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    ABSTRACT: This paper describes the operation of a new design of wave energy converter. The design consists of a buoyant tethered submerged circular cylinder which is allowed to pitch freely about an axis below its centre. Within the body of the cylinder a fluid half fills an annular tank whose shaped inner walls allow the fundamental sloshing mode of the fluid be to tuned to any period of interest. The pitching motion of the cylinder in waves induces a sloshing motion inside the annular tank which in turns drives an air turbine connecting air chambers above the two isolated internal free surfaces. The concept behind this design is to couple resonances of the pitching cylinder with natural sloshing resonances of the internal water tank and thus achieve a broadbanded power response over a wide range of physically-relevant wave periods. Mathematically, the problem introduces new techniques to solve the series of complex internal forced sloshing problems that arise and to efficiently determine key hydrodynamic coefficients needed for the calculation of the power from the device. The results show that practical configurations can be found in which the efficiency of a two-dimensional cylindrical device is close to its maximum theoretical limit over the target range of periods from 55 to 1111 seconds.
    European Journal of Mechanics - B/Fluids 09/2014;
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    ABSTRACT: Continuous action space games are ubiquitous in economics. However, whilst learning dynamics in normal form games with finite action sets are now well studied, it is not until recently that their continuous action space counterparts have been examined. We extend stochastic fictitious play to the continuous action space framework. In normal form games with finite action sets the limiting behaviour of a discrete time learning process is often studied using its continuous time counterpart via stochastic approximation. In this paper we study stochastic fictitious play in games with continuous action spaces using the same method. This requires the asymptotic pseudo-trajectory approach to stochastic approximation to be extended to Banach spaces. In particular the limiting behaviour of stochastic fictitious play is studied using the associated smooth best response dynamics on the space of finite signed measures. Using this approach, stochastic fictitious play is shown to converge to an equilibrium point in two-player zero-sum games and a stochastic fictitious play-like process is shown to converge to an equilibrium in negative definite single population games.
    Journal of Economic Theory 07/2014;
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    ABSTRACT: We consider an elastic plate of infinite length and constant width supported simply along its two parallel edges and having a finite length crack along its centreline. In particular, we look for and find trapped modes (localised oscillations) in the presence of the crack. An explicit wide-spacing approximation based on the Wiener–Hopf technique applied to incident wave scattering by semi-infinite cracks is complemented by an exact formulation of the problem in the form of integro-differential equations. An application of a Galerkin method for the numerical calculation of results from the latter method leads to a novel explicit ‘small-spacing’ approximation. In combination with the wide-spacing results this is shown to provide accurate results for all lengths of crack.
    Wave Motion 04/2014;
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    ABSTRACT: We extend to the function field setting the heuristic previously developed, by Conrey, Farmer, Keating, Rubinstein and Snaith, for the integral moments and ratios of L -functions defined over number fields. Specifically, we give a heuristic for the moments and ratios of a family of L -functions associated with hyperelliptic curves of genus g over a fixed finite field FqFq in the limit as g→∞g→∞. Like in the number field case, there is a striking resemblance to the corresponding formulae for the characteristic polynomials of random matrices. As an application, we calculate the one-level density for the zeros of these L-functions.
    Journal of Number Theory. 01/2014; 142:102–148.
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    ABSTRACT: Rationale: A recent study published in Circulation Research by Gao et al used sinoatrial node (SAN)-targeted, incomplete Ncx1 knockout in mice to explore the role of the Na(+)/Ca(2+) exchanger (NCX) in cardiac pacemaker. The authors concluded that NCX is required for increasing sinus rates, but not for maintaining resting heart rate. This conclusion was based, in part, on numeric model simulations performed by Gao et al that reproduced their experimental results of unchanged action potentials in the knockout SAN cells. The authors, however, did not simulate the NCX current (INCX), that is, the subject of the study. Objective: We extended numeric examinations to simulate INCX in their incomplete knockout SAN cells that is crucial to interpret the study results. Methods and Results: INCX and Ca(2+) dynamics were simulated using different contemporary numeric models of SAN cells. We found that minimum diastolic Ca(2+) levels and INCX amplitudes generated by remaining NCX molecules (only 20% of control) remained almost unchanged. Simulations using a new local Ca(2+) control model indicate that these powerful compensatory mechanisms involve complex local cross-talk of Ca(2+) cycling proteins and NCX. Specifically, lower NCX expression facilitates Ca(2+)-induced Ca(2+) release and larger local Ca(2+) releases that stabilize diastolic INCX. Further reduction of NCX expression results in arrhythmia and halt of automaticity. Conclusions: Remaining NCX molecules in the incomplete knockout model likely produce almost the same diastolic INCX as in wild-type cells. INCX contribution is crucially important for both basal automaticity of SAN cells and during the fight-or-flight reflex.
    Circulation Research 10/2013; 113(10):e94-e100.
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    ABSTRACT: We study reaction dynamics on a model potential energy surface exhibiting post-transition state bifurcation in the vicinity of a valley ridge inflection (VRI) point. We compute fractional yields of products reached after the VRI region is traversed, both with and without dissipation. It is found that apparently minor variations in the potential lead to significant changes in the reaction dynamics. Moreover, when dissipative effects are incorporated, the product ratio depends in a complicated and highly non-monotonic fashion on the dissipation parameter. Dynamics in the vicinity of the VRI point itself play essentially no role in determining the product ratio, except in the highly dissipative regime.
    The Journal of Chemical Physics 10/2013; 139(15):154108.
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    ABSTRACT: In 1964, Bell discovered that quantum mechanics is a nonlocal theory. Three years later, in a seemingly unconnected development, Harsanyi introduced the concept of Bayesian games. Here we show that, in fact, there is a deep connection between Bell nonlocality and Bayesian games, and that the same concepts appear in both fields. This link offers interesting possibilities for Bayesian games, namely of allowing the players to receive advice in the form of nonlocal correlations, for instance using entangled quantum particles or more general no-signalling boxes. This will lead to novel joint strategies, impossible to achieve classically. We characterize games for which nonlocal resources offer a genuine advantage over classical ones. Moreover, some of these strategies represent equilibrium points, leading to the notion of quantum/no-signalling Nash equilibrium. Finally, we describe new types of question in the study of nonlocality, namely the consideration of nonlocal advantage given a set of Bell expressions.
    Nature Communications 07/2013; 4:2057.
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    ABSTRACT: The concept of Lyapunov exponent has long occupied a central place in the theory of Anderson localization; its interest in this particular context is that it provides a reasonable measure of the localization length. The Lyapunov exponent also features prominently in the theory of products of random matrices pioneered by Furstenberg. After a brief historical survey, we describe some recent work that exploits the close connections between these topics. We review the known solvable cases of disordered quantum mechanics involving random point scatterers and discuss a new solvable case. Finally, we point out some limitations of the Lyapunov exponent as a means of studying localization properties.
    Journal of Physics A Mathematical and Theoretical 06/2013; 46(25):254003.
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    ABSTRACT: We analyze recent experiments that show that a cylinder can be suspended in a stable position by placing it on a vertically moving belt that is covered by a thin layer of very viscous oil. The weight of the cylinder is supported by viscous forces in the fluid layer, and the cylinder rotates with respect to its axis in the direction of the belt motion. We propose a simple model for stable suspension of the cylinder, based on lubrication ideas.
    Physical Review E 06/2013; 87(6-2):065001.
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    ABSTRACT: We study the evolution of an initially conical metal surface when it is heated. For all cone angles α from close to zero to 90 degrees, self-similar solutions with rounded tips are found, whose radius of curvature scales like (time)^{1/4}. For α≳3^{∘}, theoretical profiles agree very well with experiment. For smaller cone angles, we find pronounced oscillations near the tip, which presumably are responsible for the experimentally observed fragility of such tips. The amplitude and wavelength of oscillations are characterized asymptotically.
    Physical Review E 06/2013; 87(6-1):062408.
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