Search results for "MATHEMATICS"

The Homogeneous Poisson Point Process

2008

A Continuous Approach to FETI-DP Mortar Methods: Application to Dirichlet and Stokes Problem

2013

In this contribution we extend the FETI-DP mortar method for elliptic problems introduced by Bernardi et al. [2] and Chacon Vera [3] to the case of the incompressible Stokes equations showing that the same results hold in the two dimensional setting. These ideas extend easily to three dimensional problems. Finally some numerical tests are shown as a conclusion. This contribution is a condensed version of a more detailed forthcoming paper. We use standard notation, see for instance [1].

The Two-Jacobian Scheme for Systems of Conservation Laws

2006

A Domain Imbedding Method with Distributed Lagrange Multipliers for Acoustic Scattering Problems

2003

The numerical computation of acoustic scattering by bounded twodimensional obstacles is considered. A domain imbedding method with Lagrange multipliers is introduced for the solution of the Helmholtz equation with a second-order absorbing boundary condition. Distributed Lagrange multipliers are used to enforce the Dirichlet boundary condition on the scatterer. The saddle-point problem arising from the conforming finite element discretization is iteratively solved by the GMRES method with a block triangular preconditioner. Numerical experiments are performed with a disc and a semi-open cavity as scatterers.

On the spectrum of semi-classical Witten-Laplacians and Schrödinger operators in large dimension

2005

We investigate the low-lying spectrum of Witten–Laplacians on forms of arbitrary degree in the semi-classical limit and uniformly in the space dimension. We show that under suitable assumptions implying that the phase function has a unique local minimum one obtains a number of clusters of discrete eigenvalues at the bottom of the spectrum. Moreover, we are able to count the number of eigenvalues in each cluster. We apply our results to certain sequences of Schrodinger operators having strictly convex potentials and show that some well-known results of semi-classical analysis hold also uniformly in the dimension.

Openness and Discreteness

2013

The aim of this chapter is to study conditions under which a mapping of finite distortion is open (maps open sets to open sets) and discrete (preimage of each point is a discrete set).

Poincare Inequalities and Spectral Gap, Concentration Phenomenon for G-Measures

2002

We produce a new approach based upon inequalities of Poincare’s type for giving constructive estimates of the mixing rate for a family of mixing stationary processes continuously depending on their past called g-measures. We establish also exponential inequalities of Hoeffding’s type leading to a concentration phenomenon for a large class of observables; this last property permits in particular to give the typical behaviour of the n-orbits of a g-measure.

Saddle index properties, singular topology, and its relation to thermodynamic singularities for aϕ4mean-field model

2004

We investigate the potential energy surface of a ${\ensuremath{\phi}}^{4}$ model with infinite range interactions. All stationary points can be uniquely characterized by three real numbers ${\ensuremath{\alpha}}_{+},{\ensuremath{\alpha}}_{0},{\ensuremath{\alpha}}_{\ensuremath{-}}$ with ${\ensuremath{\alpha}}_{+}+{\ensuremath{\alpha}}_{0}+{\ensuremath{\alpha}}_{\ensuremath{-}}=1$, provided that the interaction strength $\ensuremath{\mu}$ is smaller than a critical value. The saddle index ${n}_{s}$ is equal to ${\ensuremath{\alpha}}_{0}$ and its distribution function has a maximum at ${n}_{s}^{\mathrm{max}}=1∕3$. The density $p(e)$ of stationary points with energy per particle $e$, as well as…

Special Functions for the Study of Economic Dynamics: The Case of the Lucas-Uzawa Model

2004

The special functions are intensively used in mathematical physics to solve differential systems. We argue that they should be most useful in economic dynamics, notably in the assessment of the transition dynamics of endogenous growth models. We illustrate our argument on the Lucas-Uzawa model, which we solve by the means of Gaussian hypergeometric functions. We show how the use of Gaussian hypergeometric functions allows for an explicit representation of the equilibrium dynamics of the variables in level. In contrast to the preexisting approaches, our method is global and does not rely on dimension reduction.

New Invariant Domain Preserving Finite Volume Schemes for Compressible Flows

2021

We present new invariant domain preserving finite volume schemes for the compressible Euler and Navier–Stokes–Fourier systems. The schemes are entropy stable and preserve positivity of density and internal energy. More importantly, their convergence towards a strong solution of the limit system has been proved rigorously in [9, 11]. We will demonstrate their accuracy and robustness on a series of numerical experiments.