11 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.
Dynamical Renormalization Group Study for a Class of Non-local Interface Equations
We provide a detailed Dynamic Renormalization Group study for a class of
stochastic equations that describe non-conserved interface growth mediated by
non-local interactions. We consider explicitly both the morphologically stable
case, and the less studied case in which pattern formation occurs, for which
flat surfaces are linearly unstable to periodic perturbations. We show that the
latter leads to non-trivial scaling behavior in an appropriate parameter range
when combined with the Kardar-Parisi-Zhang (KPZ) non-linearity, that
nevertheless does not correspond to the KPZ universality class. This novel
asymptotic behavior is characterized by two scaling laws that fix the critical
exponents to dimension-independent values, that agree with previous reports
from numerical simulations and experimental systems. We show that the precise
form of the linear stabilizing terms does not modify the hydrodynamic behavior
of these equations. One of the scaling laws, usually associated with Galilean
invariance, is shown to derive from a vertex cancellation that occurs (at least
to one loop order) for any choice of linear terms in the equation of motion and
is independent on the morphological stability of the surface, hence
generalizing this well-known property of the KPZ equation. Moreover, the
argument carries over to other systems like the Lai-Das Sarma-Villain equation,
in which vertex cancellation is known {\em not to} imply an associated symmetry
of the equation.Comment: 34 pages, 9 figures. Journal of Statistical Mechanics: Theory and
Experiments (in press
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
Implicit Model for the Hydration Free Energy Calculation in the Task of the Supercomputer Docking
Tracing the Arrows of Time
noOver the last century there have been a number of proposals to ground both local and cosmic arrows of time: from the Second law to the Growing Block Universe, from Decoherence to Earman’s time-direction heresy. The latter proposal rejects the traditional association of the Second law of thermodynamics with arrows of time. But it seems that notions like entropy and related notions – phase space volumes and typicality – are not easily banned from discussions of temporal arrows. A close reading of Eddington’s thinking on these questions reveals that his views underwent a considerable development. In particular Eddington abandoned his identification of the arrows of time with the increase in entropy and began to see the Second law as a criterion for temporal arrows. In the process, Eddington also developed an argument against Loschmidt’s reversibility objections, in terms of an expanding universe. This latter argument brings his contribution close to contemporary thinking in terms of Liouville’s theorem, the topology of phase space and typicality arguments. Their reliability to deliver arrows of time will therefore be considered.
Are there arrows of time? This question is related to the epistemological views of both Eddington and Wheeler. They insisted on the role of inferences in scientific thinking. Physical reality was to be inferred from data (Eddington) or information (Wheeler) about the physical universe. The paper will conclude that the arrows of time are equally to be regarded as conceptual inferences from various physical criteria – not just entropy – which the universe makes available to us