Splash singularities for the one-phase Muskat problem in stable regimes

This paper shows finite time singularity formation for the Muskat problem in a stable regime. The framework we found is with a dry region, where the density and the viscosity are set equal to $0$ (the gradient of the pressure is equal to $(0,0)$) in the complement of the fluid domain. The singularity is a splash-type: a smooth fluid boundary collapses due to two different particles evolve to collide at a single point. This is the first example of a splash singularity for a parabolic problem.Comment: Minor comments added, 26 pages, 1 figur

Representation, evolution and embodiment

As part of the ongoing attempt to fully naturalize the concept of human being--and, more specifically, to re-center it around the notion of agency--this essay discusses an approach to defining the content of representations in terms ultimately derived from their central, evolved function of providing guidance for action. This 'guidance theory' of representation is discussed in the context of, and evaluated with respect to, two other biologically inspired theories of representation: Dan Lloyd's dialectical theory of representation and Ruth Millikan's biosemantics

Snapshot in a Squiggle: How Painting Terminology Illuminates Short Fiction

This paper will demonstrate that painting terms can offer a helpful avenue to understand short fiction, particularly abstract short fiction. After defining abstraction, realism, and the short story, it will trace relevant stages in the evolution of both painting and short fiction to show how and why the media share similar elements. In this examination, the paper will discuss which features of painting correspond with certain features of short fiction. Based on the essential elements of short fiction, as well as the features mentioned above, the paper will analyze examples of short stories that exemplify how painting parallels short fiction and how terminology drawn from that field can help illuminate abstract short stories

Impaction of spray droplets on leaves: influence of formulation and leaf character on shatter, bounce and adhesion

This paper combines experimental data with simple mathematical models to investigate the influence of spray formulation type and leaf character (wettability) on shatter, bounce and adhesion of droplets impacting with cotton, rice and wheat leaves. Impaction criteria that allow for different angles of the leaf surface and the droplet impact trajectory are presented; their predictions are based on whether combinations of droplet size and velocity lie above or below bounce and shatter boundaries. In the experimental component, real leaves are used, with all their inherent natural variability. Further, commercial agricultural spray nozzles are employed, resulting in a range of droplet characteristics. Given this natural variability, there is broad agreement between the data and predictions. As predicted, the shatter of droplets was found to increase as droplet size and velocity increased, and the surface became harder to wet. Bouncing of droplets occurred most frequently on hard to wet surfaces with high surface tension mixtures. On the other hand, a number of small droplets with low impact velocity were observed to bounce when predicted to lie well within the adhering regime. We believe this discrepancy between the predictions and experimental data could be due to air layer effects that were not taken into account in the current bounce equations. Other discrepancies between experiment and theory are thought to be due to the current assumption of a dry impact surface, whereas, in practice, the leaf surfaces became increasingly covered with fluid throughout the spray test runs.Comment: 19 pages, 6 figures, accepted for publication by Experiments in Fluid

Jets in Hadron-Hadron Collisions

In this article, we review some of the complexities of jet algorithms and of the resultant comparisons of data to theory. We review the extensive experience with jet measurements at the Tevatron, the extrapolation of this acquired wisdom to the LHC and the differences between the Tevatron and LHC environments. We also describe a framework (SpartyJet) for the convenient comparison of results using different jet algorithms.Comment: 68 pages, 54 figure