Explicit Formulas for Non-Geodesic Biharmonic Curves of the Heisenberg Group

We consider the biharmonicity condition for maps between Riemannian manifolds (see [BK]), and study the non-geodesic biharmonic curves in the Heisenberg group H_3. First we prove that all of them are helices, and then we obtain explicitly their parametric equations.Comment: 16 pages, 2 figure

Fin de la décolonisation et printemps arabe

International audienc

Filosofia della penuria

International audienc

Entre connaissances implicites et processus explicites en intercompréhension écrite : peut-on réussir tous les transferts ?

International audienceLa méthodologie développée dans la méthode Eurom5 (édition enrichie de la méthode EuRom4 (1997) réalisée entre autres par Claire Blanche-Benveniste) permet à des lecteurs experts en L1 romane de transférer leur compétence dans plusieurs autres langues parentes peu ou pas connues. Le travail de recherche et les applications expérimentales menées durant plusieurs années ont permis de rédiger un protocole qui s’appuie sur l’exploitation de plusieurs types de stratégies relevant du processus de lecture et de compréhension. Pour chacun des paramètres qui entrent en jeu lorsqu’il s’agit de comprendre un texte, nous proposons certaines voies facilitatrices tout en mentionnant les variables sur lesquelles faire porter une attention particulière. L’originalité de cette méthodologie est d’avoir traité la dimension grammaticale des langues comme une stratégie d’accès au sens

Constant mean curvature and totally umbilical biharmonic surfaces in 3-dimensional geometries

We prove that a totally umbilical biharmonic surface in any $3$-dimensional Riemannian manifold has constant mean curvature. We use this to show that a totally umbilical surface in Thurston's 3-dimensional geometries is proper biharmonic if and only if it is a part of $S^2(1/\sqrt{2})$ in $S^3$. We also give complete classifications of constant mean curvature proper biharmonic surfaces in 3-dimensional geometries and in 3-dimensional Bianchi-Cartan-Vranceanu spaces, and a complete classifications of proper biharmonic Hopf cylinders in 3-dimensional Bianchi-Cartan-Vranceanu spaces.Comment: 15 page

Thermal boundary resistance from transient nanocalorimetry: a multiscale modeling approach

The Thermal Boundary Resistance at the interface between a nanosized Al film and an Al_{2}O_{3} substrate is investigated at an atomistic level. A room temperature value of 1.4 m^{2}K/GW is found. The thermal dynamics occurring in time-resolved thermo-reflectance experiments is then modelled via macro-physics equations upon insertion of the materials parameters obtained from atomistic simulations. Electrons and phonons non-equilibrium and spatio-temporal temperatures inhomo- geneities are found to persist up to the nanosecond time scale. These results question the validity of the commonly adopted lumped thermal capacitance model in interpreting transient nanocalorimetry experiments. The strategy adopted in the literature to extract the Thermal Boundary Resistance from transient reflectivity traces is revised at the light of the present findings. The results are of relevance beyond the specific system, the physical picture being general and readily extendable to other heterojunctions.Comment: 12 pages, 8 figure

MBOAT7 in liver and extrahepatic diseases

MBOAT7 is a protein anchored to endomembranes by several transmembrane domains. It has a catalytic dyad involved in remodelling of phosphatidylinositol with polyunsaturated fatty acids. Genetic variants in the MBOAT7 gene have been associated with the entire spectrum of non-alcoholic fatty liver (NAFLD), recently redefined as metabolic dysfunction-associated fatty liver disease (MAFLD) and, lately, steatotic liver disease (SLD), and to an increasing number of extrahepatic conditions. In this review, we will (a) elucidate the molecular mechanisms by which MBOAT7 loss-of-function predisposes to MAFLD and neurodevelopmental disorders and (b) discuss the growing number of genetic studies linking MBOAT7 to hepatic and extrahepatic diseases. MBOAT7 complete loss of function causes severe changes in brain development resulting in several neurological manifestations. Lower MBOAT7 hepatic expression at both the mRNA and protein levels, due to missense nucleotide polymorphisms (SNPs) in the locus containing the MBOAT7 gene, affects specifically metabolic and viral diseases in the liver from simple steatosis to hepatocellular carcinoma, and potentially COVID-19 disease. This body of evidence shows that phosphatidylinositol remodelling is a key factor for human health

On level line fluctuations of SOS surfaces above a wall

We study the low temperature $(2+1)$D Solid-On-Solid model on $[[1, L]]^2$ with zero boundary conditions and non-negative heights (a floor at height $0$). Caputo et al. (2016) established that this random surface typically admits either $\mathfrak h$ or $\mathfrak h+1$ many nested macroscopic level line loops $\{\mathcal L_i\}_{i\geq 0}$ for an explicit $\mathfrak h\asymp \log L$, and its top loop $\mathcal L_0$ has cube-root fluctuations: e.g., if $\rho(x)$ is the vertical displacement of $\mathcal L_0$ from the bottom boundary point $(x,0)$, then $\max \rho(x) = L^{1/3+o(1)}$ over $x\in I_0:=L/2+[[-L^{2/3},L^{2/3}]]$. It is believed that rescaling $\rho$ by $L^{1/3}$ and $I_0$ by $L^{2/3}$ would yield a limit law of a diffusion on $[-1,1]$. However, no nontrivial lower bound was known on $\rho(x)$ for a fixed $x\in I_0$ (e.g., $x=\frac L2$), let alone on $\min\rho(x)$ in $I_0$, to complement the bound on $\max\rho(x)$. Here we show a lower bound of the predicted order $L^{1/3}$: for every $\epsilon>0$ there exists $\delta>0$ such that $\min_{x\in I_0} \rho(x) \geq \delta L^{1/3}$ with probability at least $1-\epsilon$. The proof relies on the Ornstein--Zernike machinery due to Campanino--Ioffe--Velenik, and a result of Ioffe, Shlosman and Toninelli (2015) that rules out pinning in Ising polymers with modified interactions along the boundary. En route, we refine the latter result into a Brownian excursion limit law, which may be of independent interest.Comment: 48 pages, 2 figure

Bour’s theorem and helicoidal surfaces with constant mean curvature in the Bianchi–Cartan–Vranceanu spaces

In this paper, we generalize a classical result of Bour concerning helicoidal surfaces in the three-dimensional Euclidean space R3 to the case of helicoidal surfaces in the Bianchi– Cartan–Vranceanu (BCV) spaces, i.e., in the Riemannian 3-manifolds whose metrics have groups of isometries of dimension 4 or 6, except the hyperbolic one. In particular, we prove that in a BCV-space there exists a two-parameter family of helicoidal surfaces isometric to a given helicoidal surface; then, by making use of this two-parameter representation, we characterize helicoidal surfaces which have constant mean curvature, including the minimal ones