10 resultados para Number Theory

em Cambridge University Engineering Department Publications Database


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The Reynolds number influence on turbulent blocking effects by a rigid plane boundary is studied using direct numerical simulation (DNS). A new forcing method using 'simple model eddies' (Townsend 1976) for DNS of stationary homogeneous isotropic turbulence is proposed. A force field is obtained in real space by sprinkling many space-filling 'simple model eddies' whose centers are randomly but uniformly distributed in space and whose axes of rotation are random. The method is applied to a shear-free turbulent boundary layer over a rigid plane boundary and the blocking effects are investigated. The results show that stationary homogeneous isotropic turbulence is generated in real space using the present method. By using different model eddies with different sizes and rotation speeds, we could change the turbulence properties such as the integral and micro scales, the turbulent Reynolds number and the isotropy of turbulence. Turbulence intensities near the wall showed good agreements with the previous measurement and the linear analysis based on a rapid distortion theory (RDT). The splat effect (i.e., turbulence intensities of the components parallel to the boundary are amplified) occurs near the boundary and the viscous effect prohibits the splat effect at the quasi steady state at low Reynolds number.

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The Reynolds number influence on turbulent blocking effects by a rigid plane boundary is studied using direct numerical simulation (DNS). A new forcing method proposed in the second report using Townsend's "simple model eddies" for DNS was extended to generate axisymmetric anisotropic turbulence. A force field is obtained in real space by sprinkling many space-filling "simple model eddies" whose centers are randomly but uniformly distributed in space. The axes of rotation are controlled in this study to generate axisymmetric anisotropic turbulence. The method is applied to a shear-free turbulent boundary layer over a rigid plane boundary and the blocking effects for anisotropic turbulence are investigated. The results show that stationary axisymmetric anisotropic turbulence is generated using the present method. Turbulence intensities near the wall showed good agreements with the rapid distortion theory (RDT) for small t (t ≪ TL), where TL. is the eddy turnover time. The splat effect (i. e. turbulence intensities of the components parallel to the surface are amplified) occurs near the boundary and the viscous effect attenuates the splat effect at the quasi steady state at low Reynolds number as for Isotropic turbulence. Prandtl's secondary flow of the second kind does not occur for low Reynolds number flows, which qualitatively agrees with previous observetion in a mixing-box.

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In recent years, many industrial firms have been able to use roadmapping as an effective process methodology for projecting future technology and for coordinating technology planning and strategy. Firms potentially realize a number of benefits in deploying technology roadmapping (TRM) processes. Roadmaps provide information identifying which new technologies will meet firms' future product demands, allowing companies to leverage R&D investments through choosing appropriately out of a range of alternative technologies. Moreover, the roadmapping process serves an important communication tool helping to bring about consensus among roadmap developers, as well as between participants brought in during the development process, who may communicate their understanding of shared corporate goals through the roadmap. However, there are few conceptual accounts or case studies have made the argument that roadmapping processes may be used effectively as communication tools. This paper, therefore, seeks to elaborate a theoretical foundation for identifying the factors that must be considered in setting up a roadmap and for analyzing the effect of these factors on technology roadmap credibility as perceived by its users. Based on the survey results of 120 different R&D units, this empirical study found that firms need to explore further how they can enable frequent interactions between the TRM development team and TRM participants. A high level of interaction will improve the credibility of a TRM, with communication channels selected by the organization also positively affecting TRM credibility. © 2011 Elsevier Inc.

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Are there any benefits in allowing orders and products to be able to manage their own progress through a supply chain? The notion of associating (and even embedding) information management and reasoning capabilities with a physical product has been discussed for over ten years now. This talk will review the notions of product intelligence and examine the rationales for these models and the practicality of their implementation. Both theoretical and practical issues associated with product intelligence will be examined referencing a number of trial deployments in manufacturing, logistics and aerospace equipment servicing. © 2012 IFAC.

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Zeno behavior is a dynamic phenomenon unique to hybrid systems in which an infinite number of discrete transitions occurs in a finite amount of time. This behavior commonly arises in mechanical systems undergoing impacts and optimal control problems, but its characterization for general hybrid systems is not completely understood. The goal of this paper is to develop a stability theory for Zeno hybrid systems that parallels classical Lyapunov theory; that is, we present Lyapunov-like sufficient conditions for Zeno behavior obtained by mapping solutions of complex hybrid systems to solutions of simpler Zeno hybrid systems defined on the first quadrant of the plane. These conditions are applied to Lagrangian hybrid systems, which model mechanical systems undergoing impacts, yielding simple sufficient conditions for Zeno behavior. Finally, the results are applied to robotic bipedal walking. © 2012 IEEE.

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This paper presents a new formulation for trailing edge noise radiation from rotating blades based on an analytical solution of the convective wave equation. It accounts for distributed loading and the effect of mean flow and spanwise wavenumber. A commonly used theory due to Schlinker and Amiet (1981) predicts trailing edge noise radiation from rotating blades. However, different versions of the theory exist; it is not known which version is the correct one and what the range of validity of the theory is. This paper addresses both questions by deriving Schlinker and Amiet's theory in a simple way and by comparing it to the new formulation, using model blade elements representative of a wind turbine, a cooling fan and an aircraft propeller. The correct form of Schlinker and Amiet's theory (1981) is identified. It is valid at high enough frequency, i.e. for a Helmholtz number relative to chord greater than one and a rotational frequency much smaller than the angular frequency of the noise sources.