Related papers: Laplacian growth as one-dimensional turbulence
We report numerical investigations of a three-dimensional model of diffusive growth of fine particles, the internal structure of which corresponds to different crystal lattices. A growing cluster (particle) is immersed in, and exchanges…
Stochastic growth phenomena on curved interfaces are studied by means of stochastic partial differential equations. These are derived as counterparts of linear planar equations on a curved geometry after a reparametrization invariance…
These lecture notes on 2D growth processes are divided in two parts. The first part is a non-technical introduction to stochastic Loewner evolutions (SLEs). Their relationship with 2D critical interfaces is illustrated using numerical…
Galaxies comprise intricate networks of interdependent processes which together govern their evolution. Central among these are the multiplicity of feedback channels, which remain incompletely understood. One outstanding problem is the…
We study the dynamics of the Internet topology based on the empirical data on the level of the autonomous systems. It is found that the fluctuations occurring in the stochastic process of connecting and disconnecting edges are important…
We discuss shape profiles emerging in inhomogeneous growth of squeezed tissues. Two approaches are used simultaneously: i) conformal embedding of two-dimensional domain with hyperbolic metrics into the plane, and ii) a pure energetic…
Understanding the formation and evolution of young star clusters requires quantitative statistical measures of their structure. We investigate the structures of observed and modelled star-forming clusters. By considering the different…
A class of Laplacian growth models in the channel geometry is studied using the formalism of tripolar Loewner evolutions, in which three points, namely, the channel corners and infinity, are kept fixed. Initially, the problem of fingered…
The long time dynamics of large particles trapped in two inhomogeneous turbulent shear flows is studied experimentally. Both flows present a common feature, a shear region that separates two colliding circulations, but with different…
The growth of a population divided among spatial sites, with migration between the sites, is sometimes modelled by a product of random matrices, with each diagonal elements representing the growth rate in a given time period, and…
Mollusk shells are an ideal model system for understanding the morpho-elastic basis of morphological evolution of invertebrates' exoskeletons. During the formation of the shell, the mantle tissue secretes proteins and minerals that calcify…
Usual formulations of the clustering coefficient can be shown to be insufficient in the task of describing the local topology of very simple networks. Motivated by this, we review some alternatives in order to present an extension, the…
A simple theory, based on observations of snowflake distribution in a turbulent flow, is proposed to model the growth of inertial particles as a result of dynamic clustering at scales larger than the Kolmogorov length scale. Particles able…
Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…
The physics of turbulence in magnetized plasmas remains an unresolved problem. The most poorly understood aspect is intermittency -- spatio-temporal fluctuations superimposed on the self-similar turbulent motions. We employ a novel…
Can a graph specifying the pattern of connections of a dynamical network be reconstructed from statistical properties of a signal generated by such a system? In this model study, we present an evolutionary algorithm for reconstruction of…
The paper considers the application of two numerical models to simulate the evolution of steep breaking waves. The first one is a Lagrangian wave model based on equations of motion of an inviscid fluid in Lagrangian coordinates. A method…
We consider the use of N-body simulations for studying the evolution of rich star clusters (i.e. globular clusters). The dynamical processes included in this study are restricted to gravitational (point-mass) interactions, the steady tidal…
Growth and folding in one-layered model tissue sheets are studied in a stochastic, lattice-free single cell model which considers the discrete cellular structure of the tissue, and a coarse grained analytical approach. The polarity of the…
Turbulence is a key ingredient for the evolution of the intracluster medium, whose properties can be predicted with high resolution numerical simulations. We present initial results on the generation of solenoidal and compressive turbulence…