Uncertainty-based experimental validation of nonlinear reduced order models

This paper presents the first results of a combined experimental–computational investigation focused on the validation of reduced order models of geometrically nonlinear structures in the presence of uncertainty. The validation approach considered here is based on the premise that the model is valid if the experimental results can be considered as random sample responses of the stochastic system of which the reduced order model is the mean. For the situation considered here, the power spectra of the experiments should lie within the 2nd and 98th percentiles of the response (forming the uncertainty band) of the stochastic model. Nominally clamped–clamped beams are considered to demonstrate the entire process. The construction of two mean reduced order models and their stochastic counterparts are first performed. Then, the validation effort is carried out by comparing experimentally obtained power spectra and their corresponding computational uncertainty bands. This process leads, for both reduced order models, to a very good representation of the important upper envelope (98th percentile) of the experimental data but a less good fit of the lower envelope (2nd percentile).     

Characterization of the road surfaces in real time

The main factor in the propagation of traffic noise is the road surface, where the vehicles generate noise due to the contact between tire and pavement, in addition to the noise produced by the engine.     

Block renormalization group for Euclidean Fermions

Block renormalization group transformations (RGT) for lattice and continuum Euclidean Fermions in d dimensions are developed using Fermionic integrals with exponential and -function weight functions. For the free field the sequence of actionsD _k generated by the RGT from D, the Dirac operator, are shown to have exponential decay; uniform ink, after rescaling to the unit lattice. It is shown that the two-point functionD ^–1 admits a simple telescopic sum decomposition into fluctuation two-point functions which for the exponential weight RGT have exponential decay. Contrary to RG intuition the sequence of rescaled actions corresponding to the -function RGT do not have uniform exponential decay and we give examples of initial actions in one dimension where this phenomena occurs for the exponenential weight RGT also.     

Spatiotemporal and statistical symmetries

The notion of symmetries, either statistical or deterministic, can be useful for the characterization of complex systems and their bifurcations. In this paper, we investigate the connection between the (microscopic) spatiotemporal symmetries of a space-time functionu(x, t), on the one hand, and the (macroscopic) symmetries of statistical quantities such as the spatial (resp. temporal) two-point correlations and the spatial (resp. temporal) average, on the other hand. We show, how, under certain conditions, these symmetries are related to the symmetries of the orbits described byu(x, t) in the characteristic (phase) spaces. We also determine the largest group of spatiotemporal symmetries (in the sense introduced in our earlier work) satisfied by a given space-time functionu(x, t) and indicate how to extract the subgroups of point symmetries, namely those directly implemented on the space and time variables. Conversely, we determine all the functions invariant by a given space-time symmetry group. Finally, we illustrate all the previous points with specific examples.     

EDXRF and multivariate statistical analysis of fragments from Marajoara ceramics

In this work, 102 fragments of Marajoara ceramics, belonging to the National Museum collection (Rio de Janeiro, Brazil), were analyzed using energy dispersive X‐ray fluorescence (EDXRF) and principal component analysis (PCA) in order to identify possible groups of samples that present similar behaviors or different characteristics. This information will give an important aid to a more accurate classification of these artifacts. The EDXRF measurements were carried out with a portable system developed in the Nuclear Instrumentation Laboratory consisting of an Oxford TF3005 X‐ray tube, with W anode, and an Si‐PIN XR‐100CR detector from Amptek, working at 25 kV and 100 µA, acquisition time of 600 s and a beam collimation of 2 mm. PCA applied to the X‐ray fluorescence results revealed a clear cluster separation to the samples. Copyright © 2009 John Wiley & Sons, Ltd.     

Enhancement of high harmonics generated by field steering of electrons in a two-color orthogonally polarized laser field

We demonstrate enhancement by 1 order of magnitude of the high-order harmonics generated in argon by combining a fundamental field at 1300 nm (10(14) W cm(-2)) and its orthogonally polarized second harmonic at 650 nm (2 × 10(13) W cm(-2)) and by controlling the relative phase between them. This extends earlier work by ensuring that the main effect is the combined field steering the electron trajectory with negligible contribution from multiphoton effects compared to the previous schemes with 800/400 nm fields. We access a broad energy range of harmonics (from 20 eV to 80 eV) at a low laser intensity (far below the ionization saturation limit) and observe deep modulation of the harmonic yield with a period of π in the relative phase. Strong field theoretical analysis reveals that this is principally due to the steering of the recolliding electron wave packet by the two-color field. Our modeling also shows that the atto chirp can be controlled, leading to production of shorter pulses.     

Unsaturated hydrocarbons adsorbed on low coordinated Pd surface: A periodic DFT study

In this work, the adsorption of several unsaturated hydrocarbon molecules on a stepped Pd(4 2 2) surface was studied. Using a periodic method based on the Density Functional Theory (DFT) formalism, different adsorption geometries for ethylene, three butene isomers (cis/trans-2-butene and 1-butene), acetylene and 2-butyne were investigated. The results were compared with those obtained for a free defect surface as Pd(1 1 1). The 1-butene is more stable on the free defect surface than on Pd(4 2 2). On the stepped surface, the olefins adsorb tilted towards the step and increases, in almost all the cases, the magnitude of the adsorption energy. Conversely, the 3-fold site is the most stable for the alkynes adsorption on the stepped surface, as it was found on Pd(1 1 1). The analysis of the dipole moment change indicate a charge transfer from the double bond of the olefin to the metallic surface, being higher for the Pd(1 1 1) surface. In case of the alkynes, an important back-donation is produced. Except the alkynes and the 1-butene molecule, the results show the preference of ethylene and cis/trans-2-butene to be adsorbed on the stepped surface. These observations are related with experimental catalytic results.     

Glueball spectroscopy in strongly coupled lattice gauge theories

We study the mass spectrum up to –7 (1–) log of pure three-dimensional lattice gauge theories with action (g _P) for real irreducible and small . Besides the lowest excitationm ₀–4log, we find two nearly degenerate excited statesm ₁,m ₂ withm _i–6log (i=1, 2) and (m ₁–m ₂) at leastO().Work partially supported by CNPq (Brasil)     

How Focusing Phenomena in the Instructional Environment Support Individual Students' Generalizations

This article sets forth a way of connecting the classroom instructional environment with individual students' generalizations. To do so, we advance the notion of focusing phenomena, that is, regularities in the ways in which teachers, students, artifacts, and curricular materials act together to direct attention toward certain mathematical properties over others. The construct of focusing phenomena emerged from an empirical study conducted during a 5-week unit on slope and linear functions in a high school classroom using a reform curriculum. Qualitative evidence from interviews with 7 students revealed that students interpreted the m value in y = b + mx as a difference rather than a ratio as a result of counterproductive generalization afforded by focusing phenomena. Classroom analysis revealed 4 focusing phenomena, which regularly directed students' attention to various sets of differences rather than to the coordination of quantities.