Unified algebraic treatment of resonance

Energy resonance in scattering is usually investigated either directly in the complex energy plane (E-plane) or indirectly in the complex angular momentum plane (L-plane). Another formulation complementing these two approaches was introduced recently. It is an indirect algebraic method that studies resonances in a complex charge plane (Z-plane). This latter approach will be generalized to provide a unified algebraic treatment of resonances in the complex E-, L-, and Z-planes. The complex scaling (rotation) method will be used in the development of this approach. The resolvent operators (Green's functions) are formally defined in these three spaces. Bound states spectrum and resonance energies in the E-plane are mapped onto a discrete set of poles of the respective resolvent operator on the real line of the L- and Z-planes. These poles move along trajectories as the energy is varied. A finite square integrable basis is used in the numerical implementation of this approach. Stability of poles and trajectories against variation in all computational parameters is demonstrated. Resonance energies for a given potential are calculated and compared with those obtained by other studies.Comment: 15 pages, 1 Table, 7 Figures (6 are snapshots of videos

Are megaquakes clustered?

We study statistical properties of the number of large earthquakes over the past century. We analyze the cumulative distribution of the number of earthquakes with magnitude larger than threshold M in time interval T, and quantify the statistical significance of these results by simulating a large number of synthetic random catalogs. We find that in general, the earthquake record cannot be distinguished from a process that is random in time. This conclusion holds whether aftershocks are removed or not, except at magnitudes below M = 7.3. At long time intervals (T = 2-5 years), we find that statistically significant clustering is present in the catalog for lower magnitude thresholds (M = 7-7.2). However, this clustering is due to a large number of earthquakes on record in the early part of the 20th century, when magnitudes are less certain.Comment: 5 pages, 5 figure

Fe–Ga/Pb(Mg1/3Nb2/3)O3–PbTiO3 magnetoelectric laminate composites

We have found large magnetoelectric (ME) effects in long-type laminate composites of Fe–20%Ga magnetostrictive alloys and piezoelectric Pb(Mg1/3Nb2/3)O3–PbTiO3 single crystals. At lower frequencies, the ME voltage coefficient of a laminate with longitudinally magnetized and longitudinally polarized (i.e., L-L mode) layers was 1.41 V/Oe (or1.01 V/cm Oe). Near the natural resonant frequency ( ∼ 91 kHz) of the laminate, the ME voltage coefficients were found to be dramatically increased to 50.7 V/Oe (36.2 V/cm Oe)for the L-L mode. In addition, the laminate can detect a minute magnetic field as low as ∼ 2×10−12 T at resonance frequency, and ∼ 1×10−10 T at lower frequencies

Magnetostrictive and magnetoelectric behavior of Fe–20 at. % Ga/Pb(Zr,Ti)O3 laminates

The magnetostrictive and magnetoelectric (ME) properties of laminate composites of Fe–20 at. % Ga and Pb(Zr,Ti)O3 (PZT) have been studied for laminates of different geometries. The results show that (i) a long-type magnetostrictive Fe–20 at. % Ga crystal plate oriented along 〈001〉c and magnetized in its longitudinal (or length) direction has higher magnetostriction than a disk-type one; and consequently (ii) a long-type Fe–20 at. % Ga/PZT laminate has a giant ME effect, and is sensitive to low-level magnetic fields

Back-arc extension in the Andaman Sea: Tectonic and magmatic processes imaged by high-precision teleseismic double-difference earthquake relocation

The geometry, kinematics, and mode of back-arc extension along the Andaman Sea plate boundary are refined using a new set of significantly improved hypocenters, global centroid moment tensor (CMT) solutions, and high-resolution bathymetry. By applying cross-correlation and double-difference (DD) algorithms to regional and teleseismic waveforms and arrival times from International Seismological Centre and National Earthquake Information Center bulletins (1964–2009), we resolve the fine-scale structure and spatiotemporal behavior of active faults in the Andaman Sea. The new data reveal that back-arc extension is primarily accommodated at the Andaman Back-Arc Spreading Center (ABSC) at ~10°, which hosted three major earthquake swarms in 1984, 2006, and 2009. Short-term spreading rates estimated from extensional moment tensors account for less than 10% of the long-term 3.0–3.8 cm/yr spreading rate, indicating that spreading by intrusion and the formation of new crust make up for the difference. A spatiotemporal analysis of the swarms and Coulomb-stress modeling show that dike intrusions are the primary driver for brittle failure in the ABSC. While spreading direction is close to ridge normal, it is oblique to the adjacent transforms. The resulting component of E-W extension across the transforms is expressed by deep basins on either side of the rift and a change to extensional faulting along the West Andaman fault system after the Mw = 9.2 Sumatra-Andaman earthquake of 2004. A possible skew in slip vectors of earthquakes in the eastern part of the ABSC indicates an en-echelon arrangement of extensional structures, suggesting that the present segment geometry is not in equilibrium with current plate-motion demands, and thus the ridge experiences ongoing re-adjustment

The Importance of Boundary Conditions in Quantum Mechanics

We discuss the role of boundary conditions in determining the physical content of the solutions of the Schrodinger equation. We study the standing-wave, the ``in,'' the ``out,'' and the purely outgoing boundary conditions. As well, we rephrase Feynman's $+i \epsilon$ prescription as a time-asymmetric, causal boundary condition, and discuss the connection of Feynman's $+i \epsilon$ prescription with the arrow of time of Quantum Electrodynamics. A parallel of this arrow of time with that of Classical Electrodynamics is made. We conclude that in general, the time evolution of a closed quantum system has indeed an arrow of time built into the propagators.Comment: Contribution to the proceedings of the ICTP conference "Irreversible Quantum Dynamics," Trieste, Italy, July 200

The ISC-GEM Earthquake Catalogue (1904–2014): status after the Extension Project

We outline the work done to extend and improve the ISC-GEM Global Instrumental Earthquake Catalogue, a dataset which was first released in 2013 (Storchak et al., 2013, 2015). In its first version (V1) the catalogue included global earthquakes selected according to time-dependent cut-off magnitudes: 7.5 and above between 1900 and 1918 (plus significant continental earthquakes 6.5 and above); 6.25 between 1918 and 1959; 5.5 between 1960 and 2009. Such selection criteria were dictated by time and resource limitations. With the Extension Project we added both pre-1960 events below the original cut-off magnitudes (if enough station data were available to perform relocation and magnitude recomputation) and added events with magnitude 5.5 and above from 2010 to 2014. The project ran over a 4-year period during which a new version of the ISC-GEM Catalogue was released each year via the ISC website (http://http://www.isc.ac.uk/iscgem/, last access: 10 October 2018). For each year, not only have we added new events to the catalogue for a given time range but also revised events already in V1 if additional data became available or location and/or magnitude reassessments were required. Here we recall the general background behind the production of the ISC-GEM Catalogue and describe the features of the different periods in which the catalogue has been extended. Compared to the 2013 release, we eliminated earthquakes during the first 4 years (1900–1903) of the catalogue (due to lack of reliable station data), added approximately 12&thinsp;000 and 2500 earthquakes before 1960 and between 2010 and 2014, respectively, and improved the solution for approximately 2000 earthquakes already listed in previous versions. We expect the ISC-GEM Catalogue to continue to be one of the most useful datasets for studies of the Earth's global seismicity and an important benchmark for seismic hazard analyses, and, ultimately, an asset for the seismological community as well as other geoscience fields, education and outreach activities. The ISC-GEM Catalogue is freely available at https://doi.org/10.31905/D808B825.</p