Related papers: Objective barriers to the transport of dynamically…
We consider Lagrangian systems in the limit of infinitely many particles. It is shown that the corresponding discrete action functionals Gamma-converge to a continuum action functional acting on probability measures of particle…
We analyze large-scale patterns in three-dimensional turbulent convection in a horizontally extended square convection cell by Lagrangian particle trajectories calculated in direct numerical simulations. A simulation run at a Prandtl number…
Cross-jet transport of passive scalars in a kinematic model of the meandering laminar two-dimensional incompressible flow which is known to produce chaotic mixing is studied. We develop a method for detecting barriers to cross-jet transport…
We consider the relationship between Eulerian modal decompositions and Lagrangian coherent structures (LCSs). The model sensitivity framework developed by Kasz\'as and Haller (2020) is used to express data-driven modal representations of…
In probability density function (PDF) methods of turbulent flows, the joint PDF of several flow variables is computed by numerically integrating a system of stochastic differential equations for Lagrangian particles. A mathematically exact…
The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and…
Flexible barriers are increasingly used for the protection from debris flow in mountainous terrain due to their low cost and environmental impact. However, a numerical tool for rational design of such structures is still missing. In this…
In the Eulerian approach, the motion of an incompressible fluid is usually described by the velocity field which is given by the Navier--Stokes system. The velocity field generates a flow in the space of volume-preserving diffeomorphisms.…
It was shown in \cite{bloch2000optimal} that an optimal control formulation for incompressible ideal fluid flow yields Euler's equations. In this paper, we consider a variational obstacle-avoidance formulation for incompressible ideal flows…
We establish the existence and uniqueness of some smooth accelerating transonic flows governed by the three dimensional steady compressible Euler equations with an external force in cylinders with arbitrary cross sections, which include…
We examine the linear behavior of three-dimensional Lagrangian displacements in a stratified, shearing background. The isentropic and iso-rotation surfaces of the equilibrium flow are assumed to be axisymmetric, but otherwise fully…
Recent developments in dynamical systems theory have revealed long-lived and coherent Lagrangian (i.e., material) eddies in incompressible, satellite-derived surface ocean velocity fields. Paradoxically, observed drifting buoys and floating…
Motions of continuous media presenting singularities are associated with phenomena involving shocks, interfaces or material surfaces. The equations representing evolutions of these media are irregular through geometrical manifolds. A unique…
The paper deals with a family of evolution problems arising in the physical modeling of small amplitude acoustic phenomena occurring in a fluid, bounded by a surface of extended reaction. They are all derived in a Lagrangian framework. We…
Ocean flows are routinely inferred from low-resolution satellite altimetry measurements of sea surface height assuming a geostrophic balance. Recent nonlinear dynamical systems techniques have revealed that surface currents derived from…
Dynamical systems often exhibit the emergence of long-lived coherent sets, which are regions in state space that keep their geometric integrity to a high extent and thus play an important role in transport. In this article, we provide a…
In this paper, we present a novel interface-driven adaptive variational procedure using a fully Eulerian description of fluid-structure interaction. The proposed fully-Eulerian procedure involves a fixed background unstructured mesh on…
A novel smooth immersed boundary method (IBM) based on a direct-forcing formulation is proposed to simulate incompressible dense particle-laden flows. This IBM relies on a regularization of the transfer function between the Eulerian grid…
Active fluids, such as cytoskeletal filaments, bacterial colonies and epithelial cell layers, exhibit distinctive orientational coherence, often characterized by nematic order and topological defects. By contrast, little is known about…
This chapter reviews the differential geometry-based solvation and electrolyte transport for biomolecular solvation that have been developed over the past decade. A key component of these methods is the differential geometry of surfaces…