Let G be a graph and Ḡ be the complement of G. The complementary prism GḠ of G is the graph formed from the disjoint union of G and Ḡ by adding the edges of a perfect matching between the corresponding vertices of G and Ḡ. For example, if G is a 5-cycle, then GḠ is the Petersen graph. In this paper we consider domination and total domination numbers of complementary prisms. For any graph G, max {γ(G), γ(Ḡ)} ≤ γ (Ḡ)and max {γt(G), γt(Ḡ)} ≤ γt (Gγ), where γ(G) and γt(G) denote the domination and total domination numbers of G, respectively. Among other results, we characterize the graphs G attaining these lower bounds.

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This research is mainly focused on the development of the adaptive Cartesian grid methods for compressibl  e flow. At first, the ghost cell method and its applications for inviscid compressible flow on adaptive tree Cartesian grid are developed. The proposed method is successfully used to evaluate various inviscid compressible flows around complex bodies. The mass conservation of the method is also studied by numerical analysis. The extension to three-dimensional flow is presented. Then, an h-adaptive Runge–Kutta discontinuous Galerkin (RKDG) method is presented in detail for the development of high accuracy numerical method under Cartesian grid. This method combined with the ghost cell immersed boundary method is also validated by well documented test problems involving both steady and unsteady compressible flows over complex bodies in a wide range of Mach numbers. In addition, in order to suppress the failure of preserving positivity of density or pressure, which may cause blow-ups of the high order numerical algorithms, a positivity-preserving limiter technique coupled with h-adaptive RKDG method is developed. Such a method has been successfully implemented to study flows with the large Mach number, strong shock/obstacle interactions and shock diffraction. The extension of the method to viscous flow under the adaptive Cartesian grid with hybrid overlapping bodyfitted grid is developed. The method is validated by benchmark problems and has been successfully implemented to study airfoil with ice accretion. Finally, based on an open source code, the detached eddy simulation (DES) is developed for massive separation flow, and it is used to perform the research on aerodynamic performance analysis over the wing with ice accretion.

During the last years cartesian genetic programming proved to be a very perspective area of the evolutionary computing. However it has its limitations, which make its use in area of large and generic problems impossible. These limitations can be eliminated using the recent method allowing self-modification of programs in cartesian genetic programming. The purpose of this thesis is to review the development in this area done so far. Next objective is to design own solutions for solving various problems that are hardly solvable using the ordinary cartesian genetic programming. One of the problems to be considered is generating the terms of various Taylor series. Due to the fact that the solution to this problem requires generalisation, the goal is to prove that the self-modifying cartesian genetic programming scores better than classic one for this problem. Another discussed problem is using the self-modifying genetic programming for developing arbitrarily large sorting networks. In this case, the objective is to prove that self-modification brings new features to the cartesian genetic programming allowing the development of arbitrarily sized designs.

This thesis develops a disjunctivist approach to action as an alternative to the standard causal theory, or 'causalism'. The standard theory promotes a concept of action as constituted by a bodily event joined to certain mental conditions by a bond of causation. A disjunctivist approach, in contrast, claims that action must be distinguished by more than merely its etiology: action and mere movement are fundamentally different kinds. Recent objections to the causal theory of action are first surveyed, and the common causalist assumption claiming Aristotle as the progenitor of the causal theory is examined and dismissed. More refined interpretations of Aristotle's thought on action yield two different concepts: action as change, and action as a unified psychophysical process. The latter in particular is argued to hold promise as a basis for developing the disjunctivist approach to action. The remainder of the thesis therefore considers a contemporary account of psychophysicality, known as 'embodiment theory' (Hanna and Maiese 2009), with the conclusion that the intelligibility of the account depends on appeal to a recent variant of top-down causation (Steward 2012). The thesis also concludes that consideration of the concept of an animal agent makes it entirely unsurprising that the mental and physical are always found together in voluntary movement, and that the embodiment theory's central notion of ‘property fusion' potentially complements a naturalistic variant of top-down causation in explanations of agency.

Simulating transient compressible flows involving shock waves presents challenges to the CFD practitioner in terms of the mesh quality required to resolve discontinuities and prevent smearing. This document discusses a novel two-dimensional Cartesian anisotropic mesh adaptation technique implemented for transient compressible flow. This technique, originally developed for laminar incompressible flow, is efficient because it refines and coarsens cells using criteria that consider the solution in each of the cardinal directions separately. In this document the method will be applied to compressible flow. The procedure shows promise in its ability to deliver good quality solutions while achieving computational savings. Transient shock wave diffraction over a backward step and shock reflection over a forward step are considered as test cases because they demonstrate that the quality of the solution can be maintained as the mesh is refined and coarsened in time. The data structure is explained in relation to the computational mesh, and the object-oriented design and implementation of the code is presented. Refinement and coarsening algorithms are outlined. Computational savings over uniform and isotropic mesh approaches are shown to be significant.

Interface tracking methods for segregated flows such as breaking ocean waves are an important tool in marine engineering. With the development in marine renewable devices increasing and a multitude of other marine flow problems that benefit from the possibility of simulation on computer, the need for accurate free surface solvers capable of solving wave simulations has never been greater. An important component of successfully simulating segregated flow of any type is accurately tracking the position of the separating interface between fluids. It is desirable to represent the interface as a sharp, smooth, continuous entity in simulations. Popular Eulerian interface tracking methods appropriate for segregated flows such as the Marker and Cell Method (MAC) and the Volume of Fluid (VOF) were considered. However these methods have drawbacks with smearing of the interface and high computational costs in 3D simulations being among the most prevalent. This PhD project uses a level set method to implicitly represent an interface. The level set method is a signed distance function capable of both sharp and smooth representations of a free surface. It was found, over time, that the level set function ceases to represent a signed distance due to interaction of local velocity fields. This affects the accuracy to which the level set can represent a fluid interface, leading to mass loss. An advection solver, the Cubic Interpolated Polynomial (CIP) method, is presented and tested for its ability to transport a level set interface around a numerical domain in 2D. An advection problem of the level set function demonstrates the mass loss that can befall the method. To combat this, a process known as reinitialisation can be used to re-distance the level set function between time-steps, maintaining better accuracy. The goal of this PhD project is to present a new numerical gradient approximation that allows for the extension of the reinitialisation method to unstructured numerical grids. A particular focus is the Cartesian cut cell grid method. It allows geometric boundaries of arbitrary complexity to be cut from a regular Cartesian grid, allowing for flexible high quality grid generation with low computational cost. A reinitialisation routine using 1st order gradient approximation is implemented and demonstrated with 1D and 2D test problems. An additional area-conserving constraint is introduced to improve accuracy further. From the results, 1st order gradient approximation is shown to be inadequate for improving the accuracy of the level set method. To obtain higher accuracy and the potential for use on unstructured grids a novel gradient approximation based on a slope limited least squares method, suitable for level set reinitialisation, is developed. The new gradient scheme shows a significant improvement in accuracy when compared with level set reinitialisation methods using a lower order gradient approximation on a structured grid. A short study is conducted to find the optimal parameters for running 2D level set interface tracking and the new reinitialisation method. The details of the steps required to implement the current method on a Cartesian cut cell grid are discussed. Finally, suggestions for future work using the methods demonstrated in the thesis are presented.

Thesis advisor: Marilee Ogren / The suggestion of a mind-brain duality that emerges out of Descartes’ cogito argument is assessed in the context of twenty-first century neuroscience. The Cartesian texts are explored in order to qualify the extent to which the cogito necessitates such dualism and the functions that Descartes attributes to a non-corporeal soul are precisely defined. The relationship between the mind and brain is explored in the context of a number neuroscientific phenomena, including sensory perception, blindsight, amusia, phantom limb syndrome, frontal lobe lesions, and the neurodevelopmental disorder Williams syndrome, with an attempt to illuminate the physiological basis for each. Juxtaposing the two perspectives, the author concludes that Descartes hypothesis of a disembodied soul is no longer necessary and that a purely physiological understanding of the human mind is now possible, and that there is an underlying affinity between this assertion and Descartes theory of mind. / Thesis (BS) — Boston College, 2009. / Submitted to: Boston College. College of Arts and Sciences. / Discipline: College Honors Program. / Discipline: Psychology.

We present a novel dimensionally split Cartesian cut cell method to compute inviscid, viscous and turbulent flows around rigid geometries. On a cut cell mesh, the existence of arbitrarily small boundary cells severely restricts the stable time step for an explicit numerical scheme. We solve this `small cell problem' when computing solutions for hyperbolic conservation laws by combining wave speed and geometric information to develop a novel stabilised cut cell flux. The convergence and stability of the developed technique are proved for the one-dimensional linear advection equation, while its multi-dimensional numerical performance is investigated through the computation of solutions to a number of test problems for the linear advection and Euler equations. This work was recently published in the Journal of Computational Physics (Gokhale et al., 2018). Subsequently, we develop the method further to be able to compute solutions for the compressible Navier-Stokes equations. The method is globally second order accurate in the L1 norm, fully conservative, and allows the use of time steps determined by the regular grid spacing. We provide a full description of the three-dimensional implementation of the method and evaluate its numerical performance by computing solutions to a wide range of test problems ranging from the nearly incompressible to the highly compressible flow regimes. This work was recently published in the Journal of Computational Physics (Gokhale et al., 2018). It is the first presentation of a dimensionally split cut cell method for the compressible Navier-Stokes equations in the literature. Finally, we also present an extension of the cut cell method to solve high Reynolds number turbulent automotive flows using a wall-modelled Large Eddy Simulation (WMLES) approach. A full description is provided of the coupling between the (implicit) LES solution and an equilibrium wall function on the cut cell mesh. The combined methodology is used to compute results for the turbulent flow over a square cylinder, and for flow over the SAE Notchback and DrivAer reference automotive geometries. We intend to publish the promising results as part of a future publication, which would be the first assessment of a WMLES Cartesian cut cell approach for computing automotive flows to be presented in the literature.

Ma thèse a pour objet la réflexion menée par Juan Caramuel y Lobkowitz, dans ses œuvres imprimées et manuscrites, sur la philosophie de René Descartes. Notre objectif consiste à reconstruire la critique, l’interprétation et l’utilisation de la philosophie de Descartes par Caramuel à travers une étude complète, à ce jour jamais réalisée, de tous les manuscrits cartésiens de Caramuel. Cette reconstruction sera complétée par une brève recherche effectuée sur les œuvres imprimées successives aux Animadversiones. Les Animadversiones constituent une série d’objections contre les Meditationes de prima philosophia à travers lesquelles Caramuel se propose de démontrer l’échec de l’entreprise cartésienne. L’étude des Animadversiones (ch. II) a exigé d’aborder plus profondément la conception de Caramuel relative à l’existence et à la nature des entia rationis (avec lesquelles il identifie les idées matériellement fausses de la Meditatio III) dans l’ouvrage métaphysique le plus important de Caramuel, la Rationalis et Realis philosophia (ch. I) et d’analyser les lettres manuscrites sur les Animadversiones et Meditationes, dont l’étude jette une lumière plus vive sur le projet sous-jacent aux Animadversiones, leur rédaction et leur circulation manuscrite, tout en approfondissant l’analyse de certaines critiques ébauchées dans les Animadversiones. Enfin, l’analyse des autres manuscrits cartésiens de Vigevano, dans lesquels la discussion concernant la métaphysique cartésienne se développe ultérieurement et où apparaît un nouveau contexte de discussion et de remise en question des thèses cartésiennes par rapport à la physique, permet de compléter le cadre (Ch. IV). / My dissertation focuses on Juan Caramuel y Lobkowitz’s reflection on René Descartes’ Philosophy as it is developed in his printed and handwritten works. My aim is to reconstruct Caramuel’s criticism, interpretation and use of Descartes’ Philosophy through a comprehensive study of all of Caramuel’s Cartesian manuscripts, including the famous Animadversiones in Meditationes Cartesianas (1644). My reconstruction is introduced by a study of Caramuel’s main metaphysical work, Rationalis et Realis Philosophia (1642), and is complemented by a brief research conducted on his printed works published after the composition of the Animadversiones. The Animadversiones is a group of objections written against the Meditationes de prima philosophia in which Caramuel aims to demonstrate the failure of Descartes’ metaphysical project. The study of the Animadversiones (ch. II) has required, on the one hand, a preliminary enquiry on Caramuel’s metaphysical doctrine on the existence and the nature of the entia rationis, that he will later identify with the materially false ideas of Meditatio III (ch. I), and on the other hand, a detailed examination of his handwritten letters on the Animadversiones and the Meditationes. This examination is helpful in order to clarify the underlying project of the Animadversiones, as concerns both their composition and their private circulation, as well as to enlight the criticism addressed against Descartes in the Animadversiones. Finally, ch. IV completes my study by analyzing the other Cartesian manuscripts in Vigevano, that develop Caramuel’s discussion on Descartes’s Metaphysics and, at the same time, open a new discussion on Descartes’ Physics.