Search results for "equation"

Collisional Relaxation Processes Studied by Coherent Raman Spectroscopy for Major Species Present in Combustions

1992

The effects of collisional relaxation processes on the Q-branch profile of major species present in combustions have been studied by high resolution stimulated Raman spectroscopy. Particular interest has focused on the following collisional systems: N2-N2, O2-O2, CO2-CO2, O2-N2, N2-CO2 and N2-H2O. For each colliding pair, starting from accurate determinations of line broadening coefficients over a wide temperature range, state-to-state rates for rotational energy transfers have been deduced by using various fitting laws. Among these rate laws, special attention has been paid to the temperature dependence of the energy corrected scaling (ECS) law combined with a hybrid exponential-power law …

The Homogeneous Poisson Point Process

2008

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.

The Complex WKB Method

2019

In this chapter we shall study the exponential growth and asymptotic expansions of exact solutions of second-order differential equations in the semi-classical limit. As an application, we establish a Bohr-Sommerfeld quantization condition for Schrodinger operators with real-analytic complex-valued potentials.

$$\mathscr {K}$$-Convergence of Finite Volume Solutions of the Euler Equations

2020

We review our recent results on the convergence of invariant domain-preserving finite volume solutions to the Euler equations of gas dynamics. If the classical solution exists we obtain strong convergence of numerical solutions to the classical one applying the weak-strong uniqueness principle. On the other hand, if the classical solution does not exist we adapt the well-known Prokhorov compactness theorem to space-time probability measures that are generated by the sequences of finite volume solutions and show how to obtain the strong convergence in space and time of observable quantities. This can be achieved even in the case of ill-posed Euler equations having possibly many oscillatory s…

An explicit unconditionally stable numerical solution of the advection problem in irrotational flow fields

2004

[1] A new methodology for the Eulerian numerical solution of the advection problem is proposed. The methodology is based on the conservation of both the zero- and the first-order spatial moments inside each element of the computational domain and leads to the solution of several small systems of ordinary differential equations. Since the systems are solved sequentially (one element after the other), the method can be classified as explicit. The proposed methodology has the following properties: (1) it guarantees local and global mass conservation, (2) it is unconditionally stable, and (3) it applies second-order approximation of the concentration and its fluxes inside each element. Limitati…

A New Family of Deformations of Darboux-Pöschl-Teller Potentials

2004

The aim of this Letter is to present a new family of integrable functional-difference deformations of the Schrodinger equation with Darboux–Poschl–Teller potentials. The related potentials are labeled by two integers m and n, and also depend on a deformation parameter h. When h→ 0 the classical Darboux–Poschl–Teller model is recovered.

A Method of Conversion of some Coefficient Inverse Parabolic Problems to a Unified Type of Integral-Differential Equation

2011

Coefficient inverse problems are reformulated to a unified integral differential equation. The presented method of conversion of the considered inverse problems to a unified Volterra integral-differential equation gives an opportunity to distribute the acquired results also to analogous inverse problems for non-linear parabolic equations of different types.

Semi-discrete Galerkin approximation method applied to initial boundary value problems for Maxwell's equations in anisotropic, inhomogeneous media

1981

SynopsisIn this paper the semi-discrete Galerkin approximation of initial boundary value problems for Maxwell's equations is analysed. For the electric field a hyperbolic system of equations is first derived. The standard Galerkin method is applied to this system and a priori error estimates are established for the approximation.

Non-linear systems under parametric alpha-stable LÉVY WHITE NOISES

2005

In this study stochastic analysis of nonlinear dynamical systems under a-stable, multiplicative white noise has been performed. Analysis has been conducted by means of the Ito rule extended to the case of α-stable noises. In this context the order of increments of Levy process has been evaluated and differential equations ruling the evolutions of statistical moments of either parametrically and external dynamical systems have been obtained. The extended Ito rule has also been used to yield the differential equation ruling the evolution of the characteristic function for parametrically excited dynamical systems. The Fourier transform of the characteristic function, namely the probability den…