Related papers: Coarse-grained description of a passive scalar
A framework for deriving probabilistic data-driven closure models is proposed for coarse-grained numerical simulations of turbulence in statistically stationary state. The approach unites the ideal large-eddy simulation model and data…
We provide a concise PDE-based proof of anomalous diffusion in the Kraichan model -- a stochastic, white-in-time model of passive scalar turbulence. That is, we show an exponential rate of $L^2$ decay in expectation of a passive scalar…
In this work, we present a localized form of the dynamic eddy viscosity model for computationally efficient and accurate simulation of the turbulent flows governed by Euler equations. In our framework, we determine the dynamic model…
Simulating turbulent fluid flows is a computationally prohibitive task, as it requires the resolution of fine-scale structures and the capture of complex nonlinear interactions across multiple scales. This is particularly the case in direct…
In this paper, we exploit the gradient flow structure of continuous-time formulations of Bayesian inference in terms of their numerical time-stepping. We focus on two particular examples, namely, the continuous-time ensemble Kalman-Bucy…
Self-consistent closure theory for passive-scalar turbulence has been developed on the basis of the Hessian of the scalar field. As a primitive indicator of spatial structure of the scalar, we employ the Hessian into the core of the theory…
We present a computer-assisted approach to coarse-graining the evolutionary dynamics of a system of nonidentical oscillators coupled through a (fixed) network structure. The existence of a spectral gap for the coupling network graph…
Coarse-grained (CG) models are simplified representations of soft matter systems that are commonly employed to overcome size and time limitations in computational studies. Many approaches have been developed to construct and parametrise…
We establish, through coarse-grained computation, a connection between traditional, continuum numerical algorithms (initial value problems as well as fixed point algorithms) and atomistic simulations of the Larson model of micelle…
We describe in detail how to implement a coarse-grained hybrid Molecular Dynamics and Stochastic Rotation Dynamics simulation technique that captures the combined effects of Brownian and hydrodynamic forces in colloidal suspensions. The…
In the context of the recently developed "equation-free" approach to the computer-assisted analysis of complex systems, we illustrate the computation of coarsely self-similar solutions. Dynamic renormalization and fixed point algorithms for…
We consider the identification of large-scale linear and stable dynamic systems whose outputs may be the result of many correlated inputs. Hence, severe ill-conditioning may affect the estimation problem. This is a scenario often arising…
In this article, we demonstrate the use of artificial neural networks as optimal maps which are utilized for convolution and deconvolution of coarse-grained fields to account for sub-grid scale turbulence effects. We demonstrate that an…
We analyze multi-point correlation functions of a tracer in an incompressible flow at scales far exceeding the scale $L$ at which fluctuations are generated (quasi-equilibrium domain) and compare them with the correlation functions at…
A generalization to the Kraichnan gaussian, white noise in time model of turbulent velocity field is proposed. The generalization is designed to take into account the effects of stratification in the atmospheric boundary layer by…
We study coarse-grained (group-level) alignment dynamics of individual-based animal group models for {\it heterogeneous} populations consisting of informed (on preferred directions) and uninformed individuals. The orientation of each…
With the guidance offered by nonequilibrium statistical thermodynamics, simulation techniques are elevated from brute-force computer experiments to systematic tools for extracting complete, redundancy-free and consistent coarse grained…
High-dimensional recordings of dynamical processes are often characterized by a much smaller set of effective variables, evolving on low-dimensional manifolds. Identifying these latent dynamics requires solving two intertwined problems:…
Complex fluids exhibit structure on a wide range of length and time scales, and hierarchical approaches are necessary to investigate all facets of their often unusual properties. The study of idealized coarse-grained models at different…
We investigate the fixed points of a shell model for the turbulent advection of passive scalars introduced Jensen, Paladin and Vulpiani. The passive scalar field is driven by the velocity field of the popular GOY shell model. The scaling…