Hypersonic flow analysis is performed on an inflatable aerocapture device called a "Ballute" for Titan's Mission. An existing unstructured Cartesian grid methodology is used as a starting point by taking advantage of its ability to automatically generate grids over any deformed shape of the flexible ballute. The major effort for this thesis work is focused on advancing the existing unstructured Cartesian grid methodology. This includes implementing thermochemical nonequilibrium capability and porting it to a parallel computing environment using a Space-Filling-Curve (SFC) based domain decomposition technique. The implemented two temperature thermochemical nonequilibrium solver governs the finite rate chemical reactions and vibrational relaxation in the high temperature regimes of hypersonic flow. In order to avoid the stiffness problem in the explicit chemical solver, a point implicit method is adopted to calculate the chemical reaction source term. The AUSMPW+ scheme with MUSCL data reconstruction is adopted as the numerical scheme to avoid non-physical oscillations and the carbuncle phenomenon. The results for five species air model and for thirteen species N2-CH4-Ar model to simulate Titan entry are included for verification against DPLR (NASA Ames' structured grid hypersonic flow solver). The efficient parallel computation of any unstructured grid flow solver requires an adequate grid decomposition strategy because of its complex spatial data structure. The difficulties of even and block-contiguous partitioning in frequently adapting unstructured Cartesian grids are overcome by implementing the 3D Hilbert SFC. Grids constructed by the SFC for parallel environment promise short inter-CPU communication time while maintaining perfect load balancing between CPUs. The load imbalance due to the local solution adaption is simply apportioned by re-segmenting the curve into even pieces. The detailed structure of the 3D Hilbert SFC and parallel computing efficiency results based on this grid partition method are also presented. Finally, a structural dynamics tool (LS-DYNA) is loosely coupled with the present parallel thermochemical nonequilibrium flow solver to obtain the deformed surface definition of the ballute.

Phenomenology has been one of the most influential and far-reaching developments in 20th Century Philosophy and has had a great impact on the disciplines of philosophy of logic and math, theory of knowledge, and theory of meaning. The most profound influence on Edmund Husserl (1859 - 1938), the founder of phenomenology, was Rene Descartes (1596 - 1650), whose radical rethinking of philosophy’s overall project provided Husserl with both the historical and conceptual point of departure for his foundation of prima philosophia. Despite this explicit and well-known influence, there is no book- length study of their thematic parallels; numerous Journal articles focus almost entirely on the phenomenological reduction and, aside from this, are fairly unsatisfactory. The purpose of the present work is to elucidate systematic convergences (and divergences) between Descartes and Husserl throughout their respective philosophical developments. This comprises explication of several central topics: 1. The parallel between 17th C. skepticism, which Descartes attempted to overthrow, and 19th C. psychologism and relativism, which Husserl reacted against. 2. The striking similarity at the level of formal ontology between Descartes' simple and complex natures and Husserl's part-whole theory. 3. A clarification of the Cartesian sense of methodical doubt and how Husserl's mistaking of this shaped the initial formulation of the reduction. 4. Convergence in the maturation of the primitive notion of intuition as "clear and distinct seeing" and "seeing of essences" for both thinkers. 5. An analysis of the modes of methodical doubt, in terms of steps in the cognitive act of doubting, and not merely in the content of that which is doubted. 6. Far-reaching divergences in that Descartes was motivated to establish with scientific certainly an entirely new world of being, whereas Husserl was concerned to disclose an entirely new sense of the world. As such, thematic convergences between Descartes and Husserl are not due to accidental intersections of interest, nor are they curiosities of the comparative method in historical research. These parallels are intrinsic and systematic due to an overarching congruence in their visions of the starting point, methodological procedures, and reaction to pseudo-scientific matters-of-fact in the founding of a genuine philosophical project.

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This work starts from three complementary and interdependent questions: 1) How should we interpret Wittgenstein’s anti-skeptical strategy as presented in On Certainty, and especially the elusive and yet central concept of ‘hinges’? 2) Can Wittgenstein’s strategy, when properly understood and developed, provide a satisfactory response to Cartesian skepticism? 3) Does a Wittgensteinian epistemology license epistemic relativism, and if so to what extent? In Chapter 1, I present Cartesian-style skepticism and its epistemological implications along with the Dretske-Nozick’s ‘relevant alternatives’ theory, based on the rejection of the Closure principle for Knowledge which underlies the skeptical challenge. After a brief discussion of the main concerns raised against this proposal, I argue that this line is untenable and that a successful anti-skeptical proposal has to retain Closure. Having shown the shortcomings of the Dretske-Nozick proposal, I then focus my attention on G. E. Moore’s famous anti-skeptical works, namely “A Defence of Common Sense” (1925, henceforth DCS) and “Proof of an External World”, (1939, henceforth PEW). In these seminal papers, Moore famously argued that it is possible to know several ‘obvious truisms of commonsense’ such as ‘There are external objects’, I have a body’ and so on and that this knowledge can offer a direct response to skeptical worries; the aim of this strategy is then to retain both Closure and our confidence in our everyday knowledge claims. After a detailed presentation of DCS and PEW I will discuss the problems of Moore’s direct response against the skeptic, drawing on the works of distinguished commentators such as Malcolm, Clarke, Stroud and Wright. Roughly, I argue that Moore’s strategy is both unnecessary and unconvincing: unconvincing because Moore’s knowledge-claims cannot refute Cartesian skeptical arguments; unnecessary for they can ‘work’ only within our everyday ‘non-philosophical’ context, thus when no skeptical hypothesis can be sensibly raised. Even if Moore’s anti-skeptical attempts have unanimously been considered unsatisfying, for several reasons his works have nonetheless been extremely influential, to the extent that quite a few contemporary anti-skeptical proposals can be fairly described as ‘Moorean’. In Chapter 2, I present and discuss the dominant ‘Moore-Inspired’ positions, namely Pryor’s Dogmatist Reading of PEW, Neta’s interpretation of the Proof, Greco’s reliabilist account, Fara’s ‘Second Proof’, DeRose’s ‘Moorean contextualism’ and Sosa ‘Neo-Mooreanism’. I criticise these accounts in turn, in order to show that all these strategies inherit the main problems of Moore’s treatment of skepticism and also have unpalatable consequences with regard to the so-called ‘value problem for knowledge’. After having extensively criticised both Moore’s and ‘Neo-Moorean’ epistemologies, in Chapter 3 I focus my attention on Wittgenstein’s On Certainty; given the obscurity and ambiguity of this work, in this chapter I present some of the less contentious aspects of Wittgenstein’s treatment of skepticism and I emphasise the role played by ‘hinges ’ in his anti-skeptical strategy. This will give me the background to assess the different ‘Wittgensteininspired’ anti-skeptical strategies I consider in Chapter 4, namely Conant’s ‘therapeutic’ reading, Wright’s ‘rational entitlement’ account, Williams’ ‘Wittgensteinian contextualism’, McGinn’s ‘framework’ reading and Pritchard’s ‘hinge commitment’ strategy. I argue that these proposals are wanting, both as plausible interpretations of Wittgenstein’s thought and more importantly as viable anti-skeptical strategies. Moreover, I show that McGinn and Williams’ proposals can lead to a form of epistemic relativism, according to which our epistemic practices are the result of pre-rational, social commitments not subject to rational evaluation of any sort; a conclusion which is not more palatable than skepticism itself. Chapter 5 is devoted to presenting Moyal-Sharrock’s ‘non-epistemic’ reading of OC, for which ‘hinges’ such as ‘There are external objects’ or ‘I have a body’ are the expression of a pre-theoretical, animal certainty which she sees as constitutively different from knowledge. While I defend Moyal-Sharrock’s exegesis and her analogy between ‘hinges’ and 'rules of grammar’ as the most plausible interpretation of Wittgenstein’s thought, in this chapter I also criticise her ‘non-epistemic’ account; roughly, I argue that following this strategy we will be forced either to reject the Closure principle, thus inheriting the problems of the Dretske-Nozick’s line, or else to endorse skepticism. Moreover, I also consider some of the relativistic implications of Moyal-Sharrock’s account, which make her proposal vulnerable to the same objections I have raised against McGinn’s framework reading and Williams’ Wittgensteinian contextualism. In Chapter 6, I develop my own anti-skeptical proposal, which is informed by the analogy between ‘hinges’ and ‘rules of grammar’ and their peculiar status. Drawing on Wittgenstein’s reflections on grammatical rules, developed in the socalled second phase of his thought, and especially in his Philosophical Investigations, I argue that ‘hinges’ cannot be object of knowledge but are subject to an altogether different epistemic standing, namely understanding or ‘mastery of techniques’. A promising anti-skeptical implication of this account is that it will help us to dismiss Cartesian-style skepticism as the result of a logical error, based on a misleading way of representing the structure of our epistemic practices, which are not based on propositional beliefs but rather on non-propositional, normative rules. In the rest of Chapter 6, I consider a final problem that a Wittgensteinian epistemology so construed has to face in order to be considered a fully viable antiskeptical position; that is, whether Wittgenstein’s account of ‘hinges’ would lead to epistemic relativism of a kind that is generated by the proposals put forward by Williams, McGinn and Moyal-Sharrock. Chapter 7 is devoted to addressing this question in detail. Drawing on Wittgenstein’s views on mathematics, metrology and religious beliefs, I aim to show that his remarks on ‘hinges’ will help us to dissolve epistemic relativism rather than licensing it. This is so because following Wittgenstein’s remarks on the structure of reason the disagreement between epistemic communities committed to different ‘hinges’ (for instance a community which believes in oracles rather than in science) is either solvable, as different epistemic practices can be compared and assessed if they have similar aims, or is a pseudo-disagreement which stems from a misguided comparison between different practices.

My thesis examines Dubliners through the lens of Rene Descartes’s mind-body dualism to explain the relationship between contrasting themes in the text and demonstrate how they are connected. In an explication of the three words introduced by Joyce in the introductory paragraph of the first story in his collection, namely paralysis, gnomon, and simony, linking them with their more subtle but equally significant antonymic themes, which I propose are progression, epiphany, and grace, I show that Joyce was as compassionate as he was contemptuous of his countrymen. I propose that recognizing this balance helps us better understand what Joyce may have meant by making no apology for the brute-like spectacle he projects in his nicely polished looking-glass. Moreover, I argue that Dubliners serves as a fictional canvas upon which Joyce projects his dream of an Ireland that can transcend the tedium-inducing confines of its past.

Two optical design scenarios—imaging and illumination—were investigated for their use of Cartesian- and polar-based functions to generate freeform optical surfaces. The imaging scenario investigated a single-element, refracting freeform surface that converts an on-axis object field to an off-axis image point. XY polynomials (Cartesian but not orthogonal) and Zernike polynomials (Polar and orthogonal) were the two different function sets used to manipulate the surfaces to achieve the freeform imaging scenarios. The investigation discovered that the results between both function sets did not differ enough to single out a more effective surface type. However, the results did indicate that the Zernike function set typically required fewer coefficients to converge on an optimal imaging solution. The illumination scenario utilized an architectural lighting situation surrounding the Rothko exhibit for Green on Blue at the University of Arizona Museum of Art. The source location was fixed to the light track in the exhibit space and pointed in many different orientations towards the painting. For each orientation, a point cloud of a freeform optical surface was generated such that the painting surface was illuminated with uniform and low-level light. For each of these generated point clouds, a Legendre (Cartesian and orthogonal) and a Zernike (polar and orthogonal) fitting function was applied, and the convergence results were compared. In general, it was found that, after the 20th included fit term, the Legendre function resulted in a smaller RMS fit error than the Zernike function. However, if the light source was pointed near the center of the painting, the Zernike function converged on a solution with fewer fit terms than Legendre. Amidst the imaging scenario, a definition for the extent to which a surface was freeform, or the "freeformity", was given. This definition proved to be an effective solution when the image size was compared for an F/3.33, F/4, F/5, and F/6.67 system for a range of different image focusing heights: the image size trends for each F-number overlapped, indicating a universal freeform term. In addition, a recursive formula for Cartesian Zernike polynomials was defined, which was used to generate an infinite number of Zernike terms using one single recursive expression.

In this paper the Cartesian product topology for an arbitrary family of topological spaces and some of its basic properties are defined. The space is investigated to determine which of the separation properties of the component spaces are invariant.

Within the field of multi-robot control, there is a large focus in research involving consensus. In this thesis two parts will be studied. The first development of this thesis is a consensus-based robot arm platform. To implement, two robotic arms are developed and studied. The most effective robot arm is then utilized to create a robot arm network testbed. Consensus is used to coordinate several robot arms and decentralize system computation. The research explores a platform to facilitate consensus on a group of robotic arms. The second development is in Cartesian coordinate collective motion. This collective motion control combines consensus through coupling of Cartesian coordinates. The controller is presented with simulation and experimental validation. Integration of both parts of the thesis is then discussed in application. An example is provided to demonstrate usefulness. In conclusion, this thesis provides more control to a system of ground robots using collective motion and consensus-based robot arms.

Thesis--Bonn. / Includes bibliographical references (p. 223-235).

Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第14599号 / 工博第3067号 / 新制||工||1456(附属図書館) / 26951 / UT51-2009-D311 / 京都大学大学院工学研究科都市環境工学専攻 / (主査)教授 大西 有三, 教授 間瀬 肇, 准教授 西山 哲 / 学位規則第4条第1項該当