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

Thermal instabilities in protogalactic clouds

The means by which a protogalaxy can fragment to form the first generation of stars and globular clusters remains an important problem in astrophysics. Gravitational instabilities grow on timescales too long to drive fragmentation before the background density grows by many orders of magnitude (see Murray and Lin 1989a, and references therein). Thermal instability provides a much more likely mechanism. After its initial collapse, a protogalactic cloud is expected to be shock heated to its virial temperature approx. 10(exp 6) K. Cooling by H and He+ below 10(exp 6) K has a negative slope, so that the cloud is subject to strong thermal instabilities. Density enhancements may then grow rapidly, fragmenting the protogalaxy as it cools to lower temperatures. The role of dynamical effects upon the growth of perturbations is considered here. The method used is similar to that used in Murray and Lin (1989a; see also the Erratum to appear September 15), which examined the growth of thermal instabilities with a one-dimensional Lagrangian hydrodynamics code, written for spherical symmetry. Perturbed regions therefore take the form of shells. The dynamical variables are integrated explicitly, while the temperature, ionization fraction, and molecular fraction are integrated implicitly, and account is taken for non-equilibrium values of these quantities

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

Probabilistic computing with future deep sub-micrometer devices: a modelling approach

An approach is described that investigates the potential of probabilistic "neural" architectures for computation with deep sub-micrometer (DSM) MOSFETs. Initially, noisy MOSFET models are based upon those for a 0.35 /spl mu/m MOS technology with an exaggerated 1/f characteristic. We explore the manifestation of the 1/f characteristic at the output of a 2-quadrant multiplier when the key n-channel MOSFETs are replaced by "noisy" MOSFETs. The stochastic behavior of this noisy multiplier has been mapped on to a software (Matlab) model of a continuous restricted Boltzmann machine (CRBM) - an analogue-input stochastic computing structure. Simulation of this DSM CRBM implementation shows little degradation from that of a "perfect" CRBM. This paper thus introduces a methodology for a form of "technology-downstreaming" and highlights the potential of probabilistic architectures for DSM computation

Combining Biophysical and Price Simulations to Assess the Economics of Long-Term Crop Rotations

Biophysical simulation models (e.g. APSIM) using historical rainfall data are increasingly being used to provide yield and other data on crop rotations in various regions of Australia. However, to analyse the economics of these rotations it is desirable to incorporate the other main driver of profitability, price variation. Because the context was that APSIM was being used to simulate an existing trial site being monitored by a farmer group Gross Margin output was considered most appropriate. Long-run rotational gross margins were calculated for the various rotations with yields (and other physical outputs) derived from APSIM simulations over a period of 100+ years and prices simulated in @Risk based on subjective triangular price distributions elicited from farmers in the group. Rotations included chickpeas, cotton, lucerne, sorghum, wheat and different lengths of fallow. Output presented to the farmers included mean annual gross margins and distributions of gross margins presented as probability distributions, cumulative probability distributions and box and whisker plots. Cotton rotations were the most profitable but had greater declines in soil fertility and greater drainage out of the root zone.Crop Production/Industries,

Combining biophysical and price simulations to assess the economics of long-term crop rotations

Long-run rotational gross margins were calculated with yields derived from biophysical simulations in APSIM over a period of 100+ years and prices simulated in @Risk based on subjective triangular price distributions elicited from the Jimbour Plains farmer group. Rotations included chickpeas, cotton, lucerne, sorghum, wheat and different lengths of fallow. Output presented to the farmers included mean annual GMs and distributions of GMs with box and whisker plots found to be suitable. Mean-standard deviation and first and second-degree stochastic dominance efficiency measures were also calculated. Including lucerne in the rotations improved some sustainability indicators but reduced profitability.Crop Production/Industries, Farm Management,

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