Time and dark matter from the conformal symmetries of Euclidean space

The quotient of the conformal group of Euclidean 4-space by its Weyl subgroup results in a geometry possessing many of the properties of relativistic phase space, including both a natural symplectic form and non-degenerate Killing metric. We show that the general solution posesses orthogonal Lagrangian submanifolds, with the induced metric and the spin connection on the submanifolds necessarily Lorentzian, despite the Euclidean starting pont. By examining the structure equations of the biconformal space in an orthonormal frame adapted to its phase space properties, we also find that two new tensor fields exist in this geometry, not present in Riemannian geometry. The first is a combination of the Weyl vector with the scale factor on the metric, and determines the timelike directions on the submanifolds. The second comes from the components of the spin connection, symmetric with respect to the new metric. Though this field comes from the spin connection it transforms homogeneously. Finally, we show that in the absence of conformal curvature or sources, the configuration space has geometric terms equivalent to a perfect fluid and a cosmological constant.Comment: 26 pages, no figures. Appreciable introductory material added. Results substantially strengthened and explained. New results concerning dark matter and dark energy candidates added to this versio

PROBABILISTIC COST EFFECTIVENESS IN AGRICULTURAL NONPOINT POLLUTION CONTROL

Conceptual weaknesses in the use of costs of average abatement as a measure of the cost effectiveness of agricultural nonpoint pollution control are examined. A probabilistic alternative is developed. The focus is on methods for evaluating whole-farm pollution control plans rather than individual practices. As a consequence, the analysis is presented in a chance-constrained activity analysis framework because activity procedures are a practical and well developed device for screening farm planes. Reliability of control is shown to be as important as reduction targets in designing farm plans for pollution control. Furthermore, broad-axe prescriptions of technology in the form of Best Management Practices may perform poorly with respect to cost effectiveness.Environmental Economics and Policy,

The Hierarchy Solution to the LHC Inverse Problem

Supersymmetric (SUSY) models, even those described by relatively few parameters, generically allow many possible SUSY particle (sparticle) mass hierarchies. As the sparticle mass hierarchy determines, to a great extent, the collider phenomenology of a model, the enumeration of these hierarchies is of the utmost importance. We therefore provide a readily generalizable procedure for determining the number of sparticle mass hierarchies in a given SUSY model. As an application, we analyze the gravity-mediated SUSY breaking scenario with various combinations of GUT-scale boundary conditions involving different levels of universality among the gaugino and scalar masses. For each of the eight considered models, we provide the complete list of forbidden hierarchies in a compact form. Our main result is that the complete (typically rather large) set of forbidden hierarchies among the eight sparticles considered in this analysis can be fully specified by just a few forbidden relations involving much smaller subsets of sparticles.Comment: 44 pages, 2 figures. Python code providing lists of allowed and forbidden hierarchy is included in ancillary file

Loading and testing a light scattering cell with a binary fluid mixture near its critical composition

Critical phenomena has been the subject of physics research for many years. However, only in recent years has the research effort become intense. The current intensity has caused the study of critical phenomena to be grouped into a previous older era and a present contemporary era. Turbidity cell filling with methanol cyclohexane is one of the first steps toward a further understanding of critical phenomena. Work performed during the research period is outlined. During this period, research was spent developing apparatus and techniques that will make it possible to study critical phenomena through turbidity measurements on methanol cyclohexane. Topics covered range from the orientation of turbidity cell parts for assembly to the filling apparatus and procedure used when th cell is built. The last section will briefly cover some of the observations made when viewing the cell in a controlled water bath. However, before mention is made of the specifics of the summer research, a short introduction to critical phenomena and turbidity and how they relate to this experiment is provided

Edge Detecting New Physics the Voronoi Way

We point out that interesting features in high energy physics data can be determined from properties of Voronoi tessellations of the relevant phase space. For illustration, we focus on the detection of kinematic "edges" in two dimensions, which may signal physics beyond the standard model. After deriving some useful geometric results for Voronoi tessellations on perfect grids, we propose several algorithms for tagging the Voronoi cells in the vicinity of kinematic edges in real data. We show that the efficiency is improved by the addition of a few Voronoi relaxation steps via Lloyd's method. By preserving the maximum spatial resolution of the data, Voronoi methods can be a valuable addition to the data analysis toolkit at the LHC.Comment: 6 pages, 7 figure