Non-uniqueness and h-principle for H\"older-continuous weak solutions of the Euler equations

In this paper we address the Cauchy problem for the incompressible Euler equations in the periodic setting. Based on estimates developed in [Buckmaster-De Lellis-Isett-Sz\'ekelyhidi], we prove that the set of H\"older 1\slash 5-\eps wild initial data is dense in $L^2$, where we call an initial datum wild if it admits infinitely many admissible H\"older 1\slash 5-\eps weak solutions. We also introduce a new set of stationary flows which we use as a perturbation profile instead of Beltrami flows to recover arbitrary Reynolds stresses.Comment: 42 pages, minor corrections following referee comment

Combatting Skepticism Towards HR

[Excerpt] When assessing the essentiality of HR within a firm, one must first ask what is meant by the word “essential” within a business context. The trickiness here, however, is that such a definition is highly contingent on the type and size of a particular firm. If one defines “essential” as “indispensable,” then HR is almost certainly not essential in very small firms. In such instances, the work of HR can be done by other managers and the owners themselves. On the other hand, if one defines “essential” as “adding considerable value,” then innovative human resource policies can create a competitive advantage even in the smallest of firms. Instead of relying on a single definition of essentiality, this essay will focus on the reasons why human resources practices are often called into question in the first place. Furthermore, I will propose recommendations on how to combat skepticism toward HR

Lecture Notes on Gradient Flows and Optimal Transport

We present a short overview on the strongest variational formulation for gradient flows of geodesically $\lambda$-convex functionals in metric spaces, with applications to diffusion equations in Wasserstein spaces of probability measures. These notes are based on a series of lectures given by the second author for the Summer School "Optimal transportation: Theory and applications" in Grenoble during the week of June 22-26, 2009

Geometrically-exact time-integration mesh-free schemes for advection-diffusion problems derived from optimal transportation theory and their connection with particle methods

We develop an Optimal Transportation Meshfree (OTM) particle method for advection-diffusion in which the concentration or density of the diffusive species is approximated by Dirac measures. We resort to an incremental variational principle for purposes of time discretization of the diffusive step. This principle characterizes the evolution of the density as a competition between the Wasserstein distance between two consecutive densities and entropy. Exploiting the structure of the Euler-Lagrange equations, we approximate the density as a collection of Diracs. The interpolation of the incremental transport map is effected through mesh-free max-ent interpolation. Remarkably, the resulting update is geometrically exact with respect to advection and volume. We present three-dimensional examples of application that illustrate the scope and robustness of the method.Comment: 19 pages, 8 figure