On the minimization of Dirichlet eigenvalues of the Laplace operator

We study the variational problem \inf \{\lambda_k(\Omega): \Omega\ \textup{open in}\ \R^m,\ |\Omega| < \infty, \ \h(\partial \Omega) \le 1 \}, where $\lambda_k(\Omega)$ is the $k$'th eigenvalue of the Dirichlet Laplacian acting in $L^2(\Omega)$, \h(\partial \Omega) is the $(m-1)$- dimensional Hausdorff measure of the boundary of $\Omega$, and $|\Omega|$ is the Lebesgue measure of $\Omega$. If $m=2$, and $k=2,3, \cdots$, then there exists a convex minimiser $\Omega_{2,k}$. If $m \ge 2$, and if $\Omega_{m,k}$ is a minimiser, then $\Omega_{m,k}^*:= \textup{int}(\overline{\Omega_{m,k}})$ is also a minimiser, and $\R^m\setminus \Omega_{m,k}^*$ is connected. Upper bounds are obtained for the number of components of $\Omega_{m,k}$. It is shown that if $m\ge 3$, and $k\le m+1$ then $\Omega_{m,k}$ has at most $4$ components. Furthermore $\Omega_{m,k}$ is connected in the following cases : (i) $m\ge 2, k=2,$ (ii) $m=3,4,5,$ and $k=3,4,$ (iii) $m=4,5,$ and $k=5,$ (iv) $m=5$ and $k=6$. Finally, upper bounds on the number of components are obtained for minimisers for other constraints such as the Lebesgue measure and the torsional rigidity.Comment: 16 page

Parametric correlations versus fidelity decay: the symmetry breaking case

We derive fidelity decay and parametric energy correlations for random matrix ensembles where time--reversal invariance of the original Hamiltonian is broken by the perturbation. Like in the case of a symmetry conserving perturbation a simple relation between both quantities can be established.Comment: 8 pages, 8 figure

CONTROL OF END-TIDAL HALOTHANE CONCENTRATION: Part A: Anaesthesia Breathing System and Feedback Control of Gas Delivery

Conventional anaesthetic breathing systems are not designed to control end-tidal gas concentrations, nor can they be used to measure accurately the uptake of oxygen or of anaesthetic agent. We built and tested a leak-tight closed-loop anaesthetic breathing system with low solubility to volatile anaesthetic agents and with efficient gas mixing. The system included a water-sealed spirometer, a small carbon dioxide absorber, a coaxial tube to the patient a circulating pump and feedback controllers for system volume and anaesthetic concentration. Feedback control was implemented to adjust and control automatically the end-tidal anaesthetic concentration and the volume of the system with oxygen supplied through a mass flow controller and with halothane supplied by a titrating syringe. Controller gains, as a function of body weight, were found using a nine-compartment tissue uptake model. Stability was maintained with ±50% changes in alveolar ventilation and cardiac output. During subsequent investigations in an animal model, arterial, mixed venous and cerebral venous blood halothane concentrations were measured to show that the feedback-controlled halothane induction was optimized. We conclude that feedback control appears to be clinically applicable for adjusting the end-tidal Concentration and system volume to provide a rapid and optimized induction of anaesthesi

Survival Probability of a Doorway State in regular and chaotic environments

We calculate survival probability of a special state which couples randomly to a regular or chaotic environment. The environment is modelled by a suitably chosen random matrix ensemble. The exact results exhibit non--perturbative features as revival of probability and non--ergodicity. The role of background complexity and of coupling complexity is discussed as well.Comment: 19 pages 5 Figure

Optical/Near-Infrared Imaging of Infrared-Excess Palomar-Green QSOs

Ground-based high spatial-resolution (FWHM < 0.3-0.8") optical and near-infrared imaging (0.4-2.2um) is presented for a complete sample of optically selected Palomar-Green QSOs with far-infrared excesses at least as great as those of "warm" AGN-like ultraluminous infrared galaxies (L_ir/L_big-blue-bump > 0.46). In all cases, the host galaxies of the QSOs were detected and most have discernable two-dimensional structure. The QSO host galaxies and the QSO nuclei are similar in magnitude at H-band. H-band luminosities of the hosts range from 0.5-7.5 L* with a mean of 2.3 L*, and are consistent with those found in ULIGs. Both the QSO nuclei and the host galaxies have near-infrared excesses, which may be the result of dust associated with the nucleus and of recent dusty star formation in the host. These results suggest that some, but not all, optically-selected QSOs may have evolved from an infrared-active state triggered by the merger of two similarly-sized L* galaxies, in a manner similar to that of the ultraluminous infrared galaxies.Comment: Aastex format, 38 pages, 4 tables, 10 figures. Higher quality figures are available in JPG forma

Cosmological Parameter Estimation Using 21 cm Radiation from the Epoch of Reionization

A number of radio interferometers are currently being planned or constructed to observe 21 cm emission from reionization. Not only will such measurements provide a detailed view of that epoch, but, since the 21 cm emission also traces the distribution of matter in the Universe, this signal can be used to constrain cosmological parameters at 6 < z < 20. The sensitivity of an interferometer to the cosmological information in the signal may depend on how precisely the angular dependence of the 21 cm 3-D power spectrum can be measured. Utilizing an analytic model for reionization, we quantify all the effects that break the spherical symmetry of the 3-D 21 cm power spectrum and produce physically motivated predictions for this power spectrum. We find that upcoming observatories will be sensitive to the 21 cm signal over a wide range of scales, from larger than 100 to as small as 1 comoving Mpc. We consider three methods to measure cosmological parameters from the signal: (1) direct fitting of the density power spectrum to the signal, (2) using only the velocity field fluctuations in the signal, (3) looking at the signal at large enough scales such that all fluctuations trace the density field. With the foremost method, the first generation of 21 cm observations should moderately improve existing constraints on cosmological parameters for certain low-redshift reionization scenarios, and a two year observation with the second generation interferometer MWA5000 can improve constraints on Omega_w, Omega_m h^2, Omega_b h^2, Omega_nu, n_s, and alpha_s. If the Universe is substantially ionized by z = 12 or if spin temperature fluctuations are important, we show that it will be difficult to place competitive constraints on cosmological parameters with any of the considered methods.Comment: 20 pages, 12 figures, accepted by Ap

Torsion Degrees of Freedom in the Regge Calculus as Dislocations on the Simplicial Lattice

Using the notion of a general conical defect, the Regge Calculus is generalized by allowing for dislocations on the simplicial lattice in addition to the usual disclinations. Since disclinations and dislocations correspond to curvature and torsion singularities, respectively, the method we propose provides a natural way of discretizing gravitational theories with torsion degrees of freedom like the Einstein-Cartan theory. A discrete version of the Einstein-Cartan action is given and field equations are derived, demanding stationarity of the action with respect to the discrete variables of the theory

Spring-seeded smother plants for weed control in corn and soybeans

Smother plants are specialized cover crops developed for their ability to suppress weeds and may provide an alternative, non-chemical method of weed control. The goal of this project was to define the characteristics and mechanics of establishing a successful spring-seeded smother plant system and to study and exploit the competitive interactions among weeds, smother plants, and the crop

Detection of Building Damage Using Helmholtz Tomography

High‐rise buildings with dense permanent installations of continuously recording accelerometers offer a unique opportunity to observe temporal and spatial variations in the propagation properties of seismic waves. When precise, floor‐by‐floor measurements of frequency‐dependent travel times can be made, accurate models of material properties (e.g., stiffness or rigidity) can be determined using seismic tomographic imaging techniques. By measuring changes in the material properties, damage to the structure can be detected and localized after shaking events such as earthquakes. Here, seismic Helmholtz tomography is applied to simulated waveform data from a high‐rise building, and its feasibility is demonstrated. A 52‐story dual system building—braced‐frame core surrounded by an outrigger steel moment frame—in downtown Los Angeles is used for the computational basis. It is part of the Community Seismic Network and has a three‐component accelerometer installed on every floor. A finite‐element model of the building based on structural drawings is used for the computation of synthetic seismograms for 60 damage scenarios in which the stiffness of the building is perturbed in different locations across both adjacent and distributed floors and to varying degrees. The dynamic analysis loading function is a Gaussian pulse applied to the lowest level fixed boundary condition, producing a broadband response on all floors. After narrowband filtering the synthetic seismograms and measuring the maximum amplitude, the frequency‐dependent travel times and differential travel times are computed. The travel‐time and amplitude measurements are converted to shear‐wave velocity at each floor via the Helmholtz wave equation whose solutions can be used to track perturbations to wavefronts through densely sampled wavefields. These results provide validation of the method’s application to recorded data from real buildings to detect and locate structural damage using earthquake, explosion, or ambient seismic noise data in near‐real time

Detection of Building Damage Using Helmholtz Tomography

High‐rise buildings with dense permanent installations of continuously recording accelerometers offer a unique opportunity to observe temporal and spatial variations in the propagation properties of seismic waves. When precise, floor‐by‐floor measurements of frequency‐dependent travel times can be made, accurate models of material properties (e.g., stiffness or rigidity) can be determined using seismic tomographic imaging techniques. By measuring changes in the material properties, damage to the structure can be detected and localized after shaking events such as earthquakes. Here, seismic Helmholtz tomography is applied to simulated waveform data from a high‐rise building, and its feasibility is demonstrated. A 52‐story dual system building—braced‐frame core surrounded by an outrigger steel moment frame—in downtown Los Angeles is used for the computational basis. It is part of the Community Seismic Network and has a three‐component accelerometer installed on every floor. A finite‐element model of the building based on structural drawings is used for the computation of synthetic seismograms for 60 damage scenarios in which the stiffness of the building is perturbed in different locations across both adjacent and distributed floors and to varying degrees. The dynamic analysis loading function is a Gaussian pulse applied to the lowest level fixed boundary condition, producing a broadband response on all floors. After narrowband filtering the synthetic seismograms and measuring the maximum amplitude, the frequency‐dependent travel times and differential travel times are computed. The travel‐time and amplitude measurements are converted to shear‐wave velocity at each floor via the Helmholtz wave equation whose solutions can be used to track perturbations to wavefronts through densely sampled wavefields. These results provide validation of the method’s application to recorded data from real buildings to detect and locate structural damage using earthquake, explosion, or ambient seismic noise data in near‐real time