Pfair scheduling of generalized pinwheel task systems

[[abstract]]The scheduling of generalized pinwheel task systems is considered. It is shown that pinwheel scheduling is closely related to the fair scheduling of periodic task systems. This relationship is exploited to obtain new scheduling algorithms for generalized pinwheel task systems. When compared to traditional pinwheel scheduling algorithms, these new algorithms are both more efficient from a run-time complexity point of view, and have a higher density threshold, on a very large subclass of generalized pinwheel task systems.

Thermodynamics and phase transitions for the Heisenberg model on the pinwheel distorted kagome lattice

We study the Heisenberg model on the pinwheel distorted kagome lattice as observed in the material Rb_2Cu_3SnF_12. Experimentally relevant thermodynamic properties at finite temperatures are computed utilizing numerical linked-cluster expansions. We also develop a Lanczos-based, zero-temperature, numerical linked cluster expansion to study the approach of the pinwheel distorted lattice to the uniform kagome-lattice Heisenberg model. We find strong evidence for a phase transition before the uniform limit is reached, implying that the ground state of the kagome-lattice Heisenberg model is likely not pinwheel dimerized and is stable to finite pinwheel-dimerizing perturbations.Comment: 6 pages, 6 figures, 1 tabl

Pinwheel stabilization by ocular dominance segregation

We present an analytical approach for studying the coupled development of ocular dominance and orientation preference columns. Using this approach we demonstrate that ocular dominance segregation can induce the stabilization and even the production of pinwheels by their crystallization in two types of periodic lattices. Pinwheel crystallization depends on the overall dominance of one eye over the other, a condition that is fulfilled during early cortical development. Increasing the strength of inter-map coupling induces a transition from pinwheel-free stripe solutions to intermediate and high pinwheel density states.Comment: 10 pages, 4 figure

Radiative torques alignment in the presence of pinwheel torques

We study the alignment of grains subject to both radiative torques and pinwheel torques while accounting for thermal flipping of grains. By pinwheel torques we refer to all systematic torques that are fixed in grain body axes, including the radiative torques arising from scattering and absorption of isotropic radiation. We discuss new types of pinwheel torques, which are systematic torques arising from infrared emission and torques arising from the interaction of grains with ions and electrons in hot plasma. We show that both types of torques are long-lived, i.e. may exist longer than gaseous damping time. We compare these torques with the torques introduced by E. Purcell, namely, torques due to H$_2$ formation, the variation of accommodation coefficient for gaseous collisions and photoelectric emission. Furthermore, we revise the Lazarian & Draine model for grain thermal flipping. We calculate mean flipping timescale induced by Barnett and nuclear relaxation for both paramagnetic and superparamagnetic grains, in the presence of stochastic torques associated with pinwheel torques, e.g. the stochastic torques arising from H$_2$ formation, and gas bombardment. We show that the combined effect of internal relaxation and stochastic torques can result in fast flipping for sufficiently small grains and, because of this, they get thermally trapped, i.e. rotate thermally in spite of the presence of pinwheel torques. For sufficiently large grains, we show that the pinwheel torques can increase the degree of grain alignment achievable with the radiative torques by increasing the magnitude of the angular momentum of low attractor points and/or by driving grains to new high attractor points.Comment: 23 pages and 15 figures emulated ApJ style. Thermal flipping and trapping revised; paper accepted to Ap

From the SU(2)SU(2) Quantum Link Model on the Honeycomb Lattice to the Quantum Dimer Model on the Kagom\'e Lattice: Phase Transition and Fractionalized Flux Strings

We consider the $(2+1)$-d $SU(2)$ quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the Kagom\'e lattice. The model has crystalline confined phases with spontaneously broken translation invariance associated with pinwheel order, which is investigated with either a Metropolis or an efficient cluster algorithm. External half-integer non-Abelian charges (which transform non-trivially under the $\mathbb{Z}(2)$ center of the $SU(2)$ gauge group) are confined to each other by fractionalized strings with a delocalized $\mathbb{Z}(2)$ flux. The strands of the fractionalized flux strings are domain walls that separate distinct pinwheel phases. A second-order phase transition in the 3-d Ising universality class separates two confining phases; one with correlated pinwheel orientations, and the other with uncorrelated pinwheel orientations.Comment: 16 pages, 20 figures, 2 tables, two more relevant references and one short paragraph are adde

From the SU(2)SU(2) Quantum Link Model on the Honeycomb Lattice to the Quantum Dimer Model on the Kagom\'e Lattice: Phase Transition and Fractionalized Flux Strings

We consider the $(2+1)$-d $SU(2)$ quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the Kagom\'e lattice. The model has crystalline confined phases with spontaneously broken translation invariance associated with pinwheel order, which is investigated with either a Metropolis or an efficient cluster algorithm. External half-integer non-Abelian charges (which transform non-trivially under the $\mathbb{Z}(2)$ center of the $SU(2)$ gauge group) are confined to each other by fractionalized strings with a delocalized $\mathbb{Z}(2)$ flux. The strands of the fractionalized flux strings are domain walls that separate distinct pinwheel phases. A second-order phase transition in the 3-d Ising universality class separates two confining phases; one with correlated pinwheel orientations, and the other with uncorrelated pinwheel orientations.Comment: 16 pages, 20 figures, 2 tables, two more relevant references and one short paragraph are adde

Symmetry of tilings of the plane

We discuss two new results on tilings of the plane. In the first, we give sufficient conditions for the tilings associated with an inflation rule to be uniquely ergodic under translations, the conditions holding for the pinwheel inflation rule. In the second result we prove there are matching rules for the pinwheel inflation rule, making the system the first known to have complete rotational symmetry.Comment: 5 page

Imaging "Pinwheel"nebulae with optical long-baseline interferometry

Dusty Wolf-Rayet stars are few but remarkable in terms of dust production rates (up to one millionth of solar mass per year). Infrared excesses associated to mass-loss are found in the sub-types WC8 and WC9. Few WC9d stars are hosting a "pinwheel" nebula, indirect evidence of a companion star around the primary. While few other WC9d stars have a dust shell which has been barely resolved so far, the available angular resolution offered by single telescopes is insufficient to confirm if they also host "pinwheel" nebulae or not. In this article, we present the possible detection of such nebula around the star WR118. We discuss about the potential of interferometry to image more "pinwheel" nebulae around other WC9d stars.Comment: To be published soon in the conference proceedin

Pinwheel Scheduling for Fault-tolerant Broadcast Disks in Real-time Database Systems

The design of programs for broadcast disks which incorporate real-time and fault-tolerance requirements is considered. A generalized model for real-time fault-tolerant broadcast disks is defined. It is shown that designing programs for broadcast disks specified in this model is closely related to the scheduling of pinwheel task systems. Some new results in pinwheel scheduling theory are derived, which facilitate the efficient generation of real-time fault-tolerant broadcast disk programs.National Science Foundation (CCR-9308344, CCR-9596282