Search results for " Mathematics"
showing 10 items of 10797 documents
H-2, H-3(+) and the age of molecular clouds and prestellar cores
2012
Measuring the age of molecular clouds and prestellar cores is a difficult task that has not yet been successfully accomplished although the information is of paramount importance to help in understanding and discriminating between different formation scenarios. Most chemical clocks suffer from unknown initial conditions and are therefore difficult to use. We propose a new approach based on a subset of deuterium chemistry that takes place in the gas phase and for which initial conditions are relatively well known. It relies primarily on the conversion of H 3 + into H 2D + to initiate deuterium enrichment of the molecular gas. This conversion is controlled by the ortho/para ratio of H2 that i…
Minimally implicit Runge-Kutta methods for Resistive Relativistic MHD
2016
The Relativistic Resistive Magnetohydrodynamic (RRMHD) equations are a hyperbolic system of partial differential equations used to describe the dynamics of relativistic magnetized fluids with a finite conductivity. Close to the ideal magnetohydrodynamic regime, the source term proportional to the conductivity becomes potentially stiff and cannot be handled with standard explicit time integration methods. We propose a new class of methods to deal with the stiffness fo the system, which we name Minimally Implicit Runge-Kutta methods. These methods avoid the development of numerical instabilities without increasing the computational costs in comparison with explicit methods, need no iterative …
Solutions of the Einstein field equations for a bounded and finite discontinuous source, and its generalization: Metric matching conditions and jumpi…
2019
We consider the metrics of the General Relativity, whose energy-momentum tensor has a bounded support where it is continuous except for a finite step across the corresponding boundary surface. As a consequence, the first derivative of the metric across this boundary could perhaps present a finite step too. However, we can assume that the metric is ${\cal C}^1$ class everywhere. In such a case, although the partial second derivatives of the metric exhibit finite (no Dirac $\delta$ functions) discontinuities, the Dirac $\delta$ functions will still appear in the conservation equation of the energy-momentum tensor. As a consequence, strictly speaking, the corresponding metric solutions of the …
SDSS-III: Massive Spectroscopic Surveys of the Distant Universe, the Milky Way Galaxy, and Extra-Solar Planetary Systems
2011
Building on the legacy of the Sloan Digital Sky Survey (SDSS-I and II), SDSS-III is a program of four spectroscopic surveys on three scientific themes: dark energy and cosmological parameters, the history and structure of the Milky Way, and the population of giant planets around other stars. In keeping with SDSS tradition, SDSS-III will provide regular public releases of all its data, beginning with SDSS DR8 (which occurred in Jan 2011). This paper presents an overview of the four SDSS-III surveys. BOSS will measure redshifts of 1.5 million massive galaxies and Lya forest spectra of 150,000 quasars, using the BAO feature of large scale structure to obtain percent-level determinations of the…
ASYMPTOTIC ANALYSIS OF THE LINEARIZED NAVIER–STOKES EQUATION ON AN EXTERIOR CIRCULAR DOMAIN: EXPLICIT SOLUTION AND THE ZERO VISCOSITY LIMIT
2001
In this paper we study and derive explicit formulas for the linearized Navier-Stokes equations on an exterior circular domain in space dimension two. Through an explicit construction, the solution is decomposed into an inviscid solution, a boundary layer solution and a corrector. Bounds on these solutions are given, in the appropriate Sobolev spaces, in terms of the norms of the initial and boundary data. The correction term is shown to be of the same order of magnitude as the square root of the viscosity. Copyright © 2001 by Marcel Dekker, Inc.
Asymptotic stability of solutions to Volterra-renewal integral equations with space maps
2012
Abstract In this paper we consider linear Volterra-renewal integral equations (VIEs) whose solutions depend on a space variable, via a map transformation. We investigate the asymptotic properties of the solutions, and study the asymptotic stability of a numerical method based on direct quadrature in time and interpolation in space. We show its properties through test examples.
On vibrating thin membranes with mass concentrated near the boundary: an asymptotic analysis
2018
We consider the spectral problem \begin{equation*} \left\{\begin{array}{ll} -\Delta u_{\varepsilon}=\lambda(\varepsilon)\rho_{\varepsilon}u_{\varepsilon} & {\rm in}\ \Omega\\ \frac{\partial u_{\varepsilon}}{\partial\nu}=0 & {\rm on}\ \partial\Omega \end{array}\right. \end{equation*} in a smooth bounded domain $\Omega$ of $\mathbb R^2$. The factor $\rho_{\varepsilon}$ which appears in the first equation plays the role of a mass density and it is equal to a constant of order $\varepsilon^{-1}$ in an $\varepsilon$-neighborhood of the boundary and to a constant of order $\varepsilon$ in the rest of $\Omega$. We study the asymptotic behavior of the eigenvalues $\lambda(\varepsilon)$ and the eige…
A Dirichlet problem for the Laplace operator in a domain with a small hole close to the boundary
2016
We study the Dirichlet problem in a domain with a small hole close to the boundary. To do so, for each pair $\boldsymbol\varepsilon = (\varepsilon_1, \varepsilon_2 )$ of positive parameters, we consider a perforated domain $\Omega_{\boldsymbol\varepsilon}$ obtained by making a small hole of size $\varepsilon_1 \varepsilon_2 $ in an open regular subset $\Omega$ of $\mathbb{R}^n$ at distance $\varepsilon_1$ from the boundary $\partial\Omega$. As $\varepsilon_1 \to 0$, the perforation shrinks to a point and, at the same time, approaches the boundary. When $\boldsymbol\varepsilon \to (0,0)$, the size of the hole shrinks at a faster rate than its approach to the boundary. We denote by $u_{\bolds…
Discontinuous Gradient Constraints and the Infinity Laplacian
2012
Motivated by tug-of-war games and asymptotic analysis of certain variational problems, we consider a gradient constraint problem involving the infinity Laplace operator. We prove that this problem always has a solution that is unique if a certain regularity condition on the constraint is satisfied. If this regularity condition fails, then solutions obtained from game theory and $L^p$-approximation need not coincide.
Parametric and nonparametric A-Laplace problems: Existence of solutions and asymptotic analysis
2021
We give sufficient conditions for the existence of weak solutions to quasilinear elliptic Dirichlet problem driven by the A-Laplace operator in a bounded domain Ω. The techniques, based on a variant of the symmetric mountain pass theorem, exploit variational methods. We also provide information about the asymptotic behavior of the solutions as a suitable parameter goes to 0 + . In this case, we point out the existence of a blow-up phenomenon. The analysis developed in this paper extends and complements various qualitative and asymptotic properties for some cases described by homogeneous differential operators.