Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schr odinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schrödinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

Outcome of unilateral ankle arthrodesis and total ankle replacement in terms of bilateral gait mechanics.

Previous studies assessed the outcome of ankle arthrodesis (AA) and total ankle replacement (TAR) surgeries; however, the extent of postoperative recovery towards bilateral gait mechanics (BGM) is unknown. We evaluated the outcome of the two surgeries at least 2 years post rehabilitation, focusing on BGM. 36 participants, including 12 AA patients, 12 TAR patients, and 12 controls were included. Gait assessment over 50 m distance was performed utilizing pressure insoles and 3D inertial sensors, following which an intraindividual comparison was performed. Most spatiotemporal and kinematic parameters in the TAR group were indicative of good gait symmetry, while the AA group presented significant differences. Plantar pressure symmetry among the AA group was also significantly distorted. Abnormality in biomechanical behavior of the AA unoperated, contralateral foot was observed. In summary, our results indicate an altered BGM in AA patients, whereas a relatively fully recovered BGM is observed in TAR patients, despite the quantitative differences in several parameters when compared to a healthy population. Our study supports a biomechanical assessment and rehabilitation of both operated and unoperated sides after major surgeries for ankle osteoarthrosis.

A survey on the inverse integrating factor

The relation between limit cycles of planar differential systems and the inverse integrating factor was first shown in an article of Giacomini, Llibre and Viano appeared in 1996. From that moment on, many research articles are devoted to the study of the properties of the inverse integrating factor and its relationwith limit cycles and their bifurcations. This paper is a summary of all the results about this topic. We include a list of references together with the corresponding related results aiming at being as much exhaustive as possible. The paper is, nonetheless, self-contained in such a way that all the main results on the inverse integrating factor are stated and a complete overview of the subject is given. Each section contains a different issue to which the inverse integrating factor plays a role: the integrability problem, relation with Lie symmetries, the center problem, vanishing set of an inverse integrating factor, bifurcation of limit cycles from either a period annulus or from a monodromic ω-limit set and some generalizations.

Supergravity models of (3+1)-dimensional QCD

The most general black M5-brane solution of eleven-dimensional supergravity (with a flat R4 spacetime in the brane and a regular horizon) is characterized by charge, mass and two angular momenta. We use this metric to construct general dual models of large-N QCD (at strong coupling) that depend on two free parameters. The mass spectrum of scalar particles is determined analytically (in the WKB approximation) and numerically in the whole two-dimensional parameter space. We compare the mass spectrum with analogous results from lattice calculations, and find that the supergravity predictions are close to the lattice results everywhere on the two dimensional parameter space except along a special line. We also examine the mass spectrum of the supergravity Kaluza-Klein (KK) modes and find that the KK modes along the compact D-brane coordinate decouple from the spectrum for large angular momenta. There are however KK modes charged under a U(1)×U(1) global symmetry which do not decouple anywhere on the parameter space. General formulas for the string tension and action are also given.

Spontaneous Emergence of Chirality in the Limited Enantioselectivity Model: Autocatalytic Cycle Driven by an External Reagent

The emergence of chirality in enantioselective autocatalysis for compounds unable to transform according to the Frank-like reaction network is discussed with respect to the controversial limited enantioselectivity (LES) model composed of coupled enantioselective and non-enantioselective autocatalyses. The LES model cannot lead to spontaneous mirror symmetry breaking (SMSB) either in closed systems with a homogeneous temperature distribution or in closed systems with a stationary non-uniform temperature distribution. However, simulations of chemical kinetics in a two-compartment model demonstrate that SMSB may occur if both autocatalytic reactions are spatially separated at different temperatures in different compartments but coupled under the action of a continuous internal flow. In such conditions, the system can evolve, for certain reaction and system parameters, toward a chiral stationary state; that is, the system is able to reach a bifurcation point leading to SMSB. Numerical simulations in which reasonable chemical parameters have been used suggest that an adequate scenario for such a SMSB would be that of abyssal hydrothermal vents, by virtue of the typical temperature gradients found there and the role of inorganic solids mediating chemical reactions in an enzyme-like role.

Quantifying Social Asymmetric Structures

Many social phenomena involve a set of dyadic relations among agents whose actions may be dependent. Although individualistic approaches have frequently been applied to analyze social processes, these are not generally concerned with dyadic relations nor do they deal with dependency. This paper describes a mathematical procedure for analyzing dyadic interactions in a social system. The proposed method mainly consists of decomposing asymmetric data into their symmetrical and skew-symmetrical parts. A quantification of skew-symmetry for a social system can be obtained by dividing the norm of the skew-symmetrical matrix by the norm of the asymmetric matrix. This calculation makes available to researchers a quantity related to the amount of dyadic reciprocity. Regarding agents, the procedure enables researchers to identify those whose behavior is asymmetric with respect to all agents. It is also possible to derive symmetric measurements among agents and to use multivariate statistical techniques.

Extending body space in immersive virtual reality: a very long arm illusion

Recent studies have shown that a fake body part can be incorporated into human body representation through synchronous multisensory stimulation on the fake and corresponding real body part- the most famous example being the Rubber Hand Illusion. However, the extent to which gross asymmetries in the fake body can be assimilated remains unknown. Participants experienced, through a head-tracked stereo head-mounted display a virtual body coincident with their real body. There were 5 conditions in a between-groups experiment, with 10 participants per condition. In all conditions there was visuo-motor congruence between the real and virtual dominant arm. In an Incongruent condition (I), where the virtual arm length was equal to the real length, there was visuo-tactile incongruence. In four Congruent conditions there was visuo-tactile congruence, but the virtual arm lengths were either equal to (C1), double (C2), triple (C3) or quadruple (C4) the real ones. Questionnaire scores and defensive withdrawal movements in response to a threat showed that the overall level of ownership was high in both C1 and I, and there was no significant difference between these conditions. Additionally, participants experienced ownership over the virtual arm up to three times the length of the real one, and less strongly at four times the length. The illusion did decline, however, with the length of the virtual arm. In the C2-C4 conditions although a measure of proprioceptive drift positively correlated with virtual arm length, there was no correlation between the drift and ownership of the virtual arm, suggesting different underlying mechanisms between ownership and drift. Overall, these findings extend and enrich previous results that multisensory and sensorimotor information can reconstruct our perception of the body shape, size and symmetry even when this is not consistent with normal body proportions.

Thermodynamic stability of nanosized multicomponent bubbles/droplets: The square gradient theory and the capillary approach

Formation of nanosized droplets/bubbles from a metastable bulk phase is connected to many unresolved scientific questions. We analyze the properties and stability of multicomponent droplets and bubbles in the canonical ensemble, and compare with single-component systems. The bubbles/droplets are described on the mesoscopic level by square gradient theory. Furthermore, we compare the results to a capillary model which gives a macroscopic description. Remarkably, the solutions of the square gradient model, representing bubbles and droplets, are accurately reproduced by the capillary model except in the vicinity of the spinodals. The solutions of the square gradient model form closed loops, which shows the inherent symmetry and connected nature of bubbles and droplets. A thermodynamic stability analysis is carried out, where the second variation of the square gradient description is compared to the eigenvalues of the Hessian matrix in the capillary description. The analysis shows that it is impossible to stabilize arbitrarily small bubbles or droplets in closed systems and gives insight into metastable regions close to the minimum bubble/droplet radii. Despite the large difference in complexity, the square gradient and the capillary model predict the same finite threshold sizes and very similar stability limits for bubbles and droplets, both for single-component and two-component systems.

Effect of pressure on La2(WO4)3 with a modulated scheelite-type structure

We have studied the effect of pressure on the structural and vibrational properties of lanthanum tritungstate La2(WO4)3. This compound crystallizes under ambient conditions in the modulated scheelite-type structure known as the α phase. We have performed x-ray diffraction and Raman scattering measurements up to a pressure of 20 GPa, as well as ab initio calculations within the framework of the density functional theory. Up to 5 GPa, the three methods provide a similar picture of the evolution under pressure of α-La2(WO4)3. At 5 GPa, we begin to observe some structural changes, and above 6 GPa we find that the x-ray patterns cannot be indexed as a single phase. However, we find that a mixture of two phases with C2/c symmetry accounts for all diffraction peaks. Our ab initio study confirms the existence of several C2/c structures, which are very close in energy in this compression range. According to our measurements, a state with medium-range order appears at pressures above 9 and 11 GPa, from x-ray diffraction and Raman experiments, respectively. Based upon our theoretical calculations we propose several high-pressure candidates with high cationic coordinations at these pressures. The compound evolves into a partially amorphous phase at pressures above 20 GPa.

Analysis of bulk and surface contributions in the neutron skin of nuclei

The neutron skin thickness of nuclei is a sensitive probe of the nuclear symmetry energy and has multiple implications for nuclear and astrophysical studies. However, precision measurements of this observable are difficult to obtain. The analysis of the experimental data may imply some assumptions about the bulk or surface nature of the formation of the neutron skin. Here we study the bulk or surface character of neutron skins of nuclei following from calculations with Gogny, Skyrme, and covariant nuclear mean-field interactions. These interactions are successful in describing nuclear charge radii and binding energies but predict different values for neutron skins. We perform the study by fitting two-parameter Fermi distributions to the calculated self-consistent neutron and proton densities. We note that the equivalent sharp radius is a more suitable reference quantity than the half-density radius parameter of the Fermi distributions to discern between the bulk and surface contributions in neutron skins. We present calculations for nuclei in the stability valley and for the isotopic chains of Sn and Pb.

New method for measuring longitudinal fuctuations and directed flow in ultrarelativistic heavy ion reactions

It has been shown in recent ALICE@LHC measurements that the odd flow harmonics, in particular, a directed flow v1, occurred to be weak and dominated by random fluctuations. In this work we propose a new method, which makes the measurements more sensitive to the flow patterns showing global collective symmetries. We demonstrate how the longitudinal center of mass rapidity fluctuations can be identified, and then the collective flow analysis can be performed in the event-by-event center of mass frame. Such a method can be very effective in separating the flow patterns originating from random fluctuations, and the flow patterns originating from the global symmetry of the initial state.

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.

Rotational Doppler effect in magnetic resonance

We compute the shift in the frequency of the spin resonance in a solid that rotates in the field of a circularly polarized electromagnetic wave. Electron-spin resonance, nuclear magnetic resonance, and ferromagnetic resonance are considered. We show that contrary to the case of the rotating LC circuit, the shift in the frequency of the spin resonance has strong dependence on the symmetry of the receiver. The shift due to rotation occurs only when rotational symmetry is broken by the anisotropy of the gyromagnetic tensor, by the shape of the body or by magnetocrystalline anisotropy. General expressions for the resonance frequency and power absorption are derived and implications for experiment are discussed.

Une délicate rencontre entre savoirs autochtones "experts" : enjeux politiques interculturelles dans le domaine de la prévention de la violence à l'égard des femmes kichwa en Amazonie équatorienne

Cette thèse porte sur l'élaboration et la mise en pratique de politiques interculturelles dans le champ de la santé internationale, en se basant sur une ethnographie d'un programme de préven¬tion de la violence de genre dans le canton de Loreto, en Amazonie équatorienne, mis en place par la Croix-Rouge suisse et aujourd'hui géré de concert avec l'Etat équatorien et une organisation kichwa locale. Suivant une approche qui fait varier les échelles d'analyses pour articuler le niveau local, national et international, elle met en évidence les lieux d'intersection et les hiatus entre l'idéal d'interculturalité tel qu'il est conçu «par le haut» et les pratiques qui sont mises en oeuvre au quotidien par des professionnels de la santé et du développement métis équatoriens. Elle révèle ainsi qu'au-delà de l'idéal du respect des « différences culturelles autochtones » et de la symétrie entre les « cultures », les discours et les pratiques de ces professionnels consistent en une entreprise de normalisation et de moralisation des comportements des destinataires kichwa en matière de rapports de genre. Pour affiner ces analyses et dépasser une approche critique de la santé publique, cette thèse explore également les représentations et les pratiques des destinataires - femmes agents de santé et « bénéficiaires » kichwa du programme - en matière de violence et de rapports de genre. Elle montre ainsi que le transfert de normes et de valeurs via la santé publique fait l'objet de mul¬tiples processus d'appropriations, et explore les différentes d'interprétations, de négociations et d'instrumentalisations de la part des destinataires, tant au niveau individuel que collectif. -- Intercultural politics and the prevention of violence against kichwa women in the Ecuadorian Amazon This PhD thesis focuses on the development and application of intercultural policies in the field of international health. It is drawn on an ethnographic fieldwork conducted in canton Loreto, in the Ecuadorian Amazon, about a gender violence prevention program which was set up by the Swiss Red Cross and which is now managed in cooperation with the Ecuadorian State and a local kichwa organization. Following a multiple-scale analysis in order to articulate the local, national and international dynamics, it highlights the intersections and the gaps between, on the one hand, the the institutional prescriptions about the ideal of interculturality and on the other hand, the daily practices of Ecuadorian mestizo health and development profesionals. It reveals that beyond the ideal of respect for «indigenous cultural differences» and of symmetry between «cultures», the discourses and practices of these professionals consist of a normalizing and moralizing enter¬prise concerning the gendered and, more broadly, social behaviors of kichwa «beneficiaries». In order to refine the analysis and to go beyond a critical approach of public health, this thesis also explores the violence and gender relations representations and practices of kichwa women health workers and «beneficiaries», men and women. Thus it shows that the transfer of norms via public health is the subject of multiple processes of appropriation, interpretation, negotiation and instru¬mentalisation both on individual and collective levels by the «beneficiaries».