Related papers: Chaos Phenotypes in Fluids
The study of deterministic chaos continues to be one of the important problems in the field of nonlinear dynamics. Interest in the study of chaos exists both in low-dimensional dynamical systems and in large ensembles of coupled…
Complex systems often have features that can be modeled by advanced mathematical tools [1]. Of special interests are the features of complex systems that have a network structure as such systems are important for modeling technological and…
We examine the linear stability of fluid interfaces subjected to a shear flow. Our main object is to generalize previous work to arbitrary Atwood number, and to allow for surface tension and weak compressibility. The motivation derives from…
We discuss some important issues arising from computational efforts in dynamical systems and fluid dynamics. Various individuals have misunderstood these issues since the onset of these problem areas; indeed, they have been routinely…
Dynamical systems on the interval were widely studied because they are among the simplest systems and nevertheless they turn out to have complex dynamics. Many works on chaos were inspired by the behaviour of interval maps. However these…
We study phase-separating fluid mixtures as they demix in the presence of chemical reactions that maintain them away from thermodynamic equilibrium. We show that in such chemically active emulsions the interplay of chemical reactions, phase…
This work presents a tentative discussion of certain aspects of energy behavior in the context of mathematical fluid dynamics. While some observations are made regarding certain patterns in energy behavior under particular conditions, the…
Kinematical and dynamical properties of chaotic systems are reviewed and a few applications are described.
We propose an uncertainty principle for chaos, focusing on two key characteristics: alpha unpredictability and Lorenz sensitivity. This principle outlines a limitation on the relationship between two infinite sequences that underpin these…
This paper is concerned with Devaney chaos in non-autonomous discrete systems. It is shown that in its definition, the two former conditions, i.e., transitivity and density of periodic points, in a set imply the last one, i.e., sensitivity,…
This talk summarises what is currently understood about the phenomenon that has come to be known as {\it chaotic mixing}. The first part presents a concise statement as to what chaotic mixing actually is, and then explains why it should be…
Event-by-event hydrodynamics (or hydrodynamics with fluctuating initial conditions) has been developed in the past few years. Here we discuss how it may help to understand the various structures observed in two-particle correlations.
Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to…
The linear stability of pipe flow implies that only perturbations of sufficient strength will trigger the transition to turbulence. In order to determine this threshold in perturbation amplitude we study the \emph{edge of chaos} which…
We outline how unstable quantum fluctuations decohere classical fields in heavy ion collisions, leading to an equation of state and hydrodynamics. Explicit numerical realization of this framework in a scalar $\phi^4$ theory demonstrates…
Chaos is an inherently dynamical phenomenon traditionally studied for trajectories that are either permanently erratic or transiently influenced by permanently erratic ones lying on a set of measure zero. The latter gives rise to the final…
We study numerically a succession of transitions in pipe Poiseuille flow that leads from simple travelling waves to waves with chaotic time-dependence. The waves at the origin of the bifurcation cascade possess a shift-reflect symmetry and…
Linearly stable shear flows first transition to turbulence in the form of localised patches. At low Reynolds numbers, these turbulent patches tend to suddenly decay, following a memoryless process typical of rare events. How far in advance…
We give a definition of chaos for a continuous self-map of a general topological space. This definition coincides with the Devanney definition for chaos when the topological space happens to be a metric space. We show that in a uniform…
The fluidic pinball has been recently proposed as an attractive and effective flow configuration for exploring machine learning fluid flow control. In this contribution, we focus on the route to chaos in this system without actuation, as…