The Origin of Chaos in the Outer Solar System

Classical analytic theories of the solar system indicate that it is stable, but numerical integrations suggest that it is chaotic. This disagreement is resolved by a new analytic theory. The theory shows that the chaos among the Jovian planets results from the overlap of the components of a mean motion resonance among Jupiter, Saturn, and Uranus, and provides rough estimates of the Lyapunov time (10 million years) and the dynamical lifetime of Uranus (10^{18} years). The Jovian planets must have entered the resonance after all the gas and most of the planetesimals in the protoplanetary disk were removed.Comment: 19 pages, 3 figures, to appear in Scienc

Symetric Monopoles

We discuss $SU(2)$ Bogomolny monopoles of arbitrary charge $k$ invariant under various symmetry groups. The analysis is largely in terms of the spectral curves, the rational maps, and the Nahm equations associated with monopoles. We consider monopoles invariant under inversion in a plane, monopoles with cyclic symmetry, and monopoles having the symmetry of a regular solid. We introduce the notion of a strongly centred monopole and show that the space of such monopoles is a geodesic submanifold of the monopole moduli space. By solving Nahm's equations we prove the existence of a tetrahedrally symmetric monopole of charge $3$ and an octahedrally symmetric monopole of charge $4$, and determine their spectral curves. Using the geodesic approximation to analyse the scattering of monopoles with cyclic symmetry, we discover a novel type of non-planar $k$-monopole scattering process

Dynamic weight parameter for the Random Early Detection (RED) in TCP networks

This paper presents the Weighted Random Early Detection (WTRED) strategy for congestion handling in TCP networks. WTRED provides an adjustable weight parameter to increase the sensitivity of the average queue size in RED gateways to the changes in the actual queue size. This modification, over the original RED proposal, helps gateways minimize the mismatch between average and actual queue sizes in router buffers. WTRED is compared with RED and FRED strategies using the NS-2 simulator. The results suggest that WTRED outperforms RED and FRED. Network performance has been measured using throughput, link utilization, packet loss and delay

Coherence measurements on Rydberg wave packets kicked by a half-cycle pulse

A kick from a unipolar half-cycle pulse (HCP) can redistribute population and shift the relative phase between states in a radial Rydberg wave packet. We have measured the quantum coherence properties following the kick, and show that selected coherences can be destroyed by applying an HCP at specific times. Quantum mechanical simulations show that this is due to redistribution of the angular momentum in the presence of noise. These results have implications for the storage and retrieval of quantum information in the wave packet.Comment: 4 pages, 4 figures (5 figure files

Off-Diagonal Long-Range Order, Restricted Gauge Transformations, and Aharonov-Bohm Effect in Conductors

The Hamiltonian describing a conductor surrounding an external magnetic field contains a nonvanishing vector potential in the volume accessible to the electrons and nuclei of which the conductor is made. That vector potential cannot be removed by a gauge transformation. Nevertheless, a macroscopic normal conductor can experience no Aharonov-Bohm effect. That is proved by assuming only that a normal conductor lacks off-diagonal long-range order (ODLRO). Then by restricting the Hilbert space to density matrices which lack ODLRO, it is possible to introduce a restricted gauge transformation that removes the interaction of the conductor with the vector potential.Comment: Editing errors are corrected. One was slightly misleadin

Migration of giant planets in planetesimal discs

Planets orbiting a planetesimal circumstellar disc can migrate inward from their initial positions because of dynamical friction between planets and planetesimals. The migration rate depends on the disc mass and on its time evolution. Planets that are embedded in long-lived planetesimal discs, having total mass of $10^{-4}-0.01 M_{\odot}$, can migrate inward a large distance and can survive only if the inner disc is truncated or because of tidal interaction with the star. In this case the semi-major axis, a, of the planetary orbit is less than 0.1 AU. Orbits with larger $a$ are obtained for smaller value of the disc mass or for a rapid evolution (depletion) of the disc. This model may explain several of the orbital features of the giant planets that were discovered in last years orbiting nearby stars as well as the metallicity enhancement found in several stars associated with short-period planets.Comment: 21 pages; 6 encapsulated figures. Accepted by MNRA