5 research outputs found
Nonlinear equation for curved stationary flames
A nonlinear equation describing curved stationary flames with arbitrary gas
expansion , subject to the
Landau-Darrieus instability, is obtained in a closed form without an assumption
of weak nonlinearity. It is proved that in the scope of the asymptotic
expansion for the new equation gives the true solution to the
problem of stationary flame propagation with the accuracy of the sixth order in
In particular, it reproduces the stationary version of the
well-known Sivashinsky equation at the second order corresponding to the
approximation of zero vorticity production. At higher orders, the new equation
describes influence of the vorticity drift behind the flame front on the front
structure. Its asymptotic expansion is carried out explicitly, and the
resulting equation is solved analytically at the third order. For arbitrary
values of the highly nonlinear regime of fast flow burning is
investigated, for which case a large flame velocity expansion of the nonlinear
equation is proposed.Comment: 29 pages 4 figures LaTe
Flame front propagation IV: Random Noise and Pole-Dynamics in Unstable Front Propagation II
The current paper is a corrected version of our previous paper
arXiv:adap-org/9608001. Similarly to previous version we investigate the
problem of flame propagation. This problem is studied as an example of unstable
fronts that wrinkle on many scales. The analytic tool of pole expansion in the
complex plane is employed to address the interaction of the unstable growth
process with random initial conditions and perturbations. We argue that the
effect of random noise is immense and that it can never be neglected in
sufficiently large systems. We present simulations that lead to scaling laws
for the velocity and acceleration of the front as a function of the system size
and the level of noise, and analytic arguments that explain these results in
terms of the noisy pole dynamics.This version corrects some very critical
errors made in arXiv:adap-org/9608001 and makes more detailed description of
excess number of poles in system, number of poles that appear in the system in
unit of time, life time of pole. It allows us to understand more correctly
dependence of the system parameters on noise than in arXiv:adap-org/9608001Comment: 23 pages, 4 figures,revised, version accepted for publication in
journal "Combustion, Explosion and Shock Waves". arXiv admin note:
substantial text overlap with arXiv:nlin/0302021, arXiv:adap-org/9608001,
arXiv:nlin/030201
Exact Lyapunov Exponent for Infinite Products of Random Matrices
In this work, we give a rigorous explicit formula for the Lyapunov exponent
for some binary infinite products of random real matrices. All
these products are constructed using only two types of matrices, and ,
which are chosen according to a stochastic process. The matrix is singular,
namely its determinant is zero. This formula is derived by using a particular
decomposition for the matrix , which allows us to write the Lyapunov
exponent as a sum of convergent series. Finally, we show with an example that
the Lyapunov exponent is a discontinuous function of the given parameter.Comment: 1 pages, CPT-93/P.2974,late