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Topological properties of physical systems play a crucial role in our understanding of nature, yet their experimental determination remains elusive. We show that the mean helicity, a dynamical invariant in ideal flows, quantitatively…
Classical particles driven through periodically modulated potential energy landscapes are predicted to follow a Devil's staircase hierarchy of commensurate trajectories depending on the orientation of the driving force. Recent experiments…
We describe a new method for computing coherent Lagrangian vortices in two-dimensional flows according to any of the following approaches: black-hole vortices [Haller & Beron-Vera, 2013], objective Eulerian Coherent Structures (OECSs)…
We use a simple yet Earth-like atmospheric model to propose a new framework for understanding the mathematics of blocking events. Analysing error growth rates along a very long model trajectory, we show that blockings are associated with…
Urban streets are hierarchically organized in the sense that a majority of streets are trivial, while a minority of streets is vital. This hierarchy can be simply, but elegantly, characterized by the 80/20 principle, i.e. 80 percent of…
We establish a deterministic technique to investigate transport moments of arbitrary order. The theory is applied to the analysis of different kinds of intermittent one-dimensional maps and the Lorentz gas with infinite horizon: the typical…
Lagrangian stochastic models are widely used to predict and analyze turbulent dispersion in complex environments, such as in various terrestrial and marine canopy flows. However, due to a lack of empirical data, it is still not understood…
We introduce the concept of a "transitory" dynamical system---one whose time-dependence is confined to a compact interval---and show how to quantify transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case.…
An ideal compressible fluid is considered, with an equilibrium density being a given function of coordinates due to presence of some static external forces. The slow flows in such system, which do not disturb the density, are investigated…
Many situations in physics, biology, and engineering consist of the transport of some physical quantity through a network of narrow channels. The ability of a network to transport such a quantity in every direction can be described by the…
We develop efficient algorithms for a fundamental network design problem arising in potential-based flow models, which are central to many energy transport networks (e.g., hydrogen and electricity). In contrast to classical network flow…
Predicting particle transport in complex flows is traditionally achieved by solving the Navier-Stokes equations. While various numerical and experimental methods exist, they typically require deep physical insights and incur high…
This paper presents a novel spatially consistent approach for modeling line-of-sight (LOS) paths in vehicular networks. We use stochastic geometry to model transmitters, obstacles, and receivers located in three parallel lines,…
Holographic functional methods are introduced as probes of discrete time-stepped maps that lead to chaotic behavior. The methods provide continuous time interpolation between the time steps, thereby revealing the maps to be…
In this paper we review and extend our earlier recent work on thermostated systems. A description of nano-biological systems by Markov chains in coordinate space in the strongly overdamped limit is presented. Characterization of the most…
A model for traffic flow in street networks or material flows in supply networks is presented, that takes into account the conservation of cars or materials and other significant features of traffic flows such as jam formation, spillovers,…
We propose dynamical optimal transport (OT) problems constrained in a parameterized probability subset. In application problems such as deep learning, the probability distribution is often generated by a parameterized mapping function. In…
This article revolves around shape and topology optimization, in the applicative context where the objective and constraint functionals depend on the solution to a physical boundary value problem posed on the optimized domain. We introduce…
Active flows are central to mixing and transport across living systems. While Newtonian fluids remain laminar, diffusive and predictable at the microscale, living fluids like dense bacterial suspensions can exhibit highly chaotic flows like…
To comprehend the hierarchical organization of large integrated systems, we introduce the hierarchical map equation, which reveals multilevel structures in networks. In this information-theoretic approach, we exploit the duality between…