139 citations · 275 across the 13 of their papers we have counts for
14 papers
A minimal hyperbolic system for unstable shock waves
Dmitry I. Kabanov, Aslan R. Kasimov
We present a computational analysis of a 22 hyperbolic system of balance laws whose solutions exhibit complex nonlinear behavior. Traveling-wave solutions of the system are…
Linear stability analysis of detonations via numerical computation and dynamic mode decomposition
Dmitry I. Kabanov, Aslan R. Kasimov
We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler e…
On a stabilization mechanism for low velocity detonations
Aliou Sow, Roman E. Semenko, Aslan R. Kasimov
We use numerical simulations of the reactive Euler equations to analyze the nonlinear stability of steady-state one-dimensional solutions for gaseous detonations in the presence of…
Study of a model equation in detonation theory: multidimensional effects
Luiz M. Faria, Aslan R. Kasimov, Rodolfo R. Rosales
We extend the reactive Burgers equation presented in Kasimov et al. Phys. Rev. Lett., 110 (2013) and Faria et al. SIAM J. Appl. Maths, 74 (2014), to include multidimensional effect…
Qualitative modeling of the dynamics of detonations with losses
Luiz M. Faria, Aslan R. Kasimov
We consider a simplified model for the dynamics of one-dimensional detonations with generic losses. It consists of a single partial differential equation that reproduces, at a qual…
Theory of weakly nonlinear self sustained detonations
Luiz M. Faria, Aslan R. Kasimov, Rodolfo R. Rosales
We propose a theory of weakly nonlinear multi-dimensional self sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that…
Set-valued solutions for non-ideal detonation
Roman Semenko, Luiz Faria, Aslan Kasimov +1
The existence and structure of steady gaseous detonation propagating in a packed bed of solid inert particles are analyzed in the one-dimensional approximation by taking into consi…
On the Gross-Pitaevskii equation with pumping and decay: stationary states and their stability
Jesús Sierra, Aslan Kasimov, Peter Markowich +1
We investigate the behavior of solutions of the complex Gross-Pitaevskii equation, a model that describes the dynamics of pumped decaying Bose-Einstein condensates. The stationary…
Study of a model equation in detonation theory
Luiz M. Faria, Aslan R. Kasimov, Rodolfo R. Rosales
Here we analyze properties of an equation that we previously proposed to model the dynamics of unstable detonation waves [A. R. Kasimov, L. M. Faria, and R. R. Rosales. Model for s…
Sunflower detonation
A. Kasimov, S. Korneev
In this fluid dynamic video we present simulations of converging two-dimensional detonation in a radially expanding supersonic flow of ideal reactive gas. The detonation is found t…
Constructing set-valued fundamental diagrams from jamiton solutions in second order traffic models
Benjamin Seibold, Morris R. Flynn, Aslan R. Kasimov +1
Fundamental diagrams of vehicular traffic flow are generally multi-valued in the congested flow regime. We show that such set-valued fundamental diagrams can be constructed systema…
A model for shock wave chaos
Aslan Kasimov, Luiz Faria, Rodolfo R. Rosales
We propose the following model equation: \[u_{t}+1/2(u^{2}-uu_{s})_{x}=f(x,u_{s}), \] that predicts chaotic shock waves. It is given on the half-line and the shock is located…
Self-sustained nonlinear waves in traffic flow
Morris R. Flynn, Aslan R. Kasimov, Jean-Christophe Nave +2
In analogy to gas-dynamical detonation waves, which consist of a shock with an attached exothermic reaction zone, we consider herein nonlinear traveling wave solutions, termed "jam…
On "jamitons," self-sustained nonlinear traffic waves
Morris R. Flynn, Aslan R. Kasimov, Jean-Christophe Nave +2
"Phantom jams," traffic blockages that arise without apparent cause, have long frustrated transportation scientists. Herein, we draw a novel homology between phantom jams and a rel…