The NLS equation in dimension one with spatially concentrated nonlinearities: the pointlike limit

In the present paper we study the following scaled nonlinear Schr\"odinger equation (NLS) in one space dimension: $$i\frac{d}{dt} \psi^{\varepsilon}(t) =-\Delta\psi^{\varepsilon}(t) + \frac{1}{\epsilon}V\left(\frac{x}{\epsilon}\right)|\psi^{\varepsilon}(t)|^{2\mu}\psi^{\varepsilon}(t) \quad \quad \epsilon>0\ ,\quad V\in L^1(\mathbb{R},(1+|x|)dx) \cap L^\infty(\mathbb{R}) \ .$$ This equation represents a nonlinear Schr\"odinger equation with a spatially concentrated nonlinearity. We show that in the limit $\epsilon\to 0$, the weak (integral) dynamics converges in $H^1(\mathbb{R})$ to the weak dynamics of the NLS with point-concentrated nonlinearity: $$i\frac{d}{dt} \psi(t) =H_{\alpha}\psi(t) .$$ where $H_{\alpha}$ is the laplacian with the nonlinear boundary condition at the origin $\psi'(t,0+)-\psi'(t,0-)=\alpha|\psi(t,0)|^{2\mu}\psi(t,0)$ and $\alpha=\int_{\mathbb{R}}Vdx$. The convergence occurs for every $\mu\in \mathbb{R}^+$ if $V \geq 0$ and for every $\mu\in (0,1)$ otherwise. The same result holds true for a nonlinearity with an arbitrary number $N$ of concentration pointsComment: 10 page

Uncovering the species diversity of subterranean rodents at the end of the World: three new species of Patagonian tuco-tucos (Rodentia, Hystricomorpha, Ctenomys)

Ctenomys Blainville 1826 is one of the most diverse genera of South American caviomorph rodents. Currently, six species of this genus are reported from Patagonia, south of 42◦S. In this contribution, we assessed the taxonomic status of several populations from eastern and central Chubut province, northern Patagonia. Based on phylogenetic analyses of DNA sequences, morphology assessment (qualitative and quantitative), and previously published karyological data, we describe three new species of this genus, one formed by two subspecies, endemic to northern Patagonia. In addition, we include C. coyhaiquensis Kelt and Gallardo 1994 into the synonymy of C. sericeus J.A. Allen 1903. Finally, we discussed the need for additional integrative approaches, including field collection of specimens, to better understand the diversity of this highly speciose rodent genus.Fil: Teta, Pablo Vicente. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia"; ArgentinaFil: D Elía, Guillermo. Universidad Austral de Chile; Chil

Well-posedness of the three-dimensional NLS equation with sphere-concentrated nonlinearity

We discuss strong local and global well-posedness for the three-dimensional NLS equation with nonlinearity concentrated on S2 . Precisely, local well-posedness is proved for any C 2 power-nonlinearity, while global well-posedness is obtained either for small data or in the defocusing case under some growth assumptions. With respect to point-concentrated NLS models, widely studied in the literature, here the dimension of the support of the nonlinearity does not allow a direct extension of the known techniques and calls for new ideas

Vitamin D: a review on its effects on muscle strength, the risk of fall, and frailty.

Vitamin D is the main hormone of bone metabolism. However, the ubiquitary nature of vitamin D receptor (VDR) suggests potential for widespread effects, which has led to new research exploring the effects of vitamin D on a variety of tissues, especially in the skeletal muscle. In vitro studies have shown that the active form of vitamin D, calcitriol, acts in myocytes through genomic effects involving VDR activation in the cell nucleus to drive cellular differentiation and proliferation. A putative transmembrane receptor may be responsible for nongenomic effects leading to rapid influx of calcium within muscle cells. Hypovitaminosis D is consistently associated with decrease in muscle function and performance and increase in disability. On the contrary, vitamin D supplementation has been shown to improve muscle strength and gait in different settings, especially in elderly patients. Despite some controversies in the interpretation of meta-analysis, a reduced risk of falls has been attributed to vitamin D supplementation due to direct effects on muscle cells. Finally, a low vitamin D status is consistently associated with the frail phenotype. This is why many authorities recommend vitamin D supplementation in the frail patient

A Quantum Model of Feshbach Resonances

We consider a quantum model of two-channel scattering to describe the mechanism of a Feshbach resonance. We perform a rigorous analysis in order to count and localize the energy resonances in the perturbative regime, i.e., for small inter-channel coupling, and in the non-perturbative one. We provide an expansion of the effective scattering length near the resonances, via a detailed study of an effective Lippmann-Schwinger equation with energy-dependent potential.Comment: 29 pages, pdfLaTe

Patterns in research and data sharing for the study of form and function in caviomorph rodents

The combination of morphometrics, phylogenetic comparative methods, and open data sets has renewed interest in relating morphology to adaptation and ecological opportunities. Focusing on the Caviomorpha, a well-studied mammalian group, we evaluated patterns in research and data sharing in studies relating form and function. Caviomorpha encompasses a radiation of rodents that is diverse both taxonomically and ecologically. We reviewed 41 publications investigating ecomorphology in this group. We recorded the type of data used in each study and whether these data were made available, and we re-digitized all provided data. We tracked two major lines of information: collections material examined and trait data for morphological and ecological traits. Collectively, the studies considered 63% of extant caviomorph species; all extant families and genera were represented. We found that species-level trait data rarely were provided. Specimen-level data were even less common. Morphological and ecological data were too heterogeneous and sparse to aggregate into a single data set, so we created relational tables with the data. Additionally, we concatenated all specimen lists into a single data set and standardized all relevant data for phylogenetic hypotheses and gene sequence accessions to facilitate future morphometric and phylogenetic comparative research. This work highlights the importance and ongoing use of scientific collections, and it allows for the integration of specimen information with species trait data.Recientemente ha resurgido el interés por estudiar la relación entre morfología, ecología, y adaptación. Esto se debe al desarrollo de nuevas herramientas morfométricas y filogenéticas, y al acceso a grandes bases de datos para estudios comparados. Revisamos 41 publicaciones sobre ecomorfología de roedores caviomorfos, un grupo diverso y bien estudiado, para evaluar los patrones de investigación y la transparencia para la liberación de datos. Registramos los tipos de datos que se utilizaron para cada estudio y si los datos están disponibles. Cuando estos datos se compartieron, los redigitalizamos. Nos enfocamos en los ejemplares consultados, y en datos que describen rasgos ecológicos y morfológicos para las especies estudiadas. Los estudios que revisamos abarcan el 63% de las especies de caviomorfos que actualmente existen. Encontramos que raramente fueron compartidos los datos que se tomaron para especies, y menos aún para ejemplares. Los datos morfológicos y ecológicos eran demasiado heterogéneos e exiguos para consolidar en un solo banco de datos; debido a esta circunstancia, creamos tablas relacionales con los datos. Además, enlazamos todas las listas individuales de especímenes para crear un solo banco de datos y estandarizamos todos los datos pertinentes a hipótesis filogenéticas, así como los números de acceso de secuencias genéticas, para así facilitar eventuales estudios comparados de morfometría y filogenia. Este trabajo resalta la importancia de las colecciones científicas y documenta su uso, además permitiendo la futura integración de datos derivados de ejemplares con datos sobre rasgos ecomorfológicos a nivel de especie.Fil: Verde Arregoitia, Luis D.. Universidad Austral de Chile; ChileFil: Teta, Pablo Vicente. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia"; ArgentinaFil: D Elía, Guillermo. Universidad Austral de Chile; Chil

Geographic Variation in Cranial Morphology of the Southern Mountain Cavy, Microcavia australis (Rodentia, Caviidae): Taxonomic Implications, with the Description of A New Species

We analyzed the geographic variation in cranial morphology of the Southern Mountain Cavy, Microcavia australis, throughout of its distributional range. Our analysis allows us to recognize three geographically allopatric morphotypes. Thesemorphotypes differ in the general size and shape of the skull and discrete morphological traits of the zygomatic arch, palate and mesopterygoid fossa. Based on these results, we restrict the name australis to populationsdistributed in southern Argentina and west-central Andes and the name maenas to the morphotype of northwestern and central Argentina. The third morphotype occurs in the Dry Chaco ecoregion and is described here as a new species.Fil: Teta, Pablo Vicente. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia"; ArgentinaFil: Ojeda, Ricardo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto Argentino de Investigaciones de las Zonas Áridas. Provincia de Mendoza. Instituto Argentino de Investigaciones de las Zonas Áridas. Universidad Nacional de Cuyo. Instituto Argentino de Investigaciones de las Zonas Áridas; ArgentinaFil: Lucero, Sergio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia"; ArgentinaFil: D Elía, Guillermo. Universidad Austral; Chil

Wave equation with concentrated nonlinearities

In this paper we address the problem of wave dynamics in presence of concentrated nonlinearities. Given a vector field $V$ on an open subset of \CO^n and a discrete set Y\subset\RE^3 with $n$ elements, we define a nonlinear operator $\Delta_{V,Y}$ on L^2(\RE^3) which coincides with the free Laplacian when restricted to regular functions vanishing at $Y$, and which reduces to the usual Laplacian with point interactions placed at $Y$ when $V$ is linear and is represented by an Hermitean matrix. We then consider the nonlinear wave equation $\ddot \phi=\Delta_{V,Y}\phi$ and study the corresponding Cauchy problem, giving an existence and uniqueness result in the case $V$ is Lipschitz. The solution of such a problem is explicitly expressed in terms of the solutions of two Cauchy problem: one relative to a free wave equation and the other relative to an inhomogeneous ordinary differential equation with delay and principal part $\dot\zeta+V(\zeta)$. Main properties of the solution are given and, when $Y$ is a singleton, the mechanism and details of blow-up are studied.Comment: Revised version. To appear in Journal of Physics A: Mathematical and General, special issue on Singular Interactions in Quantum Mechanics: Solvable Model

Cholesterol derivatives make large part of the lipids from epidermal molts of the desert-adapted Gila monster lizard (Heloderma suspectum)

In order to understand the cutaneous water loss in the desert-adapted and venomous lizard Heloderma suspectum, the microscopic structure and lipid composition of epidermal molts have been examined using microscopic, spectroscopic and chemical analysis techniques. The molt is formed by a variably thick, superficial beta-layer, an extensive mesos-region and few alpha-cells in its lowermost layers. The beta-layer contains most corneous beta proteins while the mesos-region is much richer in lipids. The proteins in the mesos-region are more unstructured than those located in the beta-layer. Most interestingly, among other lipids, high contents of cholesteryl-β-glucoside and cholesteryl sulfate were detected, molecules absent or present in traces in other species of squamates. These cholesterol derivatives may be involved in the stabilization and compaction of the mesos-region, but present a limited permeability to water movements. The modest resistance to cutaneous water-loss of this species is compensated by adopting other physiological strategies to limit thermal damage and water transpiration as previous eco-physiological studies have indicated. The increase of steroid derivatives may also be implicated in the heat shock response, influencing the relative behavior in this desert-adapted lizard