Related papers: Bayesian Inference for Fluid Dynamics: A Case Stud…

The growing interest in creating a parametric representation of liquid sloshing inside a container stems from its practical applications in modern engineering systems. The resonant excitation, on the other hand, can cause unstable and…

In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind…

We derive stochastically-constrained Koiter shell models in line with the SALT (Stochastic Advection by Lie Transport) approach introduced by Holm [Proc. A. 471 (2015)]. First, we deduce the stochastic partial differential equations for the…

Smoothing in state-space models amounts to computing the conditional distribution of the latent state trajectory, given observations, or expectations of functionals of the state trajectory with respect to this distributions. For models that…

A particle-water discrete element based approach to describe water movement in partially saturated granular media is presented and tested. Water potential is governed by both capillary bridges, dominant at low saturations, and the pressure…

A stochastic wavevector approach is formulated to accurately represent compressible turbulence subject to rapid deformations. This approach is inspired by the incompressible particle representation model of Kassinos (1995) and preserves the…

In many applications, it is important to reconstruct a fluid flow field, or some other high-dimensional state, from limited measurements and limited data. In this work, we propose a shallow neural network-based learning methodology for such…

Smoothed particle hydrodynamics (SPH) is typically used for barotropic fluids, where the pressure depends only on the local mass density. Here, we show how to incorporate the entropy into the SPH, so that the pressure can also depend on the…

Originally introduced to describe a transition region in stars, the magnetic rotating shallow water (MRSW) model is now used in many solar physics and geophysical applications. Derived from the 3-D incompressible magnetohydrodynamic system,…

This paper introduces an energy-preserving stochastic model for studying wave effects on currents in the ocean mixing layer. The model is called stochastic forcing by Lie transport (SFLT). The SFLT model is derived here from a stochastic…

Nonlinear stochastic motion presents significant challenges for Bayesian particle tracking. To address this challenge, this paper proposes a framework to construct an invertible transformation that maps the nonlinear state-space model (SSM)…

Multi-color Stochastic Rotation Dynamics (SRDmc) has been introduced by Inoue et al. as a particle based simulation method to study the flow of emulsion droplets in non-wetting microchannels. In this work, we extend the multi-color method…

Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit…

The purpose of this paper is to examine the Lagrangian stochastic modeling of the fluid velocity seen by inertial particles in a nonhomogeneous turbulent flow. A new Langevin-type model, compatible with the transport equation of the drift…

We model filtration of a feed solution, containing both small and large foulant particles, by a membrane filter. The membrane interior is modeled as a network of pores, allowing for the simultaneous adsorption of small particles and sieving…

In this tutorial we consider the non-linear Bayesian filtering of static parameters in a time-dependent model. We outline the theoretical background and discuss appropriate solvers. We focus on particle-based filters and present Sequential…

We consider the problem of estimating a variable number of parameters with a dynamic nature. A familiar example is finding the position of moving targets using sensor array observations. The problem is challenging in cases where either the…

Filtering and smoothing algorithms for linear discrete-time state-space models with skew-t-distributed measurement noise are proposed. The algorithms use a variational Bayes based posterior approximation with coupled location and skewness…

Particle filters are computational techniques for estimating the state of dynamical systems by integrating observational data with model predictions. This work introduces a class of Localized Particle Filters (LPFs) that exploit spatial…

In the present study, we propose a modified version of the Nonlinear Shallow Water Equations (Saint-Venant or NSWE) for irrotational surface waves in the case when the bottom undergoes some significant variations in space and time. The…