Spectral Theory of Time Dispersive and Dissipative Systems

We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively determine if a given time dispersive system can be extended to a conservative one; (ii) to construct that very conservative system -- which we show is essentially unique. We illustrate the method by applying it to the spectral analysis of time dispersive dielectrics and the damped oscillator with retarded friction. In particular, we obtain a conservative extension of the Maxwell equations which is equivalent to the original Maxwell equations for a dispersive and lossy dielectric medium.Comment: LaTeX, 57 Pages, incorporated revisions corresponding with published versio

On the equivalence of the Langevin and auxiliary field quantization methods for absorbing dielectrics

Recently two methods have been developed for the quantization of the electromagnetic field in general dispersing and absorbing linear dielectrics. The first is based upon the introduction of a quantum Langevin current in Maxwell's equations [T. Gruner and D.-G. Welsch, Phys. Rev. A 53, 1818 (1996); Ho Trung Dung, L. Kn\"{o}ll, and D.-G. Welsch, Phys. Rev. A 57, 3931 (1998); S. Scheel, L. Kn\"{o}ll, and D.-G. Welsch, Phys. Rev. A 58, 700 (1998)], whereas the second makes use of a set of auxiliary fields, followed by a canonical quantization procedure [A. Tip, Phys. Rev. A 57, 4818 (1998)]. We show that both approaches are equivalent.Comment: 7 pages, RevTeX, no figure

Assessment of shallow subsea hydrocarbons as a proxy for leakage at offshore geologic CO2 storage sites

Bureau of Economic Geolog

Statistical analysis of historic hydrocarbon production data from Gulf of Mexico oil and gas fields and application to dynamic capacity assessment in CO2 storage

Bureau of Economic Geolog

Macroscopic Maxwell's equations and negative index materials

We study the linear phenomenological Maxwell's equations in the presence of a polarizable and magnetizable medium (magnetodielectric). For a dispersive, non-absorptive, medium with equal electric and magnetic permeabilities, the latter can assume the value -1 (+1 is their vacuum value) for a discrete set of frequencies, i.e., for these frequencies the medium behaves as a negative index material (NIM). We show that such systems have a well-defined time evolution. In particular the fields remain square integrable (and the electromagnetic energy finite) if this is the case at some initial time. Next we turn to the Green's function (a tensor), associated with the electric Helmholtz operator, for a set of parallel layers filled with a material. We express it in terms of the well-known scalar s and p ones. For a half space filled with the material and with a single dispersive Lorentz form for both electric and magnetic permeabilities we obtain an explicit form for the Green's function. We find the usual behavior for negative index materials, there is no refection outside the evanescent regime and the transmission (refraction) shows the usual NIM behavior. We find that the Green's function has poles, which lead to a modulation of the radiative decay probability of an excited atom. The formalism is free from ambiguities in the sign of the refractive index.Comment: 22 pages, accepted for publication in J. Math. Phys

De Dordtse Kerkorde 1619

De Dordtse Kerkorde 1619 is nog steeds de basis voor de kerkelijke orde voor gereformeerde kerken wereldwijd. Inzicht in de ontwikkeling, context en theologie van deze kerkorde kan behulpzaam zijn bij het toepassen van deze kerkorde in andere tijden en situaties. De Dordtse Kerkorde is een stadium in de ontwikkeling van het gereformeerde kerkrecht die formeel begon in 1571 in Emden. Het blijkt dat de basis van deze kerkorde nog steeds goed bruikbaar is: een ‘format van formaat’. De besluiten van de Synode van Dordrecht zijn consistent; er is ook geen discrepantie tussen de kerkorde en overige besluiten. De kerkorde is in harmonie met de Belijdenis, die door deze synode werd bevestigd als basis voor leer en leven. Alleen de positie van de diaken ten opzichte van de kerkenraad vertoont een afwijking, die te wijten kan zijn aan de invloed van de overheid op het kerkelijk leven. De positie van de overheid ten opzichte van de Kerk was een belangrijk onderwerp. De verschillende Staten vaardigden gecommitteerden af naar de Synode van Dordrecht. Een van hun taken was toezien dat niemand in zijn rechten werd aangetast. Deze gecommitteerden waren betrokken kerkleden, die eveneens het welzijn van de Kerk op het oog hadden. In de loop van ruim dertig jaren waren er veel vragen die vanuit de kerken op een antwoord wachtten. Deze vragen zijn grotendeels door middel van de Dordtse Kerkorde beantwoord. Het grondpatroon van de kerkorde is niet veranderd door de ingediende instructies en gevoerde discussies

Making the Connection: How Mentors Choose Protégés in Academic Mentoring Relationships

Among other things, mentoring research is concerned with how mentors go about the process of choosing who they should mentor. Even when mentoring relationships are assigned, mentors need to feel that the efforts they are putting forth are worth the time and energy. What protégé attributes best attract the attention of a mentor? What mentor attributes make some protégés more attractive to them than others? This study looks at 3 explanations for mentor-protégé attraction, shedding light on the mental processes that influence why some protégés find it easy to get mentors and why some have a much tougher time finding the right person to mentor them. Practical and theoretical implications of this study are included

Numerical experiments of density driven CO2 saturated brine migration in heterogeneous two-dimensional geologic fabric materials

Bureau of Economic Geolog