Traditionally, the design of complex aerospace systems requires iteration among segregated disciplines such as aerodynamic modeling and trajectory optimization. Multidisciplinary design optimization algorithms have been developed to efficiently orchestrate the interaction among these disciplines during the design process. For example, vehicle capability is generally obtained through sequential iteration among vehicle shape, aerodynamic performance, and trajectory optimization routines in which aerodynamic performance is obtained from large pre-computed tables that are a function of angle of attack, sideslip, and flight conditions. This numerical approach segregates advancements in vehicle shape design from advancements in trajectory optimization. This investigation advances the state-of-the-art in conceptual hypersonic aerodynamic analysis and trajectory optimization by removing the source of iteration between aerodynamic and trajectory analyses and capitalizing on fundamental linkages across hypersonic solutions. Analytic aerodynamic relations, like those derived in this investigation, are possible in any flow regime in which the flowfield can be accurately described analytically. These relations eliminate the large aerodynamic tables that contribute to the segregation of disciplinary advancements. Within the limits of Newtonian flow theory, many of the analytic expressions derived in this investigation provide exact solutions that eliminate the computational error of approximate methods widely used today while simultaneously improving computational performance. To address the mathematical limit of analytic solutions, additional relations are developed that fundamentally alter the manner in which Newtonian aerodynamics are calculated. The resulting aerodynamic expressions provide an analytic mapping of vehicle shape to trajectory performance. This analytic mapping collapses the traditional, segregated design environment into a single, unified, mathematical framework which enables fast, specialized trajectory optimization methods to be extended to also include vehicle shape. A rapid trajectory optimization methodology suitable for this new, mathematically integrated design environment is also developed by relying on the continuation of solutions found via indirect methods. Examples demonstrate that families of optimal hypersonic trajectories can be quickly constructed for varying trajectory parameters, vehicle shapes, atmospheric properties, and gravity models to support design space exploration, trade studies, and vehicle requirements definition. These results validate the hypothesis that many hypersonic trajectory solutions are connected through fast indirect optimization methods. The extension of this trajectory optimization methodology to include vehicle shape through the development of analytic hypersonic aerodynamic relations enables the construction of a unified mathematical framework to perform rapid, simultaneous hypersonic aerodynamic and trajectory optimization. Performance comparisons relative to state-of-the-art methodologies illustrate the computational advantages of this new, unified design environment.

Peristalsis is a mechanism of pumping fluids in ducts when a progressive wave of area contraction or expansion propagates along the length of a distensible tube containing fluid. It induces in general propulsive and mixing movements and pumps the fluids against pressure rise. Physiologically, peristaltic action is an inherent property of smooth muscle contraction. It is an automatic and vital process that drives the urine from the kidney to the bladder, food through the digestive tract, bile from the gall-bladder into the duodenum, movement of ovum in the fallopian tube and many other situations. A major industrial application of this principle is in the design of roller pumps, which are used in pumping fluids without being contaminated due to the contact with the pumping machinery. Even though peristalsis is a well-known mechanism in biological system, the first theoretical and experimental analysis of its fluid dynamics aspects were given four decades ago. In reality, the peristaltic flow problems are unsteady moving free boundary value problems where the shape of the wave on flexible tube wall is not known apriori. But the mathematical models on peristaltic transport considered in the literature deal with a prescribed train of waves moving with constant speed on the flexible boundaries and they are studied in either a fixed frame or a wave frame moving with constant velocity of the wave. In a wave frame the moving walls become stationary wavy walls. Further the motion could be treated steady under the assumptions that the peristaltic wave train is periodic, the pressure difference across the length of the tube is constant and the tube length is an integral multiple of the wavelength. Some mathematical models of peristaltic flows representing some physiological situations are studied using a wave frame of reference in this thesis. The important characteristics of these flows namely pumping (variation of time averaged flux with difference in pressures across one wavelength), trapping (splitting of streamlines enclosing a bolus which moves as a whole along with the wave), reflux phenomena (the presence of some fluid particles whose mean motion over one cycle is against the net pumping direction) are discussed in detail. A brief general introduction to the peristaltic transport and their application in physiological fluid dynamics is presented in chapter one. In the second chapter, the peristaltic transport of an incompressible viscous Newtonian fluid in an asymmetric channel is studied under long wavelength and low-Reynolds number assumptions. Choosing the peristaltic wave train on the walls to have different amplitudes and phase produces the channel asymmetry. This study is motivated by the intra-uterine fluid flow induced by uterine wall contractions which represent a peristaltic flow in an asymmetric channel and this flow is responsible for embryo transport to a successful implantation site. The solution for the stream function is obtained by neglecting inertia and curvature effects. The streamlines are plotted in both fixed and wave frames. The effects of different geometric parameters causing asymmetry like phase difference; varying channel width and wave amplitudes are investigated on the pumping characteristics, streamline pat-tern, trapping and reflux phenomena. It is observed that the pumping against pressure rise, trapping and reflux layer exists only when cross-section of the channel varies along the axis. The limits on the time averaged flux for trapping and reflux are obtained. The peristaltic waves on the walls with same amplitudes propagating in phase produce zero flux rate as the channel cross-section remains the same through out. The trapping and reflux regions reduce for asymmetric channels compared to symmetric channels. The flow of an incompressible viscous fluid driven by the traveling waves along the boundaries of an asymmetric channel is studied in the chapter three, when inertia and streamline curvature effects are not negligible. It was well documented that the inertial forces cannot be ignored in the pharyngeal phase of bolus transport. Choosing the wave train on the walls to have different amplitudes and phases produces the channel asymmetry here. An asymptotic solution is obtained in powers of a geometric parameter £, the ratio of the channel width to the wavelength, giving curvature and inertia effects. A domain transformation is used to transform the channel of variable cross section to a uniform cross section, and this facilitates in easy way of finding closed form solutions at higher orders. The solutions are presented upto second order in 6. It has been found that, the relation connecting the pressure gradient and time average flux rate is a cubic leading to a non-unique of flux for a given pressure gradient. A uniqueness criterion is derived which restricts the parameters to get a unique flux for a prescribed pressure difference. The effects of inertia and curvature on peristaltic pumping, trapping and shear stress are discussed for various parameters governing the flow for symmetric and asymmetric channels and compared with the existing results in the literature. Even under a favourable pressure gradient the possibility of fluid flow in a direction opposite to the direction of the waves propagating on the walls is detected as in the case of some non-Newtonian fluids. It is noticed that the Reynolds number and asymmetry of the wall geometry may play an important role in producing mixing. The appearance of a second trapped bolus near the down streamside of the channel for some Reynolds number is a new feature. Further, the non-zero curvature produces three trapped boluses for high Reynolds number in symmetric channel as well as for inertia free flow in an asymmetric channel. Another interesting phenomena is that the shear stress distribution on the walls vanishes at some points but it does not indicate any flow separation as the MRS criteria is not satisfied. The gastrointestinal tract is surrounded by a number of muscle layers having smooth muscle. The most important smooth muscle layers in gastrointestinal tract are submucosa and a layer of epithelial cells and these- are responsible for the absorption of nutrients and water in the intestine. These layers consist of many folds and there are pores through out the tight junctions of them. Thus a study of peristaltic transport with porous peripheral layer and porous boundaries of a duct are important. Motivated by this the flow in gastrointestinal tract is mathematically modeled by a peristaltic flow of two fluid system in a two-dimensional channel with a porous peripheral layer and a Newtonian fluid core layer, in chapter four. The fluid flow is investigated under the assumptions of long wavelength and low Reynolds number in a wave frame of reference. Brinkman extended Darcy equation is utilized to model the flow in the porous peripheral layer. A shear stress jump boundary condition of Ochoa-Tapia and Whitaker is used at the interface between porous and fluid regions together with continuity of velocity and normal stress conditions. Here one needs an extra assumption that the fluid interface and the peristaltic wave on the boundary have the same period in addition to the constant pressure difference at the ends of channel and the length of the channel to be an integral multiple of the wavelength, to consider the flow to be steady. The interface is determined as a part of the solution using the conservation of mass in both the porous and fluid regions independently. Matlab packages are used to solve the transcendental equation governing it. An interval of critical time averaged flux Q is obtained for the existence of a unique solution for the interphase. The physical quantities of importance in peristaltic transport namely, pumping, trapping and reflux are discussed for various parameters of interest governing the flow like Darcy number Da, porosity 6, shear-stress jump constant /3, viscosity ratio /i. It is observed that the peristalsis works as a pump against greater pressure rise with a porous medium in the peripheral layer than a viscous fluid. The limits on the time averaged flux Q for trapping in the core layer are obtained. The existence of reflux near the axis is observed for small values of Darcy number and large values of /?. Chapter five deals with the peristaltic transport in a tube with a poroflexible wall and having a porous material layer in the peripheral region and a Newtonian fluid in the core region. Flow in tube may be more realistic to model a flow in gastrointestinal system. At the poroflexible wall, a slip boundary condition of Saffman.type is used. The fluid flow is studied in a wave frame of reference under lubrication approach. Brinkman extended Darcy equation in cylindrical polar coordinates is considered for the porous medium with a shear-stress jump boundary condition of Ochoa-Tapia and Whitaker at the interface of porous and fluid regions together with the continuity of velocity and normal stress. The interface is found as a part of the solutions using the conservation of mass in both the regions of deformable porous medium and fluid medium independently. The interface equation turns out to be a transcendental equation involving modified Bessel functions and it is solved by using Matlab packages. The uniqueness criterion of the solutions for the interface equation in the flow region is determined for certain values of time averaged flux Q. Pumping characteristics, trapping and reflux phenomena are discussed for various parameters of interest governing the flow like, wall slip constant fc, Darcy number Da, viscosity ratio /x. shear stress jump constant f) and peripheral layer thickness 7. The slip condition at the boundary, arising due to the poroflexible nature of the wall, enhances pumping. The trapped bolus volume in the core layer is observed to decrease with a decrease in Da, /i and k and an increase in /?. The reflux phenomena is discussed in detail. The trapping limits on the flux rate Q in the core region are obtained. As the behaviour of most of the physiological fluids is known to be non-Newtonian, the peristaltic flows of power-law and micro polar fluids are investigated in the next two chapters. In chapter six, the peristaltic transport of a power-law fluid in an axisymmetric tube having poroflexible wall is studied. The power-law model of Ostwald-de Waele type is considered, which accommodates the study of both shear thinning and shear thickening fluids. The flow characteristics are studied in wave frame analysis under lubrication approach. The slip boundary conditions of Beavers-Joseph and Saffman type are considered at the wall in obtaining solutions for the flow and resulting pumping characteristics are investigated with a straight section dominated (SSD) wave form other than the sinusoidal one. It is observed that the time mean flow becomes negative in free pumping for a shear thickening fluid with a SSD expansion wave and the same is observed for a SSD contraction wave in the case of shear thinning fluid. The pressure rise increases with increasing of Darcy number Da against which the peristalsis works as a pump and decreases for an increase in Beaver-Joseph constant a. Peristalsis works as a pump against a greater pressure rise for a shear thickening fluid and the opposite happens for a shear thinning fluid compared with Newtonian fluid. Trapping and reflux phenomena are discussed for various parameters of interest governing the flow like Da, a and the fluid behaviour index n. The trapping limits on Q are derived. The trapped bolus volume for sinusoidal wave is observed to decrease as the fluid behaviour index decreases, i.e as the fluid behaviour changes from shear thickening to shear thinning, where as it increases with an increase in Darcy number. The rheological properties of fluid, wave shape and porous nature of the wall play an important role in the peristaltic transport and may be useful in understanding the transport of chyme in small intestine. The chapter seven contains the study of peristaltic transport of a micropolar fluid in an axisymmetric tube. Micropolar fluids exhibit some microscopic effects arising from the local structure and micro motion of the fluid elements. Further, they can sustain couple stresses. It is speculated that, in microcirculation, peristalsis may be involved as well in the vasomotion of small blood vessels which change their diameters periodically. Therefore, modelling blood by a micropolar fluid may be more appropriate. The closed form solutions are obtained for velocity, microrotation components, as well as the stream function under the assumption of long wavelength and low Reynolds number. The solution contains new additional parameters namely, N the coupling number and m the microploar parameter. In the case of free pumping (pressure difference Ap = 0) the difference in pumping flux is observed to be very small for Newtonian and micropolar fluids but in the case of pumping (Ap > 0) the characteristics are significantly altered for different N and m. It is observed that the peristalsis in micropolar fluids works as a pump against a greater pressure rise compared with a Newtonian fluid. Streamline patterns which depict trapping phenomena aie presented for different parameter ranges. The limit on the trapping of the center streamline is obtained. The effects of N and m on friction force for different Ap are discussed. The nomenclature of symbols in each chapter is independent of the other. Each of the chapter has its own appendix and they are numbered with the corresponding roman number of the chapters. The purpose of the study here is not to represent exactly the functioning of various physiological applications, but rather to understand the fluid-mechanical aspects inherent in the problems of peristaltic transport.

No description available.

Chemical modification is an important way to improve the properties of existing polymers, and one of the important examples is the hydrogenation of nitrile butadiene rubber (NBR) in organic solvent by homogeneous catalysis in order to extend its application. This process has been industrialized for many years to provide high performance elastomers (HNBR) for the automotive industry, especially those used to produce components in engine compartments. In the current commercial process, a batch reactor is employed for the hydrogenation step, which is labor intensive and not suitable for large volume of production. Thus, novel hydrogenation devices such as a continuous process are being developed in our research group to overcome these drawbacks. In order to make the process more practical for industrial application, high concentration polymer solutions should be targeted for the continuous hydrogenation. However, many problems are encountered due to the viscosity of the high concentration polymer solution, which increases tremendously as the reaction goes on, resulting in severe mass transfer and heat transfer problems. So, hydrogenation kinetics in high concentration NBR solution, as well as the rheological properties of this viscous solution are very essential and fundamental for the design of novel hydrogenation processes and reactor scale up. In the present work, hydrogenation of NBR in high concentration solution was carried out in a batch reactor. A commercial rhodium catalyst, Wilkinson’s catalyst, was used with triphenylphosphine as the co-catalyst and chlorobenzene as the solvent. The reactor was modified and a PID controller was tuned to fit this strong exothermic reaction. It was observed that when NBR solution is in a high concentration the kinetic behavior was greatly affected by mass transfer processes, especially the gas-liquid mass transfer. Reactor internals were designed and various agitators were investigated to improve the mechanical mixing. Experimental results show that the turbine-anchor combined agitator could provide superior mixing for this viscous reaction system. The kinetic behavior of NBR hydrogenation under low catalyst concentration was also studied. It was observed that the hydrogenation degree of the polymer could not reach 95% if less than 0.1%wt catalyst (based on polymer mass) was used, deviating from the behavior under a normal catalyst concentration. The viscosity of the NBR-MCB solutions was measured in a rotational rheometer that has a cylinder sensor under both room conditions and reaction conditions. Parameters that might affect the viscosity of the solutions were studied, especially the hydrogenation degree of polymer. Rheological properties of NBR-MEK solutions, as well as NBR melts were also studied for relevant information. It is concluded that the hydrogenation kinetics deviates from that reported by Parent et al. [6] when polymer is in high concentration and/or catalyst is in low concentration; and that the reaction solution (HNBR/NBR-MCB solution) deviates from Newtonian behavior when polymer concentration and hydrogenation degree are high.

The thesis reports a contribution to the development of neural-like network- based element-free methods for the numerical simulation of some non-Newtonian fluid flow problems. The numerical approximation of functions and solution of the governing partial differential equations are mainly based on radial basis function networks. The resultant micro-macroscopic approaches do not require any element-based discretisation and only rely on a set of unstructured collocation points and hence are truly meshless or element-free. The development of the present methods begins with the use of the multi-layer perceptron networks (MLPNs) and radial basis function networks (RBFNs) to effectively eliminate the volume integrals in the integral formulation of fluid flow problems. An adaptive velocity gradient domain decomposition (AVGDD) scheme is incorporated into the computational algorithm. As a result, an improved feed forward neural network boundary-element-only method (FFNN- BEM) is created and verified. The present FFNN-BEM successfully simulates the flow of several Generalised Newtonian Fluids (GNFs), including the Carreau, Power-law and Cross models. To the best of the author's knowledge, the present FFNN-BEM is the first to achieve convergence for difficult flow situations when the power-law indices are very small (as small as 0.2). Although some elements are still used to discretise the governing equations, but only on the boundary of the analysis domain, the experience gained in the development of element-free approximation in the domain provides valuable skills for the progress towards an element-free approach. A least squares collocation RBFN-based mesh-free method is then developed for solving the governing PDEs. This method is coupled with the stochastic simulation technique (SST), forming the mesoscopic approach for analyzing viscoelastic flid flows. The velocity field is computed from the RBFN-based mesh-free method (macroscopic component) and the stress is determined by the SST (microscopic component). Thus the SST removes a limitation in traditional macroscopic approaches since closed form constitutive equations are not necessary in the SST. In this mesh-free method, each of the unknowns in the conservation equations is represented by a linear combination of weighted radial basis functions and hence the unknowns are converted from physical variables (e.g. velocity, stresses, etc) into network weights through the application of the general linear least squares principle and point collocation procedure. Depending on the type of RBFs used, a number of parameters will influence the performance of the method. These parameters include the centres in the case of thin plate spline RBFNs (TPS-RBFNs), and the centres and the widths in the case of multi-quadric RBFNs (MQ-RBFNs). A further improvement of the approach is achieved when the Eulerian SST is formulated via Brownian configuration fields (BCF) in place of the Lagrangian SST. The SST is made more efficient with the inclusion of the control variate variance reduction scheme, which allows for a reduction of the number of dumbbells used to model the fluid. A highly parallelised algorithm, at both macro and micro levels, incorporating a domain decomposition technique, is implemented to handle larger problems. The approach is verified and used to simulate the flow of several model dilute polymeric fluids (the Hookean, FENE and FENE-P models) in simple as well as non-trivial geometries, including shear flows (transient Couette, Poiseuille flows)), elongational flows (4:1 and 10:1 abrupt contraction flows) and lid-driven cavity flows.

Κύριο αντικείμενο μελέτης της παρούσας μεταπτυχιακής διπλωματικής εργασίας είναι οι περιστρεφόμενοι αστέρες νετρονίων. Λόγω του ότι οι κλασικές διαταρακτικές μέθοδοι που εφαρμόζονται για την εύρεση της ακτίνας ενός περιστρεφόμενου πολυτροπικού μοντέλου περιορίζονται, από την επιφάνεια του αστέρα, αναπτύξαμε μία μέθοδο για τον υπολογισμό ποσοτήτων πέραν αυτού του ορίου. Αυτή η γενικευμένη μέθοδος χρησιμοποιεί τις μετανευτώνειες παραμέτρους ως όρους διαταραχής. Υλοποιώντας έναν κώδικα σε γλώσσα προγραμματισμού Fortran, υπολογίσαμε εκτεταμένους πίνακες ποσοτήτων και σταθερών. Μέσω της γενικευμένης αυτής μεθόδου επιτυγχάνεται η εύρεση της ακριβούς τιμής της ακτίνας ενός τέτοιου μοντέλου καθώς και ο καθορισμός της κρίσιμης παραμέτρου περιστροφής, η οποία αποτελεί μία μετανευτώνεια παράμετρο. Ο υπολογισμός της κρίσιμης παραμέτρου διαταραχής επιτυγχάνεται με ευκολία, κυρίως εκ του λόγου ότι η μέθοδος έχει υπολογίσει εκτεταμένους πίνακες συναρτησιακών τιμών. Οι υπολογιζόμενες κρίσιμες παράμετροι διαταραχής είναι μεγαλύτερες των αντιστοίχων τιμών της βιβλιογραφίας (κυρίως σε σύγκριση με τους Fahlman-Anand [55]), και φαίνεται να συμφωνούν καλύτερα με τις τιμές που υπολογίζονται από τις λεγόμενες επαναληπτικές μεθόδους. Τα αποτελέσματα επαληθεύουν με μεγάλη ακρίβεια τιμές συναρτήσεων και παραμέτρων σε σύγκριση με την κλασική βιβλιογραφία. Η παρούσα εργασία χωρίζεται σε πέντε μέρη, τα οποία αναπτύσσονται στα κεφάλαια 1, 2, 3, 4 και 5. Στο πρώτο κεφάλαιο, περιγράφεται ο αστέρας νετρονίων ως αστροφυσικό αντικείμενο. Δίνεται βάρος τόσο στη δομή του όσο και στα φυσικά χαρακτηριστικά του. Η ύπαρξη των αστέρων νετρονίων είναι απόλυτα συνδεδεμένη με τους πάλσαρς. Αυτοί αποτελούν ένα «ζωντανό» παράδειγμα περιστρεφομένων αστέρων νετρονίων; έτσι, γίνεται αναφορά στις φυσικές ιδιότητες και στις διεργασίες που πραγματοποιούνται σε αυτούς. Στο δεύτερο κεφάλαιο, αναφερόμαστε στις καταστατικές εξισώσεις που διέπουν το εσωτερικό των αστέρων νετρονίων, και στην έννοια του πολυτρόπου. Αφενός μεν, διότι δεν μπορεί να πραγματοποιηθεί μία μελέτη για αυτούς τους αστέρες χωρίς να υιοθετηθεί κάποια καταστατική εξίσωση, αφετέρου δε διότι μία από τις πλέον ενδεικτικές για την περιγραφή τους (και την οποία εμείς υιοθετούμε) είναι αυτή του πολυτρόπου. Επιπλέον, αναλύουμε τις εξισώσεις που διέπουν το αδιατάρακτο πολυτροπικό μοντέλο, όπως και αυτές που περιγράφουν το αντίστοιχο διαταραγμένο, σύμφωνα με τη θεωρία που ανέπτυξε ο Chandrasekhar. Στο τρίτο κεφάλαιο, χρησιμοποιούμε τη Γενική Θεωρία της Σχετικότητας στη μελέτη του πολυτροπικού μοντέλου, εστιάζοντας κυρίως στον τρόπο με τον οποίο τροποποιείται η κλασική θεώρηση, στο πώς μετασχηματίζονται η βασικές ποσότητες του μοντέλου, και στο πώς προκύπτουν οι σχέσεις της μετανευτώνειας προσέγγισης. Εξάγουμε τις μετανευτώνειες εξισώσεις της υδροδυναμικής και αναπτύσσουμε το διαταρακτικό μοντέλο επίλυσης, από το οποίο προκύπτουν οι εξισώσεις που επιλύουμε αριθμητικά. Στο τέταρτο κεφάλαιο, κάνουμε αναφορά στις διάφορες αριθμητικές μεθόδους που έχουν αναπτυχθεί για την μελέτη του σχετικιστικά περιστρεφόμενου πολυτροπικού μοντέλου. Στο πέμπτο κεφάλαιο, παρουσιάζουμε πίνακες αποτελεσμάτων και ενδιαφέρουσες γραφικές παραστάσεις. Δίνουμε επίσης ορισμένες αλγοριθμικές λεπτομέρειες για το πρόγραμμά μας. Συγκεκριμένα, γενικεύουμε τη μέθοδο των μετανευτωνείων προσεγγίσεων και αναλύουμε τα πλεονεκτήματα της. Ακολούθως, παραθέτουμε μία περιγραφή της αριθμητικής διαπραγμάτευσης της μεθόδου και την πορεία υλοποίησής της. Τέλος, παρατίθενται οι πίνακες των αποτελεσμάτων και τα τελικά συμπεράσματα. / In the present Thesis, we study rotating neutron stars. Due to the fact that the classical perturbation methods implemented to compute the radius of a polytropic rotating model are restricted by the star's surface, we develop a method for continuing integrations beyond this limit. This general approach utilises the postnewtonian parameters in terms of disturbance. By the application of a code written in Fortran, we calculate extensive tables of quantities and constants. Furthermore, we compute the radius as well as the critical rotation parameter, which plays the role of a postnewtonian term. This Thesis is organized in five chapters. In the first chapter, the neutron star is presented as an astrophysical object. Its structure and physical characteristics are of a great importance. Moreover, the existence of neutron stars is linked to pulsars, which are "living" examples of rotating neutron stars. Therefore, the physical characteristics of these objects are discussed in this chapter. The second chapter refers to the equations that describe the structure of the neutron stars and to the concept of polytropes. First, due to the difficulty in implementing a study for these stars without the adoption of any equation of state as well as due to the most indicative one for their description which is that of the polytrope. Second, the equations that refer to the undistorted and those that describe the corresponding distorted configurations are analysed in this chapter, in accordance with Chandrasekhar's perturbation theory. In the third chapter, the General Theory of Relativity is used to the study of the polytropic model, focusing on how the classical theory is corrected, on how the basic model's quantities are transformed and on how the equations of the postnewtonian approach are derived. The equations to be solved result from the latter ones. Furthermore, a a discussion on the various numerical methods that have been developed for studying the relativistic rotating polytopric model is given in the fourth chapter. In the fifth chapter of this Thesis, a number of tables illustrating results as well as some interesting diagrams are included. Certain algorithmic details for our program are given. We also discuss the generalisation of the postnewtonian approach and its advantages.

Thesis (MScEng (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2006. / When considering flow through porous media, different flow regimes may be identified. At very small Reynolds numbers the relation between the pressure gradient and the velocity of the fluid is linear. This flow regime ...

Title: Matter Models in General Relativity with a Decreasing Number of Sym- metries Author: Norman Gürlebeck Institute: Institute of theoretical physics Supervisor: Prof. RNDr. Jiří Bičák, DrSc., dr.h.c. Abstract: We investigate matter models with different symmetries in general relativity. Among these are thin (massive and massless) shells endowed with charge or dipole densities, dust distributions and rotating perfect fluid solutions. The electromagnetic sources we study are gravitating spherical symmetric condensers (including the implications of the energy conditions) and arbitrary gravitating shells endowed with a general test dipole distribution. For the latter the Israel formalism is extended to cover also general discontinuous tangential components of the electromagnetic test field, i.e., surface dipole densities. The formalism is applied to two examples and used to prove some general properties of dipole distributions. This is followed by a discussion of axially symmetric, stationary rigidly rotating dust with non-vanishing proper volume. The metric in the interior of such a configuration can be determined completely in terms of the mass density along the axis of rotation. The last matter models we consider are non-axially symmetric, stationary and rotating perfect fluid solutions. This is done with a...

Title: Sobolev-Type Spaces on Metric Measure Spaces Author: RNDr. Lukáš Malý Department: Department of Mathematical Analysis Supervisor: Prof. RNDr. Luboš Pick, CSc., DSc., Department of Mathematical Analysis Abstract: is thesis focuses on function spaces related to rst-order analysis in abstract metric measure spaces. In metric spaces, we can replace distributional gra- dients, whose de nition depends on the linear structure of Rn , by upper gradients that control the functions' behavior along all recti able curves. is gives rise to the so-called Newtonian spaces. e summability condition, considered in the thesis, is expressed using a general Banach function lattice quasi-norm and so an extensive framework is built. Sobolev-type spaces (mainly based on the Lp norm) on metric spaces, and Newtonian spaces in particular, have been under intensive study since the mid- s. Standard toolbox for the theory is set up in this general setting and Newto- nian spaces are proven complete. Summability of an upper gradient of a function is shown to guarantee the function's absolute continuity on almost all curves. Ex- istence of a unique minimal weak upper gradient is established. Regularization of Newtonian functions via Lipschitz truncations is discussed in doubling Poincaré spaces using weak boundedness of maximal...

Neste trabalho, propomos um conjunto de estratégias para enfrentar os obstáculos epistemológicos à aprendizagem da cinemática na Teoria da Relatividade Restrita. Tais estratégias são baseadas na proposta da noção de perfil conceitual de referencial (Ayala & Frezza, 2007) e visam promover uma interação cognitiva entre a Mecânica Newtoniana e Relativística. O perfil conceitual (Mortimer, 1995-2000) é um modelo para compreender a evolução conceitual em sala de aula. Para tais objetivos, foi desenvolvido um conjunto de ações em uma seqüência de aplicações de pré-testes e pós-testes com a finalidade de explicitar a concepção dos alunos sobre o aspecto a ser investigado e avaliar a evolução conceitual destes. A diferenciação entre as concepções dos alunos e aquelas cientificamente aceitas deu-se através da interpretação das concepções apresentadas, de discussões teóricas acerca do tema e da apresentação de animações construídas com o software Modellus. O público-alvo deste trabalho é formado por alunos de Licenciatura em Física, e o objetivo do mesmo é contribuir para a formação destes estudantes, futuros professores de Física. / In this work, we propose a set of strategies to face the epistemological obstacles to learning the kinematics in the Restricted Theory of Relativity. Such strategies are based on the proposal of the notion of conceptual profile of reference (Ayala & Frezza, 2007) and promote an interaction between cognitive Newtonian Mechanics and Relativistic Mechanics. The conceptual profile (Mortimer, 1995-2000) is a model for understanding the conceptual evolution of students in classroom. For these goals, we developed a set of actions in a sequence of applications of pre-tests and post-tests in order to explain the conception of students on the aspect to be investigated, and to assess your conceptual evolution. The differentiation between the students' conceptions and scientifically acceptable ones came through the interpretation of the concepts presented, theoretical discussions about the topic and the presentation of animations built with the software Modellus. The target of this work is formed by graduation students in Physics in order to contribute to your formation as future physics teachers.