The restricted two-body problem in constant curvature spaces

We perform the bifurcation analysis of the Kepler problem on $S^3$ and $L^3$. An analogue of the Delaunay variables is introduced. We investigate the motion of a point mass in the field of the Newtonian center moving along a geodesic on $S^2$ and $L^2$ (the restricted two-body problem). When the curvature is small, the pericenter shift is computed using the perturbation theory. We also present the results of the numerical analysis based on the analogy with the motion of rigid body.Comment: 29 pages, 7 figure

On the Equivalence Between Type I Liouville Dynamical Systems in the Plane and the Sphere

Producción CientíficaSeparable Hamiltonian systems either in sphero-conical coordinates on an S2 sphere or in elliptic coordinates on a R2 plane are described in a unified way. A back and forth route connecting these Liouville Type I separable systems is unveiled. It is shown how the gnomonic projection and its inverse map allow us to pass from a Liouville Type I separable system with a spherical configuration space to its Liouville Type I partners where the configuration space is a plane and back. Several selected spherical separable systems and their planar cousins are discussed in a classical context

Nonintegrability of the two-body problem in constant curvature spaces

We consider the reduced two-body problem with the Newton and the oscillator potentials on the sphere ${\bf S}^{2}$ and the hyperbolic plane ${\bf H}^{2}$. For both types of interaction we prove the nonexistence of an additional meromorphic integral for the complexified dynamic systems.Comment: 20 pages, typos correcte

Characteristic Energy of the Coulomb Interactions and the Pileup of States

Tunneling data on $\mathrm{La_{1.28}Sr_{1.72}Mn_2O_7}$ crystals confirm Coulomb interaction effects through the $\sqrt{\mathrm{E}}$ dependence of the density of states. Importantly, the data and analysis at high energy, E, show a pileup of states: most of the states removed from near the Fermi level are found between ~40 and 130 meV, from which we infer the possibility of universal behavior. The agreement of our tunneling data with recent photoemission results further confirms our analysis.Comment: 4 pages, 4 figures, submitted to PR

LHC Transverse Feedback System and its Hardware Commissioning

A powerful transverse feedback system ("Damper") has been installed in LHC. It will stabilise coupled bunch instabilities in a frequency range from 3 kHz to 20 MHz and at the same time damp injection oscillations originating from steering errors and injection kicker ripple. The transverse damper can also be used as an exciter for purposes of abort gap cleaning or tune measurement. The power and lowlevel systems layouts are described along with results from the hardware commissioning. The achieved performance is compared with earlier predictions and requirements for injection damping and instability control

LHC Transverse Feedback System: First Results of Commissionning

A powerful transverse feedback system ("Damper") has been installed in LHC. It will stabilise the high intensity beam against coupled bunch transverse instabilities in a frequency range from 3 kHz to 20 MHz and at the same time damp injection oscillations originating from steering errors and injection kicker ripple. The LHC Damper can also be used as means of exciting transverse oscillations for the purposes of abort gap cleaning and tune measurement. The LHC Damper includes 4 feedback systems on 2 circulating beams (in other words one feedback system per beam and plane). Every feedback system consists of 4 electrostatic kickers, 4 push-pull wide band power amplifiers, 8 preamplifiers, two digital processing units and 2 beam position monitors with low-level electronics. The power and low-level subsystem layout is described along with first results from the commissioning of 16 power amplifiers and 16 electrostatic kickers located in the LHC tunnel. The achieved performance is compared with earlier predictions and requirements for injection damping and instability control. Requirements and first measurements of the performance of the power and low-level subsystems are summarized

Two-body quantum mechanical problem on spheres

The quantum mechanical two-body problem with a central interaction on the sphere ${\bf S}^{n}$ is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several interactive potentials these energy levels are calculated in explicit form.Comment: 41 pages, no figures, typos corrected; appendix D was adde

Developmental malformation of the corpus callosum: a review of typical callosal development and examples of developmental disorders with callosal involvement

This review provides an overview of the involvement of the corpus callosum (CC) in a variety of developmental disorders that are currently defined exclusively by genetics, developmental insult, and/or behavior. I begin with a general review of CC development, connectivity, and function, followed by discussion of the research methods typically utilized to study the callosum. The bulk of the review concentrates on specific developmental disorders, beginning with agenesis of the corpus callosum (AgCC)—the only condition diagnosed exclusively by callosal anatomy. This is followed by a review of several genetic disorders that commonly result in social impairments and/or psychopathology similar to AgCC (neurofibromatosis-1, Turner syndrome, 22q11.2 deletion syndrome, Williams yndrome, and fragile X) and two forms of prenatal injury (premature birth, fetal alcohol syndrome) known to impact callosal development. Finally, I examine callosal involvement in several common developmental disorders defined exclusively by behavioral patterns (developmental language delay, dyslexia, attention-deficit hyperactive disorder, autism spectrum disorders, and Tourette syndrome)