Related papers: Stochastic Geometric Mechanics for Fluid Dynamics
Stochastic thermodynamics lays down a broad framework to revisit the venerable concepts of heat, work and entropy production for individual stochastic trajectories of mesoscopic systems. Remarkably, this approach, relying on stochastic…
We consider the line, surface and volume elements of fluid in stationary isotropic incompressible stochastic flow in $d$-dimensional space and investigate the long-time evolution of their statistic properties. We report the discovery of a…
Three dimensional unsteady flow of fluids in the Lagrangian description is considered as an autonomous dynamical system in four dimensions. The condition for the existence of a symplectic structure on the extended space is the frozen field…
Stochastically evolving geometric systems are studied in shape analysis and computational anatomy for modelling random evolutions of human organ shapes. The notion of geodesic paths between shapes is central to shape analysis and has a…
Fluidisation is the process by which the weight of a bed of particles is supported by a gas flow passing through it from below. When fluidised materials flow down an incline, the dynamics of the motion differ from their non-fluidised…
The state-of-the-art theoretical formalism for a covariant description of non-Gaussian fluctuation dynamics in relativistic fluids is discussed.
The building of mathematical and computer models of cities has a long history. The core elements are models of flows (spatial interaction) and the dynamics of structural evolution. In this article, we develop a stochastic model of urban…
A unified continuum-mechanical theory has been until now lacking for granular media, some believe it could not exist. Derived employing the hydrodynamic approach, GSH is such a theory, though as yet a qualitative one. The behavior being…
We apply the stochastic variational method to the action of the ideal fluid and showed that the Navier-Stokes equation is derived. In this variational method, the effect of dissipation is realized as the direct consequence of the…
Generative models have demonstrated remarkable success in domains such as text, image, and video synthesis. In this work, we explore the application of generative models to fluid dynamics, specifically for turbulence simulation, where…
Quadratic flows have the unique property of uniform strain and are commonly used in turbulence modeling and hydrodynamic analysis. While previous application focused on two-dimensional homogeneous fluid, this study examines the geometric…
The two most commonly used methods to model the behaviour of granular flows are discrete element and continuum mechanics simulations. These approaches concentrate on the deterministic description of particle or bulk material motion. Unlike…
The {\em hydrodynamic} approach to a continuum mechanical description of granular behavior is reviewed and elucidated. By considering energy and momentum conservation simultaneously, the general formalism of {\em hydrodynamics} provides a…
Stochastic Structural Stability Theory (SSST) provides an autonomous, deterministic, nonlinear dynamical system for evolving the statistical mean state of a turbulent system. In this work SSST is applied to the problem of understanding the…
Stochastic gradient descent with momentum (SGDM) methods have become fundamental optimization tools in machine learning, combining the computational efficiency of stochastic gradients with the acceleration benefits of momentum. Despite…
We introduce a finite-volume numerical scheme for solving stochastic gradient-flow equations. Such equations are of crucial importance within the framework of fluctuating hydrodynamics and dynamic density functional theory. Our proposed…
The theory of slow invariant manifolds (SIMs) is the foundation of various model-order reduction techniques for dissipative dynamical systems with multiple time-scales, e.g. in chemical kinetic models. The construction of SIMs and many…
We develop a Lie group geometric framework for the motion of fluids with permeable boundaries that extends Arnold's geometric description of fluid in closed domains. Our setting is based on the classical Hamilton principle applied to fluid…
These expository notes address certain stationary and ergodic properties of the equations of fluid dynamics subject to a spatially degenerate (i.e. frequency localized), white in time gaussian forcing. In order to provide an accessible…
Stochastic dynamics is generated by a matrix of transition probabilities. Certain eigenvectors of this matrix provide observables, and when these are plotted in the appropriate multi-dimensional space the phases (in the sense of phase…