Search results for " Discontinuities"

Nonlinear Diffusion in Transparent Media

2021

Abstract We consider a prototypical nonlinear parabolic equation whose flux has three distinguished features: it is nonlinear with respect to both the unknown and its gradient, it is homogeneous, and it depends only on the direction of the gradient. For such equation, we obtain existence and uniqueness of entropy solutions to the Dirichlet problem, the homogeneous Neumann problem, and the Cauchy problem. Qualitative properties of solutions, such as finite speed of propagation and the occurrence of waiting-time phenomena, with sharp bounds, are shown. We also discuss the formation of jump discontinuities both at the boundary of the solutions’ support and in the bulk.

Weighted Extrapolation Techniques for Finite Difference Methods on Complex Domains with Cartesian Meshes

2016

The design of numerical boundary conditions in high order schemes is a challenging problem that has been tackled in different ways depending on the nature of the problem and the scheme used to solve it numerically. In this paper we propose a technique to extrapolate the information from the computational domain to ghost cells for schemes with structured Cartesian Meshes on complex domains. This technique is based on the application of Lagrange interpolation with weighted filters for the detection of discontinuities that permits a data dependent extrapolation, with high order at smooth regions and essentially non oscillatory properties near discontinuities. This paper is a sequel of Baeza et…

Specification on the interval

1997

We study the consequences of discontinuities on the specification property for interval maps. After giving a necessary and sufficient condition for a piecewise monotonic, piecewise continuous map to have this property, we show that for a large and natural class of families of such maps (including the β \beta -transformations), the set of parameters for which the specification property holds, though dense, has zero Lebesgue measure. Thus, regarding the specification property, the general case is at the opposite of the continuous case solved by A.M. Blokh (Russian Math. Surveys 38 (1983), 133–134) (for which we give a proof).

High Order in Space and Time Schemes Through an Approximate Lax-Wendroff Procedure

2017

This paper deals with the scheme proposed by the authors in Zorio, Baeza and Mulet (J Sci Comput 71(1):246–273, 2017). This scheme is an alternative to the techniques proposed in Qiu and Shu (SIAM J Sci Comput 24(6):2185–2198, 2003) to obtain high-order accurate schemes using Weighted Essentially Non Oscillatory finite differences and approximating the flux derivatives required by the Cauchy-Kovalevskaya procedure by simple centered finite differences. We analyse how errors in first-order terms near discontinuities propagate through both versions of the Cauchy-Kovalevskaya procedure. We propose a fluctuation control, for which the approximation of the first-order derivative to be used in th…

Asset price dynamics in a “bull and bear market”

2021

Abstract We generalize an existing asset market model with heterogenous agents. In particular, we consider the case in which no-trade and low-trade intervals of chartists and fundamentalists respectively are not congruent. Thus we model chartist and fundamentalists who respond to asset prices in agent-specific neighborhoods around the fundamental value with different trade intensities. The resulting asset price dynamics is generated by a one-dimensional 5-piece linear map with discontinuities. Our analysis of this map focusses on coexisting price equilibria. Conditions for their existence and stability are determined analytically. By visualizing the results we allow for a basic bifurcation …

3D image acquisition system based on shape from focus technique

2013

agent Agrosup Dijon de l'UMREcolDurGEAPSI; This paper describes the design of a 3D image acquisition system dedicated to natural complex scenes composed of randomly distributed objects with spatial discontinuities. In agronomic sciences, the 3D acquisition of natural scene is difficult due to the complex nature of the scenes. Our system is based on the Shape from Focus technique initially used in the microscopic domain. We propose to adapt this technique to the macroscopic domain and we detail the system as well as the image processing used to perform such technique. The Shape from Focus technique is a monocular and passive 3D acquisition method that resolves the occlusion problem affecting…

Efficient FDTD analysis of discontinuities in a square coaxial waveguide

1996

G. Herglotz’ Behandlung von Beschleunigungswellen in seiner Vorlesung «Mechanik der Kontinua» angewandt auf die Stosswellen von Christoffel

1981

Following a lecture delivered by Herglotz in 1925/26 we briefly treat acceleration waves in hyperelastic materials. Our main result is a divergence equation for the squared Euclidean norm of the so-called ‘wave vector’. We then apply Herglotz’ method (devised for acceleration waves) to the propagation of such first order discontinuities in elastic bodies as were treated by Christoffel in [1].

New insights into the reading of Paleozoic plant fossil record discontinuities

2011

Studying the discontinuity patterns of Paleozoic vascular plants provides a global vision of these key events from the multivariate methods viewpoint. Non-metric multidimensional scaling, detrended correspondence analysis and cluster analysis have been employed together with a set of diversity and abundance measures and an evaluation of the geologic constraints from the plant fossil record data. The results reveal four clear significant discontinuities in terms of taxonomic composition and record representativeness during the early-middle Devonian, Devonian–Carboniferous, Mississippian–Pennsylvanian and early-late Permian. Due to the controversial character of the plant fossil record data a…

Towards nonlocal density functionals by explicit modelling of the exchange-correlation hole in inhomogeneous systems

2013

We put forward new approach for the development of a non-local density functional by a direct modeling of the shape of exchange-correlation (xc) hole in inhomogeneous systems. The functional is aimed at giving an accurate xc-energy and an accurate corresponding xc-potential even in difficult near-degeneracy situations such as molecular bond breaking. In particular we demand that: (1) the xc hole properly contains -1 electron, (2) the xc-potential has the asymptotic -1/r behavior outside finite systems and (3) the xc-potential has the correct step structure related to the derivative discontinuities of the xc-energy functional. None of the currently existing functionals satisfies all these re…