Reciprocity principle in duct acoustics

Various reciprocity relations in duct acoustics have been derived on the basis of the spatial reciprocity principle implied in Green's functions for linear waves. The derivation includes the reciprocity relations between mode conversion coefficients for reflection and transmission in nonuniform ducts, and the relation between the radiation of a mode from an arbitrarily terminated duct and the absorption of an externally incident plane wave by the duct. Such relations are well defined as long as the systems remain linear, regardless of acoustic properties of duct nonuniformities which cause the mode conversions

Towards Complexity for Quantum Field Theory States

We investigate notions of complexity of states in continuous quantum-many body systems. We focus on Gaussian states which include ground states of free quantum field theories and their approximations encountered in the context of the continuous version of Multiscale Entanglement Renormalization Ansatz. Our proposal for quantifying state complexity is based on the Fubini-Study metric. It leads to counting the number of applications of each gate (infinitesimal generator) in the transformation, subject to a state-dependent metric. We minimize the defined complexity with respect to momentum preserving quadratic generators which form $\mathfrak{su}(1,1)$ algebras. On the manifold of Gaussian states generated by these operations the Fubini-Study metric factorizes into hyperbolic planes with minimal complexity circuits reducing to known geodesics. Despite working with quantum field theories far outside the regime where Einstein gravity duals exist, we find striking similarities between our results and holographic complexity proposals.Comment: 6+7 pages, 6 appendices, 2 figures; v2: references added; acknowledgments expanded; appendix F added, reviewing similarities and differences with hep-th/1707.08570; v3: version published in PR

Equation for the superfluid gap obtained by coarse graining the Bogoliubov-de Gennes equations throughout the BCS-BEC crossover

We derive a nonlinear differential equation for the gap parameter of a superfluid Fermi system by performing a suitable coarse graining of the Bogoliubov-de Gennes (BdG) equations throughout the BCS-BEC crossover, with the aim of replacing the time-consuming solution of the original BdG equations by the simpler solution of this novel equation. We perform a favorable numerical test on the validity of this new equation over most of the temperature-coupling phase diagram, by an explicit comparison with the full solution of the original BdG equations for an isolated vortex. We also show that the new equation reduces both to the Ginzburg-Landau equation for Cooper pairs in weak coupling close to the critical temperature and to the Gross-Pitaevskii equation for composite bosons in strong coupling at low temperature.Comment: 12 pages, 8 figure

Signatures of Infinity: Nonergodicity and Resource Scaling in Prediction, Complexity, and Learning

We introduce a simple analysis of the structural complexity of infinite-memory processes built from random samples of stationary, ergodic finite-memory component processes. Such processes are familiar from the well known multi-arm Bandit problem. We contrast our analysis with computation-theoretic and statistical inference approaches to understanding their complexity. The result is an alternative view of the relationship between predictability, complexity, and learning that highlights the distinct ways in which informational and correlational divergences arise in complex ergodic and nonergodic processes. We draw out consequences for the resource divergences that delineate the structural hierarchy of ergodic processes and for processes that are themselves hierarchical.Comment: 8 pages, 1 figure; http://csc.ucdavis.edu/~cmg/compmech/pubs/soi.pd

A survey of the state-of-the-art and focused research in range systems

In this one-year renewal of NASA Contract No. 2-304, basic research, development, and implementation in the areas of modern estimation algorithms and digital communication systems have been performed. In the first area, basic study on the conversion of general classes of practical signal processing algorithms into systolic array algorithms is considered, producing four publications. Also studied were the finite word length effects and convergence rates of lattice algorithms, producing two publications. In the second area of study, the use of efficient importance sampling simulation technique for the evaluation of digital communication system performances were studied, producing two publications

Deformation due to the 17 August 1999 Izmit, Turkey, earthquake measured from SPOT images

The geometry of the ruptured areas and the coseismic slip distribution data are key to highlighting the behavior of seismic faults. This information is generally retrieved from field investigations and geodetic measurements or synthetic aperture radar (SAR) interferometry. Here we show that SPOT images can also be used to accurately map the fault zone and to determine the slip distribution by subpixel correlation of images acquired before and after an earthquake. The measured slip includes the contribution of possible distributed shear that might not be clearly expressed in surface ruptures and smoothes out possible along-strike variability due to near-surface fault complexities. We apply the technique to the M_s = 7.4, 1999, Izmit earthquake. Our results reveal a <100-m-wide and very linear fault zone that can be traced for 70 km from Gölcük to Akyazi, along which supershear rupture has been inferred. The obtained slip distribution compares well with the field measurements and is consistent with ground deformation measured at some distance from the fault zone using SAR images. Very little deformation was accommodated off the main fault plane. Maximum slip is observed near Sapanca lake at a small fault jog that has probably influenced rupture propagation