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We propose a defiltering method of turbulent flow fields for Lagrangian particle tracking using machine learning techniques. Numerical simulation of Lagrangian particle tracking is commonly used in various fields. In general, practical…
We present a setup that enables to define in a concrete way a renormalization flow for the FK-percolation models from statistical physics (that are closely related to Ising and Potts models). In this setting that is applicable in any…
Driven Langevin processes have appeared in a variety of fields due to the relevance of natural phenomena having both deterministic and stochastic effects. The stochastic currents and fluxes in these systems provide a convenient set of…
Statistical tools are crucial for studying and modeling turbulent flows, where chaotic velocity fluctuations span a wide range of spatial and temporal scales. Advances in image velocimetry, especially in tracking-based methods, now allow…
Particle Image Velocimetry (PIV) systems are often limited in their ability to fully resolve the spatiotemporal fluctuations inherent in turbulent flows due to hardware constraints. In this study, we develop models based on Rapid Distortion…
Voltage fluctuations are common disturbances in power grids. Initially, it is necessary to selectively identify individual sources of voltage fluctuations to take actions to minimize the effects of voltage fluctuations. Selective…
This paper gives a geometric description of functional spaces related to Domain Decomposition techniques for computing solutions of Laplace and Helmholtz equations. Understanding the geometric structure of these spaces leads to algorithms…
We study mathematical and physical properties of a family of recently introduced, reduced-order approximate deconvolution models. We first show a connection between these models and the NS-Voigt model, and that NS-Voigt can be re-derived in…
This paper is a short guideline to the decomposition of a compressible velocity into vortical and compressible structures using standard flow solvers. In particular, this is a fast solution to get an idea of the compressible fields inside…
Exerting a nonequilibrium drive on an otherwise equilibrium Langevin process brings the dynamics out of equilibrium but can also speedup the approach to the Boltzmann steady-state. Transverse forces are a minimal framework to achieve…
It is understood that congestion in traffic can be interpreted in terms of the instability of the equation of dynamic motion. The evolution of a traffic system from an unstable or metastable state to a globally stable state bears a strong…
The goal of this paper is to unify the lookdown representation and the stochastic flow of bridges, which are two approaches to construct the $\Lambda$-Fleming-Viot process along with its genealogy. First we introduce the stochastic flow of…
We present a derivation of a stochastic model of Navier Stokes equations that relies on a decomposition of the velocity fields into a differentiable drift component and a time uncorrelated uncertainty random term. This type of decomposition…
Whenever an It\^o-Wentsel type of formula holds for composition of flows of a certain differential dynamics, there exists locally a decomposition of the corresponding flow according to complementary distributions (or foliations, in the case…
How can we learn the laws underlying the dynamics of stochastic systems when their trajectories are sampled sparsely in time? Existing methods either require temporally resolved high-frequency observations, or rely on geometric arguments…
Salmhofer [Commun. Math. Phys. 194, 249 (1998)] has recently developed a new renormalization group method for interacting Fermi systems, where the complete flow from the bare action of a microscopic model to the effective low-energy action,…
We show an improved parallel algorithm for decomposing an undirected unweighted graph into small diameter pieces with a small fraction of the edges in between. These decompositions form critical subroutines in a number of graph algorithms.…
Electrocardiographic imaging non-invasively reconstructs activation maps of the heart from temporal body surface potential maps by post-processing solutions of an inverse problem. Typically, activation times are detected through the maximal…
Let G be a topological compact group acting on some space Y. We study a decomposition of Y-indexed stochastic processes, based on the orthogonality relations between the characters of the irreducible representations of G. In the particular…
Model reduction of Markov processes is a basic problem in modeling state-transition systems. Motivated by the state aggregation approach rooted in control theory, we study the statistical state compression of a discrete-state Markov chain…