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Series Representation (series + representation)
Selected AbstractsSimulation of coherent structures in turbulent boundary layer using Gao,Yong equations of turbulenceHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 5 2004Bo Liu Abstract The equations of incompressible turbulent flow developed by the Gao,Yong turbulence model have two important features. First, they do not contain any empirical coefficients or wall functions. Second, the series representation of turbulence energy equation reflects multi-scale structures of the nonlinearity of turbulence, and, therefore, is capable of describing both statistical mean flows and the coherent structures. This paper presents some simulation results of a two-dimensional turbulent boundary layer with zero pressure gradient based on Gao,Yong equations of turbulence. With a staggered grid arrangement, an incompressible SIMPLE code was used in the simulations. The simulated coherent structures have verified the adaptability of the newly derived equations to real intermittent turbulent flows. The effect of the orders of the energy equation and computational grid scales on the detection of coherent structures is also investigated. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(5): 287,298, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20019 [source] The Band Pass Filter*INTERNATIONAL ECONOMIC REVIEW, Issue 2 2003Lawrence J. Christiano We develop optimal finite-sample approximations for the band pass filter. These approximations include one-sided filters that can be used in real time. Optimal approximations depend upon the details of the time series representation that generates the data. Fortunately, for U.S. macroeconomic data, getting the details exactly right is not crucial. A simple approach, based on the generally false assumption that the data are generated by a random walk, is nearly optimal. We use the tools discussed here to document a new fact: There has been a significant shift in the money,inflation relationship before and after 1960. [source] Further results on the asymptotic growth of entire solutions of iterated Dirac equations in ,nMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 5 2006D. Constales Abstract In this paper, we establish some further results on the asymptotic growth behaviour of entire solutions to iterated Dirac equations in ,n. Solutions to this type of systems of partial differential equations are often called polymonogenic or k -monogenic. In the particular cases where k is even, one deals with polyharmonic functions. These are of central importance for a number of concrete problems arising in engineering and physics, such as for example in the case of the biharmonic equation for the description of the stream function in the Stokes flow regime with low Reynolds numbers and for elasticity problems in plates. The asymptotic study that we are going to perform within the context of these PDE departs from the Taylor series representation of their solutions. Generalizations of the maximum term and the central index serve as basic tools in our analysis. By applying these tools we then establish explicit asymptotic relations between the growth behaviour of polymonogenic functions, the growth behaviour of their iterated radial derivatives and that of functions obtained by applying iterations of the , operator to them. Copyright © 2005 John Wiley & Sons, Ltd. [source] Time domain characteristics of hoof-ground interaction at the onset of stance phaseEQUINE VETERINARY JOURNAL, Issue 7 2006J. F. BURN Summary Reasons for performing study: Little is known about the interaction of the hoof with the ground at the onset of stance phase although is it widely believed that high power collisions are involved in the aetiopathology of several conditions causing lameness. Objectives: To answer 3 questions regarding the fundamental nature of hoof-ground collision: (1) is the collision process deterministic for ground surfaces that present a consistent mechanical interface (2) do collision forces act on the hoof in a small or large range of directions and (3) Is the hoof decelerated to near-zero velocity by the initial deceleration peak following ground contact? Methods: Hoof acceleration during the onset of stance phase was recorded using biaxial accelerometry for horses trotting on a tarmac surface and on a sand surface. Characteristics of the collision process were identified both from vector plots and time series representations of hoof acceleration, velocity and displacement. Results: The response of the hoof to collision with smooth tarmac was predominantly deterministic and consistent with the response of a spring-damper system following shock excitation. The response to collision with sand was predominantly random. The deceleration peak following ground contact did not decelerate the hoof to near-zero velocity on tarmac but appeared to on sand. On both surfaces, collision forces acted on the hoof in a wide range of directions. Conclusions: The study suggests the presence of stiff, visco-elastic structures within the foot that may act as shock absorbers isolating the limb from large collision forces. Potential relevance: The study indicates objectives for future in vivo and in vitro research into the shock absorbing mechanism within the equine foot; and the effects of shoe type and track surface properties on the collision forces experienced during locomotion. Studies of this nature should help to establish a link between musculoskeletal injury, hoof function and hoof-ground interaction if, indeed, one exists. [source] Indirect boundary element method for unsteady linearized flow over prolate and oblate spheroids and hemispheroidal protuberancesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2004Lisa F. Shatz Abstract The indirect boundary element method was used to study the hydrodynamics of oscillatory viscous flow over prolate and oblate spheroids, and over hemispheroidal bodies hinged to a plate. Analytic techniques, such as spheroidal coordinates, method of images, and series representations, were used to make the numerical methods more efficient. A novel method for computing the hydrodynamic torque was used, since for oscillatory flow the torque cannot be computed directly from the weightings. Instead, a Green's function for torque was derived to compute the torque indirectly from the weightings. For full spheroids, the method was checked by comparing the results to exact solutions at low and high frequencies, and to results computed using the singularity method. For hemispheroids hinged to a plate, the method for low frequencies was checked by comparing the results to previous results, and to exact solutions at high frequencies. Copyright © 2004 John Wiley & Sons, Ltd. [source] | ||||||||||