Thesis (M.Sc.Eng.)PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / The exploration and production of oil and gas resources require innovative information acquisition strategies for wellbore environments to improve reservoir management. In this study, a microfluidic channel data retrieval platform was proposed for multiple sensor chip manipulation, wireless charging and information extraction in fluidic mediums. The working principle of near-field magneto inductive coupling was investigated and a prototype of a microfluidic channel integrated with a spiral reader antenna was designed and fabricated. Sensor chip manipulations and dynamic couplings between readers and sensors were demonstrated inside the proposed microfluidic channel. Furthermore, solid fluidic interaction between sensors and flows was analyzed. Comsol simulation was conducted to quantitatively characterize flow drag forces inside the channel. To prevent communication interference between sensors in the proposed coupling region, sensor separation strategies based on side channel and meander channel design were proposed and realized to separate sensors one by one by the desired distance. To enhance the efficiency of the sensor separation process, a new channel design based on a spinning blade with real-time image processing was also developed for feedback control of separation. Additionally, a 500-micron cubic sensor antenna was cut by a dicing saw and assembled into an 800-micron cubic package. Magneto inductive couplings between readers and the assembly package were conducted out of the channel. The results show that the coupling effect is strongly related with the orientation between the reader and the assembly package. Finally, the assembly package control with desired velocity and direction in oil mediums was successfully realized inside the channel. / 2999-01-01

Call number: LD2668 .T4 1985 B78 / Master of Science

Lau Kin Wing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 80-83). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.3 / Chapter 1.1 --- Heat conduction problem --- p.3 / Chapter 1.2 --- Direct problem --- p.4 / Chapter 1.3 --- Inverse problem --- p.4 / Chapter 1.4 --- Difficulty of the inverse problems --- p.5 / Chapter 1.5 --- A simple but important example for instability --- p.5 / Chapter 1.6 --- The purpose of this thesis --- p.7 / Chapter 2 --- Stability of the inverse problem --- p.9 / Chapter 2.1 --- Conditional stability results --- p.9 / Chapter 2.2 --- Stability of the inverse problems --- p.11 / Chapter 3 --- The continuous formulation --- p.30 / Chapter 3.1 --- Constrained minimization problem --- p.30 / Chapter 3.2 --- Existence of minimizers to the minimization problem --- p.31 / Chapter 4 --- Discretization and its convergence --- p.36 / Chapter 4.1 --- Finite element space --- p.36 / Chapter 4.2 --- Two important discrete projection operators --- p.37 / Chapter 4.3 --- Finite element problem --- p.39 / Chapter 4.4 --- Existence of minimizers to the finite element problem --- p.39 / Chapter 4.5 --- Discrete minimizers and global minimizers --- p.42 / Chapter 5 --- Numerical algorithms --- p.51 / Chapter 5.1 --- Gateaux derivative --- p.51 / Chapter 5.2 --- Nonlinear single-grid gradient method --- p.53 / Chapter 5.3 --- Nonlinear multigrid gradient method --- p.55 / Chapter 6 --- Numerical experiments --- p.60 / Chapter 6.1 --- One dimensional examples --- p.60 / Chapter 6.2 --- Two dimensional examples --- p.66

本論文主要研究污染源追蹤和重構的反問題以及倒向隨機微分方程的數值求解。 / 論文的第一部份考慮污染源追蹤及重構的反問題。它的目的是重構反應對流擴散系統中的未知污染源的位置以及強度。污染源的追蹤和重構在工程、化學、生物以及環境等領域有廣泛的應用。我們將同時重構靜態單點污染源的位置以及強度。在本論文中，我們提出了一個基於對偶概率的算法，它將污染源追蹤重構的反問題轉化為Volterra積分反問題。對於污染源的位置和污染物釋放強度的可重構性，文中也進行了理論上的分析和討論。數值結果表明此方法是高效穩定的。隨後，我們將對偶概率方法推廣應用與追蹤和重構動態單點污染源隨時間的軌跡以及強度。數值結果顯示，我們的方法要比多數現有的方法為有效，計算成本也大大降低。 / 論文的第二部份討論倒向隨機微分方程的數值求解。倒向隨機微分方程在隨機控制、生物、化學反應，尤其是數理金融上有重要的應用。論文中所提出的數值方法，主要是基於倒向隨機微分方程的置換解的概念。置換解的適定性分析不涉及鞅表示論，從而更靈活，更容易推廣。利用置換解的理論，文中所涉及的誤差分析都不需要用到鞅表示論。對於一般的倒向隨機微分方程，我們提出了一種簡單的倒向算法，并證明了它是半階收斂的。但是，在算法的實際應用中只可能選取有限個基函數，從而帶入了截斷誤差。截斷誤差在簡單倒向算法中會隨時間累加，導致誤差是半階增長的。為了克服這個缺點，我們提出了一種新的算法。這種算法無需進行皮卡迭代，並且在理論上我們證明了，使用這個新的算法，截斷誤差是可控的，它不會隨時間增加。隨後，我們對馬爾科夫情況的倒向隨機微分方程提出了幾個高階的數值算法，並且給出了嚴格的誤差分析。我們的數值實驗結果表明，文中所提出的方法精度高，穩定性強，且計算成本小。 / In this thesis, we shall propose some numerical methods for solving two important classes of application problems, namely the inverse heat source problems and the backward stochastic differential equations. / The inverse heat source problems are to recover the source terms in a convection-diffusion- reaction system. These inverse problems have wide applications in many areas, such as engineering, chemistry, biology, pollutant tracking, and so on. We shall first investigate the simultaneous reconstruction of the location and strength of a static singular source. An adjoint probabilistic algorithm is proposed, which turns the inverse heat source problem into an inverse Volterra integral problem. The identifiability of the location and strength of a singular source is also discussed, and numerical results are presented to show the robustness and effectiveness of the method. Then we extend the adjoint probabilistic method to reconstruct the source trace and release history of a singular moving point source. Numerical examples show that the adjoint probabilistic method is more efficient and less expensive than most existing efficient numerical methods. / The second part of the thesis is devoted to numerical solutions of some nonlinear backward stochastic differential equations (BSDEs). BSDEs are widely used in various fields like stochastic control, biology, chemistry reaction, especially mathematical finance. Our numerical methods are based on a new framework about the transposition solution to BSDEs. The proof of the well-posedness of the transposition solution does not involve Martingale representation, neither does our error analysis for the numerical schemes proposed in this thesis. For general BSDEs, we first propose a simple backward scheme, which is proved to have an accuracy of half order. However, in the real application of the scheme, it is only possible to choose a finite subset of basis functions, which will generate truncation error. The truncation error accumulates backward in time, leading to the increment of the numerical error up to a half order. To overcome this drawback, we propose a new numerical scheme without Picard iterations and prove that the truncation error is bounded independent of time partitions. Afterwards, we propose some higher order schemes for Markovian BSDEs with rigorous error analysis. Finally, numerical simulations are presented to demonstrate that the proposed methods are accurate, stable and less expensive than most existing ones. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Wang, Shiping. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 126-133). / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.v / Chapter 1 --- Introduction to inverse heat source problems and BSDEs --- p.1 / Chapter 1.1 --- Inverse heat source problems --- p.2 / Chapter 1.2 --- Backward stochastic differential equations --- p.7 / Chapter 1.3 --- Outline of the thesis --- p.11 / Chapter Part I: --- Numerical Method for Inverse Heat Source Problem --- p.13 / Chapter 2 --- Inverse heat source: static point source --- p.14 / Chapter 2.1 --- Reformulation of the forward problem --- p.15 / Chapter 2.2 --- Inverse source problem and its identifiability --- p.21 / Chapter 2.2.1 --- Identifiability of partial time in one dimensional cases --- p.21 / Chapter 2.2.2 --- Identifiability of two dimensional cases --- p.25 / Chapter 2.3 --- Algorithm to solve the inverse problem --- p.26 / Chapter 2.4 --- Numerical experiments --- p.29 / Chapter 3 --- Inverse heat source: moving point source --- p.41 / Chapter 3.1 --- Reformulation of the problem --- p.42 / Chapter 3.2 --- Algorithm and numerical examples --- p.43 / Chapter 3.2.1 --- Algorithm to recover source trace and strength --- p.44 / Chapter 3.2.2 --- Numerical examples --- p.45 / Chapter Part II: --- Numerical Methods to Backward Stochastic Differential Equations --- p.55 / Chapter 4 --- Preliminaries --- p.56 / Chapter 4.1 --- Notations and definitions --- p.56 / Chapter 4.2 --- Useful lemmas and theorems --- p.60 / Chapter 4.3 --- Existing schemes for forward SDEs --- p.66 / Chapter 5 --- Numerical algorithms to BSDEs and error estimates --- p.68 / Chapter 5.1 --- A simple backward algorithm for BSDEs and its error estimate --- p.69 / Chapter 5.1.1 --- A simple backward algorithm --- p.69 / Chapter 5.1.2 --- Error estimate for simple backward scheme --- p.71 / Chapter 5.2 --- A new explicit backward algorithm for BSDEs and its error estimates --- p.85 / Chapter 5.2.1 --- A new explicit backward algorithm --- p.85 / Chapter 5.2.2 --- Error estimate for explicit backward scheme --- p.86 / Chapter 6 --- Higher order schemes of Markovian cases and error estimates --- p.91 / Chapter 6.1 --- Error estimate of 1-order scheme for Markovian BSDEs --- p.92 / Chapter 6.2 --- 2-order scheme for Markovian BSDEs and its error estimate --- p.100 / Chapter 6.2.1 --- 2-order scheme for Markovian BSDEs --- p.100 / Chapter 6.2.2 --- Error estimate of 2-order scheme --- p.102 / Chapter 7 --- Simulation results for BSDEs --- p.106 / Chapter 7.1 --- Basis functions --- p.107 / Chapter 7.2 --- Numerical simulations --- p.108 / Chapter 7.2.1 --- Application on option pricing --- p.108 / Chapter 7.2.2 --- Numerical examples on Markovian BSDEs --- p.114 / Chapter 8 --- Conclusions and future work --- p.123 / Chapter 8.1 --- Conclusions --- p.123 / Chapter 8.2 --- Future work --- p.124 / Bibliography --- p.126

by Bai Zheng Jian. / "May 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web.

Xie Jian Li. / "August 2003." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (p. 106-109). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

by Hao-min Zhou. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references. / Abstract --- p.1 / Introduction --- p.3 / Paper I --- p.8 / Paper II --- p.28

Dans cette thèse, nous étudions les écoulements de fluides compressibles décrits par les équations de Navier-Stokes-Fourier dans les cas stationnaire et instationnaire et avec des conditions de bord assurant l’isolation thermique et mécanique du fluide. On commence par le cas stationnaire barotrope et des conditions de Navier à la frontière du domaine. La pression est donc de la forme p(%) = % où est appelé coefficient adiabatique et nous arrivons à montrer l’existence de solutions faibles pour > 1.On généralise ensuite ce résultat aux équations de Navier-Stokes-Fourier avec conduction de la chaleur et glissement (partiel ou total) au bord, toujours dans le cas stationnaire. On montre cette fois-ci l’existence de solutions faibles particulières appelées solutions entropiques variationnelles respectant l’inégalité d’entropie pour > 1 et l’existence de solutions faibles respectant le bilan de l’énergie totale au sens faible pour > 5/4. On travaille ensuite sur les écoulements instationnaires décrits par les équations de Navier-Stokes-Fourier sur une large variété de domaines non bornés, tout d’abord pour des conditions de bord d’adhérence puis pour des conditions de Navier à la frontière (ce qui restreintquelque peu la diversité des domaines non bornés admissibles). On arrive à montrer l’existence de solutions faibles particulières respectant l’inégalité d’entropie et une inégalité de dissipation remplaçant l’égalité de conservation d’énergie totale dans le volume qui n’a plus de sens dans les domaines non bornés. Par après, on met en place une inégalité dite d’entropie relative dont on montre qu’elle est respectée par certaines des solutions faibles exhibées auparavant. Ces solutions sont appelées solutions dissipatives. On parvient à prouver que pour chaque donnée initiale, il existe au moins une solution dissipative. Cette inégalité d’entropie relative nous permet de démontrer le principe d’unicité forte-faiblepour nos solutions dissipatives. Précisément, cela signifie qu’une solution dissipative et une solution forte issues des mêmes données initiales coïncident sur le temps maximal d’existence de la solution forte. La propriété d’unicité forte-faible donne un fondement à la notion de solution dissipative pour les domaines non bornés. / In this thesis, we study the Navier-Stokes-Fourier system describing the flow of compressible fluids both in the steady and unsteady case and we suppose that the fluid is thermally and mechanically isolated. We start with the case of a steady barotropic fluid and Navier boundary conditions. In this situation, the pressure law considered is of the form p(%) = %, where is called the adiabatic constant. We show the existence of weak solutions for > 1. We then extend this result to the complete Navier-Stokes-Fourier system with heat conductivity and slip or partially slip boundary conditions, once again in thesteady case. In this setup, we prove the existence of a specific type of weak solutions, called variationnal entropy solutions, which satisfy the entropy inequality for > 1 and the existence of weak solutions satisfying the conservation of total energy in its weak formulation for > 5/4. We then treat the unsteady flows described by the complete Navier-Stokes-Fourier system on a large class of unbouded domains, first with no-slip boundary conditions and then with the Navier boundary conditions which reduce the class of the admissible unbounded domains. We manage to prove the existence of a specific type of weak solutions verifying the entropy inequality and a dissipation inequality instead of the global conservation of total energy which is no more relevant in the unbounded domains. Afterwards, we establish a new inequality called relative entropy inequality and we show that it is satisfied by some of the weak solutions presented previously. These are called dissipative solutions. Next we show that for any given initial data there exists at least one dissipative solution. This observation allows us toperform the proof of the weak-strong uniqueness principle in the class of dissipative solutions. Precisely, it means that a dissipative solution and a classical one emanating from the same initial data coincide as long as the latter exists. The weak-strong uniqueness property justifies the concept of dissipative solutions in the situation of unbounded domains.

The enthalpies of solution, HS, of carbon dioxide in aqueous methyldiethanolamine were measured with an isothermal flow calorimeter over wide ranges of temperature, pressure, weight percent MDEA, and loading (gmole CO2/gmole MDEA). The values of HS (kJ/gmole CO2) were found to be constant up to the saturation concentration of CO2 in the aqueous solution. In addition, experimental data showed that HS was independent of the total pressure over the solution, but linearly dependent upon both temperature and weight percent MDEA as was given by a correlation. A computer program based upon basic thermodynamic quantities was developed to model HS of CO2 in MDEA solutions. The values of K and ΔH for each of the chemical reactions (except the MDEA protonation reaction) were fitted values from the literature. Activity coefficient correlations used in the program were also obtained from the literature. Using these data, the program was first used to find the values of K and ΔH for the MDEA protonation reaction which gave the minimum error between the model and the experimental data. Finally, the values of HS predicted by the program were compared to the experimental data and the differences were discussed.

Dans cette thèse, nous examinons la question d'existence de solutions faibles des équations de Navier-Stokes compressibles et isentropiques. Cette étude a été motivée par les travaux de P.L. Lions qui a apporté une réponse à cette question lorsque la région occupée par le fluide est régulière et sous des hypothèses pas toujours satisfaisantes d'un point de vue physique pour la constante adiabatique. Récemment, E. Feireisl a proposé une méthode permettant d'affaiblir ces hypothèses et l'a appliquée aux équations d'évolution. Dans le cas stationnaire, nous montrons l'existence d'une solution faible renormalisée à énergie bornée lorsque la région d'écoulement est bornée, à régularité Lipschitzienne et nous améliorons dans certains cas les hypothèses sur la constante adiabatique. Nous étudions ensuite les écoulements lorsque la région est non bornée et présente plusieurs sorties à l'infini. Dans cette situation, nous définissons les solutions faibles à énergie bornée en faisant apparaître dans l'inégalité d'énergie la notion de flux à travers chaque sortie ainsi que celle de saut de pression entre les sorties. Nous démontrons l'existence de ces solutions lorsque les sorties sont coniques alors que dans le cas où celles-ci sont cylindriques, nous prouvons qu'en général de telles solutions n'existent pas. Dans le cas non stationnaire, nous démontrons l'existence de solutions faibles pour un problème avec afflux et débit dans une région borée ayant une géométrie particulière. Ces travaux sont inspirés de ceux de E. Feireisl en optimisation de formes dans un écoulement compressible et visqueux.