3,030 research outputs found

    Transport in Almost Integrable Models: Perturbed Heisenberg Chains

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    The heat conductivity kappa(T) of integrable models, like the one-dimensional spin-1/2 nearest-neighbor Heisenberg model, is infinite even at finite temperatures as a consequence of the conservation laws associated with integrability. Small perturbations lead to finite but large transport coefficients which we calculate perturbatively using exact diagonalization and moment expansions. We show that there are two different classes of perturbations. While an interchain coupling of strength J_perp leads to kappa(T) propto 1/J_perp^2 as expected from simple golden-rule arguments, we obtain a much larger kappa(T) propto 1/J'^4 for a weak next-nearest neighbor interaction J'. This can be explained by a new approximate conservation law of the J-J' Heisenberg chain.Comment: 4 pages, several minor modifications, title change

    Predation Risk and the Importance of Cover for Juvenile Rainbow Trout in Lentic Systems

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    Juvenile rainbow trout Oncorhynchus mykiss stocked in midelevation reservoirs in Utah inhabit shallow nearshore areas and are vulnerable to predation from piscivorous fish and birds. We determined the use and importance of nearshore habitats by (1) measuring habitat selection by, prey availability to, and feeding of juvenile rainbow trout in two reservoirs with populations of predators, and (2) measuring survival and growth rates in the presence and absence of cover in a pond experiment where adult brown trout Salmo trutta were predators. In the reservoirs juvenile rainbow trout (60–120 mm standard length) were abundant in complex inshore habitats but avoided simple habitats such as sand and gravel during the day. At night, however, juvenile rainbow trout in both reservoirs were observed in more exposed areas, and they rested on the bottom. Measurements of gut fullness indicated that juvenile rainbow trout fed actively on large Daphnia spp. during the day but little at night. Because large daphnia were usually more abundant offshore than inshore in both reservoirs, selection of inshore cover is believed to be primarily a response to greater predation risk offshore. In the pond experiment, the presence of brown trout significantly increased mortality of juvenile rainbow trout, decreased their growth rates, and caused them to avoid open-water areas. The presence of cover significantly decreased predation rates but did not affect growth of the juvenile rainbow trout. Fisheries managers should consider augmenting cover in reservoirs and lakes where juvenile trout are stocked to minimize losses of trout to predators

    Aubry transition studied by direct evaluation of the modulation functions of infinite incommensurate systems

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    Incommensurate structures can be described by the Frenkel Kontorova model. Aubry has shown that, at a critical value K_c of the coupling of the harmonic chain to an incommensurate periodic potential, the system displays the analyticity breaking transition between a sliding and pinned state. The ground state equations coincide with the standard map in non-linear dynamics, with smooth or chaotic orbits below and above K_c respectively. For the standard map, Greene and MacKay have calculated the value K_c=.971635. Conversely, evaluations based on the analyticity breaking of the modulation function have been performed for high commensurate approximants. Here we show how the modulation function of the infinite system can be calculated without using approximants but by Taylor expansions of increasing order. This approach leads to a value K_c'=.97978, implying the existence of a golden invariant circle up to K_c' > K_c.Comment: 7 pages, 5 figures, file 'epl.cls' necessary for compilation provided; Revised version, accepted for publication in Europhysics Letter

    Shape optimisation using Computational Fluid Dynamics and Evolutionary Algorithms

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    This is the author accepted manuscript.Optimisation of designs using Computational Fluid Dynamics (CFD) are frequently performed across many fields of research, such as the optimisation of an aircraft wing to reduce drag, or to increase the efficiency of a heat exchanger. General optimisation strategies involves altering design variables with a view to improve appropriate objective function(s). Often the objective function(s) are non-linear and multi-modal, and thus polynomial time algorithms for solving such problems may not be available. In such cases, applying Evolutionary Algorithms (EAs - a class of stochastic global optimisation techniques inspired from natural evolution) may locate good solutions within a practical time frame. The traditional CFD design optimisation process is often based on a ‘trial-and-error type approach. Starting from an initial geometry, Computational Aided Design changes are introduced manually based on results from a limited number of design iterations and CFD analyses. The process is usually complex, time-consuming and relies heavily on engineering experience, thus making the overall design procedure inconsistent, i.e. different ‘best’ solutions are obtained from different designers. [...]This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant (reference number: EP/M017915/1) for the University of Exeter’s College of Engineering, Mathematics, and Physical Sciences

    Automatic shape optimisation of the turbine-99 draft tube

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    This is the author accepted manuscript.INTRODUCTION The performance of a hydraulic reaction turbine is significantly affected by the efficiency of its draft tube. Factors which impede the tube’s performance include the geometrical shape (profile), and velocity distribution at the inflow. So far, the design of draft tubes has been improved through experimental observations resulting in empirical formulae or ‘rules of thumb’. The use of Computational Fluid Dynamics (CFD) in this design process has only been a recent addition due to its robustness and cost-effectivenesses with increasing availability to computational power. The flexibility of CFD, allowing for comprehensive analysis of complex profiles, is especially appealing for optimising the design. Hence, there is a need for developing an accurate and reliable CFD approach together with an efficient optimisation strategy. Flows through a turbine draft tube are characterised as turbulent with a range of flow phenomena, e.g. unsteadiness, flow separation, and swirling flow. With the aim of improving the techniques for analysing such flows, the turbomachinery community have proposed a standard test case in the form of the Turbine-99 draft tube [1]. Along with this standard geometry, with the aim of simulating the swirling inflow, an additional runner proposed by Cervantes [2] is included in the present work. The draft tube geometry is shown in Fig.1. The purpose of this abstract is to outline the framework developed to achieve the automated shape optimisation of this draft tube.This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant (reference number: EP/M017915/1) for the University of Exeters College of Engineering, Mathematics, and Physical Sciences
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