Related papers: Topography-induced persistence of atmospheric patt…
As the parameters of a map are varied an attractor may vary continuously in the Hausdorff metric. The purpose of this paper is to explore the continuation of chaotic attractors. We argue that this is not a helpful concept for smooth…
Turbulent fluxes in the atmospheric surface layer are key input for the prediction of weather, hydrology, and carbon dioxide concentration. In numerical modelling of turbulent fluxes, a -7/3 power-law scaling in turbulence cospectra is…
Laminar-turbulent pattern formation is a distinctive feature of the intermittency regime in subcritical plane shear flows. By performing extensive numerical simulations of the plane channel flow, we show that the pattern emerges from a…
Light propagation through turbulence produces speckles, whose ensemble behavior is typically characterized by snapshot intensity statistics. Here, we track the spatiotemporal evolution of individual speckles and quantify fragmentation,…
The destruction of regular regions in two-dimensional, area-preserving maps is traditionally described in terms of the breakup of invariant curves and the persistence of transport barriers. Here, we investigate how this scenario changes…
Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features (2000) as one varies a tuning parameter. Features with short…
We consider time evolution of Turing patterns in an extended system governed by an equation of the Swift-Hohenberg type, where due to an external periodic parameter modulation long-wave and short-wave patterns with length scales related as…
Ocean motions at frequencies of the internal wave band are generally associated with freely propagating waves that are supported by stable vertical stratification in density. Previous analyses of yearlong current observations from the Bay…
The investigation of the coupled atmosphere-ocean system is not only scientifically challenging but also practically important. We consider a coupled atmosphere-ocean model, which involves hydrodynamics, thermodynamics, and random…
Wind shortwave instability of a foam layer between the atmosphere and the ocean is examined in order to reach greater understanding of the recent findings of the decrease in momentum transfer from hurricane winds to sea waves. The…
A subcritical pattern-forming system with nonlinear advection in a bounded domain is recast as a slow-fast system in space and studied using a combination of geometric singular perturbation theory and numerical continuation. Two types of…
The study of phase transitions using data-driven approaches is challenging, especially when little prior knowledge of the system is available. Topological data analysis is an emerging framework for characterizing the shape of data and has…
We consider the motion of a particle in a periodic two dimensional flow perturbed by small (molecular) diffusion. The flow is generated by a divergence free zero mean vector field. The long time behavior corresponds to the behavior of the…
This paper develops the idea of homology for 1-parameter families of topological spaces. We express parametrized homology as a collection of real intervals with each corresponding to a homological feature supported over that interval or,…
Over the last 10 years or so, advanced statistical properties, including exponential decay of correlations, have been established for certain classes of singular hyperbolic flows in three dimensions. The results apply in particular to the…
Non-stationarity is the rule in the atmospheric boundary layer (ABL). Under such conditions, the flow may experience departures from equilibrium with the underlying surface stress, misalignment of shear stresses and strain rates, and…
Paths of persistence diagrams provide a summary of the dynamic topological structure of a one-parameter family of metric spaces. These summaries can be used to study and characterize the dynamic shape of data such as swarming behavior in…
A sudden change in material properties creates a temporal interface and forces a propagating wave to change its frequency while preserving its wavenumber. In contrast to monoatomic lattices with a single frequency-wavenumber pair,…
Nontwist area-preserving maps violate the twist condition at specific orbits, resulting in shearless invariant curves that prevent chaotic transport. Plasmas and fluids with nonmonotonic equilibrium profiles may be described using nontwist…
Persistent homology provides information about the lifetime of homology classes along a filtration of cell complexes. Persistence barcode is a graphical representation of such information. A filtration might be determined by time in a set…