Related papers: Inserting Group Variables into Fluid Mechanics
We consider the motion of rigid bodies in a potential fluid subject to certain nonholonomic constraints and show that it is described by Euler--Poincar\'e--Suslov equations. In the 2-dimensional case, when the constraint is realized by a…
We consider the general formulation of nonabelian fluid dynamics based on symmetry considerations. We point out that, quite generally, this admits solitonic excitations which are the color analog of skyrmions. Some general properties of the…
Using Cartan's exterior calculus, we derive a coordinate-free formulation of the Euler equations. These equations are invariant under Galileian transformations, which constitute a global symmetry. With the introduction of an appropriate…
In 1966 V.Arnold suggested a group-theoretic approach to ideal hydrodynamics in which the motion of an inviscid incompressible fluid is described as the geodesic flow of the right-invariant $L^2$-metric on the group of volume-preserving…
In this article, I present recent methods for the numerical simulation of fluid dynamics and the associated computational algorithms. The goal of this article is to explain how to model an incompressible fluid, and how to write a computer…
Continuum mechanics can be formulated in the Lagrangian frame (addressing motion of individual continuum particles) or in the Eulerian frame (addressing evolution of fields in an inertial frame). There is a canonical Hamiltonian structure…
The two-dimensional ideal (Euler) fluids can be described by the classical fields of streamfunction, velocity and vorticity and, in an equivalent manner, by a model of discrete point-like vortices interacting in plane by a self-generated…
In 1991, Moore [20] raised a question about whether hydrodynamics is capable of performing computations. Similarly, in 2016, Tao [25] asked whether a mechanical system, including a fluid flow, can simulate a universal Turing machine. In…
Swimming involves a body's capability to navigate through a fluid by undergoing self-deformations. Typically, fluid dynamics are described by the Navier-Stokes equations, and when integrated with a swimming body, it results in a highly…
To better understand the hydrodynamic flow behavior in turbulence, Particle-Fluid flow have been studied using our Direct Numerical(DNS) based software DSM on MUSCL-QUICK and finite volume algorithm. The particle flow was studied using…
We present approaches for the study of fluid-structure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for…
In conventional fluid mechanics, the chemical composition and thermodynamic state of a fluid-solid interface are not considered when establishing velocity-field boundary conditions. As a consequence, fluid simulations are usually not able…
Living systems are chiral on multiple scales, from constituent biopolymers to large scale morphology, and their active mechanics is both driven by chiral components and serves to generate chiral morphologies. We describe the mechanics of…
The fate of small particles in turbulent flows depends strongly on the surrounding fluid's velocity gradient properties such as rotation and strain-rates. For non-inertial (fluid) particles, the Restricted Euler model provides a simple,…
We propose a new approach in Lagrangian formalism for studying the fluid dynamics on noncommutative space. Starting with the Poisson bracket for single particle, a map from canonical Lagrangian variables to Eulerian variables is constructed…
We discuss the role of the magnetic degrees of freedom of the gluon plasma in its viscosity. The main assumption is that motions of the magnetic component and of the rest of the plasma can be considered as independent. The magnetic…
The quark-gluon plasma, possibly created in ultrarelativistic heavy-ion collisions, is a strongly interacting many-body parton system. By comparison with strongly coupled electromagnetic plasmas (classical and non-relativistic) it is…
A quantum fluid dynamic control formulation is presented for optimally manipulating atomic and molecular systems. In quantum fluid dynamic the control quantum system is expressed in terms of the probability density and the quantum current.…
Quantum mechanical wave functions have phases. These phases either initial or acquired during time evolution usually do not enter the final expressions for observable physical quantities. Nevertheless in many cases the observable physical…
The relativistic fluid is a highly successful model used to describe the dynamics of many-particle systems moving at high velocities and/or in strong gravity. It takes as input physics from microscopic scales and yields as output…