Incompatible sets of gradients and metastability

We give a mathematical analysis of a concept of metastability induced by incompatibility. The physical setting is a single parent phase, just about to undergo transformation to a product phase of lower energy density. Under certain conditions of incompatibility of the energy wells of this energy density, we show that the parent phase is metastable in a strong sense, namely it is a local minimizer of the free energy in an $L^1$ neighbourhood of its deformation. The reason behind this result is that, due to the incompatibility of the energy wells, a small nucleus of the product phase is necessarily accompanied by a stressed transition layer whose energetic cost exceeds the energy lowering capacity of the nucleus. We define and characterize incompatible sets of matrices, in terms of which the transition layer estimate at the heart of the proof of metastability is expressed. Finally we discuss connections with experiment and place this concept of metastability in the wider context of recent theoretical and experimental research on metastability and hysteresis.Comment: Archive for Rational Mechanics and Analysis, to appea

Triangulation network of 1929-1944 of the first 1:500 urban map of València

[EN] Triangulation is a surveying method on which earlier maps made were based. Although the origins of the method can be traced back to the 16th century, it is still used today, with minor changes, to adjust networks observed with modern geodetic techniques. In this paper we present the geodetic survey work that was carried out for the primary triangulation network of the first 1:500 urban map of the city of València (Spain). It spanned from 1929 to 1944 and resulted in 421 maps covering about 174 square kilometres. We focus on four key elements to define the geometric framework of a map: (1) the geodetic network, (2) the cartographic projection, (3) the baseline measurements, and (4) the primary triangulation. The paper is based on the interpretation of original documents and field books recovered from the archives of the València City Council. In order to check the accuracy and consistency of the survey work, we recomputed all calculations directly from the field data, following the mathematical procedures of the time. We obtained a set of transformation parameters to convert the coordinates of 1929 to current coordinates based on the European Terrestrial Reference System of 1989 (ETRS89). Results showed that the 1929 primary triangulation angles and coordinates are accurate to 8 s of arc and 35 cm respectively, and that the coordinates transform well into the current reference system with average residuals of 26 cm across nine control points, demonstrating the high quality of the 1929 work.Villar-Cano, M.; Marqués-Mateu, Á.; Jiménez-Martínez, MJ. (2020). Triangulation network of 1929-1944 of the first 1:500 urban map of València. Survey Review (Online). 52(373):317-329. https://doi.org/10.1080/00396265.2018.1564599S31732952373Bitelli, G., Cremonini, S., & Gatta, G. (2014). Cartographic heritage: Toward unconventional methods for quantitative analysis of pre-geodetic maps. Journal of Cultural Heritage, 15(2), 183-195. doi:10.1016/j.culher.2013.04.003Blachut, T. J., Chrzanowski, A., & Saastamoinen, J. H. (1979). Urban Surveying and Mapping. doi:10.1007/978-1-4612-6145-2Brinker, R. C., & Minnick, R. (Eds.). (1987). The Surveying Handbook. doi:10.1007/978-1-4757-1188-2Gatta, G. 2010. Valorizzazione di cartografia storica attraverso moderne tecniche geomatiche: recupero metrico, elaborazione e consultazione in ambiente digitale [Valuation of historic cartography using modern geomatics techniques: metric recovering, making and use in digital environment]. Doctoral thesis. Bologna: Universitá di Bologna. 295 pages. (In Italian).Gorse, C., Johnston, D., & Pritchard, M. (2012). A Dictionary of Construction, Surveying and Civil Engineering. doi:10.1093/acref/9780199534463.001.0001Hotine, M. (1939). THE RE-TRIANGULATION OF GREAT BRITAIN IV—BASE MEASUREMENT. Empire Survey Review, 5(34), 211-225. doi:10.1179/sre.1939.5.34.211Kahmen, H., & Faig, W. (1988). Surveying. doi:10.1515/9783110845716Leick, A., Rapoport, L., & Tatarnikov, D. (2015). GPS Satellite Surveying. doi:10.1002/9781119018612Murdin, P. (2009). Full Meridian of Glory. doi:10.1007/978-0-387-75534-2Schofield, W., & Breach, M. (2007). Engineering Surveying. doi:10.1201/b12847Seeber, G. (2003). Satellite Geodesy. doi:10.1515/9783110200089Snyder, J. P. (1987). Map projections: A working manual. Professional Paper. doi:10.3133/pp139

Search for W' bosons decaying to an electron and a neutrino with the D0 detector

This Letter describes the search for a new heavy charged gauge boson W' decaying into an electron and a neutrino. The data were collected with the D0 detector at the Fermilab Tevatron proton-antiproton Collider at a center-of-mass energy of 1.96 TeV, and correspond to an integrated luminosity of about 1 inverse femtobarn. Lacking any significant excess in the data in comparison with known processes, an upper limit is set on the production cross section times branching fraction, and a W' boson with mass below 1.00 TeV can be excluded at the 95% C.L., assuming standard-model-like couplings to fermions. This result significantly improves upon previous limits, and is the most stringent to date.Comment: submitted to Phys. Rev. Let

Measurement of the Isolated Photon Cross Section in p-pbar Collisions at sqrt{s}=1.96 TeV

The cross section for the inclusive production of isolated photons has been measured in p anti-p collisions at sqrt{s}=1.96 TeV with the D0 detector at the Fermilab Tevatron Collider. The photons span transverse momenta 23 to 300 GeV and have pseudorapidity |eta|<0.9. The cross section is compared with the results from two next-to-leading order perturbative QCD calculations. The theoretical predictions agree with the measurement within uncertainties.Comment: 7 pages, 5 figures, submitted to Phys.Lett.

Measurement of the p-pbar -> Wgamma + X cross section at sqrt(s) = 1.96 TeV and WWgamma anomalous coupling limits

The WWgamma triple gauge boson coupling parameters are studied using p-pbar -> l nu gamma + X (l = e,mu) events at sqrt(s) = 1.96 TeV. The data were collected with the DO detector from an integrated luminosity of 162 pb^{-1} delivered by the Fermilab Tevatron Collider. The cross section times branching fraction for p-pbar -> W(gamma) + X -> l nu gamma + X with E_T^{gamma} > 8 GeV and Delta R_{l gamma} > 0.7 is 14.8 +/- 1.6 (stat) +/- 1.0 (syst) +/- 1.0 (lum) pb. The one-dimensional 95% confidence level limits on anomalous couplings are -0.88 < Delta kappa_{gamma} < 0.96 and -0.20 < lambda_{gamma} < 0.20.Comment: Submitted to Phys. Rev. D Rapid Communication

Measurement of the ttbar Production Cross Section in ppbar Collisions at sqrt{s} = 1.96 TeV using Kinematic Characteristics of Lepton + Jets Events

We present a measurement of the top quark pair ttbar production cross section in ppbar collisions at a center-of-mass energy of 1.96 TeV using 230 pb**{-1} of data collected by the DO detector at the Fermilab Tevatron Collider. We select events with one charged lepton (electron or muon), large missing transverse energy, and at least four jets, and extract the ttbar content of the sample based on the kinematic characteristics of the events. For a top quark mass of 175 GeV, we measure sigma(ttbar) = 6.7 {+1.4-1.3} (stat) {+1.6- 1.1} (syst) +/-0.4 (lumi) pb, in good agreement with the standard model prediction.Comment: submitted to Phys.Rev.Let

Measurement of the ttbar Production Cross Section in ppbar Collisions at sqrt(s)=1.96 TeV using Lepton + Jets Events with Lifetime b-tagging

We present a measurement of the top quark pair ($t\bar{t}$) production cross section ($\sigma_{t\bar{t}}$) in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV using 230 pb$^{-1}$ of data collected by the D0 experiment at the Fermilab Tevatron Collider. We select events with one charged lepton (electron or muon), missing transverse energy, and jets in the final state. We employ lifetime-based b-jet identification techniques to further enhance the $t\bar{t}$ purity of the selected sample. For a top quark mass of 175 GeV, we measure $\sigma_{t\bar{t}}=8.6^{+1.6}_{-1.5}(stat.+syst.)\pm 0.6(lumi.)$ pb, in agreement with the standard model expectation.Comment: 7 pages, 2 figures, 3 tables Submitted to Phys.Rev.Let

Search for a scalar or vector particle decaying into Zgamma in ppbar collisions at sqrt(s) = 1.96 TeV

We present a search for a narrow scalar or vector resonance decaying into Zgamma with a subsequent Z decay into a pair of electrons or muons. The data for this search were collected with the D0 detector at the Fermilab Tevatron ppbar collider at a center of mass energy sqrt(s) = 1.96 TeV. Using 1.1 (1.0) fb-1 of data, we observe 49 (50) candidate events in the electron (muon) channel, in good agreement with the standard model prediction. From the combination of both channels, we derive 95% C.L. upper limits on the cross section times branching fraction (sigma x B) into Zgamma. These limits range from 0.19 (0.20) pb for a scalar (vector) resonance mass of 600 GeV/c^2 to 2.5 (3.1) pb for a mass of 140 GeV/c^2.Comment: Published by Phys. Lett.