An ultradiscrete matrix version of the fourth Painleve equation

We establish a matrix generalization of the ultradiscrete fourth Painlev\'e equation (ud-PIV). Well-defined multicomponent systems that permit ultradiscretization are obtained using an approach that relies on a group defined by constraints imposed by the requirement of a consistent evolution of the systems. The ultradiscrete limit of these systems yields coupled multicomponent ultradiscrete systems that generalize ud-PIV. The dynamics, irreducibility, and integrability of the matrix valued ultradiscrete systems are studied.Comment: 12 pages, 12 figures, Latex2e, Submitted to J. Phys. A, corrections mad

Evaluation of glass resin coatings for solar cell applications

Using a variety of non-vacuum deposition techniques coatings were implemented on silicon solar cells and arrays of cells interconnected on Kapton substrates. The coatings provide both antireflection optical matching and environmental protection. Reflectance minima near 2% was achieved at a single wavelength in the visible. Reflectance averaging below 5% across the useful collection range was demonstrated. The coatings and methods of deposition were: (1) Ta2O5 spun, dipped or sprayed; (2) Ta2O5.SiO2 spun, dipped or sprayed; (3) GR908 (SiO2) spun, dipped, or sprayed. Total coating thickness were in the range of 18 microns to 25 microns. The coatings and processes are compatible with single cells or cells mounted on Kapton substrates

Thick-film materials for silicon photovoltaic cell manufacture

Thick film technology is applicable to three areas of silicon solar cell fabrication; metallization, junction formation, and coating for protection of screened ohmic contacts, particularly wrap around contacts, interconnection and environmental protection. Both material and process parameters were investigated. Printed ohmic contacts on n- and p-type silicon are very sensitive to the processing parameters of firing time, temperature, and atmosphere. Wrap around contacts are easily achieved by first printing and firing a dielectric over the edge and subsequently applying a low firing temperature conductor. Interconnection of cells into arrays can be achieved by printing and cofiring thick film metal pastes, soldering, or with heat curing conductive epoxies on low cost substrates. Printed (thick) film vitreous protection coatings do not yet offer sufficient optical uniformity and transparency for use on silicon. A sprayed, heat curable SiO2 based resin shows promise of providing both optical matching and environmental protection

Geology of the Snap Lake kimberlite intrusion, Northwest Territories, Canada: field observations and their interpretation

The Cambrian (523 Ma) Snap Lake hypabyssal kimberlite intrusion, Northwest Territories, Canada, is a complex segmented diamond-bearing ore-body. Detailed geological investigations suggest that the kimberlite is a multi-phase intrusion with at least four magmatic lithofacies. In particular, olivine-rich (ORK) and olivine-poor (OPK) varieties of hypabyssal kimberlite have been identified. Key observations are that the olivine-rich lithofacieshas a strong tendency to be located where the intrusion is thickest and that there is a good correlation between intrusion thickness, olivine crystal size and crystal content. Heterogeneities in the lithofacies are attributed to variations in intrusion thickness and structural complexities. The geometry and distribution of lithofacies points to magmaticco-intrusion, and flow segregation driven by fundamental rheological differences between the two phases. We envisage that the low-viscosity OPK magma acted as a lubricant for the highly viscous ORK magma. The presenceof such low-viscosity, crystal-poor magmas may explain how crystal-laden kimberlite magmas (>60 vol.%) are able to reach the surface during kimberlite eruptions. We also document the absence of crystal settling and the development of an unusual subvertical fabric of elongate olivine crystals, which are explained by rapid degassing-induced quench crystallization of the magmas during and after intrusio

Compton Polarimetry at a TEV Collider

An electron beam polarization of 80% or greater will be a key feature of a 1 TeV Linear Collider. Accurate measurements of the beam polarization will therefore be needed. We discuss design considerations and capabilities for a Compton-scattering polarimeter located in the extraction line from the Interaction Point. Polarization measurements with 1% accuracy taken parasitic to collision data look feasible, but detailed simulations are needed. Polarimeter design issues are similar for both electron-positron and electron-electron collider modes, though beam disruption creates more difficulties for the electron-electron mode.Comment: 7 pages, 5 figure

Resonance bifurcations from robust homoclinic cycles

We present two calculations for a class of robust homoclinic cycles with symmetry Z_n x Z_2^n, for which the sufficient conditions for asymptotic stability given by Krupa and Melbourne are not optimal. Firstly, we compute optimal conditions for asymptotic stability using transition matrix techniques which make explicit use of the geometry of the group action. Secondly, through an explicit computation of the global parts of the Poincare map near the cycle we show that, generically, the resonance bifurcations from the cycles are supercritical: a unique branch of asymptotically stable period orbits emerges from the resonance bifurcation and exists for coefficient values where the cycle has lost stability. This calculation is the first to explicitly compute the criticality of a resonance bifurcation, and answers a conjecture of Field and Swift in a particular limiting case. Moreover, we are able to obtain an asymptotically-correct analytic expression for the period of the bifurcating orbit, with no adjustable parameters, which has not proved possible previously. We show that the asymptotic analysis compares very favourably with numerical results.Comment: 24 pages, 3 figures, submitted to Nonlinearit

Ignorance can be evolutionarily beneficial

Information is increasingly being viewed as a resource used by organisms to increase their fitness. Indeed, it has been formally shown that there is a sensible way to assign a reproductive value to information and it is non-negative. However, all of this work assumed that information collection is cost-free. Here, we account for such a cost and provide conditions for when the reproductive value of information will be negative. In these instances, counter-intuitively, it is in the interest of the organism to remain ignorant. We link our results to empirical studies where Bayesian behaviour appears to break down in complex environments and provide an alternative explanation of lowered arousal thresholds in the evolution of sleep.Comment: 5 pages, submitte