Related papers: Uncertain Transport in Unsteady Flows
In this paper we study the problem of computing the effective diffusivity for a particle moving in chaotic and stochastic flows. In addition we numerically investigate the residual diffusion phenomenon in chaotic advection. The residual…
We give an algorithmic introduction to Lagrangian coherent structures (LCSs) using a newly developed computational engine, LCS Tool. LCSs are most repelling, attracting and shearing material lines that form the centerpieces of observed…
Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…
We develop a variational principle that extends the notion of a shearless transport barrier from steady to general unsteady two-dimensional flows and maps defined over a finite time interval. This principle reveals that hyperbolic…
The blooming diffusion probabilistic models (DPMs) have garnered significant interest due to their impressive performance and the elegant inspiration they draw from physics. While earlier DPMs relied upon the Markovian assumption, recent…
This paper compares the advantages, limitations, and computational considerations of using Finite-Time Lyapunov Exponents (FTLEs) and Lagrangian Descriptors (LDs) as tools for identifying barriers and mechanisms of fluid transport in…
A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of Lagrangian data is presented. Our approach partitions state space into pairs of coherent sets, which are sets of…
Using the Lagrangian transport of momentum, the Reynolds stress can be expressed in terms of basic turbulence parameters. The Reynolds stress gradient represents the lateral transport of stream-wise momentum, balanced by the u2 transport,…
A deterministic multi-scale dynamical system is introduced and discussed as prototype model for relative dispersion in stationary, homogeneous and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and…
We develop a new quantifier for forward time uncertainty for trajectories that are solutions of models generated from data sets. Our uncertainty quantifier is defined on the phase space in which the trajectories evolve and we show that it…
Understanding, quantifying and controlling transport and mixing processes are central in the study of fluid flows. Many different Lagrangian approaches have been proposed for detecting organizing flow structures that determine material…
We consider kinetic vehicular traffic flow models of BGK type. Considering different spatial and temporal scales, those models allow to derive a hierarchy of traffic models including a hydrodynamic description. In this paper, the kinetic…
We consider viscous two-dimensional steady flows of incompressible fluids past doubly periodic arrays of solid obstacles. In a class of such flows, the autocorrelations for the Lagrangian observables decay in accordance with the power law,…
Lagrangian transport structures for three-dimensional and time-dependent fluid flows are of great interest in numerous applications, particularly for geophysical or oceanic flows. In such flows, chaotic transport and mixing can play…
In recent years, research and development in nanoscale science and technology have grown significantly, with electrical transport playing a key role. A natural challenge for its description is to shed light on anomalous behaviours observed…
Lagrangian data assimilation exploits the trajectories of moving tracers as observations to recover the underlying flow field. One major challenge in Lagrangian data assimilation is the intrinsic nonlinearity that impedes using exact…
The manipulation of a collection of fluid particles in a low Reynolds number environment has several important applications. As we demonstrate in this paper, this manipulation problem is related to the scientific question of how fluid flow…
Our understanding of the material organization of complex fluid flows has recently benefited from mathematical developments in the theory of objective coherent structures. These methods have provided a wealth of approaches that identify…
This work presents an analytical investigation of anomalous diffusion and turbulence in a dusty plasma monolayer, where energy transport across scales leads to the spontaneous formation of spatially disordered patterns. Many-body…
Stochastic parametrisations of the interactions among disparate scales of motion in fluid convection are often used for estimating prediction uncertainty, which can arise due to inadequate model resolution, or incomplete observations,…