2,228 research outputs found
Using global interpolation to evaluate the Biot-Savart integral for deformable elliptical Gaussian vortex elements
This paper introduces a new method for approximating the Biot-Savart integral for elliptical Gaussian functions using high-order interpolation and compares it to an existing method based on small aspect ratio asymptotics. The new evaluation technique uses polynomials to approximate the kernel corresponding to the integral representation of the streamfunction. We determine the polynomial coefficients by interpolating precomputed values from look-up tables over a wide range of aspect ratios. When implemented in a full nonlinear vortex method, we find that the new technique is almost three times faster and unlike the asymptotic method, provides uniform accuracy over the full range of aspect ratios. As a proof-of-concept for large scale computations, we use the new technique to calculate inviscid axisymmetrization and filamentation of a two-dimensional elliptical fluid vortex. We compare our results with those from a pseudo-spectral computation and from electron vortex experiments, and find good agreement between the three approaches
Quasi-steady Monopole and Tripole Attractors in Relaxing Vortices
Using fully nonlinear simulations of the two-dimensional Navier–Stokes equations at large Reynolds number (Re), we bracket a threshold amplitude above which a perturbed Gaussian monopole will relax to a quasi-steady, rotating tripole, and below which will relax to an axisymmetric monopole. The resulting quasi-steady structures are robust to small perturbations. We propose a means of measuring the decay rate of disturbances to asymptotic vortical structures wherein streamlines and lines of constant vorticity correspond in some rotating or translating frame. These experiments support the hypothesis that small or moderate deviations from asymptotic structures decay through inviscid and viscous mixing
Slippage and Migration in Taylor-Couette Flow of a Model for Dilute Wormlike Micellar Solutions
Submitted to J. Non-Newt Fluid Mechanics, June 2005In this paper we explore a model, most appropriate for dilute or semi-dilute worm-like micellar solutions, in an axisymmetric circular Taylor-Couette geometry. This study is a natural continuation of earlier work on rectilinear shear flows. The model, based on a bead-spring microstructure with nonaffine motion, reproduces the pronounced plateau in the stress strain-rate flow curve as observed in laboratory measurements of steady shearing flows. We also carry out a linear stability analysis of the computed steady state solutions. The results show shear-banding in the form of sharp changes in velocity gradients, spatial variations in number density, and in
alignment or stretching of the micelles. The velocity profiles obtained in numerical
solutions show strong qualitative agreement with those of laboratory experiments.NSF Collaborative Research Projec
Internal Anisotropy of Collision Cascades
We investigate the internal anisotropy of collision cascades arising from the
branching structure. We show that the global fractal dimension cannot give an
adequate description of the geometrical structure of cascades because it is
insensitive to the internal anisotropy. In order to give a more elaborate
description we introduce an angular correlation function, which takes into
account the direction of the local growth of the branches of the cascades. It
is demonstrated that the angular correlation function gives a quantitative
description of the directionality and the interrelation of branches. The power
law decay of the angular correlation is evidenced and characterized by an
exponent and an angular correlation length different from the radius of
gyration. It is demonstrated that the overlapping of subcascades has a strong
effect on the angular correlation.Comment: RevteX, 8 pages, 6 .eps figures include
Dark-in-Bright Solitons in Bose-Einstein Condensates with Attractive Interactions
We demonstrate a possibility to generate localized states in effectively
one-dimensional Bose-Einstein condensates with a negative scattering length in
the form of a dark soliton in the presence of an optical lattice (OL) and/or a
parabolic magnetic trap. We connect such structures with twisted localized
modes (TLMs) that were previously found in the discrete nonlinear
Schr{\"o}dinger equation. Families of these structures are found as functions
of the OL strength, tightness of the magnetic trap, and chemical potential, and
their stability regions are identified. Stable bound states of two TLMs are
also found. In the case when the TLMs are unstable, their evolution is
investigated by means of direct simulations, demonstrating that they transform
into large-amplitude fundamental solitons. An analytical approach is also
developed, showing that two or several fundamental solitons, with the phase
shift between adjacent ones, may form stable bound states, with
parameters quite close to those of the TLMs revealed by simulations. TLM
structures are found numerically and explained analytically also in the case
when the OL is absent, the condensate being confined only by the magnetic trap.Comment: 13 pages, 7 figures, New Journal of Physics (in press
Cosmological Implications of Dynamical Supersymmetry Breaking
We provide a taxonomy of dynamical supersymmetry breaking theories, and
discuss the cosmological implications of the various types of models. Models in
which supersymmetry breaking is produced by chiral superfields which only have
interactions of gravitational strength (\eg\ string theory moduli) are
inconsistent with standard big bang nucleosynthesis unless the gravitino mass
is greater than \CO(3) \times 10^4 GeV. This problem cannot be solved by
inflation. Models in which supersymmetry is dynamically broken by
renormalizable interactions in flat space have no such cosmological problems.
Supersymmetry can be broken either in a hidden or the visible sector. However
hidden sector models suffer from several naturalness problems and have
difficulties in producing an acceptably large gluino mass.Comment: 24 pages (uses harvmac) UCSD/PTH 93-26, RU-3
- …