Related papers: 2D Smagorinsky type large eddy models as limits of…
We derive high-dimensional scaling limits and fluctuations for the online least-squares Stochastic Gradient Descent (SGD) algorithm by taking the properties of the data generating model explicitly into consideration. Our approach treats the…
For high-fidelity predictions of turbulent flows in complex practical engineering problems, the Wall-Modeled (WM) Large-Eddy Simulation (LES) has aroused great interest. In the present study, we prove that the conventional Wall-Stress…
We present a high-order implicit large eddy simulation (ILES) approach for simulating flows at the nearly incompressible regime. Our methodology based on utilization of a nodal discontinuous Galerkin (DG) discretization of the Boltzmann…
We demonstrate how to model the toppling activity in avalanching systems by stochastic differential equations (SDEs). The theory is developed as a generalization of the classical mean field approach to sandpile dynamics by formulating it as…
Understanding the properties of the stochastic phase field models is crucial to model processes in several practical applications, such as soft matters and phase separation in random environments. To describe such random evolution, this…
A previously developed modeling procedure for large eddy simulations (LESs) is extended to allow physical space implementations for inhomogeneous flows. The method is inspired by the well-established theoretical analyses and numerical…
The scaled particle theory is applied to a description of thermodynamic properties of one-dimensional hard rod fluid in disordered porous media. To this end, we extended the SPT2 approach, which had been developed previously. Analytical…
In this work we first prove the existence and uniqueness of a strong solution to stochastic GOY model of turbulence with a small multiplicative noise. Then using the weak convergence approach, Laplace principle for so- lutions of the…
We study stochastic differential equations (SDEs) of McKean-Vlasov type with distribution dependent drifts and driven by pure jump L\'{e}vy processes. We prove a uniform in time propagation of chaos result, providing quantitative bounds on…
This paper presents an in-depth analysis of a novel subgrid-scale stress model proposed in 2022, which utilizes the rotational part of the velocity gradient as the velocity scale for computing eddy viscosity. This study investigates the…
We show that the addition of a suitable Stratonovich noise prevents the explosion for ODEs with drifts of super-linear growth, in dimension $d\ge 2$. We also show the existence of an invariant measure and the geometric ergodicity for the…
This study develops invariance-embedded machine learning sub-grid-scale (SGS) stress models admitting turbulence kinetic energy (TKE) backscatter towards more accurate large eddy simulation (LES) of meso-scale turbulent hurricane boundary…
Using a multi-scaled, chaotic flow known as the KS model of turbulence, we investigate the dependence of Lyapunov exponents on various characteristics of the flow. We show that the KS model yields a power law relation between the Reynolds…
The paper is devoted to the open problem of regularization by noise of 3D Navier-Stokes equations. Opposite to several attempts made with additive noise which remained inconclusive, we show here that a suitable multiplicative noise of…
In dilute turbulent particle-laden flows, such as atmospheric dispersion of pollutants or virus particles, the dynamics of tracer-like to low inertial particles are significantly altered by the fluctuating motion of the carrier fluid phase.…
A new methodology based on energy flux similarity is suggested in this paper for large eddy simulation (LES) of transitional and turbulent flows. Existing knowledge reveals that the energy cascade generally exists in transitional and…
Large eddy simulations (LES) of a lattice Boltzmann magnetohydrodynamic (LB-MHD) model are performed for the unstable magnetized Kelvin-Helmholtz jet instability. This algorithm is an extension of Ansumali et. al. (2004) to MHD in which one…
The significance of small-scale forcing of particles on the carrier two-dimensional turbulent flow has been shown to influence the spectral scaling properties of the carrier fluid. We investigate possible consequences of such two-way…
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…
We propose new limiting dynamics for stochastic gradient descent in the small learning rate regime called stochastic modified flows. These SDEs are driven by a cylindrical Brownian motion and improve the so-called stochastic modified…