Time-Optimal Tree Computations on Sparse Meshes

The main goal of this work is to fathom the suitability of the mesh with multiple broadcasting architecture (MMB) for some tree-related computations. We view our contribution at two levels: on the one hand, we exhibit time lower bounds for a number of tree-related problems on the MMB. On the other hand, we show that these lower bounds are tight by exhibiting time-optimal tree algorithms on the MMB. Specifically, we show that the task of encoding and/or decoding n-node binary and ordered trees cannot be solved faster than Ω(log n) time even if the MMB has an infinite number of processors. We then go on to show that this lower bound is tight. We also show that the task of reconstructing n-node binary trees and ordered trees from their traversais can be performed in O(1) time on the same architecture. Our algorithms rely on novel time-optimal algorithms on sequences of parentheses that we also develop

Straits and seaways: controls, processes and implications in modern and ancient systems

Straits and seaways are connections between basins, key areas for exchange and transfer of water, heat, biota and sediments, and they can influence regional and global climate. A better understanding of strait/seaway dynamics, their evolution and preserved deposits is, therefore, fundamental to reconstructing the palaeoecology, palaeogeography and stratigraphy of interconnected basins. Straits and seaways are also important for understanding climate dynamics in Earth's past, and for safely exploiting energy resources (fossil and renewable). This volume aims at improving the knowledge on this topic, and at providing a comprehensive collection of state-of-the-art works bringing together complementary disciplines. Even though studies on modern and ancient straits and seaways exist, they are not necessarily conceived towards a better geological understanding of these features as depositional systems in their own right. In this introduction, we emphasize the geological importance of straits and seaways, summarizing the content and key findings of the contributions on this topic. The articles included in this volume explore four main research themes related to straits and seaways: (1) occurrence and classification; (2) morphological features, facies and stratigraphic variability, sedimentary processes and dynamics; (3) tectonic and climatic controls, their feedback with climate changes; and (4) palaeogeographical reconstructions and preservation of associated deposits

Aharonov-Bohm interference in the presence of metallic mesoscopic cylinders

This work studies the interference of electrons in the presence of a line of magnetic flux surrounded by a normal-conducting mesoscopic cylinder at low temperature. It is found that, while there is a supplementary phase contribution from each electron of the mesoscopic cylinder, the sum of these individual supplementary phases is equal to zero, so that the presence of a normal-conducting mesoscopic ring at low temperature does not change the Aharonov-Bohm interference pattern of the incident electron. It is shown that it is not possible to ascertain by experimental observation that the shielding electrons have responded to the field of an incident electron, and at the same time to preserve the interference pattern of the incident electron. It is also shown that the measuring of the transient magnetic field in the region between the two paths of an electron interference experiment with an accuracy at least equal to the magnetic field of the incident electron generates a phase uncertainty which destroys the interference pattern.Comment: 15 pages, 5 Postscript figure

A proposal for detecting second order topological quantum phase

Gaussian linking of a semiclassical path of a charged particle with a magnetic flux tube is responsible for the Aharonov-Bohm effect, where one observes interference proportional to the magnitude of the enclosed flux. We construct quantum mechanical wave functions where semiclassical paths can have second order linking to two magnetic flux tubes, and show there is interference proportional to the product of the two fluxes.Comment: 7 pages, 4 figure

Perturbative Study of Bremsstrahlung and Pair-Production by Spin-1/2 Particles in the Aharonov-Bohm Potential

In the presence of an external Aharonov-Bohm potential, we investigate the two QED processes of the emission of a bremsstrahlung photon by an electron, and the production of an electron-positron pair by a single photon. Calculations are carried out using the Born approximation within the framework of covariant perturbation theory to lowest non-vanishing order in \alpha. The matrix element for each process is derived, and the corresponding differential cross-section is calculated. In the non-relativistic limit, the resulting angular and spectral distributions and some polarization properties are considered, and compared to results of previous works.Comment: 15 pages, RevTex 4, 2 figures, submitted for publicatio

Electron-positron pair production in the Aharonov-Bohm potential

In the framework of QED we evaluate the cross section for electron-positron pair production by a single photon in the presence of the external Aharonov-Bohm potential in first order of perturbation theory. We analyse energy, angular and polarization distributions at different energy regimes: near the threshold and at high photon energies.Comment: LaTeX file, 13 page