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A classical problem in fluid mechanics is the motion of an axisymmetric vortex sheet evolving under the action of surface tension, surrounded by an inviscid fluid. Lagrangian descriptions of these dynamics are well‐known, involving complex nonlocal expressions for the radial and longitudinal velocities in terms of elliptic integrals. Here we use these prior results to arrive at a remarkably compact and exact Eulerian evolution equation for the sheet radius r(z, t) in an explicit flux form associated with the conservation of enclosed volume. The flux appears as an integral involving the pairwise mutual induction formula for vortex loop pairs first derived by Helmholtz and Maxwell. We show how the well‐known linear stability results for cylindrical vortex sheets in the presence of surface tension and streaming flows [A. M. Sterling and C. A. Sleicher, J. Fluid Mech.68, 477 (1975)] can be obtained directly from this formulation. Furthermore, the inviscid limit of the empirical model of Eggers and Dupont [J. Fluid Mech.262 205 (1994); SIAM J. Appl. Math.60, 1997 (2000)], which has served as the basis for understanding singularity formation in droplet pinchoff, is derived within the present formalism as the leading‐order term in an asymptotic analysis for long slender axisymmetric vortex sheets and should provide the starting point for a rigorous analysis of singularity formation. © 2019 the Authors. Communications on Pure and Applied Mathematics is published by the Courant Institute of Mathematical Sciences and Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Most undergraduates have limited experience with mathematical modeling. In an effort to respond to various initiatives, such as the recommendations outlined in [S. Garfunkel and M. Montgomery, eds., GAIMME: Guidelines for Assessment & Instruction in Mathematical Modeling Education, SIAM, 2016], this paper describes a course on the mathematical models of cancer growth and treatment. Among its aims is to provide a template for a "bridge" course between the traditional calculus and differential equations sequence and more advanced courses in mathematics and statistics. Prerequisites include a course in ordinary differential equations. Linear algebra is a useful corequisite but no previous programming experience is required. The content includes classical models of tumor growth as well as models for the growth of specific cancer types. Relevant research articles are provided for further study. Material for student projects and effective communication is supplied, as well as suggestions for homework assignments and computer labs. This paper aims to assist instructors in developing their own "Mathematics + Cancer" course. [ABSTRACT FROM AUTHOR]

We study in-group favouritism and out-group discrimination in a multiplayer dictator game in a naturally occuring group setting. An allocator divides a large sum of money among three groups of around 20 recipients each and also to themselves. The groups are supporters of two rival political movements in Thailand and politically neutral subjects. The non-rival out-group acts as a reference point and allows us to measure in-group favouritism and out-group discrimination. A treatment with artificial groups serves as a control. We find both in-group favouritism and out-group discrimination among the naturally occurring groups. In artificial groups, favouritism is observed, but not discrimination. Our results suggest that the two behaviours are not driven by the same motive, and only when groups are in conflict that out-group discrimination is likely to occur. [ABSTRACT FROM AUTHOR]