Energy spectra of vortex distributions in two-dimensional quantum turbulence

We theoretically explore key concepts of two-dimensional turbulence in a homogeneous compressible superfluid described by a dissipative two-dimensional Gross-Pitaeveskii equation. Such a fluid supports quantized vortices that have a size characterized by the healing length $\xi$. We show that for the divergence-free portion of the superfluid velocity field, the kinetic energy spectrum over wavenumber $k$ may be decomposed into an ultraviolet regime ($k\gg \xi^{-1}$) having a universal $k^{-3}$ scaling arising from the vortex core structure, and an infrared regime ($k\ll\xi^{-1}$) with a spectrum that arises purely from the configuration of the vortices. The Novikov power-law distribution of intervortex distances with exponent -1/3 for vortices of the same sign of circulation leads to an infrared kinetic energy spectrum with a Kolmogorov $k^{-5/3}$ power law, consistent with the existence of an inertial range. The presence of these $k^{-3}$ and $k^{-5/3}$ power laws, together with the constraint of continuity at the smallest configurational scale $k\approx\xi^{-1}$, allows us to derive a new analytical expression for the Kolmogorov constant that we test against a numerical simulation of a forced homogeneous compressible two-dimensional superfluid. The numerical simulation corroborates our analysis of the spectral features of the kinetic energy distribution, once we introduce the concept of a {\em clustered fraction} consisting of the fraction of vortices that have the same sign of circulation as their nearest neighboring vortices. Our analysis presents a new approach to understanding two-dimensional quantum turbulence and interpreting similarities and differences with classical two-dimensional turbulence, and suggests new methods to characterize vortex turbulence in two-dimensional quantum fluids via vortex position and circulation measurements.Comment: 19 pages, 8 figure

How Constraints Affect Content: The Case of Twitter's Switch from 140 to 280 Characters

It is often said that constraints affect creative production, both in terms of form and quality. Online social media platforms frequently impose constraints on the content that users can produce, limiting the range of possible contributions. Do these restrictions tend to push creators towards producing more or less successful content? How do creators adapt their contributions to fit the limits imposed by social media platforms? To answer these questions, we conduct an observational study of a recent event: on November 7, 2017, Twitter changed the maximum allowable length of a tweet from 140 to 280 characters, thereby significantly altering its signature constraint. In the first study of this switch, we compare tweets with nearly or exactly 140 characters before the change to tweets of the same length posted after the change. This setup enables us to characterize how users alter their tweets to fit the constraint and how this affects their tweets' success. We find that in response to a length constraint, users write more tersely, use more abbreviations and contracted forms, and use fewer definite articles. Also, although in general tweet success increases with length, we find initial evidence that tweets made to fit the 140-character constraint tend to be more successful than similar-length tweets written when the constraint was removed, suggesting that the length constraint improved tweet quality.Comment: To appear in the Proceedings of AAAI ICWSM 201

Reddit in the Time of COVID

When the COVID-19 pandemic hit, much of life moved online. Platforms of all types reported surges of activity, and people remarked on the various important functions that online platforms suddenly fulfilled. However, researchers lack a rigorous understanding of the pandemic's impacts on social platforms, and whether they were temporary or long-lasting. We present a conceptual framework for studying the large-scale evolution of social platforms and apply it to the study of Reddit's history, with a particular focus on the COVID-19 pandemic. We study platform evolution through two key dimensions: structure vs. content and macro- vs. micro-level analysis. Structural signals help us quantify how much behavior changed, while content analysis clarifies exactly how it changed. Applying these at the macro-level illuminates platform-wide changes, while at the micro-level we study impacts on individual users. We illustrate the value of this approach by showing the extraordinary and ordinary changes Reddit went through during the pandemic. First, we show that typically when rapid growth occurs, it is driven by a few concentrated communities and within a narrow slice of language use. However, Reddit's growth throughout COVID-19 was spread across disparate communities and languages. Second, all groups were equally affected in their change of interest, but veteran users tended to invoke COVID-related language more than newer users. Third, the new wave of users that arrived following COVID-19 was fundamentally different from previous cohorts of new users in terms of interests, activity, and likelihood of staying active on the platform. These findings provide a more rigorous understanding of how an online platform changed during the global pandemic.Comment: 12 pages, published in ICWSM 202

Snell's Law for a vortex dipole in a Bose-Einstein condensate

A quantum vortex dipole, comprised of a closely bound pair of vortices of equal strength with opposite circulation, is a spatially localized travelling excitation of a planar superfluid that carries linear momentum, suggesting a possible analogy with ray optics. We investigate numerically and analytically the motion of a quantum vortex dipole incident upon a step-change in the background superfluid density of an otherwise uniform two-dimensional Bose-Einstein condensate. Due to the conservation of fluid momentum and energy, the incident and refracted angles of the dipole satisfy a relation analogous to Snell's law, when crossing the interface between regions of different density. The predictions of the analogue Snell's law relation are confirmed for a wide range of incident angles by systematic numerical simulations of the Gross-Piteavskii equation. Near the critical angle for total internal reflection, we identify a regime of anomalous Snell's law behaviour where the finite size of the dipole causes transient capture by the interface. Remarkably, despite the extra complexity of the surface interaction, the incoming and outgoing dipole paths obey Snell's law.Comment: 16 pages, 7 figures, Scipost forma

Auditing Search Engines for Differential Satisfaction Across Demographics

Many online services, such as search engines, social media platforms, and digital marketplaces, are advertised as being available to any user, regardless of their age, gender, or other demographic factors. However, there are growing concerns that these services may systematically underserve some groups of users. In this paper, we present a framework for internally auditing such services for differences in user satisfaction across demographic groups, using search engines as a case study. We first explain the pitfalls of na\"ively comparing the behavioral metrics that are commonly used to evaluate search engines. We then propose three methods for measuring latent differences in user satisfaction from observed differences in evaluation metrics. To develop these methods, we drew on ideas from the causal inference literature and the multilevel modeling literature. Our framework is broadly applicable to other online services, and provides general insight into interpreting their evaluation metrics.Comment: 8 pages Accepted at WWW 201