235,830 research outputs found

    Green operators for low regularity spacetimes

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    In this paper we define and construct advanced and retarded Green operators for the wave operator on spacetimes with low regularity. In order to do so we require that the spacetime satisfies the condition of generalised hyperbolicity which is equivalent to well- posedness of the classical inhomogeneous problem with zero initial data where weak solutions are properly supported. Moreover, we provide an explicit formula for the kernel of the Green operators in terms of an arbitrary eigenbasis of H 1 and a suitable Green matrix that solves a system of second order ODEs

    Generalised hyperbolicity in spacetimes with string-like singularities

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    In this paper we present well-posedness results of the wave equation in H1H^{1} for spacetimes that contain string-like singularities. These results extend a framework able to characterise gravitational singularities as obstruction to the dynamics of test fields rather than point particles. In particular, we discuss spacetimes with cosmic strings and the relation of our results to the Strong Cosmic Censorship Conjecture.Comment: Accepted for publication in Classical and Quantum Gravit

    A salary system for the assignment problem

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    We propose a modification to the concept of the potential of agame à la Hart-Mas Colell to determine a salary system for theassignment problem. We obtain explicit formulas for the potentialof the assignment problem and for it's corresponding salarysystem. Also, we establish some properties of this salary systemand we give an interpretation in terms of the Shapley value.assignment problem

    Nonlinear chiral refrigerators

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    We investigate a mesoscopic refrigerator based on chiral quantum Hall edge channels. We discuss a three-terminal cooling device in which charge transport occurs between a pair of voltage-biased terminals only. The third terminal, which is to be cooled, is set as a voltage probe with vanishing particle flux. This largely prevents the generation of direct Joule heating which ensures a high coefficient of performance. Cooling operation is based on energy-dependent quantum transmissions. The latter are implemented with the aid of two tunable scattering resonances (quantum dots). To find the optimal performance point and the largest temperature difference created with our refrigerator, it is crucial to address the nonlinear regime of transport, accounting for electron-electron interaction effects. Our numerical simulations show that the maximal cooling power can be tuned with the quantum dot couplings and energy levels. Further, we provide analytical expressions within a weakly nonlinear scattering-matrix formalism which allow us to discuss the conditions for optimal cooling in terms of generalized thermopowers. Our results are important for the assessment of chiral conductors as promising candidates for efficient quantum refrigerators with low dissipation.Comment: 9 pages, 4 figures. v2: minor changes. Published versio

    India: the next superpower?: corruption in India

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    The momentum of last year’s hunger strike by the anti-corruption campaigner Kisan ‘Anna’ Hazare currently sees India’s parliament wrestling with the formation of a national corruption ombudsman. Hazare’s campaign rests upon the proposition that the democratic ideals with which the Indian state was formed in 1947 are all too often subverted by the self-interest of public servants. Hazare’s supporters argue that this process has two primary effects. First, corruption allows wealthier citizens to access resources and preferential state treatment to which they are not entitled. Second, corruption constitutes a drain on the coffers of many ordinary Indians, in the form of demands for bribes by state functionaries, without which their services cannot necessarily be procured