Related papers: Lagrangian Descriptors with Uncertainty
We show that, for two-dimensional space-periodic incompressible flow, the solution can be evaluated numerically in Lagrangian coordinates with the same accuracy achieved in standard Eulerian spectral methods. This allows the determination…
The Eulerian-Lagrangian approach based on Large-Eddy Simulation (LES) is one of the most promising and viable numerical tools to study turbulent dispersed flows when the computational cost of Direct Numerical Simulation (DNS) becomes too…
A study of the relationship between Lagrangian statistics and flow topology in fluid turbulence is presented. The topology is characterized using the Weiss criterion that provides a simplified tool to partition the flow into topologically…
We introduce a method based on Gaussian process regression to identify discrete variational principles from observed solutions of a field theory. The method is based on the data-based identification of a discrete Lagrangian density. It is a…
The computation of Lagrangian coherent structures (LCS) has established itself as a prominent means to reveal significant geometric structures in time-dependent vector fields. Their characterization, however, requires the selection of a…
We consider issues associated with the Lagrangian characterisation of flow structures arising in aperiodically time-dependent vector fields that are only known on a finite time interval. A major motivation for the consideration of this…
We study the Lagrangian trajectories of statistically isotropic, homogeneous, and stationary divergence free spatiotemporal random vector fields. We design this advecting Eulerian velocity field such that it gets asymptotically rough and…
Time-varying vector fields produced by computational fluid dynamics simulations are often prohibitively large and pose challenges for accurate interactive analysis and exploration. To address these challenges, reduced Lagrangian…
This paper proposes a new stochastic model of traffic dynamics in Lagrangian coordinates. The source of uncertainty is heterogeneity in driving behavior, captured using driver-specific speed-spacing relations, i.e., parametric uncertainty.…
The equation for the fluid velocity gradient along a Lagrangian trajectory immediately follows from the Navier-Stokes equation. However, such an equation involves two terms that cannot be determined from the velocity gradient along the…
These lectures notes give an introduction to the fast developing area of research dealing with perturbative descriptions of the gravitational instability in an expanding universe. I just sketch the outlines of some proofs, and many…
Accurate trajectory prediction is critical for safe autonomous navigation in crowded environments. While many trajectory predictors output Gaussian distributions to represent the multi-modal distribution over future pedestrian positions,…
Learning and predicting the dynamics of physical systems requires a profound understanding of the underlying physical laws. Recent works on learning physical laws involve generalizing the equation discovery frameworks to the discovery of…
Recently, a Lagrangian description of superfluids attracted some interest from the fluid/gravity-correspondence viewpoint. In this respect, the work of Dubovksy et al. has proposed a new field theoretical description of fluids, which has…
A first principle explanation of the origin of intermittency and nonlinear structure formation in the Lagrangian velocity increments of a turbulent flow is presented in the context of a scale invariant analytical formalism that is being…
Mining discriminative features for graph data has attracted much attention in recent years due to its important role in constructing graph classifiers, generating graph indices, etc. Most measurement of interestingness of discriminative…
In probability density function (PDF) methods a transport equation is solved numerically to compute the time and space dependent probability distribution of several flow variables in a turbulent flow. The joint PDF of the velocity…
Phase space structures such as dividing surfaces, normally hyperbolic invariant manifolds, their stable and unstable manifolds have been an integral part of computing quantitative results such as transition fraction, stability erosion in…
We formulate a perturbative approximation to gravitational instability, based on Lagrangian hydrodynamics in Newtonian cosmology. We take account of `pressure' effect of fluid, which is kinematically caused by velocity dispersion, to aim…
Lagrangian descriptors (LDs) based on the arc length of orbits previously demonstrated their utility in delineating structures governing the dynamics. Recently, a chaos indicator based on the second derivatives of the LDs, referred to as…