近年來在運用雙界二分選擇法(double-bounded dichotomous choice elicitation method)來估計受訪者願付價格(willingness to pay)的研究中，不再僅局限於單一非市場財貨的探討。這類型的模型中雖然納入了相關性的考量，但並未考慮財貨的願付價格間可能存在明確的大小關係。再者，針對抗議性樣本，以往的作法多半是丟棄不用，然而這顯然不是理想的作法。本文中，我們將建構一個模型來同時探討這兩項議題。此外我們也利用「竹東及朴子地區心臟血管疾病長期追蹤研究」第五循環中「肥胖之願付價格」的資料來進行實證分析。結果顯示，居住於竹東、有工作、曾以特定活動控制體重的受訪者願意支付較高的金額來參加減肥療程。 / Recent studies on estimating WTP prices in terms of the double-bounded dichotomous choice elicitation method are no longer restricted to the situations that discuss only one non-market good. Although a couple of models have been proposed to take the correlations into consideration when multiple scenarios are presented to the respondents, none of them pay attention to the possibilities that the prices themselves might be inherently ordered. This is one of the issues that need to be addressed. Another is about the protest samples. A common but apparently problematic approach is simply ignoring them completely. In this study, we propose a model that is able to take care of both issues simultaneously. In addition, the model is used to estimate WTP values for data collected in CVDFACTS about two weight loss treatments. The results indicate that respondents residing in Chu-Dong County, employed, and ever tried any weight controlled programs are willing to pay a higher price for the new treatments.

Most flows in nature and engineering are turbulent, and many are wall-bounded. Further, in turbulent flows, the turbulence generally has a large impact on the behavior of the flow. It is therefore important to be able to predict the effects of turbulence in such flows. The Navier-Stokes equations are known to be an excellent model of the turbulence phenomenon. In simple geometries and low Reynolds numbers, very accurate numerical solutions of the Navier-Stokes equations (direct numerical simulation, or DNS) have been used to study the details of turbulent flows. However, DNS of high Reynolds number turbulent flows in complex geometries is impractical because of the escalation of computational cost with Reynolds number, due to the increasing range of spatial and temporal scales. In Large Eddy Simulation (LES), only the large-scale turbulence is simulated, while the effects of the small scales are modeled (subgrid models). LES therefore reduces computational expense, allowing flows of higher Reynolds number and more complexity to be simulated. However, this is at the cost of the subgrid modeling problem. The goal of the current research is then to develop new subgrid models consistent with the statistical properties of turbulence. The modeling approach pursued here is that of "Optimal LES". Optimal LES is a framework for constructing models with minimum error relative to an ideal LES model. The multi-point statistics used as input to the optimal LES procedure can be gathered from DNS of the same flow. However, for an optimal LES to be truly predictive, we must free ourselves from dependence on existing DNS data. We have done this by obtaining the required statistics from theoretical models which we have developed. We derived a theoretical model for the three-point third-order velocity correlation for homogeneous, isotropic turbulence in the inertial range. This model is shown be a good representation of DNS data, and it is used to construct optimal quadratic subgrid models for LES of forced isotropic turbulence with results which agree well with theory and DNS. The model can also be filtered to determine the filtered two-point third-order correlation, which describes energy transfer among filtered (large) scales in LES. LES of wall-bounded flows with unresolved wall layers commonly exhibit good prediction of mean velocities and significant over-prediction of streamwise component energies in the near-wall region. We developed improved models for the nonlinear term in the filtered Navier-Stokes equation which result in better predicted streamwise component energies. These models involve (1) Reynolds decomposition of the nonlinear term and (2) evaluation of the pressure term, which removes the divergent part of the nonlinear models. These considerations significantly improved the performance of our optimal models, and we expect them to apply to other subgrid models as well. / text

It is well known that most fluid flows observed in nature or encountered in engineering applications are turbulent and involve separation. Fluid flows in turbines, diffusers and channels with sudden expansions are among the widely observed areas where separation substantially alters the flow field and gives rise to complex flow dynamics. Such types of flows are referred to as internal flows since they are confined within solid surfaces and predominantly involve the generation or utilization of mechanical power. However, there is also a vast variety of engineering applications where the fluid flows past solid structures, such as the flow of air around an airplane or that of water around a submarine. These are called external flows and as in the former case the downstream evolution of the flow field is crucially influenced by separation. The present doctoral thesis addresses both internal and external separated flows by means of direct numerical simulations of the incompressible Navier-Stokes equations. For internal flows, the wall-driven flow in a onesided expansion channel and the pressure-driven flow in a plane channel with a single thin-plate obstruction have been studied in the fully developed turbulent state. Since such geometrical configurations involve spatially developing turbulent flows, proper inflow conditions are to be employed in order to provide a realistic fully turbulent flow at the input. For this purpose, a newly developed technique has been used in order to mimic an infinitely long channel section upstream of the expansion and the obstruction, respectively. With this approach, we are able to gather accurate mean flow and turbulence statistics throughout each flow domain and to explore in detail the instantaneous flow topology in the separated shear layers, recirculation regions as well as the recovery zones. For external flows, on the other hand, the flow past a prolate spheroid has been studied. Here, a wide range of Reynolds numbers is taken into consideration. Based on the characteristics of the vortical structures in the wake, the flow past a prolate spheroid is classified as laminar (steady or unsteady), transitional or turbulent. In each flow regime, the characteristic features of the flow are investigated by means of detailed frequency analysis, instantaneous vortex topology and three-dimensional flow visualizations.

This thesis is focused on direct numerical simulation (DNS) of compressible and incompressible fully developed and developing turbulent flows between isothermal walls using a discontinuous Galerkin method (DGM). Three cases (Ma = 0.2, 0.7 and 1.5) of DNS of turbulent channel flows between isothermal walls with Re ~ 2800, based on bulk velocity and half channel width, have been carried out. It is found that a power law seems to scale mean streamwise velocity with Ma slightly better than the more usual log-law. Inner and outer scaling of second-order and higher-order statistics have been analyzed. The linkage between the pressure gradient and vorticity flux on the wall has been theoretically derived and confirmed and they are highly correlated very close to the wall. The correlation coefficients are influenced by Ma, and viscosity when Ma is high. The near-wall spanwise streak spacing increases with Ma. Isosurfaces of the second invariant of the velocity gradient tensor are more sparsely distributed and elongated as Ma increases. DNS of turbulent isothermal-wall bounded flow subjected to favourable and adverse pressure gradient (FPG, APG) at Ma ~ 0.2 and Reref ~ 428000, based on the inlet bulk velocity and the streamwise length of the bottom wall, is also investigated. The FPG/APG is obtained by imposing a concave/convex curvature on the top wall of a plane channel. The flows on the bottom and top walls are tripped turbulent and laminar boundary layers, respectively. It is observed that the first and second order statistics are strongly influenced by the pressure gradients. The cross-correlation coefficients of the pressure gradients and vorticity flux remain constant across the FPG/APG regions of the flat wall. High correlations between the streamwise/wallnormal pressure gradient and the spanwise vorticity are found near the separation region close to the curved top wall. The angle of inclined hairpin structure to streamwise direction of the bottom wall is smaller (flatter) in the FPG region than the APG region. / Thesis (Ph.D, Mechanical and Materials Engineering) -- Queen's University, 2009-12-21 13:59:53.084

In this dissertation we will address two types of homogenization problems. The first one is a spectral problem in the realm of lower dimensional theories, whose physical motivation is the study of waves propagation in a domain of very small thickness and where it is introduced a very thin net of heterogeneities. Precisely, we consider an elliptic operator with "ε-periodic coefficients and the corresponding Dirichlet spectral problem in a three-dimensional bounded domain of small thickness δ. We study the asymptotic behavior of the spectrum as ε and δ tend to zero. This asymptotic behavior depends crucially on whether ε and δ are of the same order (δ ≈ ε), or ε is of order smaller than that of δ (δ = ετ , τ < 1), or ε is of order greater than that of δ (δ = ετ , τ > 1). We consider all three cases. The second problem concerns the study of multiscale homogenization problems with linear growth, aimed at the identification of effective energies for composite materials in the presence of fracture or cracks. Precisely, we characterize (n+1)-scale limit pairs (u,U) of sequences {(uεLN⌊Ω,Duε⌊Ω)}ε>0 ⊂ M(Ω;ℝd) × M(Ω;ℝd×N) whenever {uε}ε>0 is a bounded sequence in BV (Ω;ℝd). Using this characterization, we study the asymptotic behavior of periodically oscillating functionals with linear growth, defined in the space BV of functions of bounded variation and described by n ∈ ℕ microscales

This thesis examines graph polynomials and particularly their complexity. We give short proofs of two results from Gessel and Sagan (1996) which present new evaluations of the Tutte polynomial concerning orientations. A theorem of Massey et al (1997) gives an expression concerning the average size of a forest in a graph. We generalise this result to any simplicial complex. We answer a question posed by Kleinschmidt and Onn (1995) by showing that the language of partitionable simplicial complexes is in NP. We prove the following result concerning the complexity of the Tutte polynomial: Theorem 1. For any fixed k, there exists a polynomial time algorithm A, which will input any graph G, with tree-width at most k, and rational numbers x and y, and evaluate the Tutte polynomial, T(G;x,y). The rank generating function S of a graphic 2-polymatroid was introduced by Oxley and Whittle (1993). It has many similarities to the Tutte polynomial and we prove the following results. Theorem 2. Evaluating S at a fixed point (u,v) is #P-hard unless uv=1 when there is a polynomial time algorithm. Theorem 3. For any fixed k, there exists a polynomial time algorithm A, which will input any graph G, with tree-width at most k, and rational numbers u and v, and evaluate S(G;u,v). We consider a class of graphs $S$, which are those graphs which are obtainable from a graph with no edges using the unsigned version of Reidemeister moves. We examine the relationship between this class and other similarly defined classes such as the delta-wye graphs. There remain many open questions such as whether S contains every graph. However we have an invariant of the moves, based on the Tutte polynomial, which allows us to determine from which graph with no edges, if any, a particular graph can be obtained. Finally we consider a new polynomial on weighted graphs which is motivated by the study of weight systems on chord diagrams. We give three states model and a recipe theorem. An unweighted version of this polynomial is shown to contain as specialisations, a wide range of graph invariants, such as the Tutte polynomial, the polymatroid polynomial of Oxley and Whittle (1993) and the symmetric function generalisation of the chromatic polynomial introduced by Stanley (1995). We close with a discussion of complexity issues proving hardness results for very restricted classes of graphs.

A new hybrid approach to model high Reynolds number wall-bounded turbulent flows is developed based on coupling the two-level simulation (TLS) approach in the inner region with conventional large eddy simulation (LES) away from the wall. This new approach is significantly different from previous near-wall approaches for LES. In this hybrid TLS-LES approach, a very fine small-scale (SS) mesh is embedded inside the coarse LES mesh in the near-wall region. The SS equations capture fine-scale temporal and spatial variations in all three cartesian directions for all three velocity components near the wall. The TLS-LES equations are derived based on defining a new scale separation operator. The TLS-LES equations in the transition region are obtained by blending the TLS large-scale and LES equations. A new incompressible parallel flow solver is developed that accurately and reliably predicts turbulent flows using TLS-LES. The solver uses a primitive variable formulation based on an artificial compressibility approach and a dual time stepping method. The advective terms are discretized using fourth-order energy conservative finite differences. The SS equations are also integrated in parallel, which reduces the overall cost of the TLS-LES approach. The TLS-LES approach is validated and investigated for canonical channel flows, channel flow with adverse pressure gradient and asymmetric plane diffuser flow. The results suggest that the TLS-LES approach yields very reasonable predictions of most of the crucial flow features in spite of using relatively coarse grids.

This thesis contains four essays that analyze the behaviors that evolve when populations of boundedly rational individuals interact strategically for a long period of time. Individuals are boundedly rational in the sense that their strategy choices are determined by simple rules of adaptation -- learning rules. Convergence results for general finite games are first obtained in a homogenous setting, where all populations consist either of stochastic imitators, who almost always imitate the most successful strategy in a sample from their own population's past strategy choices, or stochastic better repliers, who almost always play a strategy that gives at least as high expected payoff as a sample distribution of all populations' past play. Similar results are then obtained in a heterogeneous setting, where both of these learning rules are represented in each population. It is found that only strategies in certain sets are played in the limit, as time goes to infinity and the mutation rate tends to zero. Sufficient conditions for the selection of a Pareto efficient such set are also provided. Finally, the analysis is extended to natural selection among learning rules. The question is whether there exists a learning rule that is evolutionarily stable, in the sense that a population employing this learning rule cannot be invaded by individuals using a different rule. Monte Carlo simulations for a large class of learning rules and four different games indicate that only a learning rule that takes full account of hypothetical payoffs to strategies that are not played is evolutionarily stable in almost all cases. / Diss. Stockholm : Handelshögsk., 2001

On s’intéresse dans cette thèse à la PGD (Proper Generalized Decomposition), l’une des méthodes de réduction de modèles qui consiste à chercher, a priori, la solution d’une équation aux dérivées partielles sous forme de variables séparées. Ce travail est formé de cinq chapitres dans lesquels on vise à étendre la PGD aux espaces fractionnaires et aux espaces des fonctions à variation bornée, et à donner des interprétations théoriques de cette méthode pour une classe de problèmes elliptiques et paraboliques. Dans le premier chapitre, on fait un bref aperçu sur la littérature puis on présente les notions et outils mathématiques utilisés dans le corps de la thèse. Dans le second chapitre, la convergence des suites des directions alternées (AM) pour une classe de problèmes variationnels elliptiques est étudiée. Sous une condition de non-orthogonalité uniforme entre les itérés et le terme source, on montre que ces suites sont en général bornées et compactes. Alors, si en particulier la suite (AM) converge faiblement alors elle converge fortement et la limite serait la solution du problème de minimisation alternée. Dans le troisième chapitre, on introduit la notion des dérivées fractionnaires au sens de Riemann-Liouville puis on considère un problème variationnel qui est une généralisation d’ordre fractionnaire de l’équation de Poisson. En se basant sur la nature quadratique et la décomposabilité de l’énergie associée, on démontre que la suite PGD progressive converge fortement vers la solution faible de ce problème. Dans le quatrième chapitre, on profite de la structure tensorielle des espaces BV par rapport à la topologie faible étoile pour définir les suites PGD dans ce type d’espaces. La convergence de telle suite reste une question ouverte. Le dernier chapitre est consacré à l’équation de la chaleur d-dimensionnelle, où on discrétise en temps puis à chaque pas de temps on cherche la solution de l’équation elliptique en utilisant la PGD. On montre alors que la fonction affine par morceaux en temps obtenue à partir des solutions construites en utilisant la PGD converge vers la solution faible de l’équation. / In this thesis, we are interested in the PGD (Proper Generalized Decomposition), one of the reduced order models which consists in searching, a priori, the solution of a partial differential equation in a separated form. This work is composed of five chapters in which we aim to extend the PGD to the fractional spaces and the spaces of functions of bounded variation and to give theoretical interpretations of this method for a class of elliptic and parabolic problems. In the first chapter, we give a brief review of the litterature and then we introduce the mathematical notions and tools used in this work. In the second chapter, the convergence of rank-one alternating minimisation AM algorithms for a class of variational linear elliptic equations is studied. We show that rank-one AM sequences are in general bounded in the ambient Hilbert space and are compact if a uniform non-orthogonality condition between iterates and the reaction term is fulfilled. In particular, if a rank-one (AM) sequence is weakly convergent then it converges strongly and the common limit is a solution of the alternating minimization problem. In the third chapter, we introduce the notion of fractional derivatives in the sense of Riemann-Liouville and then we consider a variational problem which is a generalization of fractional order of the Poisson equation. Basing on the quadratic nature and the decomposability of the associated energy, we prove that the progressive PGD sequence converges strongly towards the weak solution of this problem. In the fourth chapter, we benefit from tensorial structure of the spaces BV with respect to the weak-star topology to define the PGD sequences in this type of spaces. The convergence of this sequence remains an open question. The last chapter is devoted to the d-dimensional heat equation, we discretize in time and then at each time step one seeks the solution of the elliptic equation using the PGD. Then, we show that the piecewise linear function in time obtained from the solutions constructed using the PGD converges to the weak solution of the equation.

Cette thèse porte sur des propriétés d'approximation généralisant la moyennabilité pour les groupes localement compacts. Ces propriétés sont définies à partir des multiplicateurs de certaines algèbres associés aux groupes. La première partie est consacrée à l'étude de la propriété p-AP, qui est une extension de la AP de Haagerup et Kraus au cadre des opérateurs sur les espaces Lp. Le résultat principal dit que les groupes de Lie simples de rang supérieur et de centre fini ne satisfont p-AP pour aucun p entre 1 et l'infini. La deuxième partie se concentre sur les multiplicateurs de Schur radiaux sur les graphes. L'étude de ces objets est motivée par les liens avec les actions de groupes discrets et la moyennabilité faible. Les trois résultats principaux donnent des conditions nécessaires et suffisantes pour qu'une fonction sur les nombres naturels définisse un multiplicateur radial sur des différentes classes de graphes généralisant les arbres. Plus précisément, les classes de graphes étudiées sont les produits d'arbres, les produits de graphes hyperboliques et les complexes cubiques CAT(0) de dimension finie. / This thesis focusses on some approximation properties which generalise amenability for locally compact groups. These properties are defined by means of multipliers of certain algebras associated to the groups. The first part is devoted to the study of the p-AP, which is an extension of the AP of Haagerup and Kraus to the context of operators on Lp spaces. The main result asserts that simple Lie groups of higher rank and finite centre do not satisfy p-AP for any p between 1 and infinity. The second part concentrates on radial Schur multipliers on graphs. The study of these objects is motivated by some connections with actions of discrete groups and weak amenability. The three main results give necessary and sufficient conditions for a function of the natural numbers to define a radial multiplier on different classes of graphs generalising trees. More precisely, the classes of graphs considered here are products of trees, products hyperbolic graphs and finite dimensional CAT(0) cube complexes.