Analyse de groupe d’un modèle de la plasticité idéale planaire et sur les solutions en termes d’invariants de Riemann pour les systèmes quasilinéaires du premier ordre

Les objets d’étude de cette thèse sont les systèmes d’équations quasilinéaires du premier ordre. Dans une première partie, on fait une analyse du point de vue du groupe de Lie classique des symétries ponctuelles d’un modèle de la plasticité idéale. Les écoulements planaires dans les cas stationnaire et non-stationnaire sont étudiés. Deux nouveaux champs de vecteurs ont été obtenus, complétant ainsi l’algèbre de Lie du cas stationnaire dont les sous-algèbres sont classifiées en classes de conjugaison sous l’action du groupe. Dans le cas non-stationnaire, une classification des algèbres de Lie admissibles selon la force choisie est effectuée. Pour chaque type de force, les champs de vecteurs sont présentés. L’algèbre ayant la dimension la plus élevée possible a été obtenues en considérant les forces monogéniques et elle a été classifiée en classes de conjugaison. La méthode de réduction par symétrie est appliquée pour obtenir des solutions explicites et implicites de plusieurs types parmi lesquelles certaines s’expriment en termes d’une ou deux fonctions arbitraires d’une variable et d’autres en termes de fonctions elliptiques de Jacobi. Plusieurs solutions sont interprétées physiquement pour en déduire la forme de filières d’extrusion réalisables. Dans la seconde partie, on s’intéresse aux solutions s’exprimant en fonction d’invariants de Riemann pour les systèmes quasilinéaires du premier ordre. La méthode des caractéristiques généralisées ainsi qu’une méthode basée sur les symétries conditionnelles pour les invariants de Riemann sont étendues pour être applicables à des systèmes dans leurs régions elliptiques. Leur applicabilité est démontrée par des exemples de la plasticité idéale non-stationnaire pour un flot irrotationnel ainsi que les équations de la mécanique des fluides. Une nouvelle approche basée sur l’introduction de matrices de rotation satisfaisant certaines conditions algébriques est développée. Elle est applicable directement à des systèmes non-homogènes et non-autonomes sans avoir besoin de transformations préalables. Son efficacité est illustrée par des exemples comprenant un système qui régit l’interaction non-linéaire d’ondes et de particules. La solution générale est construite de façon explicite.The objects under consideration in this thesis are systems of first-order quasilinear equations. In the first part of the thesis, a study is made of an ideal plasticity model from the point of view of the classical Lie point symmetry group. Planar flows are investigated in both the stationary and non-stationary cases. Two new vector fields are obtained. They complete the Lie algebra of the stationary case, and the subalgebras are classified into conjugacy classes under the action of the group. In the non-stationary case, a classification of the Lie algebras admissible under the chosen force is performed. For each type of force, the vector fields are presented. For monogenic forces, the algebra is of the highest possible dimension. Its classification into conjugacy classes is made. The symmetry reduction method is used to obtain explicit and implicit solutions of several types. Some of them can be expressed in terms of one or two arbitrary functions of one variable. Others can be expressed in terms of Jacobi elliptic functions. Many solutions are interpreted physically in order to determine the shape of realistic extrusion dies. In the second part of the thesis, we examine solutions expressed in terms of Riemann invariants for first-order quasilinear systems. The generalized method of characteristics, along with a method based on conditional symmetries for Riemann invariants are extended so as to be applicable to systems in their elliptic regions. The applicability of the methods is illustrated by examples such as non-stationary ideal plasticity for an irrotational flow as well as fluid mechanics equations. A new approach is developed, based on the introduction of rotation matrices which satisfy certain algebraic conditions. It is directly applicable to non-homogeneous and non-autonomous systems. Its efficiency is illustrated by examples which include a system governing the non-linear superposition of waves and particles. The general solution is constructed in explicit form

Symmetry group analysis of an ideal plastic flow

In this paper, we study the Lie point symmetry group of a system describing an ideal plastic plane flow in two dimensions in order to find analytical solutions. The infinitesimal generators that span the Lie algebra for this system are obtained. We completely classify the subalgebras of up to codimension two in conjugacy classes under the action of the symmetry group. Based on invariant forms, we use Ansatzes to compute symmetry reductions in such a way that the obtained solutions cover simultaneously many invariant and partially invariant solutions. We calculate solutions of the algebraic, trigonometric, inverse trigonometric and elliptic type. Some solutions depending on one or two arbitrary functions of one variable have also been found. In some cases, the shape of a potentially feasible extrusion die corresponding to the solution is deduced. These tools could be used to thin, curve, undulate or shape a ring in an ideal plastic material

Replication fork collisions cause pathological chromosomal amplification in cells lacking RecG DNA translocase

Duplication and transmission of chromosomes require precise control of chromosome replication and segregation. Here we present evidence that RecG is a major factor influencing these processes in bacteria. We show that the extensive DnaA-independent stable DNA replication observed without RecG can lead to replication of any area of the chromosome. This replication is further elevated following irradiation with UV light and appears to be perpetuated by secondary events that continue long after the elimination of UV lesions. The resulting pathological cascade is associated with an increased number of replication forks traversing the chromosome, sometimes with extensive regional amplification of the chromosome, and with the accumulation of highly branched DNA intermediates containing few Holliday junctions. We propose that the cascade is triggered by replication fork collisions that generate 3′ single-strand DNA flaps, providing sites for PriA to initiate re-replication of the DNA and thus to generate linear duplexes that provoke recombination, allowing priming of even further replication. Our results shed light on why termination of replication in bacteria is normally limited to a single encounter of two forks and carefully orchestrated within a restricted area, and explain how a system of multiple forks and random termination can operate in eukaryotes

Assessing European wheat sensitivities to parastagonospora nodorum necrotrophic effectors and fine-mapping the Snn3-B1 locus conferring sensitivity to the effector SnTox3

© 2018 Downie, Bouvet, Furuki, Gosman, Gardner, Mackay, Campos Mantello, Mellers, Phan, Rose, Tan, Oliver and Cockram. Parastagonospora nodorum is a necrotrophic fungal pathogen of wheat (Triticum aestivum L.), one of the world’s most important crops. P. nodorum mediates host cell death using proteinaceous necrotrophic effectors, presumably liberating nutrients that allow the infection process to continue. The identification of pathogen effectors has allowed host genetic resistance mechanisms to be separated into their constituent parts. In P. nodorum, three proteinaceous effectors have been cloned: SnToxA, SnTox1, and SnTox3. Here, we survey sensitivity to all three effectors in a panel of 480 European wheat varieties, and fine-map the wheat SnTox3 sensitivity locus Snn3-B1 using genome-wide association scans (GWAS) and an eight-founder wheat multi-parent advanced generation inter-cross (MAGIC) population. Using a Bonferroni corrected P = 0.05 significance threshold, GWAS identified 10 significant markers defining a single locus, Snn3-B1, located on the short arm of chromosome 5B explaining 32% of the phenotypic variation [peak single nucleotide polymorphisms (SNPs), Excalibur_c47452_183 and GENE-3324_338, -log10P = 20.44]. Single marker analysis of SnTox3 sensitivity in the MAGIC population located Snn3-B1 via five significant SNPs, defining a 6.2-kb region that included the two peak SNPs identified in the association mapping panel. Accordingly, SNP Excalibur_c47452_183 was converted to the KASP genotyping system, and validated by screening a subset of 95 wheat varieties, providing a valuable resource for marker assisted breeding and for further genetic investigation. In addition, composite interval mapping in the MAGIC population identified six minor SnTox3 sensitivity quantitative trait loci, on chromosomes 2A (QTox3.niab-2A.1, P-value = 9.17-7), 2B (QTox3.niab-2B.1, P = 0.018), 3B (QTox3.niab-3B.1, P = 48.51-4), 4D (QTox3.niab-4D.1, P = 0.028), 6A (QTox3.niab-6A.1, P = 8.51-4), and 7B (QTox3.niab-7B.1, P = 0.020), each accounting for between 3.1 and 6.0 % of the phenotypic variance. Collectively, the outcomes of this study provides breeders with knowledge and resources regarding the sensitivity of European wheat germplasm to P. nodorum effectors, as well as simple diagnostic markers for determining allelic state at Snn3-B1

Evidence for cognitive vestibular integration impairment in idiopathic scoliosis patients

<p>Abstract</p> <p>Background</p> <p>Adolescent idiopathic scoliosis is characterized by a three-dimensional deviation of the vertebral column and its etiopathogenesis is unknown. Various factors cause idiopathic scoliosis, and among these a prominent role has been attributed to the vestibular system. While the deficits in sensorimotor transformations have been documented in idiopathic scoliosis patients, little attention has been devoted to their capacity to integrate vestibular information for cognitive processing for space perception. Seated idiopathic scoliosis patients and control subjects experienced rotations of different directions and amplitudes in the dark and produced saccades that would reproduce their perceived spatial characteristics of the rotations (vestibular condition). We also controlled for possible alteration of the oculomotor and vestibular systems by measuring the subject's accuracy in producing saccades towards memorized peripheral targets in absence of body rotation and the gain of their vestibulo-ocular reflex.</p> <p>Results</p> <p>Compared to healthy controls, the idiopathic scoliosis patients underestimated the amplitude of their rotations. Moreover, the results revealed that idiopathic scoliosis patients produced accurate saccades to memorized peripheral targets in absence of body rotation and that their vestibulo-ocular reflex gain did not differ from that of control participants.</p> <p>Conclusion</p> <p>Overall, results of the present study demonstrate that idiopathic scoliosis patients have an alteration in cognitive integration of vestibular signals. It is possible that severe spine deformity developed partly due to impaired vestibular information travelling from the cerebellum to the vestibular cortical network or alteration in the cortical mechanisms processing the vestibular signals.</p