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

H\"older equicontinuity of the integrated density of states at weak disorder

H\"older continuity, $|N_\lambda(E)-N_\lambda(E')|\le C |E-E'|^\alpha$, with a constant $C$ independent of the disorder strength $\lambda$ is proved for the integrated density of states $N_\lambda(E)$ associated to a discrete random operator $H = H_o + \lambda V$ consisting of a translation invariant hopping matrix $H_o$ and i.i.d. single site potentials $V$ with an absolutely continuous distribution, under a regularity assumption for the hopping term.Comment: 15 Pages, typos corrected, comments and ref. [1] added, theorems 3,4 combine

Evaluation of health effects of air pollution in the Chestnut Ridge area : preliminary analysis

This project involves several tasks designed to take advantage of (1) a very extensive air pollution monitoring system that is operating ..n the Chestnut Ridge.region of Western Pennsylvania and (2) -the very well developed analytic dispersion models that have been previously fine-tuned to this particular area.. The major task in this project is to establish, through several distinct epidemiolopic approaches, health data to be used to test hypotheses about relations of air pollution exposures to morbidity and mortality rates in this region. Because the air quality monitoring network involves no expense to this contract this project affords a very cost-effective 6pportunity-for state-of-the-art techniques to be used in both costly areas of air pollution and health -effects data col1 ection. . The closely spaced network of monitors, plus the dispersion modeling capabilities,.allow for the investigation- of health impacts of. various pollutant gradients in neighboring geographic areas, thus minimizing -the confounding effects of social, ethnic, and economic factors. The pollutants that are monitored in this network include total gaseous sulfur, sulfates, total suspended particulates, NOx, NO, ozone/oxidants, and coefficient of haze. In addition to enabling the simulation of exposure profiles between monitors, the air quality2 modeling, along with extensive source and background inventories, will allow for upgrading the quality of the monitored data. as well as simulating the exposure levels for about 25 additional air pollutants. Another important goal of this project is to collect and test the many available models for associating.health effects with air pollution, to determine their predictive validity and their usefulness in the choice and siting of future energy facilities

Thermoacoustically driven flame motion and heat release variation in a swirl-stabilized gas turbine burner investigated by LIF and chemiluminescence

Laser-induced fluorescence and chemiluminescence, both phase-locked to the dominant acoustic oscillation, are used to investigate phenomena related to thermoacoustic instability in a swirl-stabilized industrial scale gas turbine burner. The observed sinusoidal phase-averaged flame motion in axial (main flow) direction is analyzed using different schemes for defining the flame position. Qualitative agreement between experimental data and theoretical analysis of the observed flame motion is obtained, interpreted as originating primarily from variation of the burning velocity. The heat release variation during an acoustic cycle is determined from the sinusoidally varying total OH* chemiluminescence intensit

Birth and closure of the Kallipetra Basin: Late Cretaceous reworking of the Jurassic Pelagonian-Axios/Vardar contact (northern Greece)

Some 20 Myr after the Late Jurassic to Early Cretaceous obduction and collision at the eastern margin of Adria, the eroded Pelagonia (Adria) Axios/Vardar (oceanic complex) contact collapsed, forming the Kallipetra Basin, described around the Aliakmon River near Veroia (northern Greece). Clastic and carbonate marine sediments deposited from the early Cenomanian to the end of the Turonian, with abundant olistoliths and slope failures at the base due to active normal faults. The middle part of the series is characterized by red and green pelagic limestones, with a minimal contribution of terrigenous debris. Rudist mounds in the upper part of the basin started forming on the southwestern slope, and their growth competed with a flux of ophiolitic debris, documenting the new fault scarps affecting the Vardar oceanic complex (VOC). Eventually, the basin was closed by overthrusting of the VOC towards the northeast and was buried and heated up to ~ 180 °C. A strong reverse geothermal gradient with temperatures increasing up-section to near 300 °C is recorded beneath the VOC by illite crystallinity and by the crystallization of chlorite during deformation. This syntectonic heat partially reset the zircon fission track ages bracketing the timing of closure just after the deposition of the ophiolitic debris in the Turonian. This study documents the reworking of the Pelagonian Axios/Vardar contact, with Cenomanian extension and basin widening followed by Turonian compression and basin inversion. Thrusting occurred earlier than previously reported in the literature for the eastern Adria and shows a vergence toward the northeast, at odds with the regional southwest vergence of the whole margin but in accordance to some reports about 50 km north

Hamiltonian structure for dispersive and dissipative dynamical systems

We develop a Hamiltonian theory of a time dispersive and dissipative inhomogeneous medium, as described by a linear response equation respecting causality and power dissipation. The proposed Hamiltonian couples the given system to auxiliary fields, in the universal form of a so-called canonical heat bath. After integrating out the heat bath the original dissipative evolution is exactly reproduced. Furthermore, we show that the dynamics associated to a minimal Hamiltonian are essentially unique, up to a natural class of isomorphisms. Using this formalism, we obtain closed form expressions for the energy density, energy flux, momentum density, and stress tensor involving the auxiliary fields, from which we derive an approximate, ``Brillouin-type,'' formula for the time averaged energy density and stress tensor associated to an almost mono-chromatic wave.Comment: 68 pages, 1 figure; introduction revised, typos correcte

From self-efficacy to imposter syndrome: The intrapersonal traits of surgeons

BACKGROUND: Demographic differences among surgical trainees regarding intrapersonal traits, such as imposter syndrome and assertiveness, have become widely acknowledged. However, many of these characteristics have not been examined in tandem, nor among both trainees and surgeons in practice. This study aimed to address these knowledge gaps. METHODS: This was an anonymous, voluntary survey study comprised of validated measures of (1) self-efficacy, (2) imposter syndrome, (3) assertiveness, (4) perfectionism, and (5) self-rated likeability. A multimodal recruitment strategy was used and surgeons across all subspecialties were eligible for inclusion. RESULTS: A total of 296 participants were included, with 54% identifying as female (n = 161) and 72% between the ages of 25 and 40 years of age (n = 212). Imposter syndrome, assertiveness, and perfectionism scales were normally distributed; self-efficacy and self-rated likeability scales demonstrated slight negative skew. Self-identified male sex was associated with less imposter syndrome (P \u3c 0.001) and perfectionism (P = 0.035) and higher assertiveness (P \u3c 0.001). Imposter syndrome was less common among older age groups (P = 0.001). CONCLUSIONS: Surgeons are a self-efficacious group of perfectionists with widespread variability in imposter syndrome and assertiveness. Female sex and younger age were associated with more imposter syndrome and less assertiveness, highlighting an opportunity for early career coaching

Eigenvector localization for random band matrices with power law band width

It is shown that certain ensembles of random matrices with entries that vanish outside a band around the diagonal satisfy a localization condition on the resolvent which guarantees that eigenvectors have strong overlap with a vanishing fraction of standard basis vectors, provided the band width $W$ raised to a power $\mu$ remains smaller than the matrix size $N$. For a Gaussian band ensemble, with matrix elements given by i.i.d. centered Gaussians within a band of width $W$, the estimate $\mu \le 8$ holds.Comment: 30 pages; corrected typo

Evidence for Low Extinction in Actively Star Forming Galaxies at z>>6.5

We present a search for the [CII] 158micron fine structure line (a main cooling line of the interstellar medium) and the underlying far-infrared (FIR) continuum in three high-redshift (6.6<z<8.2) star-forming galaxies using the IRAM Plateau de Bure interferometer. We targeted two Lyman-Alpha-selected galaxies (Lyman-Alpha-Emitters, LAEs) with moderate UV-based star formation rates (SFR~20 M_sun/yr; Himiko at z=6.6 and IOK-1 at z=7.0) and a Gamma Ray Burst (GRB) host galaxy (GRB 090423 at z~8.2). Based on our 3 sigma rest-frame FIR continuum limits, previous (rest-frame) UV continuum measurements and spectral energy distribution (SED) fitting, we rule out SED shapes similar to highly obscured galaxies (e.g. Arp220, M82) and less extreme dust-rich nearby spiral galaxies (e.g. M51) for the LAEs. Conservatively assuming a SED shape typical of local spiral galaxies we derive upper limits for the FIR-based star formation rates (SFRs) of ~70 M_sun/yr, ~50 M_sun/yr and ~40 M_sun/yr for Himiko, IOK-1 and GRB 090423, respectively. For the LAEs these limits are only a factor ~3 higher than the published UV-based SFRs (uncorrected for extinction). This indicates that the dust obscuration in the z>6 LAEs studied here is lower by a factor of a few than what has recently been found in some LAEs at lower redshift (2<z<3.5) with similar UV-based SFRs. A low obscuration in our z>6 LAE sample is consistent with recent rest-frame UV studies of z~7 Lyman-Break-Galaxies (LBGs).Comment: Accepted for publication in the Astrophysical Journa