Alexander Zaitzeff

Alexander Zaitzeff, Selim Esedoglu, Krishna Garikipati

We present careful numerical convergence studies, using parameterized curves to reach very high resolutions in two dimensions, of a level set method for multiphase curvature motion known as the Voronoi implicit interface method. Our tests demonstrate that in the unequal, additive surface tension case, the Voronoi implicit interface method does not converge to the desired limit. We then present a variant that maintains the spirit of the original algorithm, and appears to fix the non-convergence. As a bonus, the new variant extends the Voronoi implicit interface method to unequal mobilities.

Alexander Zaitzeff, Samuel Blazek

We place geo-targeted advertisements on Facebook to encourage users to fill out an online survey, following a process known as river sampling. We discovered a large number and variety of users also came to our survey through snowball sampling, including shared social media posts and other word-of-mouth referral methods. In this article, we analyze the differences between the respondents from river and snowball sampling. We present evidence that the respondents obtained by snowball sampling are more likely to complete the survey and contain a higher fraction of new users and women than those obtained by river sampling. Additionally, the evidence indicates that users from snowball sampling give shorter responses and take less time on the survey than users from river sampling. We hope these findings provide insight for other researchers who incorporate social media strategies when fielding surveys.