# Model for shock wave chaos.

@article{Kasimov2013ModelFS, title={Model for shock wave chaos.}, author={Aslan R. Kasimov and Luiz M. Faria and Rodolfo Ruben Rosales}, journal={Physical review letters}, year={2013}, volume={110 10}, pages={ 104104 } }

We propose the following model equation, u(t) + 1/2(u(2)-uu(s))x = f(x,u(s)) that predicts chaotic shock waves, similar to those in detonations in chemically reacting mixtures. The equation is given on the half line, x<0, and the shock is located at x = 0 for any t ≥ 0. Here, u(s)(t) is the shock state and the source term f is taken to mimic the chemical energy release in detonations. This equation retains the essential physics needed to reproduce many properties of detonations in gaseous… Expand

#### 27 Citations

Study of a Model Equation in Detonation Theory

- Physics, Computer Science
- SIAM J. Appl. Math.
- 2014

The nature of the steady-state solutions of this nonlocal hyperbolic balance law, the linear stability of these solutions, and the nonlinear dynamics are investigated. Expand

Numerical Computation of Detonation Stability

- Physics
- 2018

Numerical computation of detonation stability Dmitry I. Kabanov Detonation is a supersonic mode of combustion that is modeled by a system of conservation laws of compressible fluid mechanics coupled… Expand

Multiplicity of detonation regimes in systems with a multi-peaked thermicity

- Physics, Chemistry
- 2012

The study investigates detonations with multiple quasi-steady velocities that have been observed in the past in systems with multi-peaked thermicity, using Fickett's detonation analogue. A… Expand

Study of the Instability and Dynamics of Detonation Waves using Fickett's Analogue to the Reactive Euler Equations

- Physics
- 2013

The instability behaviour of detonation waves are studied using Fickett’s model with a 2-step reaction model with separately controlled induction and reaction zones. This model acts as a simplified… Expand

Influence of discrete sources on detonation propagation in a Burgers equation analog system.

- Physics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2015

The measurement of the average velocity of the leading shock front for systems of both regular, fixed-period and randomized sources is found to be in close agreement with the Velocity of the equivalent CJ detonation in a uniform medium, wherein the sources have been spatially homogenized. Expand

Two separate decay timescales of a detonation wave modeled by the Burgers equation and their relation to its chaotic dynamics.

- Medicine, Physics
- Physical review. E
- 2021

A simplified detonation model is used to investigate the behavior of detonations with galloping-like pulsations, revealing a sawtooth evolution of the front velocity with a period-averaged detonation speed equal to the Chapman-Jouguet velocity. Expand

Study of a Model Equation in Detonation Theory: Multidimensional Effects

- Physics, Mathematics
- SIAM J. Appl. Math.
- 2016

The proposed model is a forced version of the unsteady small disturbance transonic flow equations and it is demonstrated that multidimensional effects play an important role in the stability and dynamics of the traveling waves. Expand

A nonlinear evolution equation for pulsating detonations using Fickett's model with chain branching kinetics

- Physics
- 2014

The detonation wave stability is addressed using Fickett's equation, i.e., the reactive form of Burgers' equation. This serves as a simple analogue to the reactive Euler equations, permitting one to… Expand

Stability of viscous detonations for Majda’s model

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- 2013

Abstract Using analytical and numerical Evans-function techniques, we examine the spectral stability of strong-detonation-wave solutions of a version of Majda’s scalar model for a reacting gas… Expand

Mean structure of one-dimensional unstable detonations with friction

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- Journal of Fluid Mechanics
- 2014

Abstract This investigation deals with the study of the mean structure of a mildly unstable non-ideal detonation wave. The analysis is based on the integration of one-dimensional reactive Euler… Expand

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