Related papers: Laplacian growth as one-dimensional turbulence
Motivated by systems in which droplets grow and shrink in a turbulence-driven supersaturation field, we investigate the problem of turbulent condensation in a general manner. Using direct numerical simulations we show that the turbulent…
Two-dimensional turbulent flows, and to some extent, geophysical flows, are systems with a large number of degrees of freedom, which, albeit fluctuating, exhibit some degree of organization: coherent structures emerge spontaneously at large…
Nucleation and growth is the dominant relaxation mechanism driving first order phase transitions. In two-dimensional at systems nucleation has been applied to a wide range of problems in physics, chemistry and biology. Here we study…
Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates…
Spectral clustering is a powerful unsupervised machine learning algorithm for clustering data with non convex or nested structures. With roots in graph theory, it uses the spectral properties of the Laplacian matrix to project the data in a…
We develop a model in two dimensions to characterise the growth rate of a tracer gradient mixed by a statistically homogeneous flow with rapid temporal variations. % % The model is based on the orientation dynamics of the passive-tracer…
The structure of cloud complexes appears to be well described by a "tree structure" representation when the image is partitioned into "clouds". In this representation, the parent-child relationships are assigned according to containment.…
First, we revisit the stochastic Luria-Delbr\"uck model: a classic two-type branching process which describes cell proliferation and mutation. We prove limit theorems and exact results for the mutation times, clone sizes, and number of…
Dynamical behavior of the clusters during relaxation is studied in two-dimensional Potts model using cluster algorithm. Average cluster size and cluster formation velocity are calculated on two different lattice sizes for different number…
The cosmic web is a complex spatial pattern of walls, filaments, cluster nodes and underdense void regions. It emerged through gravitational amplification from the Gaussian primordial density field. Here we infer analytical expressions for…
The emergence of clustering and coarsening in crowded ensembles of self-propelled agents is studied using a lattice model in one-dimension. The persistent exclusion process, where particles move at directions that change randomly at a low…
One-dimensional models are presented for transitional shear flows. The models have two variables corresponding to turbulence intensity and mean shear. These variables evolve according to simple equations based on known properties of…
We study Turing pattern formation in a system undergoing radial growth in two dimensions. The Lengyel-Epstein two variable model is implemented in COMSOL Multiphysics and solved on domains growing at different speeds while sweeping other…
A central question in developmental biology is how size and position are determined. The genetic code carries instructions on how to control these properties in order to regulate the pattern and morphology of structures in the developing…
We study the conditions under which and how an imposed cluster of fixed colloidal particles at prescribed positions triggers crystal nucleation from a metastable colloidal fluid. Dynamical density functional theory of freezing and Brownian…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
Dynamics of coarsening of a statistically homogeneous fractal cluster, created by a morphological instability of diffusion-controlled growth, is investigated theoretically. An exact mathematical setting of the problem is presented that…
This work is intended to be a contribution to the study of the morphology of the rising convective columns, for a better representation of the processes of entrainment and detrainment. We examine technical methods for the description of the…
The non-modal transient growth of perturbations in horizontal and inclined channel flows of two immiscible fluids is studied. 3D perturbations are examined in order to find the optimal perturbations that attain the maximum amplification of…
We present a numerical investigation of two-dimensional decaying turbulence in the Lagrangian framework. Focusing on single particle statistics, we investigate Lagrangian trajectories in a freely evolving turbulent velocity field. The…