A new method of imposing boundary conditions for hyperbolic equations

A new method to impose boundary conditions for pseudospectral approximations to hyperbolic equations is suggested. This method involves the collocation of the equation at the boundary nodes as well as satisfying boundary conditions. Stability and convergence results are proven for the Chebyshev approximation of linear scalar hyperbolic equations. The eigenvalues of this method applied to parabolic equations are shown to be real and negative

Homoclinic snaking of localized states in doubly diffusive convection

Numerical continuation is used to investigate stationary spatially localized states in two-dimensional thermosolutal convection in a plane horizontal layer with no-slip boundary conditions at top and bottom. Convectons in the form of 1-pulse and 2-pulse states of both odd and even parity exhibit homoclinic snaking in a common Rayleigh number regime. In contrast to similar states in binary fluid convection, odd parity convectons do not pump concentration horizontally. Stable but time-dependent localized structures are present for Rayleigh numbers below the snaking region for stationary convectons. The computations are carried out for (inverse) Lewis number \tau = 1/15 and Prandtl numbers Pr = 1 and Pr >> 1

High-order discretization of backward anisotropic diffusion and application to image processing

Anisotropic diffusion is a well recognized tool in digital image processing, including edge detection and focusing. We present here a particular nonlinear time-dependent operator together with an appropriate high-order discretization for the space variable. In just a single step, the procedure emphasizes the contour lines encircling the objects, paving the way to accurate reconstructions at a very low cost. One of the main features of such an approach is the possibility of relying on a rather large set of invariant discontinuous images, whose edges can be determined without introducing any approximation

Electromagnetic fields simulating a rotating sphere and its exterior with implications to the modeling of the heliosphere

Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a ball. The fields satisfy the set of Maxwell's equations, and some connections with magnetohydrodynamics can also be established. The solutions are extended with continuity outside the ball. In order to avoid peripheral velocities of arbitrary magnitude, as it may happen for a rigid rotating body, they are organized to form successive encapsulated shells, with substructures recalling ball-bearing assemblies. A recipe for the construction of these solutions is provided by playing with the eigenfunctions of the vector Laplace operator. Some applications relative to astronomy are finally discussed

Numerical Approximations Using Chebyshev Polynomial Expansions

We present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the Chebyshev polynomial of order N (El-gendi's method). The solutions are exact at these points, apart from round-off computer errors and the convergence of other numerical methods used in connection to solving the linear system of equations. Applications to initial value problems in time-dependent quantum field theory, and second order boundary value problems in fluid dynamics are presented.Comment: minor wording changes, some typos have been eliminate

A Decision-Making Machine Learning Approach in Hermite Spectral Approximations of Partial Differential Equations

The accuracy and effectiveness of Hermite spectral methods for the numerical discretization of partial differential equations on unbounded domains are strongly affected by the amplitude of the Gaussian weight function employed to describe the approximation space. This is particularly true if the problem is under-resolved, i.e., there are no enough degrees of freedom. The issue becomes even more crucial when the equation under study is time-dependent, forcing in this way the choice of Hermite functions where the corresponding weight depends on time. In order to adapt dynamically the approximation space, it is here proposed an automatic decision-making process that relies on machine learning techniques, such as deep neural networks and support vector machines. The algorithm is numerically tested with success on a simple 1D problem, but the main goal is its exportability in the context of more serious applications. As a matter of fact we also show at the end an application in the framework of plasma physics

Effects of angiotensin-converting enzyme inhibition on left ventricular geometric patterns in patients with essential hypertension

Although angiotensin-converting enzyme inhibitors have been shown to affect left ventricular (LV) remodeling favorably in several conditions, it remains unclear whether they can influence LV geometric pattern in hypertension. To address this issue, 122 patients (71 men and 51 women; mean age = 51 +/- 20 years) with mild to moderate hypertension were studied prospectively. All underwent clinical evaluation and Doppler echocardiography at entry and more than 2 years of quinapril therapy (10-40 mg/day). According to either LV mass (normal if <131 g/m(2) for men or <100 g/m(2) for women) or the ratio of LV posterior wall thickness to diastolic diameter (RWT; normal if <0.45) at baseline, 58 patients had normal mass and RWT, 18 patients had concentric remodeling (i.e., normal mass but increased RWT), 24 patients had eccentric hypertrophy (i.e., increased mass but normal RWT), and 22 patients had concentric hypertrophy (i.e., increase in both mass and RWT). After 6 months of quinapril therapy, all patients with normal left ventricles showed the maintenance of mass and RWT within normal limits. Patients with concentric remodeling showed no increase in mass but had a significant decrease in RWT. Patients with eccentric hypertrophy exhibited a significant reduction in mass with no substantial change in RWT. Patients with concentric hypertrophy had a significant reduction in both mass and RWT. Changes in LV mass and geometry were maintained during the 2-year period of treatment and were paralleled by improvements in Doppler in dices of LV diastolic function in each group. It is concluded that quinapril, with its well-known effects on LV hypertrophy, modifies the LV geometric pattern of hypertensive patients favorably, regardless of the presence of an abnormal LV mass or RWT

Second order averaging for the nonlinear Schroedinger equation with strongly anisotropic potential

International audienceWe consider the three dimensional Gross-Pitaevskii equation (GPE) describing a Bose-Einstein Condensate (BEC) which is highly confi ned in vertical z direction. The highly confi ned potential induces high oscillations in time. If the confi nement in the z direction is a harmonic trap (which is widely used in physical experiments), the very special structure of the spectrum of the confi nement operator will imply that the oscillations are periodic in time. Based on this observation, it can be proved that the GPE can be averaged out with an error of order of epsilon, which is the typical period of the oscillations. In this article, we construct a more accurate averaged model, which approximates the GPE up to errors of order epsilon squared. Then, expansions of this model over the eigenfunctions (modes) of the vertical Hamiltonian Hz are given in convenience of numerical application. Effi cient numerical methods are constructed for solving the GPE with cylindrical symmetry in 3D and the approximation model with radial symmetry in 2D, and numerical results are presented for various kinds of initial data

Efecto de la densidad de plantas y distancia entre surcos sobre el rendimiento de materia seca de maíces forrajeros en Santa Rosa, La Pampa

Whole plant and its components dry matter of an experimental fodder corn population (crossing between Zea mays L. x Zea diploperennis I.) and a commercial hybrid was evaluated with respect to three plant densities (50.000; 65.000 y 80.000 plants.ha-1) and two row spacings (50 y 70 cm). No response to row spacing was found, and no interaction with plant density and genotype could be determined. The results showed interaction of plant density and genotype on dry matter production of whole and leaves. The experimental population responded to the lowest plant density (5 plant m^) with the highest whole plant and leaf dry matter, while the commercial hybrid produced higher dry matter at intermediate plant density (6.5 plant.m-2). Future studies will corroborate the information on dry matter production and evaluation of digestibility of plant material should be carried out to better characterize the potential of the experimental population.Se evalúa la producción de la materia seca de planta completa y sus componentes en una población forrajera experimental originada de la cruza entre Zea mays L. x Zea diploperennis I. y un híbrido comercial con respecto a tres densidades de siembra (50.000; 65.000 y 80.000 pl.ha-1) y en dos distancias entre hileras (50 y 70 cm). No se evidenció respuesta para el espaciamiento entre surcos como tampoco interacción con la densidad de siembra ni genotipos. Se encontró interacción entre la densidad de siembra y los genotipos para la producción de materia seca de la planta completa y de hojas. La población experimental respondió mejor en la densidad menor (5 pl. m-2) donde obtuvo el mayor rendimiento de planta completa y de hojas. El hibrido lo logra con una densidad de plantas intermedia (6.5 pl.m-2). La repetición del experimento y la evaluación de la digestibilidad ampliarían la información aportada con el rendimiento de la materia seca

Contribution of NADPH Oxidase to Membrane CD38 Internalization and Activation in Coronary Arterial Myocytes

The CD38-ADP-ribosylcyclase-mediated Ca2+ signaling pathway importantly contributes to the vasomotor response in different arteries. Although there is evidence indicating that the activation of CD38-ADP-ribosylcyclase is associated with CD38 internalization, the molecular mechanism mediating CD38 internalization and consequent activation in response to a variety of physiological and pathological stimuli remains poorly understood. Recent studies have shown that CD38 may sense redox signals and is thereby activated to produce cellular response and that the NADPH oxidase isoform, NOX1, is a major resource to produce superoxide (O2·−) in coronary arterial myocytes (CAMs) in response to muscarinic receptor agonist, which uses CD38-ADP-ribosylcyclase signaling pathway to exert its action in these CAMs. These findings led us hypothesize that NOX1-derived O2·− serves in an autocrine fashion to enhance CD38 internalization, leading to redox activation of CD38-ADP-ribosylcyclase activity in mouse CAMs. To test this hypothesis, confocal microscopy, flow cytometry and a membrane protein biotinylation assay were used in the present study. We first demonstrated that CD38 internalization induced by endothelin-1 (ET-1) was inhibited by silencing of NOX1 gene, but not NOX4 gene. Correspondingly, NOX1 gene silencing abolished ET-1-induced O2·− production and increased CD38-ADP-ribosylcyclase activity in CAMs, while activation of NOX1 by overexpression of Rac1 or Vav2 or administration of exogenous O2·−significantly increased CD38 internalization in CAMs. Lastly, ET-1 was found to markedly increase membrane raft clustering as shown by increased colocalization of cholera toxin-B with CD38 and NOX1. Taken together, these results provide direct evidence that Rac1-NOX1-dependent O2·− production mediates CD38 internalization in CAMs, which may represent an important mechanism linking receptor activation with CD38 activity in these cells