scholarly journals Winding of a Brownian particle around a point vortex

2019 ◽  
Vol 377 (2158) ◽  
pp. 20180347
Author(s):  
Huanyu Wen ◽  
Jean-Luc Thiffeault
Keyword(s):  
Numerical Simulations ◽  
Gamma Distribution ◽  
Theta Function ◽  
Vortex Dynamics ◽  
Brownian Particle ◽  
Point Vortex ◽  
Theme Issue ◽  
Drift Term ◽  
Inverse Gamma ◽  
Winding Angle

We derive the asymptotic winding law for a Brownian particle in the plane subjected to a tangential drift due to a point vortex. For winding around a point, the normalized winding angle converges to an inverse Gamma distribution. For winding around a disc, the angle converges to a distribution given by an elliptic theta function. For winding in an annulus, the winding angle is asymptotically Gaussian with a linear drift term. We validate our results with numerical simulations. This article is part of the theme issue ‘Topological and geometrical aspects of mass and vortex dynamics’.

scholarly journals Variance Adaptive Shrinkage (vash): Flexible Empirical Bayes estimation of variances

2016 ◽  
Author(s):  
Mengyin Lu ◽  
Matthew Stephens
Keyword(s):  
Gamma Distribution ◽  
Empirical Bayes ◽  
Variance Estimation ◽  
R Package ◽  
Bayes Estimation ◽  
Inverse Gamma Distribution ◽  
Inverse Gamma ◽  
Tissues Expression ◽  
Flexible Model ◽  
Better Than

AbstractMotivationWe consider the problem of estimating variances on a large number of “similar” units, when there are relatively few observations on each unit. This problem is important in genomics, for example, where it is often desired to estimate variances for thousands of genes (or some other genomic unit) from just a few measurements on each. A common approach to this problem is to use an Empirical Bayes (EB) method that assumes the variances among genes follow an inverse-gamma distribution. Here we describe a more flexible EB method, whose main assumption is that the distribution of the variances (or, as an alternative, the precisions) is unimodal.ResultsWe show that this more flexible assumption provides competitive performance with existing methods when the variances truly come from an inverse-gamma distribution, and can outperform them when the distribution of the variances is more complex. In analyses of several human gene expression datasets from the Genotype Tissues Expression (GTEx) consortium, we find that our more flexible model often fits the data appreciably better than the single inverse gamma distribution. At the same time we find that, for variance estimation, the differences between methods is often small, suggesting that the simpler methods will often suffice in practice.AvailabilityOur methods are implemented in an R package vashr available from http://github.com/mengyin/vashr.

Point vortex dynamics in a magnetized plasma

1994 ◽  
Author(s):  
Mitsuo Kono ◽  
Hideaki Shibahara ◽  
Kentaro Yabuki
Keyword(s):  
Vortex Dynamics ◽  
Point Vortex ◽  
Magnetized Plasma

Point vortex dynamics within a background vorticity patch

2001 ◽  
Vol 13 (3) ◽  
pp. 677-691 ◽  
Author(s):  
Dezhe Z. Jin ◽  
Daniel H. E. Dubin
Keyword(s):  
Vortex Dynamics ◽  
Point Vortex

scholarly journals Network-theoretic approach to sparsified discrete vortex dynamics

2015 ◽  
Vol 768 ◽  
pp. 549-571 ◽  
Author(s):  
Aditya G. Nair ◽  
Kunihiko Taira
Keyword(s):  
Vortex Dynamics ◽  
Point Vortex ◽  
Spectral Graph Theory ◽  
Theoretic Approach ◽  
Dynamics Model ◽  
Discrete Vortex ◽  
Sparse Graphs ◽  
Graph Representations ◽  
Vortex Interactions ◽  
Two Dimensional Flow

We examine discrete vortex dynamics in two-dimensional flow through a network-theoretic approach. The interaction of the vortices is represented with a graph, which allows the use of network-theoretic approaches to identify key vortex-to-vortex interactions. We employ sparsification techniques on these graph representations based on spectral theory to construct sparsified models and evaluate the dynamics of vortices in the sparsified set-up. Identification of vortex structures based on graph sparsification and sparse vortex dynamics is illustrated through an example of point-vortex clusters interacting amongst themselves. We also evaluate the performance of sparsification with increasing number of point vortices. The sparsified-dynamics model developed with spectral graph theory requires a reduced number of vortex-to-vortex interactions but agrees well with the full nonlinear dynamics. Furthermore, the sparsified model derived from the sparse graphs conserves the invariants of discrete vortex dynamics. We highlight the similarities and differences between the present sparsified-dynamics model and reduced-order models.

Sign in / Sign up

Export Citation Format

Share Document