title: Rapid dissipation in a current sheet driven by footpoints motions

authors: Fruit, G.

subjects: Magnetohydrodynamics

abstract: Context.Wave energy dissipation by viscous and resistive damping in magnetic coronal plasmas is addressed. A two and one half dimensional, line-tied magnetic channel is considered whose footpoints are disturbed by buffeting motions of the photosphere.
Aims.The aim of the analysis is to determine how effectively shear Alfvén waves, driven by footpoint motions and resonating in the channel, can be damped by visco-resistive friction.
Methods.The problem is analyzed using a mixture of numerical and analytic techniques. Dynamic simulations, based on a cyclic footpoint driver, show that phase mixing resulting from variations in the magnetic field of the channel is instrumental in setting up a permanent "resonance regime" for the system. Analytic methods are used to analyze the resonance regime and to develop scaling laws for the rate of energy dissipation.
Results.We show that in the general case where the Alfvén velocity profile may be linearized around the resonance, the dissipation rate is "fast" in that it is not limited by small damping coefficients. Although large energies can accumulate within the channel in the limit of very small damping, we show that by tuning the driver to low frequencies, both the energy level and the dissipation rate can be made insensitive to the level of the damping.

text: Rapid dissipation in a current sheet driven by footpoints motions Context.Wave energy dissipation by viscous and resistive damping in magnetic coronal plasmas is addressed. A two and one half dimensional, line-tied magnetic channel is considered whose footpoints are disturbed by buffeting motions of the photosphere.
Aims.The aim of the analysis is to determine how effectively shear Alfvén waves, driven by footpoint motions and resonating in the channel, can be damped by visco-resistive friction.
Methods.The problem is analyzed using a mixture of numerical and analytic techniques. Dynamic simulations, based on a cyclic footpoint driver, show that phase mixing resulting from variations in the magnetic field of the channel is instrumental in setting up a permanent "resonance regime" for the system. Analytic methods are used to analyze the resonance regime and to develop scaling laws for the rate of energy dissipation.
Results.We show that in the general case where the Alfvén velocity profile may be linearized around the resonance, the dissipation rate is "fast" in that it is not limited by small damping coefficients. Although large energies can accumulate within the channel in the limit of very small damping, we show that by tuning the driver to low frequencies, both the energy level and the dissipation rate can be made insensitive to the level of the damping.

year: 2006

title: Optimal Task Scheduling in a Flexible Manufacturing System using Model Checking

authors: Malik, Robi

subjects: Applications

abstract: This paper demonstrates the use of model checking to solve the problem of optimal task scheduling in a flexible manufacturing system. The system is modelled as a discrete event system, for which the least restrictive safe behaviour is synthesised according to supervisory control theory. Then timing constraints are added to the model in the form of extended finite-state machines, and time-optimal schedules are computed using the discrete event systems and model checking tool Supremica. In the case study considered in this paper, which previously was only solved heuristically, the method successfully produces optimal schedules to manufacture up to 30 products of two different types. The method is furthermore used to find an optimal cycle, solving the scheduling problem of the case study for an arbitrary number of products in optimal or asymptotically close to optimal time.

text: Optimal Task Scheduling in a Flexible Manufacturing System using Model Checking This paper demonstrates the use of model checking to solve the problem of optimal task scheduling in a flexible manufacturing system. The system is modelled as a discrete event system, for which the least restrictive safe behaviour is synthesised according to supervisory control theory. Then timing constraints are added to the model in the form of extended finite-state machines, and time-optimal schedules are computed using the discrete event systems and model checking tool Supremica. In the case study considered in this paper, which previously was only solved heuristically, the method successfully produces optimal schedules to manufacture up to 30 products of two different types. The method is furthermore used to find an optimal cycle, solving the scheduling problem of the case study for an arbitrary number of products in optimal or asymptotically close to optimal time.

year: 2018

title: Katoa: A descriptive, comparative and historical analysis

authors: Wessels, Kanauhea Janion

subjects: discontinuous quantification

abstract: Katoa, approximately translated as ‘all, every’, functions as the universal quantifier in te reo Māori (the Māori language), inherited from Proto Polynesian *katoa. Less well known is its occurrence as a postnominal modifier in singular noun phrases, contributing the meaning of ‘whole’, and as a nominal head meaning ‘all (of them), the whole (of it)’. As a postverbal modifier, katoa can quantify a subject noun phrase with the same meanings of ‘all, every’ and ‘whole’, and it can modify situations expressed by the verb, meaning ‘wholly, completely’. In this paper, we examine the behaviour of katoa in te reo Māori, comparing some properties of katoa with the behaviour of quantifiers in related Polynesian languages. This, in turn, informs our understanding of the prehistory of quantification in Polynesian, where we observe evidence of both retention and replacement of quantifier forms.

text: Katoa: A descriptive, comparative and historical analysis Katoa, approximately translated as ‘all, every’, functions as the universal quantifier in te reo Māori (the Māori language), inherited from Proto Polynesian *katoa. Less well known is its occurrence as a postnominal modifier in singular noun phrases, contributing the meaning of ‘whole’, and as a nominal head meaning ‘all (of them), the whole (of it)’. As a postverbal modifier, katoa can quantify a subject noun phrase with the same meanings of ‘all, every’ and ‘whole’, and it can modify situations expressed by the verb, meaning ‘wholly, completely’. In this paper, we examine the behaviour of katoa in te reo Māori, comparing some properties of katoa with the behaviour of quantifiers in related Polynesian languages. This, in turn, informs our understanding of the prehistory of quantification in Polynesian, where we observe evidence of both retention and replacement of quantifier forms.

year: 2024