Modal stability theory

This article contains a review of modal stability theory. It covers local stability analysis of parallel flows including temporal stability, spatial stability, phase velocity, group velocity, spatio-temporal stability, the linearized Navier-Stokes equations, the Orr-Sommerfeld equation, the Rayleigh equation, the Briggs-Bers criterion, Poiseuille flow, free shear flows, and secondary modal instability. It also covers the parabolized stability equation (PSE), temporal and spatial biglobal theory, 2D eigenvalue problems, 3D eigenvalue problems, spectral collocation methods, and other numerical solution methods. Computer codes are provided for tutorials described in the article. These tutorials cover the main topics of the article and can be adapted to form the basis of research codes. Copyright © 2014 by ASME.

Small-scale turbulent fluctuations beyond Taylor's frozen-flow hypothesis

The space-time cross-correlation function C-T(r, tau) of local temperature fluctuations in turbulent Rayleigh-Benard convection is obtained from simultaneous two-point time series measurements. The obtained C-T(r, tau) is found to have the scaling form C-T(r(E), 0) with r(E)=[(r-U tau)(2)+ V-2 tau(2)](1/2), where U and V are two characteristic velocities associated with the mean and rms velocities of the flow. The experiment verifies the theory and demonstrates its applications to a class of turbulent flows in which the requirement of Taylor's frozen flow hypothesis is not met.

Non-modal instabilities of two-dimensional disturbances in plane Couette flow of a power-law fluid

Instabilities of fluid flows have traditionally been investigated by normal mode analysis, i.e. by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In this paper we study the instabilities of two-dimensional Couette flow of a polymeric fluid in the framework of non-modal stability theory rather than normal mode analysis. A power-law model is used to describe the polymeric liquid. We focus on the response to external excitations and initial conditions by examining the pseudospectra structures and the transient energy growths. For both Newtonian and non-Newtonian flows, the results show that there can be a rather large transient growth even though the linear operator of Couette flow has no unstable eigenvalue. The effects of non-Newtonian viscosity on the transient behaviors are examined in this study. The results show that the "shear-thinning/shear-thickening" effect increases/decreases the amplitude of responses to external excitations and initial conditions. (C) 2010 Elsevier B.V. All rights reserved.

The kinetics study in liquid-liquid systems with constant interfacial area cell with Laminar flow

A novel constant interfacial cell with laminar flow is proposed as an approach to obtain extraction kinetics data in liquid-liquid systems. Applications and theoretical fundamentals of the apparatus have been elaborated.. The equation which can express the mass transfer of liquid-liquid system run in the constant interfacial cell with laminar flow is deduced. Simulations from the equations indicate that diffusivity is a suitable factor to represent the characteristics of extraction kinetics rather than the extraction rate in the diffusion controlling step. The dependence of the aqueous phase concentration on time is recommended to determine the extraction regime. The diffusivities of the EuCl3-HDEHP extraction system obtained by different methods are compared to certify the hydrodynamic theory of the cell. The diffusivities of the ErCl3-HEH/EHP extraction system are determined, which show that this technique is a convenient method to obtain the diffusivities in the liquid-liquid system and to determine the extraction regime. (C) 1998 Elsevier Science Ltd. All rights reserved.

Qualitative Process Theory

Objects move, collide, flow, bend, heat up, cool down, stretch, compress and boil. These and other things that cause changes in objects over time are intuitively characterized as processes. To understand common sense physical reasoning and make programs that interact with the physical world as well as people do we must understand qualitative reasoning about processes, when they will occur, their effects, and when they will stop. Qualitative Process theory defines a simple notion of physical process that appears useful as a language in which to write dynamical theories. Reasoning about processes also motivates a new qualitative representation for quantity in terms of inequalities, called quantity space. This report describes the basic concepts of Qualitative Process theory, several different kinds of reasoning that can be performed with them, and discusses its impact on other issues in common sense reasoning about the physical world, such as causal reasoning and measurement interpretation. Several extended examples illustrate the utility of the theory, including figuring out that a boiler can blow up, that an oscillator with friction will eventually stop, and how to say that you can pull with a string but not push with it. This report also describes GIZMO, an implemented computer program which uses Qualitative Process theory to make predictions and interpret simple measurements. The represnetations and algorithms used in GIZMO are described in detail, and illustrated using several examples.

Choices of approaches in e-moderation: conclusions from a grounded theory study

Much has been published in recent years about the desirable nature of facilitated interactions in on-line discussions with educational purposes. However little has been reported about the roles which tutors actually adopt in real life learning contexts, how these range between ‘tutoring, ‘managing’ and ‘facilitating’, and what the distinctions between these three roles may be. In this paper choices of priorities in e-moderation, which were made in three naturalistic (real life) case studies by three higher education practitioners, are identified and discussed. These contrasting approaches were captured and analysed using grounded theory principles. The paper also discusses these occasions when the facilitation was less effective than might have been desired. It finally summarises the potential of various approaches within e-moderation – and some of the attendant risks. The finding is that principles and practices developed for face-to-face support of student-directed learning were found equally applicable in e-moderated online group work, despite several significant differences between the two types of setting. Keywords: higher education, e-learning, e-moderation, asynchronous discussions, learning outcomes, grounded theory

Generalized semi-geostrophic theory on a sphere

Douglas, Robert; Cullen, M.J.P.; Roulston, I.; Sewell, M.J., (2005) 'Generalized semi-geostrophic theory on a sphere', Journal of Fluid Mechanics 531 pp.123-157 RAE2008

Computational inference of neural information flow networks.

Determining how information flows along anatomical brain pathways is a fundamental requirement for understanding how animals perceive their environments, learn, and behave. Attempts to reveal such neural information flow have been made using linear computational methods, but neural interactions are known to be nonlinear. Here, we demonstrate that a dynamic Bayesian network (DBN) inference algorithm we originally developed to infer nonlinear transcriptional regulatory networks from gene expression data collected with microarrays is also successful at inferring nonlinear neural information flow networks from electrophysiology data collected with microelectrode arrays. The inferred networks we recover from the songbird auditory pathway are correctly restricted to a subset of known anatomical paths, are consistent with timing of the system, and reveal both the importance of reciprocal feedback in auditory processing and greater information flow to higher-order auditory areas when birds hear natural as opposed to synthetic sounds. A linear method applied to the same data incorrectly produces networks with information flow to non-neural tissue and over paths known not to exist. To our knowledge, this study represents the first biologically validated demonstration of an algorithm to successfully infer neural information flow networks.

Design of Scheduling Algorithms Using Game Theoretic Ideas

Scheduling a set of jobs over a collection of machines to optimize a certain quality-of-service measure is one of the most important research topics in both computer science theory and practice. In this thesis, we design algorithms that optimize {\em flow-time} (or delay) of jobs for scheduling problems that arise in a wide range of applications. We consider the classical model of unrelated machine scheduling and resolve several long standing open problems; we introduce new models that capture the novel algorithmic challenges in scheduling jobs in data centers or large clusters; we study the effect of selfish behavior in distributed and decentralized environments; we design algorithms that strive to balance the energy consumption and performance.

The technically interesting aspect of our work is the surprising connections we establish between approximation and online algorithms, economics, game theory, and queuing theory. It is the interplay of ideas from these different areas that lies at the heart of most of the algorithms presented in this thesis.

The main contributions of the thesis can be placed in one of the following categories.

1. Classical Unrelated Machine Scheduling: We give the first polygorithmic approximation algorithms for minimizing the average flow-time and minimizing the maximum flow-time in the offline setting. In the online and non-clairvoyant setting, we design the first non-clairvoyant algorithm for minimizing the weighted flow-time in the resource augmentation model. Our work introduces iterated rounding technique for the offline flow-time optimization, and gives the first framework to analyze non-clairvoyant algorithms for unrelated machines.

2. Polytope Scheduling Problem: To capture the multidimensional nature of the scheduling problems that arise in practice, we introduce Polytope Scheduling Problem (\psp). The \psp problem generalizes almost all classical scheduling models, and also captures hitherto unstudied scheduling problems such as routing multi-commodity flows, routing multicast (video-on-demand) trees, and multi-dimensional resource allocation. We design several competitive algorithms for the \psp problem and its variants for the objectives of minimizing the flow-time and completion time. Our work establishes many interesting connections between scheduling and market equilibrium concepts, fairness and non-clairvoyant scheduling, and queuing theoretic notion of stability and resource augmentation analysis.

3. Energy Efficient Scheduling: We give the first non-clairvoyant algorithm for minimizing the total flow-time + energy in the online and resource augmentation model for the most general setting of unrelated machines.

4. Selfish Scheduling: We study the effect of selfish behavior in scheduling and routing problems. We define a fairness index for scheduling policies called {\em bounded stretch}, and show that for the objective of minimizing the average (weighted) completion time, policies with small stretch lead to equilibrium outcomes with small price of anarchy. Our work gives the first linear/ convex programming duality based framework to bound the price of anarchy for general equilibrium concepts such as coarse correlated equilibrium.

Wave transformation and wave-driven flow across a steep coral reef

Observations of waves, setup, and wave-driven mean flows were made on a steep coral forereef and its associated lagoonal system on the north shore of Moorea, French Polynesia. Despite the steep and complex geometry of the forereef, and wave amplitudes that are nearly equal to the mean water depth, linear wave theory showed very good agreement with data. Measurements across the reef illustrate the importance of including both wave transport (owing to Stokes drift), as well as the Eulerian mean transport when computing the fluxes over the reef. Finally, the observed setup closely follows the theoretical relationship derived from classic radiation stress theory, although the two parameters that appear in the model-one reflecting wave breaking, the other the effective depth over the reef crest-must be chosen to match theory to data. © 2013 American Meteorological Society.

A new heuristic for three-machine flow shop scheduling

This paper considers the problem of sequencing n jobs in a three-machine flow shop with the objective of minimizing the makespan, which is the completion time of the last job. An O(n log n) time heuristic that is based on Johnson's algorithm is presented. It is shown to generate a schedule with length at most 5/3 times that of an optimal schedule, thereby reducing the previous best available worst-case performance ratio of 2. An application to the general flow shop is also discussed.

Approximation algorithms for two-machine flow shop scheduling with batch setup times

In many practical situations, batching of similar jobs to avoid setups is performed while constructing a schedule. This paper addresses the problem of non-preemptively scheduling independent jobs in a two-machine flow shop with the objective of minimizing the makespan. Jobs are grouped into batches. A sequence independent batch setup time on each machine is required before the first job is processed, and when a machine switches from processing a job in some batch to a job of another batch. Besides its practical interest, this problem is a direct generalization of the classical two-machine flow shop problem with no grouping of jobs, which can be solved optimally by Johnson's well-known algorithm. The problem under investigation is known to be NP-hard. We propose two O(n logn) time heuristic algorithms. The first heuristic, which creates a schedule with minimum total setup time by forcing all jobs in the same batch to be sequenced in adjacent positions, has a worst-case performance ratio of 3/2. By allowing each batch to be split into at most two sub-batches, a second heuristic is developed which has an improved worst-case performance ratio of 4/3. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.

The implementation of an aeronautical CFD flow code onto distributed memory parallel systems

The parallelization of an industrially important in-house computational fluid dynamics (CFD) code for calculating the airflow over complex aircraft configurations using the Euler or Navier–Stokes equations is presented. The code discussed is the flow solver module of the SAUNA CFD suite. This suite uses a novel grid system that may include block-structured hexahedral or pyramidal grids, unstructured tetrahedral grids or a hybrid combination of both. To assist in the rapid convergence to a solution, a number of convergence acceleration techniques are employed including implicit residual smoothing and a multigrid full approximation storage scheme (FAS). Key features of the parallelization approach are the use of domain decomposition and encapsulated message passing to enable the execution in parallel using a single programme multiple data (SPMD) paradigm. In the case where a hybrid grid is used, a unified grid partitioning scheme is employed to define the decomposition of the mesh. The parallel code has been tested using both structured and hybrid grids on a number of different distributed memory parallel systems and is now routinely used to perform industrial scale aeronautical simulations. Copyright © 2000 John Wiley & Sons, Ltd.

A semi-Lagrangian finite volume method for Newtonian contraction flows

A new finite volume method for solving the incompressible Navier--Stokes equations is presented. The main features of this method are the location of the velocity components and pressure on different staggered grids and a semi-Lagrangian method for the treatment of convection. An interpolation procedure based on area-weighting is used for the convection part of the computation. The method is applied to flow through a constricted channel, and results are obtained for Reynolds numbers, based on half the flow rate, up to 1000. The behavior of the vortex in the salient corner is investigated qualitatively and quantitatively, and excellent agreement is found with the numerical results of Dennis and Smith [Proc. Roy. Soc. London A, 372 (1980), pp. 393-414] and the asymptotic theory of Smith [J. Fluid Mech., 90 (1979), pp. 725-754].

A computational model for defect prediction in shape castings based on the interaction of free surface flow, heat transfer, and solidification phenomena

High-integrity castings require sophisticated design and manufacturing procedures to ensure they are essentially macrodefect free. Unfortunately, an important class of such defects—macroporosity, misruns, and pipe shrinkage—are all functions of the interactions of free surface flow, heat transfer, and solidication in complex geometries. Because these defects arise as an interaction of the preceding continuum phenomena, genuinely predictive models of these defects must represent these interactions explicitly. This work describes an attempt to model the formation of macrodefects explicitly as a function of the interacting continuum phenomena in arbitrarily complex three-dimensional geometries. The computational approach exploits a compatible set of finite volume procedures extended to unstructured meshes. The implementation of the model is described together with its testing and a measure of validation. The model demonstrates the potential to predict reliably shrinkage macroporosity, misruns, and pipe shrinkage directly as a result of interactions among free-surface fluid flow, heat transfer, and solidification.