Ensemble Dependence of the Transient Fluctuation Theorem

The Fluctuation Theorem gives an analytical expression for the probability of observing second law violating dynamical fluctuations, in nonequilibrium systems. At equilibrium statistical mechanical fluctuations are known to be ensemble dependent. In this paper we generalise the Transient and Steady State Fluctuation Theorems to various nonequilibrium dynamical ensembles. The Transient and Steady State Fluctuation Theorem for an isokinetic ensemble of isokinetic trajectories is tested using nonequilibrium molecular dynamics simulations of shear flow.We would like to thank the Australian Research Council for the support of this project

Ensemble Dependence of the Transient Fluctuation Theorem

The Fluctuation Theorem gives an analytical expression for the probability of observing second law violating dynamical fluctuations, in nonequilibrium systems. At equilibrium statistical mechanical fluctuations are known to be ensemble dependent. In this paper we generalise the Transient and Steady State Fluctuation Theorems to various nonequilibrium dynamical ensembles. The Transient and Steady State Fluctuation Theorem for an isokinetic ensemble of isokinetic trajectories is tested using nonequilibrium molecular dynamics simulations of shear flow.Comment: 16 pages, 1 table, 4 figures; presentation of generalised formulae and discussion clarifie

The Fluctuation Theorem and Green-Kubo Relations

Green-Kubo and Einstein expressions for the transport coefficients of a fluid in a nonequilibrium steady state can be derived using the Fluctuation Theorem and by assuming the probability distribution of the time-averaged dissipative flux is Gaussian. These expressions are consistent with those obtained using linear response theory and are valid in the linear regime. It is shown that these expressions are however, not valid in the nonlinear regime where the fluid is driven far from equilibrium. We advance an argument for why these expression are only valid in the linear response, zero field limit.Comment: 32 pages, inc. 6 figures Discussion and notation improve

Lorenz-Mie theory for 2D scattering and resonance calculations

This PhD tutorial is concerned with a description of the two-dimensional generalized Lorenz-Mie theory (2D-GLMT), a well-established numerical method used to compute the interaction of light with arrays of cylindrical scatterers. This theory is based on the method of separation of variables and the application of an addition theorem for cylindrical functions. The purpose of this tutorial is to assemble the practical tools necessary to implement the 2D-GLMT method for the computation of scattering by passive scatterers or of resonances in optically active media. The first part contains a derivation of the vector and scalar Helmholtz equations for 2D geometries, starting from Maxwell's equations. Optically active media are included in 2D-GLMT using a recent stationary formulation of the Maxwell-Bloch equations called steady-state ab initio laser theory (SALT), which introduces new classes of solutions useful for resonance computations. Following these preliminaries, a detailed description of 2D-GLMT is presented. The emphasis is placed on the derivation of beam-shape coefficients for scattering computations, as well as the computation of resonant modes using a combination of 2D-GLMT and SALT. The final section contains several numerical examples illustrating the full potential of 2D-GLMT for scattering and resonance computations. These examples, drawn from the literature, include the design of integrated polarization filters and the computation of optical modes of photonic crystal cavities and random lasers.Comment: This is an author-created, un-copyedited version of an article published in Journal of Optics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from i

Earnouts: A Study of Financial Contracting in Acquisition Agreements

We empirically examine earnout contracts, which provide for contingent payments in acquisition agreements. Our analysis reveals considerable heterogeneity in the terms of earnout contracts, i.e. the potential size of the earnout, the performance measure on which the contingent payment is based, the period over which performance is measured, the frequency with which performance is measured, and the form of payment for the earnout. Consistent with the costly contracting hypothesis, we find that the terms of earnout contracts are associated with measures of target valuation uncertainty, target growth opportunities, and the degree of post-acquisition integration between target and acquirer. We conclude that earnouts are structured to minimize the costs of adverse selection and moral hazard in acquisition negotiations.

On the Application of the Gallavotti-Cohen Fluctuation Relation to Thermostatted Steady States Near Equilibrium

The fluctuation relation of the Gallavotti-Cohen Fluctuation Theorem (GCFT) concerns fluctuations in the phase space compression rate of dissipative, reversible dynamical systems. It has been proven for Anosov systems, but it is expected to apply more generally. This raises the question of which non-Anosov systems satisfy the fluctuation relation. We analyze time dependent fluctuations in the phase space compression rate of a class of N-particle systems that are at equilibrium or in near equilibrium steady states. This class does not include Anosov systems or isoenergetic systems, however, it includes most steady state systems considered in molecular dynamics simulations of realistic systems. We argue that the fluctuations of the phase space compression rate of these systems at or near equilibrium do not satisfy the fluctuation relation of the GCFT, although the discrepancies become somewhat smaller as the systems move further from equilibrium. In contrast, similar fluctuation relations for an appropriately defined dissipation function appear to hold both near and far from equilibrium.Comment: 46 pages, for publication in PR

Generalised Fluctuation Formula

We develop a General Fluctuation Formula for phase variables that are odd under time reversal. Simulations are used to verify the new formula.Comment: 10 pages, 5 figures, submitted to Procedings of the 3rd Tohwa University International Conference of Statistical Physics, Nov 8-12, 1999 (AIP Conferences Series