Variational Methods and Planar Elliptic Growth

A nested family of growing or shrinking planar domains is called a Laplacian growth process if the normal velocity of each domain's boundary is proportional to the gradient of the domain's Green function with a fixed singularity on the interior. In this paper we review the Laplacian growth model and its key underlying assumptions, so that we may consider a generalization to so-called elliptic growth, wherein the Green function is replaced with that of a more general elliptic operator--this models, for example, inhomogeneities in the underlying plane. In this paper we continue the development of the underlying mathematics for elliptic growth, considering perturbations of the Green function due to those of the driving operator, deriving characterizations and examples of growth, developing a weak formulation of growth via balayage, and discussing of a couple of inverse problems in the spirit of Calder\'on. We conclude with a derivation of a more delicate, reregularized model for Hele-Shaw flow

Periodic homogenization with an interface

We consider a diffusion process with coefficients that are periodic outside of an 'interface region' of finite thickness. The question investigated in the articles [1,2] is the limiting long time / large scale behaviour of such a process under diffusive rescaling. It is clear that outside of the interface, the limiting process must behave like Brownian motion, with diffusion matrices given by the standard theory of homogenization. The interesting behaviour therefore occurs on the interface. Our main result is that the limiting process is a semimartingale whose bounded variation part is proportional to the local time spent on the interface. We also exhibit an explicit way of identifying its parameters in terms of the coefficients of the original diffusion. Our method of proof relies on the framework provided by Freidlin and Wentzell for diffusion processes on a graph in order to identify the generator of the limiting process.Comment: ISAAC 09 conference proceeding

Comment on "Biases in the Quasar Mass-Luminosity Plane"

Comment on "Biases in the Quasar Mass-Luminosity Plane"Comment: Comment on Biases in the Quasar Mass-Luminosity Plane; 3 page

Professional Ethics in the Construction Industry

The results are provided of a small, but reprersentative, questionnaire survey of typical project managers, architects and building contractors concerning their views and experiences on a range of ethical issues surrounding construction industry activities. Most (90%) subscribed to a professional Code of Ethics and many (45%) had an Ethical Code of Conduct in their employing organisations, with the majority (84%) considering good ethical practice to be an important organisational goal. 93% of the respondents agreed that "Business Ethics" should be driven or governed by "Personal Ethics", with 84% of respondents stating that a balance of both the requirements of the client and the impact on the public should be maintained. No respondents were aware of any cases of employers attempting to force their employees to initiate, or participate in, unethical conduct. Despite this, all the respondents had witnessed or experienced some degree of unethical conduct, in the form of unfair conduct (81%), negligence (67%), conflict of interest (48%), collusive tendering (44%), fraud (35%), confidentiality and propriety breach (32%), bribery (26%) and violation of environmental ethics (20%)

The Quasar Mass-Luminosity Plane I: A Sub-Eddington Limit for Quasars

We use 62185 quasars from the Sloan Digital Sky Survey Data Release 5 sample to explore the relationship between black hole mass and luminosity. Black hole masses were estimated based on the widths of their H{\beta}, MgII and CIV lines and adjacent continuum luminosities using standard virial mass estimate scaling laws. We find that, over the range 0.2 < z < 4.0, the most luminous low-mass quasars are at their Eddington luminosity, but the most luminous high-mass quasars in each redshift bin fall short of their Eddington luminosities, with the shortfall of the order of 10 or more at 0.2 < z < 0.6. We examine several potential sources of measurement uncertainty or bias and show that none of them can account for this effect. We also show the statistical uncertainty in virial mass estimation to have an upper bound of ~0.15 dex, smaller than the 0.4 dex previously reported. We also examine the highest mass quasars in every redshift bin in an effort to learn more about quasars that are about to cease their luminous accretion. We conclude that the quasar mass-luminosity locus contains a number of new puzzles that must be explained theoretically.Comment: 14 pages, MNRA

Why Water Markets Are Not Quick Fixes for Droughts in the Western United States

Water in the western United States can be bought and sold, but the transactions will always be complicated. Transfers of water will always be expensive and time consuming because of the hydrologic and institutional interconnections inherent to water. Our data show that most of the water rights in the West are messy. Therefore, markets cannot be quick fixes, and using markets for future water allocation, even if it is economically efficient, will take time and resources to set up. Untangling serial uses and negotiating multiple ownership claims are hurdles, not barriers, and they can be overcome in time but will require both time and money. Buying existing water rights may be less costly than building infrastructure to transport available water from long distances or desalinating seawater, but the transactions will come at a price. Municipalities may purchase water from farmers and thus bear the transaction costs directly, or the private sector may purchase agricultural water (e.g., Two Rivers Water and Farming, Colorado (Landry 2012)), bear the associated risk and transaction costs, and sell it on to municipalities. In either case, the end users will inevitably pay higher prices for water. Markets can and will be part of western U.S. water allocation, but they do not provide quick solutions. Droughts can focus public attention on the value of water and potentially increase the willingness-to-pay prices that reflect the transaction costs of tangled western water markets

The habitability of the Universe through 13 billion years of cosmic time

The field of astrobiology has made tremendous progress in modelling galactic-scale habitable zones which offer a stable environment for life to form and evolve in complexity. Recently, this idea has been extended to cosmological scales by studies modelling the habitability of the local Universe in its entirety (e.g. Dayal et al. 2015; Li & Zhang 2015). However, all of these studies have solely focused on estimating the potentially detrimental effects of either Type II supernovae (SNII) or Gamma Ray Bursts (GRBs), ignoring the contributions from Type Ia supernovae (SNIa) and active galactic nuclei (AGN). In this study we follow two different approaches, based on (i) the amplitude of deleterious radiation and (ii) the total planet-hosting volume irradiated by deleterious radiation. We simultaneously track the contributions from the key astrophysical sources (SNII, SNIa, AGN and GRBs) for the entire Universe, for both scenarios, to determine its habitability through 13.8 billion years of cosmic time. We find that SNII dominate the total radiation budget and the volume irradiated by deleterious radiation at any cosmic epoch closely followed by SNIa (that contribute half as much as SNII), with GRBs and AGN making up a negligible portion (<1%). Secondly, as a result of the total mass in stars (or the total number of planets) slowly building-up with time and the total deleterious radiation density, and volume affected, falling-off after the first 3 billion years, we find that the Universe has steadily increased in habitability through cosmic time. We find that, depending on the exact model assumptions, the Universe is 2.5 to 20 times more habitable today compared to when life first appeared on the Earth 4 billion years ago. We find that this increase in habitability will persist until the final stars die out over the next hundreds of billions of years.Comment: Under refereeing in Ap

Method and apparatus for determining optical absorption and emission characteristics of a crystal or non-crystalline fiber

This invention relates generally to spectroscopy and, more particularly, to a method and apparatus for performing spectroscopic analysis of crystal and noncrystalline fibers. The invention provides a complete absorption curve for a material using a crystal fiber which can be more easily produced than the types of samples required for other methods of obtaining substantially the same absorption curve for identical materials