Related papers: The edge as a Lagrangian Coherent Structure in a h…
Systems that can be described with the same mathematical models that account for the properties of electrons in graphene are known as graphene-like systems. These include magnons, photons, polaritons, acoustic waves, and electrons in…
Robust states emerging at the boundary of a system constitute a hallmark for topological band structures. Other than in closed systems, topologically protected states can occur even in systems with a trivial band structure, if exposed to…
We consider Lagrangian coherent structures (LCSs) as the boundaries of material subsets whose advective evolution is metastable under weak diffusion. For their detection, we first transform the Eulerian advection-diffusion equation to…
The detection of coherent structures is an important problem in fluid dynamics, particularly in geophysical applications. For instance, knowledge of how regions of fluid are isolated from each other allows prediction of the ultimate fate of…
Lagrangian statistics and particle transport in edge plasma turbulence are investigated using the Hasegawa-Wakatani model and its modified version. The latter shows the emergence of pronounced zonal flows. Different values of the…
Over the past decade, the edge of chaos has proven to be a fruitful starting point for investigations of shear flows when the laminar base flow is linearly stable. Numerous computational studies of shear flows demonstrated the existence of…
The concept of edge state is investigated in the asymptotic suction boundary layer in relation with the receptivity process to noisy perturbations and the nucleation of turbulent spots. Edge tracking is first performed numerically, without…
An approach is presented for identifying separatrices in phase space generated from noisy time series data sets representative of measured experimental data. These separatrices are identified as ridges in the phase space distribution of…
Symmetries -- whether explicit, latent, or hidden -- are fundamental to understanding topological materials. This work introduces a prototypical spring-mass model that extends beyond established canonical models, revealing topological edge…
Spontaneous emergence of organized states in materials driven by non-equilibrium conditions is of significant fundamental and technological interest. In many cases, the organized states are complex, hence, with some well-studied exceptions,…
Measurements of Lagrangian single-point and multiple-point statistics in a quasi-two-dimensional stratifed layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced…
Active fluids, such as cytoskeletal filaments, bacterial colonies and epithelial cell layers, exhibit distinctive orientational coherence, often characterized by nematic order and topological defects. By contrast, little is known about…
We explore a two-dimensional dynamical system modeling transition in shear flows to try to understand the nature of an 'edge' state. The latter is an invariant set in phase space separating the basin of attraction B of the laminar state…
The evolution of organismal populations is not typically thought of in terms of classical mechanics. However, many of the conceptual models used to approximate evolutionary trajectories have implicit parallels to dynamic physical systems.…
Recurrence in the phase space of complex systems is a well-studied phenomenon, which has provided deep insights into the nonlinear dynamics of such systems. For dissipative systems, characteristics based on recurrence plots have recently…
Many complex flows such as those arising from ocean plastics in geophysics or moving cells in biology are characterized by sparse and noisy trajectory datasets. We introduce techniques for identifying Lagrangian Coherent Structures (LCSs)…
Topological states have been widely investigated in different types of systems and lattices. In the present work, we report on topological edge states in double-wave (DW) chains, which can be described by a generalized Aubry-Andr\'e-Harper…
We identify materially defined regions in unsteady two-dimensional flows that combine finite-time contraction with elevated accumulated intrinsic rotation along trajectories, which we term \emph{Lagrangian rotating contracting structures}…
A new geometric approach to systems with boundary energy flow is developed using infinite-dimensional Dirac structures within the Lagrangian formalism. This framework satisfies a list of consistency criteria with the geometric setting of…
In an experiment on a turbulent jet, we detect interfacial turbulent layers in a frame that moves, on average, along with the \tnti. This significantly prolongs the observation time of scalar and velocity structures and enables the…