Phase II of the ASCE Benchmark Study on SHM

The task group on structural health monitoring of the Dynamic Committee of ASCE was formed in 1999 at the 12 th Engineering Mechanics Conference. The task group has designed a number of analytical studies on a benchmark structure and there are plans to follow these with an experimental program. The first phase of the analytical studies was completed in 2001. The second phase, initiated in the summer of 2001, was formulated in the light of the experience gained on phase I and focuses on increasing realism in the simulation of the discrepancies between the actual structure and the mathematical model used in the analysis. This paper describes the rational that lead the SHM task group to the definition of phase II and presents the details of the cases that are being considered

Small-Recoil Approximation

In this review we discuss a technique to compute and to sum a class of Feynman diagrams, and some of its applications. These are diagrams containing one or more energetic particles that suffer very little recoil in their interactions. When recoil is completely neglected, a decomposition formula can be proven. This formula is a generalization of the well-known eikonal formula, to non-abelian interactions. It expresses the amplitude as a sum of products of irreducible amplitudes, with each irreducible amplitude being the amplitude to emit one, or several mutually interacting, quasi-particles. For abelian interaction a quasi-particle is nothing but the original boson, so this decomposition formula reduces to the eikonal formula. In non-abelian situations each quasi-particle can be made up of many bosons, though always with a total quantum number identical to that of a single boson. This decomposition enables certain amplitudes of all orders to be summed up into an exponential form, and it allows subleading contributions of a certain kind, which is difficult to reach in the usual way, to be computed. For bosonic emissions from a heavy source with many constituents, a quasi-particle amplitude turns out to be an amplitude in which all bosons are emitted from the same constituent. For high-energy parton-parton scattering in the near-forward direction, the quasi-particle turns out to be the Reggeon, and this formalism shows clearly why gluons reggeize but photons do not. The ablility to compute subleading terms in this formalism allows the BFKL-Pomeron amplitude to be extrapolated to asymptotic energies, in a unitary way preserving the Froissart bound. We also consider recoil corrections for abelian interactions in order to accommodate the Landau-Pomeranchuk-Migdal effect.Comment: 21 pages with 4 figure

Generalized Background-Field Method

The graphical method discussed previously can be used to create new gauges not reachable by the path-integral formalism. By this means a new gauge is designed for more efficient two-loop QCD calculations. It is related to but simpler than the ordinary background-field gauge, in that even the triple-gluon vertices for internal lines contain only four terms, not the usual six. This reduction simplifies the calculation inspite of the necessity to include other vertices for compensation. Like the ordinary background-field gauge, this generalized background-field gauge also preserves gauge invariance of the external particles. As a check of the result and an illustration for the reduction in labour, an explicit calculation of the two-loop QCD $\beta$-function is carried out in this new gauge. It results in a saving of 45% of computation compared to the ordinary background-field gauge.Comment: 17 pages, Latex, 18 figures in Postscrip

Weighing the Cosmological Energy Contents with Weak Gravitational Lensing

Bernardeau et al. (1997), using perturbation theory, showed that the skewness of the large-scale lensing-convergence, or projected mass density, could be used to constrain $\Omega_m$, the matter content of the universe. On the other hand, deep weak-lensing field surveys in the near future will likely measure the convergence on small angular scales (< 10 arcmin.), where the signal will be dominated by highly nonlinear fluctuations. We develop a method to compute the small-scale convergence skewness, using a prescription for the highly nonlinear three-point function developed by Scoccimarro and Frieman (1998). This method gives predictions that agree well with existing results from ray-tracing N-body simulations, but is significantly faster, allowing the exploration of a large number of models. We demonstrate that the small-scale convergence skewness is insensitive to the shape and normalization of the primordial (CDM-type) power spectrum, making it dependent almost entirely on the cosmological energy contents, through their influence on the global geometrical distances and fluctuation growth rate. Moreover, nonlinear clustering appears to enhance the differences between predictions of the convergence skewness for a range of models. Hence, in addition to constraining $\Omega_m$, the small-scale convergence skewness from future deep several- degree-wide surveys can be used to differentiate between curvature dominated and cosmological constant ($\Lambda$) dominated models, as well as to constrain the equation of state of a quintessence component, thereby distinguishing $\Lambda$ from quintessence as well. Finally, our method can be easily generalized to other measures such as aperture mass statistics.Comment: 13 pages, 2 ps figures, submitted to ApJ

Lake and climate models linkage: a 3-D hydrodynamic contribution

International audienceUnder a Canadian Foundation for Climate and Atmospheric Sciences (CFCAS) project, targeted to study the feasibility to link regional climate models with lake models, one of the tasks was to consider such a coupling in large lakes. The objective is to provide detailed information on temperature and circulation distributions of the lake to take into account the spatial variability for temperature and the heat exchange through the water's surface. The major contribution of this work is focused on realistic representation of the heat fluxes and temperature distributions to and from lakes especially during the thermally stratified ice-free periods. This paper presents the detailed 3-D ELCOM model applied in Lake Erie in order to produce, at the surface layer of the lake, the spatial distribution of temperature and heat exchanges that eventually can be coupled with a regional climate model (CRCM). Preliminary results will be presented on how this lake model may improve the regional climate models, which currently do not consider such large lake circulation effects

Combinatorial Hopf algebras and Towers of Algebras

Bergeron and Li have introduced a set of axioms which guarantee that the Grothendieck groups of a tower of algebras $\bigoplus_{n\ge0}A_n$ can be endowed with the structure of graded dual Hopf algebras. Hivert and Nzeutzhap, and independently Lam and Shimozono constructed dual graded graphs from primitive elements in Hopf algebras. In this paper we apply the composition of these constructions to towers of algebras. We show that if a tower $\bigoplus_{n\ge0}A_n$ gives rise to graded dual Hopf algebras then we must have $\dim(A_n)=r^nn!$ where $r = \dim(A_1)$.Comment: 7 page

Activation Energy of Metastable Amorphous Ge2Sb2Te5 from Room Temperature to Melt

Resistivity of metastable amorphous Ge2Sb2Te5 (GST) measured at device level show an exponential decline with temperature matching with the steady-state thin-film resistivity measured at 858 K (melting temperature). This suggests that the free carrier activation mechanisms form a continuum in a large temperature scale (300 K - 858 K) and the metastable amorphous phase can be treated as a super-cooled liquid. The effective activation energy calculated using the resistivity versus temperature data follow a parabolic behavior, with a room temperature value of 333 meV, peaking to ~377 meV at ~465 K and reaching zero at ~930 K, using a reference activation energy of 111 meV (3kBT/2) at melt. Amorphous GST is expected to behave as a p-type semiconductor at Tmelt ~ 858 K and transitions from the semiconducting-liquid phase to the metallic-liquid phase at ~ 930 K at equilibrium. The simultaneous Seebeck (S) and resistivity versus temperature measurements of amorphous-fcc mixed-phase GST thin-films show linear S-T trends that meet S = 0 at 0 K, consistent with degenerate semiconductors, and the dS/dT and room temperature activation energy show a linear correlation. The single-crystal fcc is calculated to have dS/dT = 0.153 {\mu}V/K for an activation energy of zero and a Fermi level 0.16 eV below the valance band edge.Comment: 5 pages, 5 figure

Multiple Reggeon Exchange from Summing QCD Feynman Diagrams

Multiple reggeon exchange supplies subleading logs that may be used to restore unitarity to the Low-Nussinov Pomeron, provided it can be proven that the sum of Feynman diagrams to all orders gives rise to such multiple regge exchanges. This question cannot be easily tackled in the usual way except for very low-order diagrams, on account of delicate cancellations present in the sum which necessitate individual Feynman diagrams to be computed to subleading orders. Moreover, it is not clear that sums of high-order Feynman diagrams with complicated criss-crossing of lines can lead to factorization implied by the multi-regge scenario. Both of these difficulties can be overcome by using the recently developed nonabelian cut diagrams. We are then able to show that the sum of $s$-channel-ladder diagrams to all orders does lead to such multiple reggeon exchanges.Comment: uu-encoded latex file with 11 postscript figures (20 pages