Simultaneous denoising and enhancement of signals by a fractal conservation law

In this paper, a new filtering method is presented for simultaneous noise reduction and enhancement of signals using a fractal scalar conservation law which is simply the forward heat equation modified by a fractional anti-diffusive term of lower order. This kind of equation has been first introduced by physicists to describe morphodynamics of sand dunes. To evaluate the performance of this new filter, we perform a number of numerical tests on various signals. Numerical simulations are based on finite difference schemes or Fast and Fourier Transform. We used two well-known measuring metrics in signal processing for the comparison. The results indicate that the proposed method outperforms the well-known Savitzky-Golay filter in signal denoising. Interesting multi-scale properties w.r.t. signal frequencies are exhibited allowing to control both denoising and contrast enhancement

Simulation of flows with violent free surface motion and moving objects using unstructured grids

This is the peer reviewed version of the following article: [Löhner, R. , Yang, C. and Oñate, E. (2007), Simulation of flows with violent free surface motion and moving objects using unstructured grids. Int. J. Numer. Meth. Fluids, 53: 1315-1338. doi:10.1002/fld.1244], which has been published in final form at https://doi.org/10.1002/fld.1244. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.A volume of fluid (VOF) technique has been developed and coupled with an incompressible Euler/Navier–Stokes solver operating on adaptive, unstructured grids to simulate the interactions of extreme waves and three-dimensional structures. The present implementation follows the classic VOF implementation for the liquid–gas system, considering only the liquid phase. Extrapolation algorithms are used to obtain velocities and pressure in the gas region near the free surface. The VOF technique is validated against the classic dam-break problem, as well as series of 2D sloshing experiments and results from SPH calculations. These and a series of other examples demonstrate that the ability of the present approach to simulate violent free surface flows with strong nonlinear behaviour.Peer ReviewedPostprint (author's final draft

Asymptotic stability of the multidimensional wave equation coupled with classes of positive-real impedance boundary conditions

This paper proves the asymptotic stability of the multidimensional wave equation posed on a bounded open Lipschitz set, coupled with various classes of positive-real impedance boundary conditions, chosen for their physical relevance: time-delayed, standard diffusive (which includes the Riemann-Liouville fractional integral) and extended diffusive (which includes the Caputo fractional derivative). The method of proof consists in formulating an abstract Cauchy problem on an extended state space using a dissipative realization of the impedance operator, be it finite or infinite-dimensional. The asymptotic stability of the corresponding strongly continuous semigroup is then obtained by verifying the sufficient spectral conditions derived by Arendt and Batty (Trans. Amer. Math. Soc., 306 (1988)) as well as Lyubich and V\~u (Studia Math., 88 (1988))

Competitive effects between stationary chemical reaction centres: a theory based on off-center monopoles.

The subject of this paper is competitive effects between multiple reaction sinks. A theory based on off-center monopoles is developed for the steady-state diffusion equation and for the convection-diffusion equation with a constant flow field. The dipolar approximation for the diffusion equation with two equal reaction centres is compared with the exact solution. The former turns out to be remarkably accurate, even for two touching spheres. Numerical evidence is presented to show that the same holds for larger clusters (with more than two spheres). The theory is extended to the convection-diffusion equation with a constant flow field. As one increases the convective velocity, the competitive effects between the reactive centres gradually become less significant. This is demonstrated for a number of cluster configurations. At high flow velocities, the current methodology breaks down. Fixing this problem will be the subject of future research. The current method is useful as an easy-to-use tool for the calibration of other more complicated models in mass and/or heat transfer

Fractional equations and diffusive systems: an overview

The aim of this discussion is to give a broad view of the links between fractional differential equations (FDEs) or fractional partial differential equations (FPDEs) and so-called diffusive representations (DR). Many aspects will be investigated: theory and numerics, continuous time and discrete time, linear and nonlinear equations, causal and anti-causal operators, optimal diffusive representations, fractional Laplacian. Many applications will be given, in acoustics, continuum mechanics, electromagnetism, identification, ..

Delocalization and spin-wave dynamics in ferromagnetic chains with long-range correlated random exchange

We study the one-dimensional quantum Heisenberg ferromagnet with exchange couplings exhibiting long-range correlated disorder with power spectrum proportional to $1/k^{\alpha}$, where $k$ is the wave-vector of the modulations on the random coupling landscape. By using renormalization group, integration of the equations of motion and exact diagonalization, we compute the spin-wave localization length and the mean-square displacement of the wave-packet. We find that, associated with the emergence of extended spin-waves in the low-energy region for $\alpha > 1$, the wave-packet mean-square displacement changes from a long-time super-diffusive behavior for $\alpha <1$ to a long-time ballistic behavior for $\alpha > 1$. At the vicinity of $\alpha =1$, the mobility edge separating the extended and localized phases is shown to scale with the degree of correlation as $E_c\propto (\alpha -1)^{1/3}$.Comment: PRB to appea

Superdiffusion of energy in a chain of harmonic oscillators with noise

We consider a one dimensional infinite chain of har- monic oscillators whose dynamics is perturbed by a stochastic term conserving energy and momentum. We prove that in the unpinned case the macroscopic evolution of the energy converges to a fractional diffusion. For a pinned system we prove that energy evolves diffusively, generalizing some of the results of [4].Comment: New version with corrections. Diffusion of phonon modes remouved, it will appear in a forthcoming not