2,766 research outputs found
Structure And Dynamics Of Modulated Traveling Waves In Cellular Flames
We describe spatial and temporal patterns in cylindrical premixed flames in
the cellular regime, , where the Lewis number is the ratio of
thermal to mass diffusivity of a deficient component of the combustible
mixture. A transition from stationary, axisymmetric flames to stationary
cellular flames is predicted analytically if is decreased below a critical
value. We present the results of numerical computations to show that as is
further decreased traveling waves (TWs) along the flame front arise via an
infinite-period bifurcation which breaks the reflection symmetry of the
cellular array. Upon further decreasing different kinds of periodically
modulated traveling waves (MTWs) as well as a branch of quasiperiodically
modulated traveling waves (QPMTWs) arise. These transitions are accompanied by
the development of different spatial and temporal symmetries including period
doublings and period halvings. We also observe the apparently chaotic temporal
behavior of a disordered cellular pattern involving creation and annihilation
of cells. We analytically describe the stability of the TW solution near its
onset+ using suitable phase-amplitude equations. Within this framework one of
the MTW's can be identified as a localized wave traveling through an underlying
stationary, spatially periodic structure. We study the Eckhaus instability of
the TW and find that in general they are unstable at onset in infinite systems.
They can, however, become stable for larger amplitudes.Comment: to appear in Physica D 28 pages (LaTeX), 11 figures (2MB postscript
file
Theory of Spike Spiral Waves in a Reaction-Diffusion System
We discovered a new type of spiral wave solutions in reaction-diffusion
systems --- spike spiral wave, which significantly differs from spiral waves
observed in FitzHugh-Nagumo-type models. We present an asymptotic theory of
these waves in Gray-Scott model. We derive the kinematic relations describing
the shape of this spiral and find the dependence of its main parameters on the
control parameters. The theory does not rely on the specific features of
Gray-Scott model and thus is expected to be applicable to a broad range of
reaction-diffusion systems.Comment: 4 pages (REVTeX), 2 figures (postscript), submitted to Phys. Rev.
Let
Theory of weakly nonlinear self sustained detonations
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 these equations can be reduced to a model
consisting of a forced, unsteady, small disturbance, transonic equation and a
rate equation for the heat release. In one spatial dimension, the model
simplifies to a forced Burgers equation. Through analysis, numerical
calculations and comparison with the reactive Euler equations, the model is
demonstrated to capture such essential dynamical characteristics of detonations
as the steady-state structure, the linear stability spectrum, the
period-doubling sequence of bifurcations and chaos in one-dimensional
detonations and cellular structures in multi- dimensional detonations
A wildland fire model with data assimilation
A wildfire model is formulated based on balance equations for energy and
fuel, where the fuel loss due to combustion corresponds to the fuel reaction
rate. The resulting coupled partial differential equations have coefficients
that can be approximated from prior measurements of wildfires. An ensemble
Kalman filter technique with regularization is then used to assimilate
temperatures measured at selected points into running wildfire simulations. The
assimilation technique is able to modify the simulations to track the
measurements correctly even if the simulations were started with an erroneous
ignition location that is quite far away from the correct one.Comment: 35 pages, 12 figures; minor revision January 2008. Original version
available from http://www-math.cudenver.edu/ccm/report
A model for shock wave chaos
We propose the following model equation:
that predicts chaotic shock waves.
It is given on the half-line and the shock is located at for any
. Here is the shock state and the source term is assumed
to satisfy certain integrability constraints as explained in the main text. We
demonstrate that this simple equation reproduces many of the properties of
detonations in gaseous mixtures, which one finds by solving the reactive Euler
equations: existence of steady traveling-wave solutions and their instability,
a cascade of period-doubling bifurcations, onset of chaos, and shock formation
in the reaction zone.Comment: 4 pages, 4 figure
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