Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.

Mastectomy, Body De-Construction and Impact on Identity: A qualitative study

Objectives: This qualitative study aims at understanding the consequences of body deconstruction through mastectomy on corporality and identity in women with breast cancer. Design: Nineteen women were contacted through the hospital. All had to undergo mastectomy. Some were offered immediate breast reconstruction, others, because of cancer treatments, had no planned reconstruction. A qualitative reflexive methodological background was chosen. Method: Women were invited to participate in three semi-structured interviews, one shortly before or after mastectomy, and the other interviews later in their illness courses, after surgery. All interviews were transcribed verbatim. Thematic analysis was performed. The analysis of the first interview of each woman is presented in this article. Results: Mastectomy provokes a painful experience of body deconstruction. Even when immediate reconstruction is proposed, contrasted feelings and dissonance are expressed when comparing the former healthy body to the present challenged body entity. Body transformations are accompanied with experiences of mutilation, strangeness, and modify the physical, emotional social, symbolic and relational dimensions of the woman's gendered identity. Although the opportunity of breast reconstruction is seen as a possible recovery of a lost physical symmetry and body integrity, grieving the past body and integrating a new corporality leads to a painful identity crisis. Conclusion: With mastectomy, the roots of the woman's identity are challenged, leading to a re-evaluation of her existential values. The consequences of mastectomy transform the woman's corporality and embodiment, and question her identity. Psychological support is discussed in the perspective of our results.

Percolation and three-dimensional structure of supercritical water

It is well established that at ambient and supercooled conditions water can be described as a percolating network of H bonds. This work is aimed at identifying, by neutron diffraction experiments combined with computer simulations, a percolation line in supercritical water, where the extension of the H-bond network is in question. It is found that in real supercritical water liquidlike states are observed at or above the percolation threshold, while below this threshold gaslike water forms small, sheetlike configurations. Inspection of the three-dimensional arrangement of water molecules suggests that crossing of this percolation line is accompa- nied by a change of symmetry in the first neighboring shell of molecules from trigonal below the line to tetrahedral above.

Viral self-assembly as a thermodynamic process

The protein shells, or capsids, of nearly all spherelike viruses adopt icosahedral symmetry. In the present Letter, we propose a statistical thermodynamic model for viral self-assembly. We find that icosahedral symmetry is not expected for viral capsids constructed from structurally identical protein subunits and that this symmetry requires (at least) two internal switching configurations of the protein. Our results indicate that icosahedral symmetry is not a generic consequence of free energy minimization but requires optimization of internal structural parameters of the capsid proteins

Sedimentation of pairs of hydrodynamically interacting semiflexible filaments

We describe the effect of hydrodynamic interactions in the sedimentation of a pair of inextensible semiflexible filaments under a uniform constant force at low Reynolds numbers. We have analyzed the different regimes and the morphology of such polymers in simple geometries, which allow us to highlight the peculiarities of the interplay between elastic and hydrodynamic stresses. Cooperative and symmetry breaking effects associated to the geometry of the fibers gives rise to characteristic motion which give them distinct properties from rigid and elastic filaments.

Fluctuation relation for weakly ergodic aging systems

A fluctuation relation for aging systems is introduced and verified by extensive numerical simulations. It is based on the hypothesis of partial equilibration over phase-space regions in a scenario of entropy-driven relaxation. The relation provides a simple alternative method, amenable of experimental implementation, to measure replica symmetry breaking parameters in aging systems. The connection with the effective temperatures obtained from the fluctuation-dissipation theorem is discussed

Origin of needle fibre calcite (NFC) : a geochemical approach

ABSTRACTNeedle fibre calcite (NFC) is one of the most widespread habits of pedogenic calcite. It is a monocrystal of calcite, in the shape of a needle, with a diameter of one micron and a length between 4 and 103 times its width. NFC occurs in soils with different macroscopic and microscopic morphologies. Macroscopically, two main habits of NFC exist: "cotton ball'Mike clusters and as "powder" coating on pebbles inside the soil. It can also act as nucleation sites for precipitation of calcite cements of purely physicochemical origin (LCC - Late Calcitic Cement). Although many studies have been conducted on needle fibre calcite, its origin remains a subject of debate. The NFC having never been reproduced in the laboratory whatever the considered approach, the processes responsible for its precipitation as a so particular morphology remain unexplained. The shift between the length orientation of the needle crystal and the normal axis of calcite growth (c-axis) is also unresolved.Samples taken in two soils observed in quarries (Villiers and Savagnier) in the Swiss Jura Mountains are used to investigate the processes involved in the formation of these calcite crystals in pedogenic environments. Three groups of microscopic morphologies are distinguished: (i) simple needles (SN), (ii) simple needles with overgrowths (SNO), and (iii) simple needles with nanofibres (SNN), nanofibres being either organic or mineral in nature. These groups correspond to different stages in the formation and evolution of NFC.Comparison of carbon and oxygen isotope compositions of NFC with LCC, in relationship with the composition of the carbonate host rock (CHR), and the carbon isotope signature of dissolved inorganic carbon (DIC) from the soil waters, indicates that both NFC and LCC are precipitated in isotopic equilibrium with the soil solution. Similar Ô13C and Ô180 values of the elongated NFC and the rhombohedral calcite crystals of the LCC suggest that the precipitation of these different calcite habits is not due to changes in physicochemical conditions. The growth of NFC crystals inside an organic mould formed by the fungal hyphae could explain the formation of calcite ciystals in the shape of a needle in isotopic equilibrium with the local environment.Strontium and calcium isotope compositions of the three microscopic groups of NFC and LCC were also studied, in order to determine the origin of calcium (Ca2+) entrapped in the calcite lattice and to elucidate the processes responsible for the precipitation of NFC. The 87Sr/86Sr ratio of the SN is closer to the 87Sr/86Sr ratio of the carbonate host rock than the LCC, SNO, and SNN. This could be another clue for the formation of SN inside fungal hyphae, because fungi are known to dissolve the rocks to release and translocate through their hyphae nutrients necessary for their growth. SN and SNN are depleted in Sr and enriched in ^Ca compared to the LCC. In the context of Villiers quarry, where the two ciystal shapes precipitate at similar temperature (in a range of 0,6°C), such variations are the result of a slower precipitation rate of NFC, which is inconsistent with a purely physicochemically precipitated elongate crystal.Finally, NFC is enriched in major and trace elements (i.e. Fe, Zn, Cu, and Mo) compared to the LCC. This enrichment is ascribed to modification in precipitation processes between the NFC and LCC. Right now, it is not possible to preclude the influence of the particular shape of NFC or the biological influence. REEs are not fractionated in NFC, contrary to LCC. Thus, NFC does not precipitate from a percolation solution circulating downward the soil, which should lead to the fractionation of the REEs. As explained above, fungi, are able to dissolve and translocate nutrients. This kind of processes allows releasing elements in the soil solution without fractionation and could explain the particular chemical signature of NFC regarding the REEs.The geochemical approach to investigate the origin of NFC presented in this study does not allow providing direct clues to the fungal origin of NFC, but brings several new insights in the understanding of the formation of such a particular mineral, calcite needles, by precluding definitively their physicochemical origin.RESUMELa calcite en aiguilles (NFC) est l'une des formes les plus ubiquiste de calcite pédogénique. Il s'agit d'un monocrystal de calcite d'un diamètre d'un micron et d'une longueur 4 à 102 fois supérieure à sa largeur. A l'échelle macroscopique, la NFC a été observée sous deux principaux aspects : l'une « cotonneuse » et l'autre formant un mince croûte autour des graviers du sol. La NFC peut également servir de support à la nucléation de ciments secondaires précipités de manière purement physico-chimique (LCC). Malgré les nombreuses études menées sur la NFC, son origine demeure encore inconnue. A ce jour, aucune expérience en laboratoire n'a permis de créer de la calcite en aiguilles, et ce, quelque soit l'approche abordée. Par conséquent, les processus précis responsables de la précipitation calcite avec une telle morphologie restent inconnus. Le décalage existant entre l'axe d'allongement des aiguilles de calcite et l'axe normal de croissance de la calcite (axe c) reste inexpliqué.Des échantillons de NFC, LCC, roche mère, eau de pluie des différents horizons du sol ont été prélevés principalement au front de deux carrières de graviers, ainsi que dans un profil de sol adjacent à ces carrières, dans le but de mieux comprendre les processus à l'origine de la précipitation de calcite en forme d'aiguille. Trois micro-morphologies ont été distinguées: les aiguilles simples (SN), les aiguilles simples avec surcroissances calcitiques (SNO) et enfin les aiguilles simples avec nanofibres (SNN), celles-ci pouvant être de minérales ou organiques. Ces groupes, d'après nos résultats et les études antérieures pourraient correspondre à différentes étapes de formation de la calcite en aiguilles.Dans un premier temps, la comparaison des signatures isotopiques de la calcite en aiguilles, du LCC, de la roche mère et du carbone inorganique dissout dans la solution du sol (CID) indique que la NFC, tout comme le LCC, précipite en équilibre avec la solution du sol. Les valeurs similaires en Ô13C et δ180 de cristaux de calcite allongés (NFC) et rhombohédriques (LCC) formés dans un même milieu suggère que ces différences morphologiques ne peuvent pas être attribuées à des modifications purement physico-chimiques. La croissance de NFC à l'intérieur d'un moule organique comme les hyphes de champignons semble être la seule hypothèse plausible permettant d'expliquer la formation de monocrystaux allongés de calcite en équilibre avec leur environnement.La composition isotopique en strontium (Sr) et calcium (Ca) des LCC et des trois micro¬morphologies de la NFC ont été étudiées également, afin de déterminer l'origine du Ca2+ présent dans le réseau cristallin de la calcite en aiguilles, ainsi que les processus responsables de la formation de NFC. Les valeurs du rapport 87Sr/86$r de la forme SN sont les plus proches de celles de la roche mère par rapport aux formes SNN et SNO et du LCC. Ceci pourrait être un nouvel indice de l'implication des champignons dans la précipitation de calcite en aiguilles, puisqu'ils sont connus pour avoir la capacité de dissoudre les roches afin de libérer les nutriments nécessaires à leur croissance, ainsi que de les transloquer par leurs hyphes. De plus, les formes SN et SNN sont appauvries en Sr et enrichies en "Ca, comparativement au LCC. Dans le sol étudié, tous les carbonates de calcium précipitent à la même température, par conséquent, de telles variations sont dues à un taux de précipitation plus lent de SN et SNN, ce qui est contradictoire avec l'hypothèse physico-chimique. Pour finir, la NFC est enrichie en certains éléments majeurs et traces (i.e. Fe, Zn, Cu et Mo) par rapport au LCC. Ceci peut être attribué à différents processus de formation entre la NFC et le LCC. Pour le moment il est impossible d'exclure l'influence de la forme particulière de la NFC ou celle du champignon. Les terres rares (REEs) ne sont pas fractionnées dans la NFC, contrairement au LCC. Ceci peut être expliqué par le fait que la NFC précipite à partir d'une solution qui n'a pas percolé à travers le sol. Les champignons en dissolvant les roches mettent en solution éléments sans les fractionner. L'approche géochimique de l'étude de la calcite en aiguilles ne permets pas de produire des preuves directes sur sa potentielle origine fongique, mais permet de mieux comprendre comment un minéral aussi singulier que la NFC peut se former. D'autre pare cette étude permets d'exclure définitivement l'hypothèse physico-chimique de l'origine de la calcite en aiguilles

Effects of 2 different prior endurance exercises on whole-body fat oxidation kinetics: light vs. heavy exercise.

This study aimed to compare the effects of 2 different prior endurance exercises on subsequent whole-body fat oxidation kinetics. Fifteen men performed 2 identical submaximal incremental tests (Incr2) on a cycle ergometer after (i) a ∼40-min submaximal incremental test (Incr1) followed by a 90-min continuous exercise performed at 50% of maximal aerobic power-output and a 1-h rest period (Heavy); and (ii) Incr1 followed by a 2.5-h rest period (Light). Fat oxidation was measured using indirect calorimetry and plotted as a function of exercise intensity during Incr1 and Incr2. A sinusoidal equation, including 3 independent variables (dilatation, symmetry and translation), was used to characterize the fat oxidation kinetics and to determine the intensity (Fat(max)) that elicited the maximal fat oxidation (MFO) during Incr. After the Heavy and Light trials, Fat(max), MFO, and fat oxidation rates were significantly greater during Incr2 than Incr1 (p < 0.001). However, Δ (i.e., Incr2-Incr1) Fat(max), MFO, and fat oxidation rates were greater in the Heavy compared with the Light trial (p < 0.05). The fat oxidation kinetics during Incr2(Heavy) showed a greater dilatation and rightward asymmetry than Incr1(Heavy), whereas only a greater dilatation was observed in Incr2(Light) (p < 0.05). This study showed that although to a lesser extent in the Light trial, both prior exercise sessions led to an increase in Fat(max), MFO, and absolute fat oxidation rates during Incr2, inducing significant changes in the shape of the fat oxidation kinetics.

Topological phases in small quantum Hall samples

Topological order has proven a useful concept to describe quantum phase transitions which are not captured by the Ginzburg-Landau type of symmetry-breaking order. However, lacking a local order parameter, topological order is hard to detect. One way to detect it is via direct observation of anyonic properties of excitations which are usually discussed in the thermodynamic limit, but so far has not been realized in macroscopic quantum Hall samples. Here we consider a system of few interacting bosons subjected to the lowest Landau level by a gauge potential, and theoretically investigate vortex excitations in order to identify topological properties of different ground states. Our investigation demonstrates that even in surprisingly small systems anyonic properties are able to characterize the topological order. In addition, focusing on a system in the Laughlin state, we study the robustness of its anyonic behavior in the presence of tunable finite-range interactions acting as a perturbation. A clear signal of a transition to a different state is reflected by the system's anyonic properties.

Large D gravity and low D strings

We show that in the limit of a large number of dimensions a wide class of nonextremal neutral black holes has a universal near-horizon limit. The limiting geometry is the two-dimensional black hole of string theory with a two-dimensional target space. Its conformal symmetry explains the properties of massless scalars found recently in the large-D limit. For black branes with string charges, the near-horizon geometry is that of the three-dimensional black strings of Horne and Horowitz. The analogies between the α′ expansion in string theory and the large-D expansion in gravity suggest a possible effective string description of the large-D limit of black holes. We comment on applications to several subjects, in particular to the problem of critical collapse.

Characterization of phosphate structures in biochar from swine bones

The objective of this work was to develop an alternative methodology to study and characterize the phosphate crystalline properties, directly associated with solubility and plant availability, in biochar from swine bones. Some phosphate symmetry properties of pyrolyzed swine bones were established, using solid state nuclear magnetic resonance spectroscopy, principal component analysis, and multivariate curve resolution analysis, on four pyrolyzed samples at different carbonization intensities. Increasing carbonization parameters (temperature or residence time) generates diverse phosphate structures, increasing their symmetry and decreasing the crossed polarizability of the pair ¹H-31P, producing phosphates with, probably, lower solubility than the ones produced at lower carbonization intensity. Additionally, a new methodology is being developed to study and characterize phosphate crystalline properties directly associated with phosphate solubility and availability to plants.

Synchronization of symmetric chaotic systems

This paper contains a study of the synchronization by homogeneous nonlinear driving of systems that are symmetric in phase space. The main consequence of this symmetry is the ability of the response to synchronize in more than just one way to the driving systems. These different forms of synchronization are to be understood as generalized synchronization states in which the motions of drive and response are in complete correlation, but the phase space distance between them does not converge to zero. In this case the synchronization phenomenon becomes enriched because there is multistability. As a consequence, there appear multiple basins of attraction and special responses to external noise. It is shown, by means of a computer simulation of various nonlinear systems, that: (i) the decay to the generalized synchronization states is exponential, (ii) the basins of attraction are symmetric, usually complicated, frequently fractal, and robust under the changes in the parameters, and (iii) the effect of external noise is to weaken the synchronization, and in some cases to produce jumps between the various synchronization states available

Multi-scale systems analysis of plant development : beyond cellular signaling and tissue morphodynamics

Les plantes sont essentielles pour les sociétés humaines. Notre alimentation quotidienne, les matériaux de constructions et les sources énergétiques dérivent de la biomasse végétale. En revanche, la compréhension des multiples aspects développementaux des plantes est encore peu exploitée et représente un sujet de recherche majeur pour la science. L'émergence des technologies à haut débit pour le séquençage de génome à grande échelle ou l'imagerie de haute résolution permet à présent de produire des quantités énormes d'information. L'analyse informatique est une façon d'intégrer ces données et de réduire la complexité apparente vers une échelle d'abstraction appropriée, dont la finalité est de fournir des perspectives de recherches ciblées. Ceci représente la raison première de cette thèse. En d'autres termes, nous appliquons des méthodes descriptives et prédictives combinées à des simulations numériques afin d'apporter des solutions originales à des problèmes relatifs à la morphogénèse à l'échelle de la cellule et de l'organe. Nous nous sommes fixés parmi les objectifs principaux de cette thèse d'élucider de quelle manière l'interaction croisée des phytohormones auxine et brassinosteroïdes (BRs) détermine la croissance de la cellule dans la racine du méristème apical d'Arabidopsis thaliana, l'organisme modèle de référence pour les études moléculaires en plantes. Pour reconstruire le réseau de signalement cellulaire, nous avons extrait de la littérature les informations pertinentes concernant les relations entre les protéines impliquées dans la transduction des signaux hormonaux. Le réseau a ensuite été modélisé en utilisant un formalisme logique et qualitatif pour pallier l'absence de données quantitatives. Tout d'abord, Les résultats ont permis de confirmer que l'auxine et les BRs agissent en synergie pour contrôler la croissance de la cellule, puis, d'expliquer des observations phénotypiques paradoxales et au final, de mettre à jour une interaction clef entre deux protéines dans la maintenance du méristème de la racine. Une étude ultérieure chez la plante modèle Brachypodium dystachion (Brachypo- dium) a révélé l'ajustement du réseau d'interaction croisée entre auxine et éthylène par rapport à Arabidopsis. Chez ce dernier, interférer avec la biosynthèse de l'auxine mène à la formation d'une racine courte. Néanmoins, nous avons isolé chez Brachypodium un mutant hypomorphique dans la biosynthèse de l'auxine qui affiche une racine plus longue. Nous avons alors conduit une analyse morphométrique qui a confirmé que des cellules plus anisotropique (plus fines et longues) sont à l'origine de ce phénotype racinaire. Des analyses plus approfondies ont démontré que la différence phénotypique entre Brachypodium et Arabidopsis s'explique par une inversion de la fonction régulatrice dans la relation entre le réseau de signalisation par l'éthylène et la biosynthèse de l'auxine. L'analyse morphométrique utilisée dans l'étude précédente exploite le pipeline de traitement d'image de notre méthode d'histologie quantitative. Pendant la croissance secondaire, la symétrie bilatérale de l'hypocotyle est remplacée par une symétrie radiale et une organisation concentrique des tissus constitutifs. Ces tissus sont initialement composés d'une douzaine de cellules mais peuvent aisément atteindre des dizaines de milliers dans les derniers stades du développement. Cette échelle dépasse largement le seuil d'investigation par les moyens dits 'traditionnels' comme l'imagerie directe de tissus en profondeur. L'étude de ce système pendant cette phase de développement ne peut se faire qu'en réalisant des coupes fines de l'organe, ce qui empêche une compréhension des phénomènes cellulaires dynamiques sous-jacents. Nous y avons remédié en proposant une stratégie originale nommée, histologie quantitative. De fait, nous avons extrait l'information contenue dans des images de très haute résolution de sections transverses d'hypocotyles en utilisant un pipeline d'analyse et de segmentation d'image à grande échelle. Nous l'avons ensuite combiné avec un algorithme de reconnaissance automatique des cellules. Cet outil nous a permis de réaliser une description quantitative de la progression de la croissance secondaire révélant des schémas développementales non-apparents avec une inspection visuelle classique. La formation de pôle de phloèmes en structure répétée et espacée entre eux d'une longueur constante illustre les bénéfices de notre approche. Par ailleurs, l'exploitation approfondie de ces résultats a montré un changement de croissance anisotropique des cellules du cambium et du phloème qui semble en phase avec l'expansion du xylème. Combinant des outils génétiques et de la modélisation biomécanique, nous avons démontré que seule la croissance plus rapide des tissus internes peut produire une réorientation de l'axe de croissance anisotropique des tissus périphériques. Cette prédiction a été confirmée par le calcul du ratio des taux de croissance du xylème et du phloème au cours de développement secondaire ; des ratios élevés sont effectivement observés et concomitant à l'établissement progressif et tangentiel du cambium. Ces résultats suggèrent un mécanisme d'auto-organisation établi par un gradient de division méristématique qui génèrent une distribution de contraintes mécaniques. Ceci réoriente la croissance anisotropique des tissus périphériques pour supporter la croissance secondaire. - Plants are essential for human society, because our daily food, construction materials and sustainable energy are derived from plant biomass. Yet, despite this importance, the multiple developmental aspects of plants are still poorly understood and represent a major challenge for science. With the emergence of high throughput devices for genome sequencing and high-resolution imaging, data has never been so easy to collect, generating huge amounts of information. Computational analysis is one way to integrate those data and to decrease the apparent complexity towards an appropriate scale of abstraction with the aim to eventually provide new answers and direct further research perspectives. This is the motivation behind this thesis work, i.e. the application of descriptive and predictive analytics combined with computational modeling to answer problems that revolve around morphogenesis at the subcellular and organ scale. One of the goals of this thesis is to elucidate how the auxin-brassinosteroid phytohormone interaction determines the cell growth in the root apical meristem of Arabidopsis thaliana (Arabidopsis), the plant model of reference for molecular studies. The pertinent information about signaling protein relationships was obtained through the literature to reconstruct the entire hormonal crosstalk. Due to a lack of quantitative information, we employed a qualitative modeling formalism. This work permitted to confirm the synergistic effect of the hormonal crosstalk on cell elongation, to explain some of our paradoxical mutant phenotypes and to predict a novel interaction between the BREVIS RADIX (BRX) protein and the transcription factor MONOPTEROS (MP),which turned out to be critical for the maintenance of the root meristem. On the same subcellular scale, another study in the monocot model Brachypodium dystachion (Brachypodium) revealed an alternative wiring of auxin-ethylene crosstalk as compared to Arabidopsis. In the latter, increasing interference with auxin biosynthesis results in progressively shorter roots. By contrast, a hypomorphic Brachypodium mutant isolated in this study in an enzyme of the auxin biosynthesis pathway displayed a dramatically longer seminal root. Our morphometric analysis confirmed that more anisotropic cells (thinner and longer) are principally responsible for the mutant root phenotype. Further characterization pointed towards an inverted regulatory logic in the relation between ethylene signaling and auxin biosynthesis in Brachypodium as compared to Arabidopsis, which explains the phenotypic discrepancy. Finally, the morphometric analysis of hypocotyl secondary growth that we applied in this study was performed with the image-processing pipeline of our quantitative histology method. During its secondary growth, the hypocotyl reorganizes its primary bilateral symmetry to a radial symmetry of highly specialized tissues comprising several thousand cells, starting with a few dozens. However, such a scale only permits observations in thin cross-sections, severely hampering a comprehensive analysis of the morphodynamics involved. Our quantitative histology strategy overcomes this limitation. We acquired hypocotyl cross-sections from tiled high-resolution images and extracted their information content using custom high-throughput image processing and segmentation. Coupled with an automated cell type recognition algorithm, it allows precise quantitative characterization of vascular development and reveals developmental patterns that were not evident from visual inspection, for example the steady interspace distance of the phloem poles. Further analyses indicated a change in growth anisotropy of cambial and phloem cells, which appeared in phase with the expansion of xylem. Combining genetic tools and computational modeling, we showed that the reorientation of growth anisotropy axis of peripheral tissue layers only occurs when the growth rate of central tissue is higher than the peripheral one. This was confirmed by the calculation of the ratio of the growth rate xylem to phloem throughout secondary growth. High ratios are indeed observed and concomitant with the homogenization of cambium anisotropy. These results suggest a self-organization mechanism, promoted by a gradient of division in the cambium that generates a pattern of mechanical constraints. This, in turn, reorients the growth anisotropy of peripheral tissues to sustain the secondary growth.

Transonic flow past on enlarged missile nose parts

Numerical computation of a viscid heat-conducting transonic flow over a generic commercial rocket profile with symmetric oversized nose part was carried out. It has been shown that at zero angle of attack for some free-streamvelocity value flow pattern loses its symmetry. This results in non-uniform pressure distribution on rocket surface in angle direction which may yield in additional oscillating stress on the rocket. Also it has been found that obtained non-symmetric flow patterns are stable for small velocity perturbations.

Dynamical sectors of a relativistic two particle model

We reconsider a model of two relativistic particles interacting via a multiplicative potential, as an example of a simple dynamical system with sectors, or branches, with different dynamics and degrees of freedom. The presence or absence of sectors depends on the values of rest masses. Some aspects of the canonical quantization are described. The model could be interpreted as a bigravity model in one dimension.