7 research outputs found
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
Flame front propagation V: Stability Analysis of Flame Fronts: Dynamical Systems Approach in the Complex Plane
We consider flame front propagation in channel geometries. The steady state
solution in this problem is space dependent, and therefore the linear stability
analysis is described by a partial integro-differential equation with a space
dependent coefficient. Accordingly it involves complicated eigenfunctions. We
show that the analysis can be performed to required detail using a finite order
dynamical system in terms of the dynamics of singularities in the complex
plane, yielding detailed understanding of the physics of the eigenfunctions and
eigenvalues.Comment: 17 pages 7 figure
A note on the extension of the polar decomposition for the multidimensional Burgers equation
It is shown that the generalizations to more than one space dimension of the
pole decomposition for the Burgers equation with finite viscosity and no force
are of the form u = -2 viscosity grad log P, where the P's are explicitly known
algebraic (or trigonometric) polynomials in the space variables with polynomial
(or exponential) dependence on time. Such solutions have polar singularities on
complex algebraic varieties.Comment: 3 pages; minor formatting and typos corrected. Submitted to Phys.
Rev. E (Rapid Comm.
Continuous dielectric permittivity II: An Iterative Method for Calculating the Polar Component of the Molecular Solvation Gibbs Energy Under a Smooth Change in the Dielectric Permittivity of a Solution
An iterative method for calculating the polar component of the solvation
Gibbs energy under a smooth change in dielectric permittivity, both between a
substrate and a solvent and in a solvent is formulated on the basis of a
previously developed model. The method is developed in the approximation of the
local relationship D = \eps (r) E between the displacement vectors D and the
electric field intensity E.Comment: 36 pages,3 Figures, in English and in Russia
Flame front propagation I: The Geometry of Developing Flame Fronts: Analysis with Pole Decomposition
The roughening of expanding flame fronts by the accretion of cusp-like
singularities is a fascinating example of the interplay between instability,
noise and nonlinear dynamics that is reminiscent of self-fractalization in
Laplacian growth patterns. The nonlinear integro-differential equation that
describes the dynamics of expanding flame fronts is amenable to analytic
investigations using pole decomposition. This powerful technique allows the
development of a satisfactory understanding of the qualitative and some
quantitative aspects of the complex geometry that develops in expanding flame
fronts.Comment: 4 pages, 2 figure