Dynamical Systems On Three Manifolds Part II: 3-Manifolds,Heegaard Splittings and Three-Dimensional Systems

The global behaviour of nonlinear systems is extremely important in control and systems theory since the usual local theories will only give information about a system in some neighbourhood of an operating point. Away from that point, the system may have totally different behaviour and so the theory developed for the local system will be useless for the global one. In this paper we shall consider the analytical and topological structure of systems on 2- and 3- manifolds and show that it is possible to obtain systems with 'arbitrarily strange' behaviour, i.e., arbitrary numbers of chaotic regimes which are knotted and linked in arbitrary ways. We shall do this by considering Heegaard Splittings of these manifolds and the resulting systems defined on the boundaries.Comment: 15 pages with 9 pictures. Accepted by Int. J. of Bifurcation and Chao

Collision frequencies and energy transfer-ions Scientific report no. 272

Ion energy transfer, collision frequencies, and resonance charge exchange of neutral gases for studying thermal behavior of ion

Thermal Conduction and Ion Temperatures in the Ionosphere

Ion energy balance equation analyzed in study of thermal conduction and ion temperatures in ionospher

Charged Particle Temperatures and Electron Thermal Conductivity in the Upper Atmosphere Scientic Report No. 276

Charged particle temperatures and electron thermal conductivity in upper atmospher

The Temperature Coupling of Ions in the Ionosphere

Temperature coupling investigated of oxygen, helium, and hydrogen ions in ionosphere by theoretical analysi

Collision Frequencies and Energy Transfer- Electrons

Elastic collisions and energy transfer between gases with separate Maxwellian velocity distribution

Modelling dynamic decision making with the ACT-R cognitive architecture

This paper describes a model of dynamic decision making in the Dynamic Stocks and Flows (DSF) task, developed using the ACT-R cognitive architecture. This task is a simple simulation of a water tank in which the water level must be kept constant whilst the inflow and outflow changes at varying rates. The basic functions of the model are based around three steps. Firstly, the model predicts the water level in the next cycle by adding the current water level to the predicted net inflow of water. Secondly, based on this projection, the net outflow of the water is adjusted to bring the water level back to the target. Thirdly, the predicted net inflow of water is adjusted to improve its accuracy in the future. If the prediction has overestimated net inflow then it is reduced, if it has underestimated net inflow it is increased. The model was entered into a model comparison competition-the Dynamic Stocks and Flows Challenge-to model human performance on four conditions of the DSF task and then subject the model to testing on five unseen transfer conditions. The model reproduced the main features of the development data reasonably well but did not reproduce human performance well under the transfer conditions. This suggests that the principles underlying human performance across the different conditions differ considerably despite their apparent similarity. Further lessons for the future development of our model and model comparison challenges are considered

Embedding the Pentagon

The Pentagon Model is an explicit supersymmetric extension of the Standard Model, which involves a new strongly-interacting SU(5) gauge theory at TeV-scale energies. We show that the Pentagon can be embedded into an SU(5) x SU(5) x SU(5) gauge group at the GUT scale. The doublet-triplet splitting problem, and proton decay compatible with experimental bounds, can be successfully addressed in this context. The simplest approach fails to provide masses for the lighter two generations of quarks and leptons; however, this problem can be solved by the addition of a pair of antisymmetric tensor fields and an axion.Comment: 39 page

A Pyramid Scheme for Particle Physics

We introduce a new model, the Pyramid Scheme, of direct mediation of SUSY breaking, which is compatible with the idea of Cosmological SUSY Breaking (CSB). It uses the trinification scheme of grand unification and avoids problems with Landau poles in standard model gauge couplings. It also avoids problems, which have recently come to light, associated with rapid stellar cooling due to emission of the pseudo Nambu-Goldstone Boson (PNGB) of spontaneously broken hidden sector baryon number. With a certain pattern of R-symmetry breaking masses, a pattern more or less required by CSB, the Pyramid Scheme leads to a dark matter candidate that decays predominantly into leptons, with cross sections compatible with a variety of recent observations. The dark matter particle is not a thermal WIMP but a particle with new strong interactions, produced in the late decay of some other scalar, perhaps the superpartner of the QCD axion, with a reheat temperature in the TeV range. This is compatible with a variety of scenarios for baryogenesis, including some novel ones which exploit specific features of the Pyramid Scheme.Comment: JHEP Latex, 32 pages, 1 figur

Baryogenesis, Dark Matter and the Pentagon

We present a new mechanism for baryogenesis, which links the baryon asymmetry of the universe to the dark matter density. The mechanism arises naturally in the Pentagon model of TeV scale physics. In that context, it forces a re-evaluation of some of the assumptions of the model, and we detail the changes that are required in order to fit observations.Comment: JHEP3 LaTeX, 15 pages. New version corrects errors in the electroweak baryon violating and matter radiation temperatures, which were pointed out by the referee. Substantial quantitative but no qualitative change to our conclusion