Related papers: Network-theoretic approach to sparsified discrete …
A network community-based reduced-order model is developed to capture key interactions amongst coherent structures in high-dimensional unsteady vortical flows. The present approach is data-inspired and founded on network-theoretic…
We introduce a network (graph) theoretic community-based framework to extract vortical structures that serve the role of connectors for the vortical interactions in two- and three-dimensional isotropic turbulence. The present framework…
Two-dimensional arrays of nonlinear electric oscillators are considered theoretically, where nearest neighbors are coupled by relatively small, constant, but non-equal capacitors. The dynamics is approximately reduced to a weakly…
The present paper reports on our effort to characterize vortical interactions in complex fluid flows through the use of network analysis. In particular, we examine the vortex interactions in two-dimensional decaying isotropic turbulence and…
The coupling interactions between deformable structures and unsteady fluid flows occur across a wide range of spatial and temporal scales in many engineering applications. These fluid-structure interactions (FSI) pose significant challenges…
The network of interactions among fluid elements and coherent structures gives rise to the incredibly rich dynamics of vortical flows. These interactions can be described with the use of mathematical tools from the emerging field of network…
Cardiac blood flow patterns contain rich information about disease severity and clinical interventions, yet current imaging and computational methods fail to capture underlying relational structures of coherent flow features. We propose a…
The complex interactions of localized vortices with waves is investigated using a model of point vortices in the presence of a transverse or longitudinal wave. This simple model shows a rich dynamical behavior including oscillations of a…
We integrate a discrete vortex method with complex network analysis to strategize dynamic stall mitigation over a pitching airfoil with active flow control. The objective is to inform actuator placement and timing to introduce control…
The point vortex model is an idealized model for describing the dynamics of many vortices with numerical efficiency, and has been shown to be powerful in modeling the dynamics of vortices in a superfluid. The model can be extended to…
This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…
Separated flows past complex geometries are modelled by discrete vortex techniques. The flows are assumed to be rotational and inviscid, and a new technique is described to determine the streamfunctions for linear shear profiles. The…
We introduce a new algorithmic framework for designing dynamic graph algorithms in minor-free graphs, by exploiting the structure of such graphs and a tool called vertex sparsification, which is a way to compress large graphs into small…
Network (or graph) sparsification compresses a graph by removing inessential edges. By reducing the data volume, it accelerates or even facilitates many downstream analyses. Still, the accuracy of many sparsification methods, with…
Graph neural networks have emerged as a powerful tool for learning spatiotemporal interactions. However, conventional approaches often rely on predefined graphs, which may obscure the precise relationships being modeled. Additionally,…
Graph drawings are useful tools for exploring the structure and dynamics of data that can be represented by pair-wise relationships among a set of objects. Typical real-world social, biological or technological networks exhibit high…
At the very heart of turbulent fluid flows are many interacting vortices that produce a chaotic and seemingly unpredictable velocity field. Gaining new insight into the complex motion of vortices and how they can lead to topological changes…
In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…
Numerical and experimental turbulence simulations are nowadays reaching the size of the so-called big data, thus requiring refined investigative tools for appropriate statistical analyses and data mining. We present a new approach based on…
Vortex is a central concept in the understanding of turbulent dynamics. Objective algorithms for the detection and extraction of vortex structures can facilitate the physical understanding of turbulence regeneration dynamics by enabling…