We give an elementary proof of the convergence of the point vortex method (PVM) to a classical weak solution for the two-dimensional incompressible Euler equations with initial vorticity being a finite Radon measure of distinguished sign and the initial velocity of locally bounded energy. This includes the important example of vortex sheets, which exhibits the classical Kelvin-Helmholtz instabi...

Background The vortex ring formed in the left ventricle (LV) of the human heart during early diastolic inflow (corresponding to the Doppler E-wave) contains information about the normal and pathophysiologic aspects of diastole. Previous studies suggest that the volume of the vortex ring is an important characteristic of vortex ring formation. However, due to lack of quantitative methods, vortex...

The generation of initial or inflow synthetic turbulent velocity scalar fields reproducing statistical characteristics realistic turbulence is still a challenge. eddy method, previously introduced in the context conditions for large simulations, based on assumption that can be regarded as superposition coherent structures. In this paper, new type method proposed, where fundamental constructed b...

In this thesis we investigate the locomotion of fish and birds by applying both new and well known mathematical techniques. The two-dimensional model is first studied using Krasny’s vortex blob method, and then a new numerical method based on Wu’s theory1 is developed. To begin with, we will implement Krasny’s ideas for a couple of examples and then switch to the numerical implementation of the...

We study the vortex glass transition in disordered high temperature superconductors using Monte Carlo simulations. We use a random pinning model with strong point-correlated quenched disorder, a net applied magnetic field, long-range vortex interactions, and periodic boundary conditions. From a finite size scaling study of the helicity modulus, the rms current, and the resistivity, we obtain cr...

We report time and frequency domain studies of spin-torque-driven vortex self-oscillations at zero magnetic field. We observe two types of abrupt fluctuations in the frequency and amplitude, with very long random mean lifetimes 102 to 104 oscillation cycles . First, we observe fluctuations between two center frequencies separated by 10s of MHz that we identify with switching between quasiunifor...

We study the pinning dynamics of magnetic flux (vortex) lines in a disordered type-II superconductor. Using numerical simulations of a directed elastic line model, we extract the pinning time distributions of vortex line segments. We compare different model implementations for the disorder in the surrounding medium: discrete, localized pinning potential wells that are either attractive and repu...

The system of N -point vortices on R2 is considered under the hypothesis that vortex intensities are independent and identically distributed random variables with respect to a law P supported on (0, 1]. It is shown that, in the limit as N approaches∞, the 1-vortex distribution is a minimizer of the free energy functional and is associated to (some) solutions of the following non-linear Poisson ...