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

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.

An algorithm for two-dimensional mesh generation based on the pinwheel tiling

We propose a new two-dimensional meshing algorithm called PINW able to generate meshes that accurately approximate the distance between any two domain points by paths composed only of cell edges. This technique is based on an extension of pinwheel tilings proposed by Radin and Conway. We prove that the algorithm produces triangles of bounded aspect ratio. This kind of mesh would be useful in cohesive interface finite element modeling when the crack propagation pathis an outcome of a simulation process.Comment: Short version appears in Proceedings of 2004 International Meshing Roundtable at http://www.imr.sandia.go

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

Symmetry considerations and development of pinwheels in visual maps

Neurons in the visual cortex respond best to rod-like stimuli of given orientation. While the preferred orientation varies continuously across most of the cortex, there are prominent pinwheel centers around which all orientations a re present. Oriented segments abound in natural images, and tend to be collinear}; neurons are also more likely to be connected if their preferred orientations are aligned to their topographic separation. These are indications of a reduced symmetry requiring joint rotations of both orientation preference and the underl ying topography. We verify that this requirement extends to cortical maps of mo nkey and cat by direct statistical analysis. Furthermore, analytical arguments and numerical studies indicate that pinwheels are generically stable in evolving field models which couple orientation and topography