Non-Hamiltonian dynamics in optical microcavities resulting from wave-inspired corrections to geometric optics

We introduce and investigate billiard systems with an adjusted ray dynamics that accounts for modifications of the conventional reflection of rays due to universal wave effects. We show that even small modifications of the specular reflection law have dramatic consequences on the phase space of classical billiards. These include the creation of regions of non-Hamiltonian dynamics, the breakdown of symmetries, and changes in the stability and morphology of periodic orbits. Focusing on optical microcavities, we show that our adjusted dynamics provides the missing ray counterpart to previously observed wave phenomena and we describe how to observe its signatures in experiments. Our findings also apply to acoustic and ultrasound waves and are important in all situations where wavelengths are comparable to system sizes, an increasingly likely situation considering the systematic reduction of the size of electronic and photonic devices.Comment: 6 pages, 4 figures, final published versio

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

Detecting failure events in buildings: a numerical and experimental analysis

A numerical method is used to investigate an approach for detecting the brittle fracture of welds associated with beam -column connections in instrumented buildings in real time through the use of time-reversed Green’s functions and wave propagation reciprocity. The approach makes use of a prerecorded catalog of Green’s functions for an instrumented building to detect failure events in the building during a later seismic event by screening continuous data for the presence of waveform similarities to one of the prerecorded events. This study addresses whether a set of Green’s functions in response to an impulsive force load can be used to approximate the response of the structure to a localized failure event such as a brittle weld fracture. Specifically, we investigate whether prerecorded Green’s functions can be used to determine the absolute time and location of a localized failure event in a building. We also seek to differentiate between sources such as a weld fracture that are structurally damaging and sources such as falling or colliding furniture and other non-structural elements that do not contribute to structural failure. This is explored numerically by comparing the dynamic response of a finite-element cantilevered beam model structure to a variety of loading mechanisms. A finite-element method is employed to determine the behavior of the resulting elastic waves and to obtain a general understanding of the structural response

Complex scattering within D" observed on the very dense Los Angeles Region Seismic Experiment passive array

Several seismic phases that scattered within a few hundred kilometers of the base of the mantle are observed in a very dense seismic section. The Los Angeles Region Seismic Experiment passive phase array was composed of 88 seismometers placed along a 175 km profile. Records from two deep earthquakes in Tonga and one earthquake near Honshu, Japan show a secondary arrival between clear P and PcP arrivals. Modeling with layered structures shows that the Tonga and Honshu seismic sections are consistent with an increase in seismic velocity 140 and 240 km above the core-mantle boundary, respectively, and a ≃10-km thick low-velocity zone at the base of the mantle beneath a region in the mid Pacific. Several of these arrivals are not coherent enough to appear in higher resolution stacks from the much larger Southern California Seismic Network. This experiment illustrates that fine-scale passive array data can reveal small-scale deep Earth structure invisible to larger-scale seismic networks

Earthquake and ambient vibration monitoring of the steel frame UCLA Factor building

Dynamic property measurements of the moment-resisting steel-frame University of California, Los Angeles, Factor building are being made to assess how forces are distributed over the building. Fourier amplitude spectra have been calculated from several intervals of ambient vibrations, a 24-hour period of strong winds, and from the 28 March 2003 Encino, California (M_L =2.9), the 3 September 2002 Yorba Linda, California (M_L=4.7), and the 3 November 2002 Central Alaska (M_w=7.9) earthquakes. Measurements made from the ambient vibration records show that the first-mode frequency of horizontal vibration is between 0.55 and 0.6 Hz. The second horizontal mode has a frequency between 1.6 and 1.9 Hz. In contrast, the first-mode frequencies measured from earthquake data are about 0.05 to 0.1 Hz lower than those corresponding to ambient vibration recordings indicating softening of the soil-structure system as amplitudes become larger. The frequencies revert to pre-earthquake levels within five minutes of the Yorba Linda earthquake. Shaking due to strong winds that occurred during the Encino earthquake dominates the frequency decrease, which correlates in time with the duration of the strong winds. The first shear wave recorded from the Encino and Yorba Linda earthquakes takes about 0.4 sec to travel up the 17-story building

Compartmental Bone Morphometry in the Mouse Femur: Reproducibility and Resolution Dependence of Microtomographic Measurements

Microcomputed tomography (μCT) is widely used for nondestructive bone phenotyping in small animals, especially in the mouse. Here, we investigated the reproducibility and resolution dependence of μCT analysis of microstructural parameters in three different compartments in the mouse femur. Reproducibility was assessed with respect to precision error (PE%CV) and intraclass correlation coefficient (ICC). We examined 14 left femurs isolated postmortem from two strains of mice (seven per group). Measurements and analyses were repeated five times on different days. In a second step, analysis was repeated again five times for a single measurement. Resolution dependence was assessed by high-resolution measurements (10μm) in one strain and subsequent image degrading. Reproducibility was better in full bone compartment and in cortical bone compartment in the diaphysis (PE%CV = 0.06-2.16%) than in trabecular compartment in the distal metaphysis (PE%CV = 0.59-5.24%). Nevertheless, ICC (0.92-1.00) showed a very high reliability of the assessed parameters in all regions, indicating very small variances within repeated measurements compared to the population variances. Morphometric indices computed from lower- and higher-resolution images displayed in general only weak dependence and were highly correlated with each other (R2 = 0.91-0.99). The results show that parameters in the full and cortical compartments were very reproducible, whereas precision in the trabecular compartment was somewhat lower. Nevertheless, all compartmental analysis methods were very robust, as shown by the high ICC values, demonstrating high suitability for application in inbred strains, where highest precision is needed due to small population variance

Macroscopic aspects of relativistic x-ray assisted high-order harmonic generation

A theoretical model is developed describing high-order harmonic generation (HHG) from a gas of multiply-charged ions driven by a laser field of relativistic intensity. Macroscopic propagation of harmonics is investigated in a relativistic HHG setup where the relativistic drift is suppressed by means of x-ray field assistance of the driving laser field. The possibility of phase-matched emission of the harmonics is shown. The laser field geometry is optimized to maximize the HHG yield with the corresponding phase-matching schemes. Crucial issues determining the macroscopic HHG yield are discussed in detail