Related papers: Detecting coherent structures using braids
The statistical properties of fluid particles transported by a fully developed turbulent flow are investigated by means of high resolution direct numerical simulations. Single trajectory statistics is investigated in a time range spanning…
We describe a method for analyzing the phase space structures of Hamiltonian systems. This method is based on a time-frequency decomposition of a trajectory using wavelets. The ridges of the time-frequency landscape of a trajectory, also…
Long-lived flow patterns in the atmosphere such as weather fronts, mid-latitude blockings or tropical cyclones often induce extreme weather conditions. As a consequence, their description, detection, and tracking has received increasing…
Recent theoretical and experimental investigations have demonstrated the role of certain invariant manifolds, termed burning invariant manifolds (BIMs), as one-way dynamical barriers to reaction fronts propagating within a flowing fluid.…
Robust 3D object detection in adverse weather is highly challenging due to the varying reliability of different sensors. While existing LiDAR-4D radar fusion methods improve robustness, they predominantly rely on fixed or weakly adaptive…
To a closed braid in a solid torus we associate a trace graph in a thickened torus in such a way that closed braids are isotopic if and only if their trace graphs can be related by trihedral and tetraherdal moves. For closed braids with a…
In this paper, we design linear time algorithms to recognize and determine topological invariants such as the genus and homology groups in 3D. These properties can be used to identify patterns in 3D image recognition. This has tremendous…
We introduce a new global Lagrangian descriptor that is applied to flows with general time dependence (altimetric datasets). It succeeds in detecting simultaneously, with great accuracy, invariant manifolds, hyperbolic and non-hyperbolic…
We derive a theory for material surfaces that maximally inhibit the diffusive transport of a dynamically active vector field, such as the linear momentum, the angular momentum or the vorticity, in general fluid flows. These special material…
Weather regimes provide a useful framework for describing large-scale atmospheric variability and its impacts on regional weather. Despite extensive study, there is still no universally accepted definition or method for identifying weather…
We explore the mechanisms of heat transfer in a turbulent constant heat flux-driven Rayleigh-B\'enard convection flow, which exhibits a hierarchy of flow structures from granules to supergranules. Our computational framework makes use of…
Accurately predicting the future fluid is vital to extensive areas such as meteorology, oceanology, and aerodynamics. However, since the fluid is usually observed from the Eulerian perspective, its moving and intricate dynamics are…
Dynamic and temporal graphs are rich data structures that are used to model complex relationships between entities over time. In particular, anomaly detection in temporal graphs is crucial for many real world applications such as intrusion…
We present a simple method to efficiently compute a lower limit of the topological entropy and its spatial distribution for two-dimensional mappings. These mappings could represent either two-dimensional time-periodic fluid flows or…
We consider turbulence in a stratified 'Kolmogorov' flow, driven by horizontal shear in the form of sinusoidal body forcing in the presence of an imposed background linear stable stratification in the third direction. This flow…
In the first half of the paper we construct a Morse-type theory on certain spaces of braid diagrams. We define a topological invariant of closed positive braids which is correlated with the existence of invariant sets of parabolic flows…
Continuum lattice grid structures which consist of joined elastic beams subject to flexural deformations are ubiquitous. In this work, we establish a theoretical framework of the topological dynamics of continuum lattice grid structures,…
We develop a methodology to identify finite-time Lagrangian structures from data and models using an extension of the Koopman operator-theoretic methods developed for velocity fields with simple (periodic, quasi-periodic) time-dependence.…
This text describes a method to simultaneously reconstruct flow states and determine particle properties from Lagrangian particle tracking (LPT) data. LPT is a popular measurement strategy for fluids in which particles in a flow are…
Lagrangian properties obtained from a Particle Tracking Velocimetry experiment in a turbulent flow at intermediate Reynolds number are presented. Accurate sampling of particle trajectories is essential in order to obtain the Lagrangian…