Related papers: Stochastically-constrained Koiter shell models
The Navier-Stokes-Voigt (NSV) model of viscoelastic incompressible fluid has been recently proposed as a regularization of the 3D Navier-Stokes equations for the purpose of direct numerical simulations. In this work we investigate its…
Advanced measurement techniques and high performance computing have made large data sets available for a wide range of turbulent flows that arise in engineering applications. Drawing on this abundance of data, dynamical models can be…
Using rigorous constitutive linearization of second variation introduced in [6] we study weak stability of homogeneous deformation of the axially compressed circular cylindrical shell, regarded as a 3-dimensional hyperelastic body. We show…
We consider a microscopic model of $n$ identical axis-symmetric rigid Brownian particles suspended in a Stokes flow. We rigorously derive in the homogenization limit of many small particles a classical formula for the viscoelastic stress…
In this article, we derive a mathematical model for a shell (i.e. a thin elastic body) bonded to an elastic foundation by modifying Koiter's linear shell equations. We prove the existence and the uniqueness of solutions, and we explicitly…
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…
In the "stochastic $\delta N$ formalism", the statistics of the inflationary density perturbation are obtained from the first passage distribution of a stochastic process. We develop a general framework in which to evaluate the rare tail of…
We study nonlinear wave equations perturbed by transport noise acting either on the displacement or on the velocity. Such noise models random advection and, under suitable scaling of space covariance, may generate an effective dissipative…
Our work is part of the close link between continuous-time dissipative dynamical systems and optimization algorithms, and more precisely here, in the stochastic setting. We aim to study stochastic convex minimization problems through the…
Starting from a three-dimensional model based on the Ciarlet-Geymonat energy, we derive nonlinear shell models within the classical elasticity theory of compressible isotropic materials. The Neo-Hookean term involving the norm of the…
In this paper we linearise the recently introduced geometrically nonlinear constrained Cosserat-shell model. In the framework of the linear constrained Cosserat-shell model, we provide a comparison of our linear models with the classical…
We analyze a system of PDEs governing the interaction between two compressible mutually noninteracting fluids and a shell of Koiter type encompassing a time dependent 3D domain filled by the fluids. The dynamics of the fluids is modelled by…
A stochastic data-driven reduced-order model applicable to a wide range of turbulent natural and engineering flows is presented. Combining ideas from Koopman theory and spectral model order reduction, the stochastic low-dimensional inflated…
We consider stochastic inviscid dyadic models with energy-preserving noise. It is shown that the models admit weak solutions which are unique in law. Under a certain scaling limit of the noise, the stochastic models converge weakly to a…
In this paper we derive, by two$-$scale convergence, periodically wrinked shell models starting from three dimensional linear elasticity, depending of the behaviour of the small parameter $\varepsilon>0$ and $p>1$, differents theories…
We consider the stochastic nonlinear Schr\"odinger equation driven by linear multiplicative noise in the mass-supercritical case. Given arbitrary $K$ solitary waves with distinct speeds, we construct stochastic multi-solitons pathwisely in…
This paper introduces a novel mathematical framework for examining the regularity and energy dissipation properties of solutions to the stochastic Navier-Stokes equations. By integrating Sobolev-Besov hybrid spaces, fractional differential…
We develop a computational model to study the interaction of a fluid with a poroelastic material. The coupling of Stokes and Biot equations represents a prototype problem for these phenomena, which feature multiple facets. On one hand it…
We study the coupling of a viscoelastic deformation governed by a Kelvin-Voigt model at equilibrium, based on the concept of second-grade nonsimple materials, with a plastic deformation due to volumetric swelling, described via a…
Stochastic models for pore collapse in granular materials are developed. First, a general fluctuating stress-strain relation for a plastic flow rule is derived. The fluctuations account for non-associativity in plastic deformations…