Related papers: Detecting coherent structures using braids
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…
Modeling fluid turbulence using a 'skeleton' of coherent structures has traditionally progressed by focusing on a few canonical experiments, such as pipe flow and Taylor-Couette flow. We here consider an alternative canonical experiment,…
Transport and mixing in dynamical systems are important properties for many physical, chemical, biological, and engineering processes. The detection of transport barriers for dynamics with general time dependence is a difficult, but…
This study proposes a novel topology optimization method for unsteady fluid flows induced by actively moving rigid bodies. The key idea of the proposed method is to decouple the design and analysis domains by using separate grids. The…
In this work we propose algorithms to explicitly construct a conservative estimate of the configuration spaces of rigid objects in 2D and 3D. Our approach is able to detect compact path components and narrow passages in configuration space…
The curvature field is measured from tracer particle trajectories in a two-dimensional fluid flow that exhibits spatiotemporal chaos, and is used to extract the hyperbolic and elliptic points of the flow. These special points are pinned to…
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…
Mixing, and coherence are fundamental issues at the heart of understanding transport in fluid dynamics and other non-autonomous dynamical systems. Recently, the notion of coherence has come to a more rigorous footing, and particularly…
In many engineering systems operating with a working fluid, the best efficiency is reached close to a condition of flow separation, which makes its prediction very crucial in industry. Providing that wall-based quantities can be measured,…
We introduce a new Lagrangian particle tracking algorithm that tracks particles in three dimensions to separations between trajectories approaching contact. The algorithm also detects low Weber number binary collisions that result in…
To facilitate the understanding and to quantitatively assess the material transport in fluids, a modern characterisation method has emerged in fluid dynamics in the last decades footed in dynamical systems theory. It allows to examine the…
The Lagrangian derivatives of finite-time Lyapunov exponents and the corresponding characteristic directions are shown to satisfy time-asymptotic differential constraints in chaotic flows. The constraints are valid for any metric tensor,…
Analysis of Lagrangian Coherent Structures (LCSs) has been showed to be a valid mathematical approach to explain the formation of transport barriers in magnetized plasmas. Such LCSs, borrowed from fluid dynamics theory, can be considered as…
Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…
We present a continuous-time collision detection algorithm for quickly detecting whether certain polynomial trajectories in time intersect with convex obstacles. The algorithm is used in conjunction with an existing multicopter trajectory…
We propose a new method for determining the stochastic or ordered nature of trajectories in non-integrable Hamiltonian dynamical systems. The method consists of constructing a time-series from the divergence of nearby trajectories and then…
We present TOPGN, a novel method for real-time transparent obstacle detection for robot navigation in unknown environments. We use a multi-layer 2D grid map representation obtained by summing the intensities of lidar point clouds that lie…
Turbulent flows, despite their apparent randomness, exhibit coherent structures that underpin their dynamics. Proper orthogonal decomposition (POD) has been widely used to extract these structures from experimental data. While periodic…
We present a braided circuit topology framework for investigating topology and structural phase transitions in aggregates of semiflexible polymers. In the conventional approach to circuit topology, which specifically applies to single…
Motion prediction of surrounding vehicles is one of the most important tasks handled by a self-driving vehicle, and represents a critical step in the autonomous system necessary to ensure safety for all the involved traffic actors. Recently…