Potts Models on Feynman Diagrams

We investigate numerically and analytically Potts models on ``thin'' random graphs -- generic Feynman diagrams, using the idea that such models may be expressed as the N --> 1 limit of a matrix model. The thin random graphs in this limit are locally tree-like, in distinction to the ``fat'' random graphs that appear in the planar Feynman diagram limit, more familiar from discretized models of two dimensional gravity. The interest of the thin graphs is that they give mean field theory behaviour for spin models living on them without infinite range interactions or the boundary problems of genuine tree-like structures such as the Bethe lattice. q-state Potts models display a first order transition in the mean field for q>2, so the thin graph Potts models provide a useful test case for exploring discontinuous transitions in mean field theories in which many quantities can be calculated explicitly in the saddle point approximation.Comment: 10 pages, latex, + 6 postscript figure

Decorating Random Quadrangulations

On various regular lattices (simple cubic, body centred cubic..) decorating an edge with an Ising spin coupled by bonds of strength L to the original vertex spins and competing with a direct anti-ferromagnetic bond of strength alpha L can give rise to three transition temperatures for suitable alpha. The system passes through ferromagnetic, paramagnetic, anti-ferromagnetic and paramagnetic phases respectively as the temperature is increased. For the square lattice on the other hand multiple decoration is required to see this effect. We note here that a single decoration suffices for the Ising model on planar random quadrangulations (coupled to 2D quantum gravity). Other random bipartite lattices such as the Penrose tiling are more akin to the regular square lattice and require multiple decoration to have any affect.Comment: 6 pages + 5 figure

The Gonihedric Ising Model and Glassiness

The Gonihedric 3D Ising model is a lattice spin model in which planar Peierls boundaries between + and - spins can be created at zero energy cost. Instead of weighting the area of Peierls boundaries as the case for the usual 3D Ising model with nearest neighbour interactions, the edges, or "bends" in an interface are weighted, a concept which is related to the intrinsic curvature of the boundaries in the continuum. In these notes we follow a roughly chronological order by first reviewing the background to the formulation of the model, before moving on to the elucidation of the equilibrium phase diagram by various means and then to investigation of the non-equilibrium, glassy behaviour of the model.Comment: To appear as Chapter 7 in Rugged Free-Energy Landscapes - An Introduction, Springer Lecture Notes in Physics, 736, ed. W. Janke, (2008

Automated mixed traffic transit vehicle microprocessor controller

An improved Automated Mixed Traffic Vehicle (AMTV) speed control system employing a microprocessor and transistor chopper motor current controller is described and its performance is presented in terms of velocity versus time curves. The on board computer hardware and software systems are described as is the software development system. All of the programming used in this controller was implemented using FORTRAN. This microprocessor controller made possible a number of safety features and improved the comfort associated with starting and shopping. In addition, most of the vehicle's performance characteristics can be altered by simple program parameter changes. A failure analysis of the microprocessor controller was generated and the results are included. Flow diagrams for the speed control algorithms and complete FORTRAN code listings are also included

Potts Models with (17) Invisible States on Thin Graphs

The order of a phase transition is usually determined by the nature of the symmetry breaking at the phase transition point and the dimension of the model under consideration. For instance, q-state Potts models in two dimensions display a second order, continuous transition for q = 2,3,4 and first order for higher q. Tamura et al recently introduced Potts models with "invisible" states which contribute to the entropy but not the internal energy and noted that adding such invisible states could transmute continuous transitions into first order transitions. This was observed both in a Bragg-Williams type mean-field calculation and 2D Monte-Carlo simulations. It was suggested that the invisible state mechanism for transmuting the order of a transition might play a role where transition orders inconsistent with the usual scheme had been observed. In this paper we note that an alternative mean-field approach employing 3-regular random ("thin") graphs also displays this change in the order of the transition as the number of invisible states is varied, although the number of states required to effect the transmutation, 17 invisible states when there are 2 visible states, is much higher than in the Bragg-Williams case. The calculation proceeds by using the equivalence of the Potts model with 2 visible and r invisible states to the Blume-Emery-Griffiths (BEG) model, so a by-product is the solution of the BEG model on thin random graphs.Comment: (2) Minor typos corrected, references update

Intrinsic Variability and Field Statistics for the Vela Pulsar: 3. Two-Component Fits and Detailed Assessment of Stochastic Growth Theory

The variability of the Vela pulsar (PSR B0833-45) corresponds to well-defined field statistics that vary with pulsar phase, ranging from Gaussian intensity statistics off-pulse to approximately power-law statistics in a transition region and then lognormal statistics on-pulse, excluding giant micropulses. These data are analyzed here in terms of two superposed wave populations, using a new calculation for the amplitude statistics of two vectorially-combined transverse fields. Detailed analyses show that the approximately power-law and lognormal distributions observed are fitted well at essentially all on-pulse phases by Gaussian-lognormal and double-lognormal combinations, respectively. These good fits, plus the smooth but significant variations in fit parameters across the source, provide strong evidence that the approximately power-law statistics observed in the transition region are not intrinsic. Instead, the data are consistent with normal pulsar emission having lognormal statistics at all phases. This is consistent with generation in an inhomogeneous source obeying stochastic growth theory (SGT) and with the emission mechanism being purely linear (either direct or indirect). A nonlinear mechanism is viable only if it produces lognormal statistics when suitably ensemble-averaged. Variations in the SGT fit parameters with phase imply that the radiation is relatively more variable near the pulse edges than near the center, as found in earlier work. In contrast, Vela's giant micropulses come from a very restricted phase range and have power-law statistics with indices ($6.7 \pm 0.6$) not inconsistent with nonlinear wave collapse. These results imply that normal pulses have a different source and generation mechanism than giant micropulses, as suggested previously on other grounds.Comment: 10 pages and 14 figures. Accepted by Monthly Notices of the Royal Astronomical Society in April 200

Automated mixed traffic vehicle design AMTV 2

The design of an improved and enclosed Automated Mixed Traffic Transit (AMTT) vehicle is described. AMTT is an innovative concept for low-speed tram-type transit in which suitable vehicles are equipped with sensors and controls to permit them to operate in an automated mode on existing road or walkway surfaces. The vehicle chassis and body design are presented in terms of sketches and photographs. The functional design of the sensing and control system is presented, and modifications which could be made to the baseline design for improved performance, in particular to incorporate a 20-mph capability, are also discussed. The vehicle system is described at the block-diagram-level of detail. Specifications and parameter values are given where available