Main goal of this thesis is to design exhaust manifold for Formula Student car Dragon 3. Construction parameters follow requirements on high engine power and also have to meet some restrictions given by competition rules. Lotus Engine Simulation software was used for modelling the engine (originally from Husaberg FE 570 motorcycle) and for determination of influence of the exhaust parameters on power characteristics. This thesis is also dedicated to noise emitted by the exhaust system which is important due to Formula Student rules.

We study the relationship between subdivision rules, 3-dimensional manifolds, and circle packings. We find explicit subdivision rules for closed right-angled hyperbolic manifolds, a large family of hyperbolic manifolds with boundary, and all 3-manifolds of the E^3,H^2 x R, S^2 x R, SL_2(R), and S^3 geometries (up to finite covers). We define subdivision rules in all dimensions and find explicit subdivision rules for the n-dimensional torus as an example in each dimension. We define a graph and space at infinity for all subdivision rules, and use that to show that all subdivision rules for non-hyperbolic manifolds have mesh not going to 0. We provide an alternate proof of the Combinatorial Riemann Mapping Theorem using circle packings (although this has been done before). We provide a new definition of conformal for subdivision rules of unbounded valence, show that the subdivision rules for the Borromean rings complement are conformal and show that barycentric subdivision is almost conformal. Finally, we show that subdivision rules can be degenerate on a dense set, while still having convergent circle packings.

Estimativas de erro são estabelecidas em termos do número de Rossby para a aproximação de Galerkin não linear nas soluções do modelo atmosférico balanceado de Lorenz com massa forçante. Desse modo a aproximação espectral da aproximação de Galerkin não linear é ligada ao número de Rossby. / Error estimates are established in terms of the Rossby number for a nonlinear Galerkin approximation to the solutions of the balanced atmosphere model of Lorenz with mass forcing. Thereby, the approximation spectral dimension of the nonlinear Galerkin approximation is linked to the Rossby number.

Estimativas de erro são estabelecidas em termos do número de Rossby para a aproximação de Galerkin não linear nas soluções do modelo atmosférico balanceado de Lorenz com massa forçante. Desse modo a aproximação espectral da aproximação de Galerkin não linear é ligada ao número de Rossby. / Error estimates are established in terms of the Rossby number for a nonlinear Galerkin approximation to the solutions of the balanced atmosphere model of Lorenz with mass forcing. Thereby, the approximation spectral dimension of the nonlinear Galerkin approximation is linked to the Rossby number.

Le sujet de cette thèse est l'étude d'idéaux monomiaux de l'anneau de polynômes S qui ont une résolution linéaire. D'après un résultat remarquable de Bayer et Stilman et en utilisant la polarisation, la classification des idéaux monomiaux ayant une résolution linéaire est équivalente à la classification des idéaux monomiaux libres de carrés ayant une résolution linéaire. Pour cette raison dans cette thèse nous considérons seulement le cas d'idéaux monomiaux libres de carrés. De plus, le théorème de Eagon-Reiner établit une dualité entre les idéaux monomiaux libres de carrés ayant une résolution linéaire et les idéaux monomiaux libres de carrés Cohen-Macaulay, ce qui montre que le problème de classification des idéaux monomiaux libres de carrés ayant une résolution linéaire est très difficile. Nous rappelons que les idéaux monomiaux libres de carrés sont en correspondance biunivoque avec les complexes simpliciaux d'une part, et d'autre part avec les clutters. Ces correspondances nous motivent pour utiliser les propriétés combinatoires des complexes simpliciaux et des clutters pour obtenir des résultats algébriques. La classification des idéaux monomiaux libres de carrés ayant une résolution linéaire engendrés en degré 2 a été faite par Froberg en 1990. Froberg a observé que l'idéal des circuits d'un graphe G a une résolution 2-linéaire si et seulement si G est un graphe de cordes, i.e. il n'a pas de cycles minimaux de longueur plus grande que 4. Dans [Em, ThVt, VtV, W] les auteurs ont partiellement généralisé les résultats de Froberg à des idéaux engendrés en degré >2. Ils ont introduit plusieurs définitions de clutters de cordes et démontré que les idéaux de circuits correspondant ont une résolution linéaire. Nous pouvons voir les cycles du point de vue topologique, comme la triangulation d'une courbe fermée, dans cette thèse nous utiliserons cette idée pour étudier des clutters associés à des triangulation de pseudo-manifolds en vue d'obtenir une généralisation partielle des résultats de Froberg à des idéaux engendrés en degré >2. Nous comparons notre travail à ceux de [Em, ThVt, VtV, W]. Nous présentons nos résultats dans le chapitres 4 et 5. / In this thesis, we study square-free monomial ideals of the polynomial ring S which have a linear resolution. By remarkable result of Bayer and Stilman [BS] and the technique of polarization, classification of ideals with linear resolution is equivalent to classification of square-free monomial ideals with linear resolution. For this reason, we consider only square-free monomial ideals in S. However, classification of square-free monomial ideals with linear resolution seems to be so difficult because by Eagon-Reiner Theorem [ER], this is equivalent to classification of Cohen-Macaulay ideals. It is worth to note that, square-free monomial ideals in S are in one-to-one correspondence to Stanley-Reisener ideals of simplicial complexes on one hand and the circuit ideal of clutters from another hand. This correspondence motivated mathematicians to use the combinatorial and geometrical properties of these objects in order to get the desired algebraic results. Classification of square-free monomial ideals with 2-linear resolution, was successfully done by Froberg [Fr] in 1990. Froberg observed that the circuit ideal of a graph G has a 2-linear resolution if and only if G is chordal, that is, G does not have an induced cycle of length > 3. In [Em, ThVt, VtV, W] the authors have partially generalized the Fr¨oberg's theorem for degree greater than 2. They have introduced several definitions of chordal clutters and proved that, their corresponding circuit ideals have linear resolutions. Viewing cycles as geometrical objects (triangulation of closed curves), in this thesis we try to generalize the concept of cycles to triangulation of pseudo-manifolds and get a partial generalization of Froberg's theorem for higher dimensional hypergraphs. All the results in Chapters 4 and 5 and some results in Chapter 3 are devoted to be the original results.

Estimativas de erro são estabelecidas em termos do número de Rossby para a aproximação de Galerkin não linear nas soluções do modelo atmosférico balanceado de Lorenz com massa forçante. Desse modo a aproximação espectral da aproximação de Galerkin não linear é ligada ao número de Rossby. / Error estimates are established in terms of the Rossby number for a nonlinear Galerkin approximation to the solutions of the balanced atmosphere model of Lorenz with mass forcing. Thereby, the approximation spectral dimension of the nonlinear Galerkin approximation is linked to the Rossby number.

In many areas of science one often has a given matrix, representing for example a measured data set and is required to find a matrix that is closest in a suitable norm to the matrix and possesses additionally a structure, inherited from the model used or coming from the application. We call these problems structured matrix nearness problems. We look at three different groups of these problems that come from real applications, analyze the properties of the corresponding matrix structure, and propose algorithms to solve them efficiently. The first part of this thesis concerns the nearness problem of finding the nearest k factor correlation matrix C(X) = diag(I_n -XX T)+XX T to a given symmetric matrix, subject to natural nonlinear constraints on the elements of the n x k matrix X, where distance is measured in the Frobenius norm. Such problems arise, for example, when one is investigating factor models of collateralized debt obligations (CDOs) or multivariate time series. We examine several algorithms for solving the nearness problem that differ in whether or not they can take account of the nonlinear constraints and in their convergence properties. Our numerical experiments show that the performance of the methods depends strongly on the problem, but that, among our tested methods, the spectral projected gradient method is the clear winner. In the second part we look at two two-sided optimization problems where the matrix of unknowns Y ε R {n x p} lies in the Stiefel manifold. These two problems come from an application in atomic chemistry where one is looking for atomic orbitals with prescribed occupation numbers. We analyze these two problems, propose an analytic optimal solution of the first and show that an optimal solution of the second problem can be found by solving a convex quadratic programming problem with box constraints and p unknowns. We prove that the latter problem can be solved by the active-set method in at most 2p iterations. Subsequently, we analyze the set of optimal solutions C}= {Y ε R n x p:Y TY=I_p,Y TNY=D} of the first problem for N symmetric and D diagonal and find that a slight modification of it is a Riemannian manifold. We derive the geometric objects required to make an optimization over this manifold possible. We propose an augmented Lagrangian-based algorithm that uses these geometric tools and allows us to optimize an arbitrary smooth function over C. This algorithm can be used to select a particular solution out of the latter set C by posing a new optimization problem. We compare it numerically with a similar algorithm that ,however, does not apply these geometric tools and find that our algorithm yields better performance. The third part is devoted to low rank nearness problems in the Q-norm, where the matrix of interest is additionally of linear structure, meaning it lies in the set spanned by s predefined matrices U₁,..., U_s ε {0,1} n x p. These problems are often associated with model reduction, for example in speech encoding, filter design, or latent semantic indexing. We investigate three approaches that support any linear structure and examine further the geometric reformulation by Schuermans et al. (2003). We improve their algorithm in terms of reliability by applying the augmented Lagrangian method and show in our numerical tests that the resulting algorithm yields better performance than other existing methods.

The master´s thesis is focused on the design of the intake and exhaust ducts for V8 engine. Home work is focused on the description of the construction of the intake and exhaust pipes for a given engine. Another part deals with creating a thermodynamic model of the engine, and the design of the intake and exhaust pipes. The last part deals with verifying the proposed pipeline construction.

Diplomová práce je zaměřena na konstrukční návrh sacího potrubí pro vůz Formula Student. Pro pohon vozu je použit jednoválcový atmosférický benzinový motor Husaberg FE 570. Sací potrubí je navrhováno tak, aby bylo v souladu s pravidly Formula Student. Pro zvýšení plnící účinnosti sací potrubí využívá resonančního efektu. Délky sacího potrubí byly spočítány v software Lotus Engine simulation.

The aim of this diploma thesis is supercharging of SI engines and design influence on performance. The main objective of this thesis is to propose appropriate modifications on AR67203 engine of Alfa Romeo 155Q4 personal vehicle in order to achieve significantly better performance parameters and a constant torque in the widest possible speed range. That is why I analyze design and modifications that affect the overall engine performance and their appropriate application to the selected engine. An important point of this thesis is the right choice of turbocharger, in order to have an effective cooperation with a modified engine. The calculation study and the simulation in Lotus Engine Simulation software serve this purpose. I also give information about ECU programming. The results, as well as a practical output in the form of measured performance parameters of modified engine, are evaluated at the end.