Exact Analysis of Level-Crossing Statistics for (d+1)-Dimensional Fluctuating Surfaces

We carry out an exact analysis of the average frequency $\nu_{\alpha x_i}^+$ in the direction $x_i$ of positive-slope crossing of a given level $\alpha$ such that, $h({\bf x},t)-\bar{h}=\alpha$, of growing surfaces in spatial dimension $d$. Here, $h({\bf x},t)$ is the surface height at time $t$, and $\bar{h}$ is its mean value. We analyze the problem when the surface growth dynamics is governed by the Kardar-Parisi-Zhang (KPZ) equation without surface tension, in the time regime prior to appearance of cusp singularities (sharp valleys), as well as in the random deposition (RD) model. The total number $N^+$ of such level-crossings with positive slope in all the directions is then shown to scale with time as $t^{d/2}$ for both the KPZ equation and the RD model.Comment: 22 pages, 3 figure

Clusters in the inner spiral arms of M51: the cluster IMF and the formation history

We study the cluster population in a region of 3.2x3.2 kpc^2 in the inner spiral arms of the intergacting galaxy M51, at a distance of about 1 to 3 kpc from the nucleus, based on HST--WFPC2 images taken through five broadband and two narrowband filters. We found 877 cluster candidates and we derived their ages, initial masses and extinctions by comparing their energy distribution with the Starburst99 cluster models. We describe the 3 and 2-dimensional least-square energy fitting method that was used (3DEF, 2DEF). The lack of [OIII] emission in even the youngest clusters with strong H-alpha emission, indicates the absence of the most massive stars and suggests a mass upper limit of about 25 to 30 solar masses. The mass versus age distribution of the clusters shows a drastic decrease in the number of clusters with age, which indicates that cluster disruption is occurring on a timescale of about 10 Myr for low mass clusters. The cluster initial mass function for clusters younger than 10 Myr has an exponent of alpha = 2.0 (+- 0.05) We derived the cluster formation history from clusters with an initial mass larger than 10^4 solar masses. There is no evidence for a peak in the cluster formation rate within a factor two at about 200 to 400 Myr ago, i.e. at the time of the interaction with the companion galaxy NGC 5194.Comment: 15 pages, 15 figures. Accepted for publication by Astronomy and Astrophysic

Synthesis of accelerograms compatible with the Chinese GB 50011-2001 design spectrum via harmonic wavelets: artificial and historic records

A versatile approach is employed to generate artificial accelerograms which satisfy the compatibility criteria prescribed by the Chinese aseismic code provisions GB 50011-2001. In particular, a frequency dependent peak factor derived by means of appropriate Monte Carlo analyses is introduced to relate the GB 50011-2001 design spectrum to a parametrically defined evolutionary power spectrum (EPS). Special attention is given to the definition of the frequency content of the EPS in order to accommodate the mathematical form of the aforementioned design spectrum. Further, a one-to-one relationship is established between the parameter controlling the time-varying intensity of the EPS and the effective strong ground motion duration. Subsequently, an efficient auto-regressive moving-average (ARMA) filtering technique is utilized to generate ensembles of non-stationary artificial accelerograms whose average response spectrum is in a close agreement with the considered design spectrum. Furthermore, a harmonic wavelet based iterative scheme is adopted to modify these artificial signals so that a close matching of the signals’ response spectra with the GB 50011-2001 design spectrum is achieved on an individual basis. This is also done for field recorded accelerograms pertaining to the May, 2008 Wenchuan seismic event. In the process, zero-phase high-pass filtering is performed to accomplish proper baseline correction of the acquired spectrum compatible artificial and field accelerograms. Numerical results are given in a tabulated format to expedite their use in practice

An Introduction to random vibrations and spectral analysis, 2nd.ed./ Newland

377 hal. : ill. ; 24 cm

An Introduction to random vibrations and spectral analysis, 2nd.ed./ Newland

377 hal. : ill. ; 24 cm