Equidistribution results for geodesic flows

Using the works of Ma\~n\'e \cite{Ma} and Paternain \cite{Pat} we study the distribution of geodesic arcs with respect to equilibrium states of the geodesic flow on a closed manifold, equipped with a $\mathcal{C}^{\infty}$ Riemannian metric. We prove large deviations lower and upper bounds and a contraction principle for the geodesic flow in the space of probability measures of the unit tangent bundle. We deduce a way of approximating equilibrium states for continuous potentials.Comment: 25 page

Ácido hialurónico e neocolagénese: a importância na harmonização orofacial – uma revisão narrativa

O ácido hialurónico desempenha um papel fundamental no funcionamento da matriz extracelular. É um seu componente fundamental, importante na morfogénese e contribui significativamente para a hidrodinâmica dos tecidos, migração e proliferação celular. O objectivo desta revisão narrativa, é analisar o papel do ácido hialurónico em harmonização orofacial e simultaneamente compreender o seu papel na neocolagénese enquanto bioestimulador de colagénio. Procedeu-se ao levantamento de artigos nas bases de dados PubMed, Bon, Elsevier, Science Direct, considerando essencialmente os últimos 5 anos de publicação (2016 a 2021). A presença de ácido hialurónico tem sido associada ao aumento da síntese de colagénio nos tecidos mediante a ligação a receptores membranares tais como cluster de diferenciação 44 e o receptores para a motilidade mediada por hialurano. A introdução de ácido hialurónico na derme, estimula os fibroblastos a produzir colagénio tipo I. Essa estimulação está associada a um aumento localizado das forças mecânicas, indicado pelo alongamento dos fibroblastos, sendo mediada por uma regulação positiva do receptor do fator de crescimento transformante beta e do fator de crescimento do tecido conjuntivo. O conhecimento dos princípios de bioestimulação e neocolagénese são fundamentais para melhor compreender o mecanismo de acção dos vários bioestimuladores, bem como selecionar a melhor opção em função da biologia do paciente. Será este conhecimento dos profissionais de saúde em harmonização orofacial, que os capacitará – a mais do que dominar um conjunto de técnicas injetáveis – a entender que os princípios da harmonização orofacial integram biomedicina, biomateriais, farmacologia, engenharia e vão ciência fora, longe de encontrar fronteiras!Hyaluronic acid plays a key role in the functioning of the extracellular matrix. It is a fundamental component, important in morphogenesis and significantly contributes to tissue hydrodynamics, cell migration and proliferation. The aim of this narrative review is to analyze the role of hyaluronic acid in orofacial harmonization and simultaneously understand its role in neocollagenesis as a collagen biostimulator. Articles were surveyed in the PubMed, Bon, Elsevier, Science Direct databases, essentially considering the last 5 years of publication (2016 to 2021). The presence of hyaluronic acid has been associated with increased collagen synthesis in tissues through binding to membrane receptors such as the differentiation cluster 44 and the receptor for hyaluronan-mediated motility. The introduction of hyaluronic acid in the dermis stimulates the fibroblasts to produce collagen type I. This stimulation is associated with a localized increase in mechanical forces, indicated by the elongation of the fibroblasts, being mediated by a positive regulation of the transforming growth factor beta receptor and of connective tissue growth factor. Knowledge of the principles of biostimulation and neocollagenesis are essential to better understand the mechanism of action of the various biostimulators, as well as to select the best option depending on the patient's biology. It will be this knowledge of health professionals in orofacial harmonization that will enable them - more than mastering a set of injectable techniques - to understand that the principles of orofacial harmonization integrate biomedicine, biomaterials, pharmacology, engineering and go beyond science, far from finding borders

Space-time laser instabilities in homogeneously broadened dense media

We investigate the space-time dynamics of a homogeneously broadened single-mode laser when local field correction (LFC) is taken into account. We demonstrate that the Maxwell-Bloch equations modified by LFC admit travelling-wave solutions, as when LFC is not taken into account. Their stability is discussed and compared to the case without LFC

Flexoelectric fluid membrane vesicles in spherical confinement

The morphology of spherically confined flexoelectric fluid membrane vesicles in an external uniform electric field is studied numerically. Due to the deformations induced by the confinement, the membrane becomes polarized resulting in an interaction with the external field. The equilibrium shapes of the vesicle without electric field can be classified in a geometrical phase diagram as a function of scaled area and reduced volume [1,2]. When the area of the membrane is only slightly larger than the area of the confining sphere, a single axisymmetric invagination appears. A non-vanishing electric field induces an additional elongation of the confined vesicle which is either perpendicular or parallel depending on the sign of the electric field parameter. Higher values of the surface area or the electric field parameter can reduce the symmetry of the system leading to more complex folding. We present the resulting shapes and show that transition lines are shifted in the presence of an electric field. The obtained folding patterns could be of interest for biophysical and technological applications alike.Comment: main text: 9 pages, 4 figures supplemental: 5 pages, 2 figure

Effect of Mn Doped and Mn+Sn Co-doping on the Properties of ZnO Thin Films

Mn doped and Mn/Sn co-doped ZnO thin films nanoparticles have been successfully synthesized by Spray pyrolysis technique at 300 0C. X-ray diffraction study showed that all the films have the hexagonal wurtzite structure with the preferential orientation (002) plane. The optical measurement exhibited an increase in the average transmittance from 77% for Mn doped ZnO to 84% for Mn/Sn co-doped ZnO films in the visible region. Further the optical band gap changes from 3.18 eV for undoped ZnO films to 3.27 eV for Mn/Sn co-doped ZnO films. The electrical resistivity has decreased with incorporation of Mn and Sn ions to reach the minimum value of 11 (Ω.cm) for Mn doped ZnO film

Stabilization of space–time laser instability through the finite transverse extension of pumping

We investigate the space–time dynamics of a homogeneously broadened single-mode laser when diffraction is taken into account. It is well known that such a laser displays instability when pumping reaches the second laser threshold. We show that the laser dynamics can be stabilized by pumping in a domain of finite width. The analysis of stationary solutions to the Maxwell–Bloch equations (evanescent waves, travelling waves, localized solutions) allows the stabilization mechanism to be explained

Analyse de dynamiques spatio-temporelles d’un laser

La dynamique spatio-temporelle d’un système laser avec diffraction est étudiée. La correspondance entre la structure du portrait de phase et l’organisation relative desdéfauts topologiques dans les diagrammes spatio-temporels est clairement mise en évidence. Ainsi, une dynamique de type chaos toroïdal est associée à des défauts apparaissant périodiquement (dans l’espace et dans le temps). En revanche, il n’y a plus de périodicité des défauts sur les diagrammes spatio-temporels lorsque le régime est un chaos développé