Ontological aspects of the Casimir Effect

The role of the vacuum, in the Casimir Effect, is a matter of some dispute: the Casimir force has been variously described as a phenomenon resulting "from the alteration, by the boundaries, of the zero-point electromagnetic energy", or a "Van der Waals force between the metal plates" that can be "computed without reference to zero point energies". Neither of these descriptions are grounded in a consistently quantum mechanical treatment of matter interacting with the electromagnetic field. However, the Casimir Effect has been canonically described within the framework of macroscopic quantum electrodynamics. On this account, the force is seen to arise due to the coupling of fluctuating currents to the zero-point radiation, and it is in this restricted sense that the phenomenon requires the existence of zero-point fields. The conflicting descriptions of the Casimir Effect, on the other hand, appear to arise from inadequate ontologies in which an unwarranted metaphysical priority is assigned either to the matter or the fields. Such ontological errors may have a direct bearing on the problem of the cosmological constant and the correct prediction of the Casimir force in a state of thermal equilibrium.Comment: 6 page

The paradox of the Casimir force in inhomogeneous transformation media

It has recently been argued that Casimir-Lifshitz forces depend in detail on the microphysics of a system; calculations of the Casimir force in inhomogeneous media yield results that are cutoff-dependent. This result has been shown to hold generally. But suppose we introduce an inhomogeneous metamaterial into a cavity that effectively implements a simple distortion of the coordinate system. Considered in its 'virtual space', the optical properties of such a material are homogeneous and consequently free from the cutoff-dependency associated with inhomogeneous media. This conclusion should be reconciled with recent advances in our understanding of Casimir-Lifshitz forces. We consider an example of such a system here and demonstrate that, whilst the size of the Casimir force is modified by the inhomogeneous medium, the force is cutoff-independent and can be stated exactly. The apparent paradox dissolves when we recognise that an idealised metamaterial that could implement a virtual geometry for all frequencies would be devoid of internal scattering, and would not give rise to a cutoff-dependency in the Casimir force for that reason.Comment: 7 page

A weighted dispersive estimate for Schr\"{o}dinger operators in dimension two

Let $H=-\Delta+V$, where $V$ is a real valued potential on $\R^2$ satisfying |V(x)|\les \la x\ra^{-3-}. We prove that if zero is a regular point of the spectrum of $H=-\Delta+V$, then \|w^{-1} e^{itH}P_{ac}f\|_{L^\infty(\R^2)}\les \f1{|t|\log^2(|t|)} \|w f\|_{L^1(\R^2)}, |t| >2, with $w(x)=\log^2(2+|x|)$. This decay rate was obtained by Murata in the setting of weighted $L^2$ spaces with polynomially growing weights.Comment: 23 page

Sediment management for Southern California mountains, coastal plains and shoreline

The Environmental Quality Laboratory at Caltech and the Shore Processes Laboratory at Scripps Institution of Oceanography have jointly undertaken a study of regional sediment balance problems in coastal southern California (see map in Figure 1). The overall objective in this study is to define specific alternatives in sediment management that may be implemented to alleviate a) existing sediment imbalance problems (e.g. inland debris disposal, local shoreline erosion) and b) probable future problems that have not yet manifested themselves. These alternatives will be identified through a consideration of economic, legal, and institutional issues as well as an analysis of governing physical processes and engineering constraints. The first part of this study (Phase I), which is currently under way, involves a compilation and analysis of all available data in an effort to obtain an accurate definition of the inland/coastal regional sediment balance under natural conditions, and specific quantitative effects man-made controls have on the overall natural process. During FY77, substantial progress was made at EQL and SPL in achieving the objectives of the initial Planning and Assessment Phase of the CIT/SIO Sediment Management Project. Financial support came from Los Angeles County, U.S. Geological Survey, Orange County, U.S. Army Corps of Engineers, and discretionary funding provided by a grant from the Ford Foundation. The current timetable for completion of this phase is Fall 1978. This report briefly describes the project status, including general administration, special activities, and research work as of January 1978

The Politics of Hydroelectric Power in Alaska: Rampart and Devil Canyon -- A Case Study

Originally published January 1978, revised October 1978. OWRT Agreement No. 14-34-0001-7003 Project No. A-060-ALAS. Completion Report.Hydroelectric power in Alaska has had a curious history--and an instructive one. This study focuses on three separate projects: Eklutna, Rampart, and Devil Canyon. The Eklutna project functions today; Rampart was not constructed; and the Devil Canyon project is still in the planning stage. Yet for all their differences in location, goals, and fate, the projects were related; and, taken together, their histories highlight all the essential political elements involved in hydroelectric power construction. There is still a fourth project which is functioning today--the Snettisham installation near Juneau which is not considered in this paper. A complex decision-making process determines the progress of such large projects. In following these three Alaskan projects, we can gain a better perspective on the roles of the several government agencies and the public; thus we can assess some of the inherent complexities. Such an assessment fully substantiates the conclusion that it takes more than moving dirt to build a dam.The work upon which this completion report is based was supported by funds provided by the U. S. Department of the Interior, Office of Water Research and Technology as authorized under the Water Resources Research Act of 1964, Public Law 88-379, as amended

Nanoparticle transport in saturated porous medium using magnetic resonance imaging

Transport study of nanoparticle (NP) through matrix flow dominated aquifer sand and soils have significant influence in natural systems. To quantify the transport behaviour, magnetic resonance imaging (MRI) was used to image the iron oxide based nanoparticle, Molday ION (carboxyl terminated) through saturated sandstone rock core. T2-weighted images were acquired and the changes in image intensity were calibrated to get a quantitative concentration profiles at various time intervals. These profiles were evaluated through CXTFIT transport model to estimate the transport parameters. These parameters are estimated at various points along the length of the column while classical breakthrough curve analysis cannot provide these details. NP–surface interactions were investigated using DLVO (Derjaguin–Landau–Verwey–Overbeek) theory. The dispersion coefficients (2.55–1.21 × 10−7 m2/s) were found to be decrease with distance, deposition rate constant k (6.70–9.13 × 10−4 (1/s)) and fast deposition rate constant kfast (4.32–8.79 × 10−2 (1/s)) were found to be increase with distance. These parameter variations over length will have a scaling up impact in developing transport models for environmental remediation and risk assessment schemes

Dispersive estimates for massive Dirac operators in dimension two

We study the massive two dimensional Dirac operator with an electric potential. In particular, we show that the $t^{-1}$ decay rate holds in the $L^1\to L^\infty$ setting if the threshold energies are regular. We also show these bounds hold in the presence of s-wave resonances at the threshold. We further show that, if the threshold energies are regular that a faster decay rate of $t^{-1}(\log t)^{-2}$ is attained for large $t$, at the cost of logarithmic spatial weights. The free Dirac equation does not satisfy this bound due to the s-wave resonances at the threshold energies.Comment: 40 page