A critical set in a Latin square of order n is a set of entries in an n×n array which can be embedded in precisely one Latin square of order n, with the property that if any entry of the critical set is deleted, the remaining set can be embedded in more than one Latin square of order n. The number of critical sets grows super-exponentially as the order of the Latin square increases. It is difficult to find patterns in Latin squares of small order (order 5 or less) which can be generalised in the process of creating new theorems. Thus, I have written many algorithms to find critical sets with various properties in Latin squares of order greater than 5, and to deal with other related structures. Some algorithms used in the body of the thesis are presented in Chapter 3; results which arise from the computational studies and observations of the patterns and subsequent results are presented in Chapters 4, 5, 6, 7 and 8. The cardinality of the largest critical set in any Latin square of order n is denoted by lcs(n). In 1978 Curran and van Rees proved that lcs(n)<=n²-n. In Chapter 4, it is shown that lcs(n)<=n²-3n+3. Chapter 5 provides new bounds on the maximum number of intercalates in Latin squares of orders m×2^α (m odd, α>=2) and m×2^α+1 (m odd, α>=2 and α≠3), and a new lower bound on lcs(4m). It also discusses critical sets in intercalate-rich Latin squares of orders 11 and 14. In Chapter 6 a construction is given which verifies the existence of a critical set of size n²÷ 4 + 1 when n is even and n>=6. The construction is based on the discovery of a critical set of size 17 for a Latin square of order 8. In Chapter 7 the representation of Steiner trades of volume less than or equal to nine is examined. Computational results are used to identify those trades for which the associated partial Latin square can be decomposed into six disjoint Latin interchanges. Chapter 8 focusses on critical sets in Latin squares of order at most six and extensive computational routines are used to identify all the critical sets of different sizes in these Latin squares.

Thesis (Ph.D.); Submitted to the University of California at Berkeley, Berkeley, CA (US); 1 Sep 2003. / Published through the Information Bridge: DOE Scientific and Technical Information. "LBNL--55023" Li, Liang-shi. USDOE Director. Office of Science. Office of Basic Energy Sciences (US) 09/01/2003. Report is also available in paper and microfiche from NTIS.

Made available in DSpace on 2014-06-11T19:26:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-02-27Bitstream added on 2014-06-13T20:08:06Z : No. of bitstreams: 1 rayzaro_os_me_sjrp.pdf: 628267 bytes, checksum: 09181fbba2d539fd6135f0b473b3b345 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho vemos que a imagem de um ideal do anel dos inteiros dos corpos de números, via o homomorfismo de Minkowski, é um reticulado, chamado de reticulado algébrico. Assim, o principal objetivo deste trabalho é a construção de reticulados algébricos de dimensão 2; 4; 6 e 8, com densidade de centro ótimo. / In this work, we see that the image of an ideal from the algebraic integer ring of the numbers ¯elds by the Minkowski homomorphism is a lattice, named algebraic lattice. In this way, the main aim of this work is the construction of algebraic lattices of dimensions 2,4,6 and 8, with the center density excellent.

Made available in DSpace on 2014-06-11T19:26:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2005-12-10Bitstream added on 2014-06-13T20:08:00Z : No. of bitstreams: 1 ramos_gm_me_sjrp.pdf: 353629 bytes, checksum: 1030312b97bd0bb7f95093162b227e48 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O objetivo principal deste trabalho é estudar a densidade de centro de reticulados obtidos por meio do Método de Minkowski em subcorpos de Q(?pq), com p e q primos ímpares distintos e satisfazendo a condição oq(p) = op(q) = 1 (mod 2). O cálculo da densidade de centro é feito a partir do discriminante do corpo, da norma do ideal e da minimização da forma traço. / This work aims at studying the center density of the lattices got through the Minkowski's Method in subfields of Q(?pq), p and q prime number and oq(p) = op(q) = 1 (mod 2). The calcule of the center density is done using the discriminant of the field, the norm of the ideal and the minimization of trace form.

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Hydrocarbon chains are a basic component in a number of systems as diverse as biological membranes, phospholipids and polymers. A better understanding of the physical properties of n-alkane chains should provide a better understanding of these more complex systems. With this aim, vibrational spectroscopy has been extensively used. This technique, sensitive to molecular details, is the only one able to both identify and quantify conformational disorder present in paraffinic systems. To achieve this, methyl deformations have been widely used as "internal standards" for the normalisation of peak areas. However, in the case of n-alkanes with short chain length, such as n-C[44]H[90] for example, the infrared spectra recorded at liquid nitrogen temperature and reported here show the sensitivity of these latter peaks to the various crystal structures formed. Indeed, the main frequencies of the symmetric methyl bending mode were found between 1384 cm[-1] and 1368 cm[-1] as a function of the crystal form. Changes in the frequency of the first order of the L.A.M. present in the Raman spectra were also observed. At higher temperatures, non all-trans conformers, inferred from different infrared bands present in the wagging mode region, were found to be essentially placed at the end of the n-alkane chains. At the monoclinic phase transition, the concentration of end-gauche conformers, proportional to the area of the infrared band at 1342 cm[-1], increases abruptly. On the contrary, in the spectra recorded at liquid nitrogen temperature no such band is observed. We also studied the degree of disorder in two purely monodisperse long chain n-alkanes, namely n-C[198]H[398] and n-C[246]H[494]. The chain conformation as well as the tilt angle of the chains from the crystal surfaces were determined by means of low frequency Raman spectroscopy and S.A.X.S. measurements on solution-crystallised samples. The increase in the number of end-gauche conformers which was expected to occur with the increase of the tilt angle as a function of the temperature was not detected due to a perfecting of the crystals. Indeed, due to successive heating and cooling to -173&deg;C, the concentration of non all-trans conformers was found to decrease within the crystals. Their numbers were found to be up to six times higher in n-C[198]H[398] crystallised in once folded form than when crystallised in extended form. The C-C stretching mode region of the spectra was used to identify the chain conformation and to estimate the length of the all-trans stem passing through the crystal layers at -173&deg;C. The transition between once folded and extended form crystals was indicated by the presence of additional bands in this region at 1089 cm[-1], 1078 cm[-1] and 1064 cm[-1]. Some of those bands may be related to the fold itself. At the same time, a strong decrease of the intensity of the infrared bands present in the wagging mode region was observed. Finally, the triple layered structure proposed on the basis of X-ray measurements obtained from the crystals of a binary mixture of long chain n-alkanes, namely n-C[162]H[326] and n-C[246]H[494], was confirmed from the study of the C-C stretching mode region of the infrared spectra.

Au cours de cette thèse, nous avons étudiés théoriquement les propriétés structurelles et électroniques des super-réseaux d'oxyde de manganèse en structure perovskiteö au moyen de calculs ab initio.Les oxydes de manganèse au lanthane, donnés avec la formule générique La(1-x)A(x)MnO(3) (LAMO) (A un élément divalent), constituent une classe importante d'oxydes de manganèse en raison de leurs diverses propriétés, telles que l'effet de magnétorésistance colossale, leur riche diagramme de phase en fonction du dopage, de la température ou de champs externes, et leur grande température Curie. Ces propriétés peuvent être exploitées dans de nombreuses applications technologiques potentielles telles que les valves de spin ou les injecteurs de spin. Le contrôle des propriétés de ces matériaux peut se faire par dépôt sous forme de films minces ou comme blocs de construction dans des super-réseaux. Lorsque x = 1/3, le La(1-x)A(x)MnO(3) massif est ferromagnétique et métallique grâce au mécanisme de double échange dans la electrons 3d de Mn. Lorsque Mn est dans un état de valence mixte, les orbitales eg (dx2-y2 and dz2) sont partiellement occupées et peuvent se délocaliser sur les atomes de Mn voisins, seulement si ceux-ci sont alignés ferromagnétiquement. Dans des films très minces, puisque la direction perpendiculaire au substrat, c, n'a que quelques cellules unitaires d'épaisseur, seules les interactions dans le plan (ab) sont importantes pour les propriétés thermodynamiques. En agissant sur la géométrie de la couche LAMO, on peut ainsi maximiser l'occupation de l'orbitales dx2-y2 et augmenter l'échange magnétique et la température Curie associée.Notre but était donc de concevoir de nouveaux matériaux avec un ordre orbital 3d spécifique afin d'assurer les propriétés magnétiques souhaitées.Dans cette thèse, nous avons travaillé sur deux types de super-réseaux. Le premier était constitué de deux oxydes de manganèse antiferromagnétiques, non dopés, LaMnO(3) et SrMnO(3), c'est-à-dire des super-réseaux [LaMnO(3)]n/[SrMnO(3)]m. Nous avons étudié l'état fondamental magnétique pour différentes valeurs n et m afin d'expliquer les résultats expérimentaux surprenants. Le deuxième type de super-réseaux que nous avons étudiés est composé de couches métalliques LAMO en alternance avec des couches isolantes. En effet, les super-réseaux avec des interfaces métal-isolant ont un grand potentiel dans les applications de valves de spin. Ainsi, nous avons d'abord considéré des super-réseaux entre composés ferromagnétiques-métalliques et ferroélectriques-isolantes [LAMO](3)/[BTiO(3)](3) (A = Sr ou Ba, B = Ba ou Pb). Dans ces super-réseaux, les propriétés magnétiques sont malheuresement réduites en raison de la délocalisation d'électrons dz2 à l'interface entre Mn et Ti. Dans de tels super-réseaux , nous avons clarifié le rôle de la polarisation des couches ferroélectriques et le rôle des mouvements antiferrodistortifs dans les couches de manganite. Enfin, de manierè à 'éviter que la délocalisation ait lieu à l'interface, nous avons conçu un autre super-réseau avec interface métal-isolant dans lequel nous avons remplacé l'isolant (BTiO(3)) par un oxyde simple (BO): [LAMO]n/[BO]p superlattices (A = Sr ou Ba, B = Ba, Sr ou Mg et n = 3 ou 6, p = 6 ou 2). Dans ces nouveaux super-réseaux, nous avons réussi à promouvoir les occupations des orbitales dx2-y2 dans les interfaces assurant un fort moment magnetique à l'interface et a priori une fort temperature de Curie. Nous avons également montré une faible corrélation entre la conductivité électrique et l'ordre orbitaire. / This thesis theoretically studies structural and electronic properties of perovskite manganese oxide superlattices by means of ab-initio calculations.Lanthanum manganese oxides, given with the generic formula La1−xAxMnO3 (LAMO) (A a divalent element), are an important class of perovskite manganese oxides due to their various exotic properties, such as giant and colossal magnetoresistance effect, rich phase diagrams with respect to doping, temperature or external fields, and intinsic large Curie temperature. These properties can be exploited in many potential technological applications such as spin valves or spin injectors. Controlling the properties of these materials can be done through deposition as thin films or as building blocks in superlattices. When x = 1/3, bulk La1−xAxMnO3 is ferromagnetic and metallic due to the double-exchange mechanism in the Mn 3d shell. When Mn is in a mixed valence state, the eg orbitals (dx2-y2 and dz2) are partially occupied, and can delocalize on neighboring Mn atoms only if the latter are ferromagnetically aligned. In very thin films, since the direction perpendicular to the substrate, c, is only a few unit cell thick, only in-plane (ab) interactions are important for the thermodynamic properties. By acting on the LAMO layer geometry, one can thus maximize the dx2-y2 occupancy and increase the magnetic exchange and related Curie temperature.Our aim was thus to design new materials with desired 3d orbital order so that to ensure desired magnetic properties.In this thesis, we worked on two types of superlattices. The first one was made of two undoped antiferromagnetic manganese oxides LaMnO3 and SrMnO3, i.e. [LaMnO3]n/[SrMnO3]m superlattices. We investigated the magnetic ground state for different n and m values in order to explain suprising experimental results. The second type of superlattices is composed of metallic LAMO layers with alternated insulating layers. Indeed, the superlattices with metal-insulator interfaces have a great potential in spin valves applications. Thus, we first considered the ferromagnetic-metallic/ferroelectric-insulating [LAMO]3/[BTiO3]3 superlattices (A= Sr or Ba, B=Ba or Pb) where the magnetic properties are reduced due to delocalization of dz2 electrons at the interface from Mn to Ti. In such superlattices, we clarified the role of the polarization of the ferroelectric layers and the role of the antiferrodistortive motions in the manganite layers. In order to prevent the delocalization taking place at the interface, we designed another superlattice with metallic-insulator interface where we replaced the insulator (BTiO3) with a simple oxide (BO); that is [LAMO]n/[BO]p superlattices (A= Sr or Ba, B=Ba, Sr or Mg and n=3 or 6, p=6 or 2). Within this new superlattice, we successully managed to promote dx2-y2 orbital occupancies at the interfaces which ensures a large magnetic moment at the interfaces and an expected large Curie temperature. We also showed the weak correlation between electrical conductivity and orbital ordering.

Le mélange de solutés par les écoulements en milieux poreux contrôle les réactions chimiques dans un grand nombre d'applications souterraines, dont le transport et la remédiation des contaminants, le stockage et l'extraction souterrains d'énergie, et la séquestration du CO2. Nous étudions les mécanismes du mélange à l'échelle du pore et plus précisément comment la topologie de l'écoulement est reliée à la dynamique du mélange d'espèces conservatives; en particulier, l'émergence d'un mélange chaotique est-elle possible dans un milieu poreux tridimensionnel (3D) ? Nous calculons donc numériquement ou mesurons expérimentalement les vitesses d'écoulement et l'évolution temporelle des champs de concentration afin de caractériser la déformation et le mélange à l'échelle du pore. Une première étude, expérimentale, permet de caractériser le mélange dans un fluide s’écoulant à travers un milieu poreux bidimensionnel (2D). Nous mesurons les vitesses par suivi de microparticules solides (''PTV''). L’évolution temporelle de la distance séparant deux particules permet de caractériser la dynamique de la déformation lagrangienne. Des mesures de transport conservatif dans le même milieu fournissent l'évolution temporelle du gradient de concentration moyen (une mesure du mélange). À partir de ces résultats expérimentaux nous proposons la première validation expérimentale à l'échelle du pore de la théorie lamellaire du mélange, reliant les propriétés de la déformation du fluide à la dynamique du mélange. Dans une deuxième étude nous examinons les conditions d'apparition du mélange chaotique dans l’écoulement dans des milieux poreux 3D granulaires ordonnés. Nous effectuons des calculs numériques hautement résolus de d'écoulement de Stokes entre des sphères empilées selon une structure cristalline (cubique simple ou cubique centrée), périodique. La déformation lagrangienne, obtenue à partir des champs de vitesse à l'aide d'outils numériques développés spécifiquement, met en lumière une large variété de dynamiques de la déformation dans ces milieux 3D, selon l'orientation de l'écoulement. Quand la direction de l'écoulement n'est pas normale à l'un des plans de symétrie de réflection du cristal, l'évolution temporelle de la déformation est exponentielle, traduisant une advection chaotique. L’émergence (ou non) du chaos est contrôlée par un mécanisme similaire à la ''transformation du boulanger'': les particules fluides se déplaçant autour d'un grain solide se retrouvent séparées par une surface virtuelle (appelée “variété”) qui émerge de la surface du grain. De multiples variétés existent dans l’écoulement, et la façon dont elles s'intersectent contrôle la nature - chaotique ou non - du mélange, et l'intensité du chaos. En particulier, l'exposant de Lyapunov (une mesure du chaos), est contrôlé par la fréquence spatiale des intersections appropriées à la génération du chaos, nommées ''connections hétéroclinines'' entre variétés. L'image conventionnelle, 2D, des mécanismes du mélange, impose des contraintes topologiques qui ne permettent pas le développement de ces mécanismes 3D. Elle pourrait donc être inadaptée aux milieux poreux naturels. La troisième étude a deux objectifs: (i) fournir une preuve expérimentale de la nature chaotique de l'advection, par la visualisation des variétés et par l'obtention d'une mesure de l'exposant de Lyapunov; et (ii), évaluer si nos résultats numériques obtenus pour des milieux granulaires ordonnés peuvent être généralisés à des milieux désordonnés, plus proches des milieux naturels. L’expérience est fondée sur un empilement désordonné de sphères rendu transparent par l'ajustement optique du liquide avec les sphères. La fluorescence induite par laser (''LIF'') permet de détecter les variétés au sein de l'écoulement, et des techniques PTV de mesurer les vitesses d'écoulement et quantifier l'exposant de Lyapunov. Les premiers résultats expérimentaux sont prometteurs. / Solute mixing in porous media flows plays a central role in driving chemical reactions in a number of subsurface applications, including contaminant transport and remediation, subsurface energy storage and extraction, and CO2 sequestration. We study the mechanisms of solute mixing, in particular how the pore scale flow topology is related to the mixing dynamics of conservative solutes, with a particular emphasis on the possible emergence of chaotic mixing processes in three-dimensional (3D) porous media. To do so, we perform numerical computations or experimental measurements of the flow velocities and temporal evolution of the concentration fields, and characterize fluid deformation and mixing at the pore scale. This PhD work consists of three main studies. In the first study, we experimentally characterize mixing in a fluid flowing through a two-dimensional (2D) porous medium built by lithography. We measure the velocity distributions from Particle Tracking Velocimetry (PTV). The time evolution of the separation distance between two particles is analyzed to characterize the Lagrangian deformation dynamics. In parallel we perform conservative transport experiments with the same porous media, and quantify the temporal evolution of the mean concentration gradient, which is a measure of the mixing rate. From these experimental results we obtain the first experimental pore scale validation of the lamella mixing theory, which relates the fluid deformation properties to the mixing dynamics. In the second study, we investigate the conditions of emergence of chaotic mixing in the flow through 3D ordered granular porous media. In these periodic cubic crystalline packings (Simple Cubic - SC - and Body-Centered Cubic - BCC) of spheres, we are able to perform highly resolved computations of the 3D Stokes flow. Using custom-developed numerical tools to measure the Lagrangian deformation from the computed velocity fields, we uncover the existence of a rich array of Lagrangian deformation dynamics in these 3D media, depending on the flow orientation. When the flow direction is not normal to one of the reflection symmetry planes of the crystalline lattice, we find that the Lagrangian deformation dynamics follow an exponential law, which indicates chaotic advection. This chaotic behavior is controlled by a mechanism akin to the baker's transformation: fluid particles traveling around a solid grain along different paths end up either separated by, or on the same side of, a virtual surface projecting from the grain surface and called a manifold. Multiple such manifolds exist within the flow, and the way they intersect controls the nature of mixing (that is, either non-chaotic or chaotic), and the strength of chaos. We show in particular that the magnitude of the Lyapunov exponent (a measure of the vigor of chaos) is controlled by the spatial frequency of transverse connections between the manifolds (called heteroclinic intersections). We thus demonstrate that the conventional 2D picture of the mechanisms of mixing may not be adapted for natural porous media because that picture imposes topological constraints which cannot account for these important 3D mechanisms. The third study has two objectives: (i) provide experimental evidence of the chaotic nature of pore scale advection/mixing, both by visualizing the manifolds and by obtaining a quantitative estimate of the Lyapunov exponent; and (ii) assess if the results obtained numerically in ordered packings of spheres extend to random packings, which are closer to natural porous media. The experiment features a random packing of glass beads rendered transparent by optical index-matching between the fluid and solid grains. We use Laser Induced Fluorescence (LIF) to detect the manifolds, and PTV techniques to measure flow velocities and subsequently quantify Lyapunov exponent. The first experimental results are promising.

La classification d'images s'articule généralement autour des deux étapes que sont l'étape d'extraction de signatures suivie de l'étape d'analyse des données extraites, ces dernières étant généralement quantitatives. De nombreux modèles de classification ont été proposés dans la littérature, le choix du modèle le plus adapté est souvent guidé par les performances en classification ainsi que la lisibilité du modèle. L'arbre de classification et le treillis de Galois sont deux modèles symboliques connus pour leur lisibilité. Dans sa thèse [Guillas 2007], Guillas a utilisé efficacement les treillis de Galois pour la classification d'images, et des liens structurels forts avec les arbres de classification ont été mis en évidence. Les travaux présentés dans ce manuscrit font suite à ces résultats, et ont pour but de définir un modèle hybride entre ces deux modèles, qui réunissent leurs avantages (leur lisibilité respective, la robustesse du treillis et le faible espace mémoire de l'arbre). A ces fins, l'étude des liens existants entre les deux modèles a permis de mettre en avant leurs différences. Tout d'abord, le type de discrétisation, les arbres utilisent généralement une discrétisation locale tandis que les treillis, initialement définis pour des données binaires, utilisent une discrétisation globale. A partir d'une étude des propriétés des treillis dichotomiques (treillis définis après une discrétisation), nous proposons une discrétisation locale pour les treillis permettant d'améliorer ses performances en classification et de diminuer sa complexité structurelle. Puis, le processus de post-élagage mis en œuvre dans la plupart des arbres a pour objectif de diminuer la complexité de ces derniers, mais aussi d'augmenter leurs performances en généralisation. Les simplifications de la structure de treillis (exponentielle en la taille de données dans les pires cas), quant à elles, sont motivées uniquement par une diminution de la complexité structurelle. En combinant ces deux simplifications, nous proposons une simplification de la structure du treillis obtenue après notre discrétisation locale et aboutissant à un modèle de classification hybride qui profite de la lisibilité des deux modèles tout en étant moins complexe que le treillis mais aussi performant que celui-ci. / Image classification is generally based on two steps namely the extraction of the image signature, followed by the extracted data analysis. Image signature is generally numerical. Many classification models have been proposed in the literature, among which most suitable choice is often guided by the classification performance and the model readability. Decision trees and Galois lattices are two symbolic models known for their readability. In her thesis {Guillas 2007}, Guillas efficiently used Galois lattices for image classification. Strong structural links between decision trees and Galois lattices have been highlighted. Accordingly, we are interested in comparing models in order to design a hybrid model between those two. The hybrid model will combine the advantages (robustness of the lattice, low memory space of the tree and readability of both). For this purpose, we study the links between the two models to highlight their differences. Firstly, the discretization type where decision trees generally use a local discretization while Galois lattices, originally defined for binary data, use a global discretization. From the study of the properties of dichotomic lattice (specific lattice defined after discretization), we propose a local discretization for lattice that allows us to improve its classification performances and reduces its structural complexity. Then, the process of post-pruning implemented in most of the decision trees aims to reduce the complexity of the latter, but also to improve their classification performances. Lattice filtering is solely motivated by a decrease in the structural complexity of the structures (exponential in the size of data in the worst case). By combining these two processes, we propose a simplification of the lattice structure constructed after our local discretization. This simplification leads to a hybrid classification model that takes advantage of both decision trees and Galois lattice. It is as readable as the last two, while being less complex than the lattice but also efficient.