In this Note we present some results concerning the concentration of sequences of first eigenfunctions on the limit sets of a Morse–Smale dynamical system on a compact Riemannian manifold. More precisely a renormalized sequence of eigenfunctions converges to a measure μ concentrated on the hyperbolic sets of the field. The coefficients which appear in the limit measure can be characterized usin...

Artificial viscosity can be combined with a higher-order discontinuous Galerkin finite element discretization to resolve a shock layer within a single cell. However, when a non-smooth artificial viscosity model is employed with an otherwise higherorder approximation, element-to-element variations induce oscillations in state gradients and pollute the downstream flow. To alleviate these difficul...

In order to explore a new approach to construct surfaces bounded by geodesics or lines of curvature, a method of surface modeling based on fourth-order partial differential equations (PDEs) is presented. Compared with the free-form surface modeling based on finding control points, PDE-based surface modeling has the following three advantages. First, the corresponding biharmonic surface can natu...

A method for trimming surfaces generated as solutions to Partial Differential Equations (PDEs) is presented. The work we present here utilises the 2D parameter space on which the trim curves are defined whose projection on the parametrically represented PDE surface is then trimmed out. To do this we define the trim curves to be a set of boundary conditions which enable us to solve a low order e...

This article is concerned with effective numerical techniques for partial differential equation (PDE)based image restoration. Numerical realizations of most PDE-based denoising models show a common drawback: loss of fine structures. In order to overcome the drawback, the article introduces a new timestepping procedure, called the method of nonflat time evolution (MONTE), in which the timestep s...

Inactivation of the cyclic nucleotide signal in granulosa cells depends on a complex array of cyclic nucleotide phosphodiesterases (PDE). In order to examine the role of PDE in cyclic AMP (cAMP) signaling in granulosa cells, the present study examined the expression of PDE4D proteins and regulation of cAMP-PDE activities in cultured rat granulosa cells. The results of immunoblot analyses showed...

The accurate simulation of supersonic and hypersonic flows is well suited to higher-order (p > 1), adaptive computational fluid dynamics (CFD). Since these cases involve flow velocities greater than the speed of sound, an appropriate shock capturing for higher-order, adaptive methods is necessary. Artificial viscosity can be combined with a higher-order discontinuous Galerkin finite element dis...

Modelling correlation between financial quantities is important in the accurate pricing of financial derivatives. In this paper, we introduce some stochasticity in correlation, by considering a regime-switching correlation model, in which the transition rates between regimes are given. We present a derivation of the associated Partial Differential Equation (PDE) problem. The problem involves a ...