다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Benard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.

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Pattern formation outside of equilibrium

Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has been a surge of interest in saddle point problems, and numerous solution techniques have been proposed for this type of system. The aim of this paper is to present and discuss a large selection of solution methods for linear systems in saddle point form, with an emphasis on iterative methods for large and sparse problems.

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Numerical solution of saddle point problems

Description of the NCAR Community Atmosphere Model (CAM 3.0)

저작근 근전도에 관한 정상교합자와 ii급 부정교합자의 비교 연구

Polynomial approximations are arguably the most common representation of uncertainty [2]. Such approximations are computed by either local Taylor expansions, e.g., first-order derivatives, or by fitting the approximation at well-chosen sample points, e.g., collocation or surface response methods [4,6]. In this work we present a hybrid approach, where the polynomial approximation is computed based on function and derivative information at sample points in the uncertainty region. This approach is shown to efficiently approximate both the distribution and the major global sensitivity effects of the target functional.

Stochastic Finite-Element Approach in Nuclear Reactor Uncertainty Quantification

LES and no-model LES (coarse-grid DNS) have been performed of turbulent flow in a plane asymmetric diffuser by the Spectral-Element Method (SEM). Mean profile and turbulent stresses compare well to LES results from Herbst e, however the SEM generally predicts a later (i.e. further downstream) separation. It can be concluded that the use of a high-order method is advantageous for flows featuring pressure-induced separation.

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Large-Eddy Simulation of Turbulent Flow in a Plane Asymmetric Diffuser by the Spectral-Element Method

Predictions in CFD simulations of wire-wrapped SFR fuel assemblies

Nek5000 developments in support of industry and the NRC

Transient growth of linearly stable disturbances is believed to play an important role in the subcritical transition of laminar boundary layers and the self-sustained nature of boundary layer fluctuations in a fully turbulent flow. Prior work on transient growth has focused on identifying the optimum initial disturbances that result in maximum transient growth. This paper addresses the companion issue of receptivity of those disturbances, the mechanism that determines the actual magnitudes of transient growth that are realized in a given physical situation. A synergistic combination of experimental, computational, and theoretical approaches is used to quantify the flow receptivity to surface roughness in a Blasius boundary layer. Results reveal the non-optimality of the transient growth factors involved as well as the sensitive dependence of flow perturbations to the geometric characteristics of the roughness distribution. Direct numerical simulations (DNS) are compared in detail with experimental results, results obtained from linear receptivity theory and optimal disturbance calculations. DNS shows good agreement with the experimental results. Differences between the linear theory and DNS are attributed to nonlinear receptivity mechanisms. Results also support the proposal by Fransson et al. (2004) that disagreement between optimal disturbances and experiments/DNS may be attributed to differences involving the wall normal location of the streamwise vortex initiating the transient growth. INTRODUCTION The transient growth phenomenon refers to an algebraic amplification of small-amplitude disturbances prior to an exponential decay farther downstream. Transient growth has been proposed as a likely mechanism behind laminar-turbulent transition scenarios that cannot be explained by the classical paradigm of hydrodynamic instabilities. Transient growth is also believed to play an important role in the self-generation of turbulence in fully turbulent wall shear flows (Butler and Farrell 1993; Chernyshenko and Baig 2005). Physically, the occurrence of transient growth can be explained by Landahl’s (1980) “lift-up” mechanism, where a pair of stable, counter-rotating, streamwise-oriented vortices transfers momentum across the boundary layer, creating a significantly stronger streamwise velocity perturbation. The mathematical foundation of transient growth has been described by Schmid and Henningson (2001) and Reshotko (2001). Transient growth arises because the linearized disturbance equations are not self-adjoint and, therefore, have nonorthogonal eigenmodes. In boundary layers, the correct representation of disturbances is the superposition of the discrete and continuous eigenmodes of the Orr–Sommerfeld (OS) equation. In classical linear stability analysis, the most amplified discrete eigenmode represents the dominant disturbance observed in an experiment. However, even in the subcritical region where the TS waves are damped, a suitable mixture of continuous spectrum modes (each of which has a different decay rate) can exhibit temporary algebraic growth before the exponential decay manifests itself. A particular combination of the modes will form an initial disturbance that experiences the maximum amount of growth. Such a disturbance is called the optimal disturbance (Farrell 1988) and many investigators have contributed to the modelling of spatially growing optimal disturbances (Andersson et al. 1999; Luchini 2000; Tumin and Reshotko 2001). For a laminar Blasius boundary layer, the optimal initial disturbance has been shown to consist of an array of stationary streamwise vortices with a dimensionless spanwise wavenumber of 0.45. Andersson et al. (1999) also found that the measured evolution of low-frequency boundary-layer disturbances excited via freestream turbulence is in agreement with the optimal growth theory. On the other hand, there is a significant mismatch between the optimal growth theory and measured (i.e. realizable) disturbances due to controlled surface roughness. White (2002) finds that roughness-induced disturbances show suboptimal behavior. Fransson et al. (2004) confirm this observation and attribute the mismatch to differences between the initial disturbance profiles used in optimal disturbance studies and those induced by surface roughness. The former corresponds to a streamwise vortex that is not confined to the boundary layer. Unlike the case of freestream turbulence, however, disturbances generated by low amplitude surface roughness are mostly confined to the boundary layer region. Transient disturbances are extremely sensitive to initial disturbance conditions as these determine the spectrum of modes that make up the disturbance and, hence, its algebraic growth rate. Since the maximum disturbance energy attained downstream of the source is mostly specified by the algebraic growth rate, understanding the receptivity mechanism that determines the initial disturbance condition is crucial. The objective of this work is to summarize the recent progress in experimental, computational and theoretical investigations of roughness-induced transient growth, with an emphasis on detailed comparisons between the respective findings for specific roughness configurations. Remaining challenges to assessing the relevance of the optimal growth theory to roughness effects on boundary-layer transition are also outlined. EXPERIMENTS White and coworkers (White and Ergin 2003; White et al. 2005; Ergin and White 2005) at Case Western Reserve University (Case) have conducted a number of experiments on the behavior of roughness-induced transient disturbances. Present efforts are focused on generating disturbance data that is suitable for comparison with DNS and theoretical models. A brief description of the experimental setup and data analysis procedure is given below. Measurements are obtained in the boundary layer of a flat plate with an elliptical leading edge and disturbances are generated by a spanwise array of cylindrical roughness elements. Roughness arrays provide considerable flexibility in varying the controlled disturbance inputs, via variations in the height, spacing and diameter of the roughness elements. Various averaging techniques, such as spatial phase-locked averaging, can be utilized to improve the signal-to-noise characteristics during data analysis. Throughout this paper, k denotes the roughness height, λk is the spanwise roughness spacing (19 mm), xk is the array’s streamwise location relative to the physical leading edge (300 mm), and Rek is the roughness Reynolds number, U(k)k/ν. Hotwire velocity measurements are performed in planes perpendicular to the streamwise flow. An illustration of the experimental setup is given in Figure 1. The main data analysis technique is to decompose the kinetic energy associated with the steady disturbance into spanwise wavelength components by performing a spanwise Fourier transform, computing the energy of each and examining the downstream evolution of these energies. The energy is defined by

Paul Fischer

Papers

Stochastic Finite-Element Approach in Nuclear Reactor Uncertainty Quantification

Large-Eddy Simulation of Turbulent Flow in a Plane Asymmetric Diffuser by the Spectral-Element Method

Predictions in CFD simulations of wire-wrapped SFR fuel assemblies

Nek5000 developments in support of industry and the NRC

Transient growth: Experiments, DNS and theory