and the
Cotton-Mouton birefringences in vacuum, thus providing a unified treatment of
various polarization schemes, including those involving static fields
Euler configurations and quasi-polynomial systems
In the Newtonian 3-body problem, for any choice of the three masses, there
are exactly three Euler configurations (also known as the three Euler points).
In Helmholtz' problem of 3 point vortices in the plane, there are at most three
collinear relative equilibria. The "at most three" part is common to both
statements, but the respective arguments for it are usually so different that
one could think of a casual coincidence. By proving a statement on a
quasi-polynomial system, we show that the "at most three" holds in a general
context which includes both cases. We indicate some hard conjectures about the
configurations of relative equilibrium and suggest they could be attacked
within the quasi-polynomial framework.Comment: 21 pages, 6 figure
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