Self-similar solutions of the localized induction approximation: singularity formation

Self-similar Solutions of the Localized Induction Approximation: Singularity Formation

Renewal of Singularity Sets of Statistically Self-similar Measures

This paper investigates new properties concerning the multifractal structure of a class of statistically self-similar measures. These measures include the well-known Mandelbrot multiplicative cascades, sometimes called independent random cascades. We evaluate the scale at which the multifractal structure of these measures becomes discernible. The value of this scale is obtained through what we ...

Quasi-static solutions for quantum vortex motion under the localized induction approximation

The motion of a quantum vortex is considered in the context of the localized induction approximation (LIA). In this context, the instantaneous vortex velocity is proportional to the local curvature and is parallel to the vector which is a linear combination of the local binormal and the principal normal to the vortex line. This implies that the quantum vortex shrinks, which is in contrast to th...

Fast Approximation of Self-Similar Network Traffic

Recent network traffic studies argue that network arrival processes are much more faithfully modeled using statistically self-similarprocesses instead of traditional Poisson processes [LTWW94a, PF94]. One difficulty in dealing with selfsimilar models is how to efficiently synthesize traces (sample paths) corresponding to self-similar traffic. We present a fast Fourier transform method for synth...

A Numerical Study of the Self-Similar Solutions of the Schrödinger Map

We present a numerical study of the self-similar solutions of the Localized Induction Approximation of a vortex filament. These self-similar solutions, which constitute a one-parameter family, develop a singularity at finite time. We study a number of boundary conditions that allow us reproduce the mechanism of singularity formation. Some related questions are also considered.