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We consider a damped linear hyperbolic system modelling the propagation of pressure waves in a network of pipes. Well-posedness is established via semi-group theory and the existence of a unique steady state is proven in the absence of…

Numerical Analysis · Mathematics 2016-05-11 Herbert Egger , Thomas Kugler

We report a systematic and detailed numerical study of statistics of the reflection coefficient $(|R(L)|^2)$ and its associated phase ($\theta$) for a plane wave reflected from a one-dimensional (1D) disordered medium beyond the random…

Mesoscale and Nanoscale Physics · Physics 2008-02-03 Prabhakar Pradhan

This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation subject to a nonmonotone distributed damping. A well-posedness result is provided together with a precise characterization of the asymptotic…

Analysis of PDEs · Mathematics 2019-02-07 Swann Marx , Yacine Chitour , Christophe Prieur

Spontaneous rhythmic oscillations are widely observed in various real-world systems. In particular, biological rhythms, which typically arise via synchronization of many self-oscillatory cells, often play important functional roles in…

Adaptation and Self-Organizing Systems · Physics 2021-06-11 Hiroya Nakao

Scroll waves are three-dimensional analogs of spiral waves. The linear stability spectrum of untwisted and twisted scroll waves is computed for a two-variable reaction-diffusion model of an excitable medium. Different bands of modes are…

Condensed Matter · Physics 2007-05-23 Herve Henry , Vincent Hakim

We study stability of monostable waves for reaction-diffusion systems. When the solution is initially close to a fast wave profile in optimal topology, we prove convergence to a shifted profile. The proof relies on explicit resolvent…

Analysis of PDEs · Mathematics 2026-02-27 Louis Garénaux

In chaotic reaction-diffusion systems with two degrees of freedom, the modes governing the exponential relaxation to the thermodynamic equilibrium present a fractal structure which can be characterized by a Hausdorff dimension. For long…

Statistical Mechanics · Physics 2009-11-07 I. Claus , P. Gaspard

Spatial distributions of heavy particles suspended in an incompressible isotropic and homogeneous turbulent flow are investigated by means of high resolution direct numerical simulations. In the dissipative range, it is shown that particles…

Chaotic Dynamics · Physics 2007-05-23 J. Bec , L. Biferale , M. Cencini , A. Lanotte , S. Musacchio , F. Toschi

In contrast to the prevailing view in the literature, it is shown that even extremely stiff sets of ordinary differential equations may be solved efficiently by explicit methods if limiting algebraic solutions are used to stabilize the…

Solar and Stellar Astrophysics · Physics 2016-08-01 Mike Guidry

We study the planar front solution for a class of reaction diffusion equations in multidimensional space in the case when the essential spectrum of the linearization in the direction of the front touches the imaginary axis. At the linear…

Analysis of PDEs · Mathematics 2017-12-11 Anna Ghazaryan , Yuri Latushkin , Xinyao Yang

Spiral waves emerge in numerous pattern forming systems and are commonly modeled with reaction-diffusion systems. Some systems used to model biological processes, such as ion-channel models, fall under the reaction-diffusion category and…

Dynamical Systems · Mathematics 2021-10-29 Stephanie Dodson , Bjorn Sandstede

We address the propagation into an unstable state of a localised disturbance in a forward-backward diffusion pseudo-parabolic equation. Three asymptotic regimes are distinguished as t tends to infinity, the first being a regime ahead of the…

Analysis of PDEs · Mathematics 2016-05-27 C. M. Cuesta , J. R. King

The velocity relaxation of an impulsively forced spherical particle in a fluid confined by two parallel plane walls is studied using a direct numerical simulation approach. During the relaxation process, the momentum of the particle is…

Fluid Dynamics · Physics 2015-06-15 Rei Tatsumi , Ryoichi Yamamoto

Understanding the timescales associated with relaxation to equilibrium in closed quantum many-body systems is one of the central focuses in the study of their non-equilibrium dynamics. At late times, these relaxation processes exhibit…

Statistical Mechanics · Physics 2026-01-19 Kadir Çeven , Lukas Peinemann , Fabian Heidrich-Meisner

We study classical particles on the sites of an open chain which diffuse, coagulate and decoagulate preferentially in one direction. The master equation is expressed in terms of a spin one-half Hamiltonian $H$ and the model is shown to be…

Condensed Matter · Physics 2015-06-25 Haye Hinrichsen , Klaus Krebs , Ingo Peschel

We consider a scalar reaction-diffusion equation in one spatial dimension with bistable nonlinearity and a nonlocal space-fractional diffusion operator of Riesz-Feller type. We present our analytical results on the existence, uniqueness (up…

Numerical Analysis · Mathematics 2017-02-28 Franz Achleitner , Christian Kuehn

We establish sharp estimates for the convergence rate of the Kranosel'ski\v{\i}-Mann fixed point iteration in general normed spaces, and we use them to show that the asymptotic regularity bound recently proved in [11] (Israel Journal of…

Optimization and Control · Mathematics 2017-01-31 Mario Bravo , Roberto Cominetti

Wall-resolved large-eddy simulations are performed to study the impact of spanwise traveling transversal surface waves in zero-pressure gradient turbulent boundary layer flow. Eighty variations of wavelength, period, and amplitude of the…

We investigate front propagation in a reacting particle system in which particles perform scale-free random walks known as Levy flights. The system is described by a fractional generalization of a reaction-diffusion equation. We focus on…

Statistical Mechanics · Physics 2007-05-23 D. Brockmann , L. Hufnagel

In this paper we develop a new statistical model for the irradiance fluctuations of an unbounded optical wavefront (plane and spherical waves) propagating through a turbulent medium under all irradiance fluctuation conditions in…