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

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References

SHOWING 1-10 OF 59 REFERENCES
Stability of the square-wave detonation in a model system
Abstract Using a set of model equations for reactive flow, we study the stability of a “square-wave” detonation, in which each particle of the fluid reacts instantaneously after an induction timeExpand
Supersonic Flow and Shock Waves
TWENTY-FIVE years ago what was known on the dynamics of gases, if acoustics and the study of steady motion at speeds small compared with that of sound (when the flow resembles that of a liquid) beExpand
Simulations of pulsating one-dimensional detonations with true fifth order accuracy
TLDR
A novel, highly accurate numerical scheme based on shock-fitting coupled with fifth order spatial and temporal discretizations is applied to a classical unsteady detonation problem to generate solutions with unprecedented accuracy, enabling more precise verification of known results and prediction of heretofore unknown phenomena. Expand
Qualitative model for dynamic combustion
A qualitative model for studying shock-wave chemistry interactions in combustion theory is introduced. The model which we study bears the analogous relationship to reacting gas flow as Burgers’Expand
Nonlinear dynamics and chaos analysis of one-dimensional pulsating detonations
To understand the nonlinear dynamical behaviour of a one-dimensional pulsating detonation, results obtained from numerical simulations of the Euler equations with simple one-step Arrhenius kineticsExpand
Weakly Nonlinear Detonation Waves
The authors develop a simplified asymptotic model for studying nonlinear detonation waves in chemically reacting fluids which propagate with wave speed close to the acoustical sound speed. In thisExpand
Nonlinear dynamics of self-sustained supersonic reaction waves: Fickett's detonation analogue.
TLDR
The results obtained clarify the physical origin of detonation wave instability in chemical detonations previously observed experimentally and clarify the spatiotemporal variability in the dynamics of self-sustained supersonic reaction waves propagating through an excitable medium. Expand
A mathematical model illustrating the theory of turbulence
Publisher Summary This chapter discusses that the application of methods of statistical analysis and statistical mechanics to the problem of turbulent fluid motion has attracted much attention inExpand
Stability of Detonation Profiles in the ZND Limit
Confirming a conjecture of Lyng–Raoofi–Texier–Zumbrun, we show that stability of strong detonation waves in the ZND, or small-viscosity, limit is equivalent to stability of the limiting ZNDExpand
An equation for continuous chaos
Abstract A prototype equation to the Lorenz model of turbulence contains just one (second-order) nonlinearity in one variable. The flow in state space allows for a “folded” Poincare map (horseshoeExpand
...
1
2
3
4
5
...