Related papers: Probabilistic representation of helicity in viscou…
In this thesis we study field theoretic viewpoints on certain fluid mechanical phenomena. In the Higgs mechanism, the weak gauge bosons acquire masses by interacting with a scalar field, leading to a vector boson mass matrix. On the other…
A visualization of three-dimensional incompressible flows by divergence-free quasi-two-dimensional projections of velocity field on three coordinate planes is proposed. It is argued that such divergence-free projections satisfying all the…
Recent numerical simulations showed that the mean flow is generated in inhomogeneous turbulence of an incompressible fluid accompanied with helicity and system rotation. In order to investigate the mechanism of this phenomenon, we carry out…
Using fluctuating hydrodynamics we describe the slow build-up of long range spatial correlations in a freely evolving fluid of inelastic hard spheres. In the incompressible limit, the behavior of spatial velocity correlations (including…
We use confocal microscopy to directly visualize the spatial fluctuations in fluid flow through a three-dimensional porous medium. We find that the velocity magnitudes and the velocity components both along and transverse to the imposed…
A new microscopic formula for the viscosity of liquids and solids is derived rigorously from a first-principles (microscopically reversible) Hamiltonian for particle-bath atomistic motion. The derivation is done within the framework of…
Assume that a stochastic processes can be approximated, when some scale parameter gets large, by a fluid limit (also called "mean field limit", or "hydrodynamic limit"). A common practice, often called the "fixed point approximation"…
Viscous hydrodynamics gives a satisfactory description of the transverse momentum spectra, of the elliptic and triangular flow, and of the femtoscopic correlations for particles produced in relativistic heavy-ion collisions. On general…
Helicity, a topological degree that measures the winding and linking of vortex lines, is preserved by ideal (barotropic) fluid dynamics. In the context of the Hamiltonian description, the helicity is a Casimir invariant characterizing a…
The energy of the stochastic magnetic field is bounded from below by a topological quantity expressing the degree of linkage of the field lines. When the bound is saturated one can assume that the storage of a certain magnetic energy…
This paper presents a streamfunction-vorticity formulation for the Navier--Stokes and Euler equations on general surfaces. Notably, this includes non-simply connected surfaces, on which the harmonic components of the velocity field play a…
In the present paper we study the fast rotation limit for viscous incompressible fluids with variable density, whose motion is influenced by the Coriolis force. We restrict our analysis to two dimensional flows. In the case when the initial…
It is shown that the incompressible Navier-Stokes equation can be derived from an infinite dimensional mean-field stochastic differential equation.
In this paper we have continued the calculations made recently concerning he generalization of the minimal coupling prescription. We have obtained the Navier-Stokes equation for the charged fluid embedded into an electromagnetic field. We…
In this paper a rigorous proof of the mean field limit for a pedestrian flow model in two dimensions is given by using a probabilistic method. The model under investigation is an interacting particle system coupled to the eikonal equation…
We prove existence and regularity of the stochastic flows used in the stochastic Lagrangian formulation of the incompressible Navier-Stokes equations (with periodic boundary conditions), and consequently obtain a $\holderspace{k}{\alpha}$…
Blood flow in arterial systems can be described by the three-dimensional Navier-Stokes equations within a time-dependent spatial domain that accounts for the elasticity of the arterial walls. In this article blood is treated as an…
We derive the vorticity equation for an incompressible fluid on a 2-dimensional surface with arbitrary topology embedded in 3-dimensional Euclidean space by using a tailored Clebsch parametrization of the flow. In the inviscid limit, we…
We derive a formula for the entropy of two dimensional incompressible inviscid flow, by determining the volume of the space of vorticity distributions with fixed values for the moments Q_k= \int_w(x)^k d^2 x. This space is approximated by a…
Viscous streaming has emerged as an effective method to transport, trap, and cluster inertial particles in a fluid. Previous work has shown that this transport is well described by the Maxey-Riley equation augmented with a term representing…