Search results for "hyperbolic"
showing 10 items of 156 documents
The eigen-structure of the Jacobian in multi-class Lighthill-Whitham-Richards traffic flow models
2007
Characteristic-based High Resolution Shock Capturing schemes for hyperbolic systems of conservation laws require, in their basic design structure, knowledge on the complete eigen-decomposition of the Jacobian matrix of the system. For the Multi-Class Lighthill-Witham-Richards (MCLWR) Traffic flow model considered in [4], there is no explicit formula for the eigenvalues of the Jacobian matrix, which can only be determined numerically. However, once they are determined, the eigen-vectors are easily computed and straightforward formulas can be obtained by exploiting the specific structure of the Jacobian matrix in these models. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
On global solutions of the Maxwell-Dirac equations
1987
We prove, for the Maxwell-Dirac equations in 1+3 dimensions, that modified wave operators exist on a domain of small entire test functions of exponential type and that the Cauchy problem, inR+×R3, has a unique solution for each initial condition (att=0) which is in the image of the wave operator. The modification of the wave operator, which eliminates infrared divergences, is given by approximate solutions of the Hamilton-Jacobi equation, for a relativistic electron in an electromagnetic potential. The modified wave operator linearizes the Maxwell-Dirac equations to their linear part.
MR 3079286 Reviewed Hoshi Y. On a problem of Matsumoto and Tamagawa concerning monodromic fullness of hyperbolic curves: genus zero case. Tohoku Math…
2014
Let \emph{Primes} be the set of all prime numbers, $k$ be a finite extension of the field of rational numbers and $\bar{k}$ be an algebraic closure of $k$. Let $(g, r)$ be a pair of nonnegative integers such that $2g - 2 + r > 0$ and $X$ be a hyperbolic curve of type $(g, r)$ over $k$. The author observes that, for each $l \in \emph{Primes}$, there are two natural outer representations on $\pi^{\{ l\}}_{1} (X \otimes_{k} \bar{k})$: $$\rho_{X / k} ^{\{ l\}}: G_{k} := Gal(\bar{k} / k) \rightarrow Out (\pi^{\{ l\}}_{1} (X \otimes_{k} \bar{k}))$$ and $$ \rho_{g, [r]} ^{\{ l\}}: \pi_{1}(M_{g, [r]}) \rightarrow Out (\pi^{\{ l\}}_{1} (X \otimes_{k} \bar{k})),$$ where $\pi^{\{ l\}}_{1} (X \otimes_{…
Multiscale Particle Method in Solving Partial Differential Equations
2007
A novel approach to meshfree particle methods based on multiresolution analysis is presented. The aim is to obtain numerical solutions for partial differential equations by avoiding the mesh generation and by employing a set of particles arbitrarily placed in problem domain. The elimination of the mesh combined with the properties of dilation and translation of scaling and wavelets functions is particularly suitable for problems governed by hyperbolic partial differential equations with large deformations and high gradients.
Nonlocal dispersion anomalies of Dyakonov-like surface waves at hyperbolic media interfaces
2016
Dyakonov-like surface waves (DSWs) propagating obliquely on an anisotropic nanostructure have been theoretically proved in a few cases including 2D photonic crystals and metal-insulator (MI) layered metamaterials. Up to now, the long-wavelength approximation has been employed in order to obtain effective parameters to be introduced in the Dyakonov equation, which is largely restricted to material inhomogeneities of a few nanometers when including metallic elements. Here, we explore DSWs propagating obliquely at the interface between an insulator and a hyperbolic metamaterial, the latter consisting of a 1D MI bandgap grating using realistic slab sizes. We found unexpected favorable condition…
Singular hyperbolic systems
1999
We construct a class of vector fields on 3-manifolds containing the hyperbolic ones and the geometric Lorenz attractor. Conversely, we shall prove that nonhyperbolic systems in this class resemble the Lorenz attractor: they have Lorenz-like singularities accumulated by periodic orbits and they cannot be approximated by flows with nonhyperbolic critical elements.
Global attractors from the explosion of singular cycles
1997
Abstract In this paper we announce recent results on the existence and bifurcations of hyperbolic systems leading to non-hyperbolic global attractors.
On a nonlinear flux-limited equation arising in the transport of morphogens
2012
Abstract Motivated by a mathematical model for the transport of morphogens in biological systems, we study existence and uniqueness of entropy solutions for a mixed initial–boundary value problem associated with a nonlinear flux-limited diffusion system. From a mathematical point of view the problem behaves more as a hyperbolic system than a parabolic one.
Capturing Shock Reflections: An Improved Flux Formula
1996
Godunov type schemes, based on exact or approximate solutions to the Riemann problem, have proven to be an excellent tool to compute approximate solutions to hyperbolic systems of conservation laws. However, there are many instances in which a particular scheme produces inappropriate results. In this paper we consider several situations in which Roe's scheme gives incorrect results (or blows up all together) and we propose an alternative flux formula that produces numerical approximations in which the pathological behavior is either eliminated or reduced to computationally acceptable levels.
Well-balanced bicharacteristic-based scheme for multilayer shallow water flows including wet/dry fronts
2013
The aim of this paper is to present a new well-balanced finite volume scheme for two-dimensional multilayer shallow water flows including wet/dry fronts. The ideas, presented here for the two-layer model, can be generalized to a multilayer case in a straightforward way. The method developed here is constructed in the framework of the Finite Volume Evolution Galerkin (FVEG) schemes. The FVEG methods couple a finite volume formulation with evolution operators. The latter are constructed using the bicharacteristics of multidimensional hyperbolic systems. However, in the case of multilayer shallow water flows the required eigenstructure of the underlying equations is not readily available. Thus…