Post-Newtonian Dynamics in Dense Star Clusters: Highly-Eccentric, Highly-Spinning, and Repeated Binary Black Hole Mergers

We present models of realistic globular clusters with post-Newtonian dynamics for black holes. By modeling the relativistic accelerations and gravitational-wave emission in isolated binaries and during three- and four-body encounters, we find that nearly half of all binary black hole mergers occur inside the cluster, with about 10% of those mergers entering the LIGO/Virgo band with eccentricities greater than 0.1. In-cluster mergers lead to the birth of a second generation of black holes with larger masses and high spins, which, depending on the black hole natal spins, can sometimes be retained in the cluster and merge again. As a result, globular clusters can produce merging binaries with detectable spins regardless of the birth spins of black holes formed from massive stars. These second-generation black holes would also populate any upper mass gap created by pair-instability supernovae.Comment: 9 pages, 3 figures, 2 appendices. To appear in Physical Review Letter

A match coefficient approach for damage imaging in structural components by ultrasonic synthetic aperture focus

Ultrasonic Synthetic Aperture Focus (SAF) techniques are commonly used to image structural defects. In this paper, a variation of SAF based on ideas borrowed from Matched Field Processing (MFP) is evaluated to reduce artifacts and sidelobes of the resulting images. In particular, instead of considering the full RF ultrasonic waveforms for the SAF time backpropagation, only selected features from the waveforms are utilized to form a “data vector” and a “replica” (expected) vector of MFP. These vectors are adaptive for the pair of transmitter-receiver and the focus point. The image is created as a matched filter between these two vectors. Experimental results are shown for an isotropic and homogenous metallic plate with simulated defects, probed by six piezoelectric patches used as receivers or transmitters

Adaptive walks in a gene network model of morphogenesis: insights into the Cambrian explosion

The emergence of complex patterns of organization close to the Cambrian boundary is known to have happened over a (geologically) short period of time. It involved the rapid diversification of body plans and stands as one of the major transitions in evolution. How it took place is a controversial issue. Here we explore this problem by considering a simple model of pattern formation in multicellular organisms. By modeling gene network-based morphogenesis and its evolution through adaptive walks, we explore the question of how combinatorial explosions might have been actually involved in the Cambrian event. Here we show that a small amount of genetic complexity including both gene regulation and cell-cell signaling allows one to generate an extraordinary repertoire of stable spatial patterns of gene expression compatible with observed anteroposterior patterns in early development of metazoans. The consequences for the understanding of the tempo and mode of the Cambrian event are outlined.Comment: to appear in International Journal of Developmental Biology, special issue on Evo-Devo (2003

Sowing the seeds of massive black holes in small galaxies: Young clusters as the building blocks of Ultra-Compact-Dwarf Galaxies

Interacting galaxies often have complexes of hundreds of young stellar clusters of individual masses $\sim 10^{4-6}~M_\odot$ in regions that are a few hundred parsecs across. These cluster complexes interact dynamically, and their coalescence is a candidate for the origin of some ultracompact dwarf galaxies (UCDs). Individual clusters with short relaxation times are candidates for the production of intermediate-mass black holes of a few hundred solar masses, via runaway stellar collisions prior to the first supernovae in a cluster. It is therefore possible that a cluster complex hosts multiple intermediate-mass black holes that may be ejected from their individual clusters due to mergers or binary processes, but bound to the complex as a whole. Here we explore the dynamical interaction between initially free-flying massive black holes and clusters in an evolving cluster complex. We find that, after hitting some clusters, it is plausible that the massive black hole will be captured in an ultracompact dwarf forming near the center of the complex. In the process, the hole typically triggers electromagnetic flares via stellar disruptions, and is also likely to be a prominent source of gravitational radiation for the advanced ground-based detectors LIGO and VIRGO. We also discuss other implications of this scenario, notably that the central black hole could be considerably larger than expected in other formation scenarios for ultracompact dwarfs.Comment: 15 pages, published in ApJ; for movies, please visit http://members.aei.mpg.de/amaro-seoane/ultra-compact-dwarf-galaxie

Composition operators acting on weighted Dirichlet spaces

We study composition operators acting on weighted Dirichlet spaces. We obtain estimates for the essential norm, describe the membership in Schatten-Von Neumann ideals and characterize the composition operators with closed range

On the length and area spectrum of analytic convex domains

Area-preserving twist maps have at least two different (p, q)-periodic orbits and every (p, q)-periodic orbit has its (p, q)-periodic action for suitable couples (p, q). We establish an exponentially small upper bound for the differences of (p, q)-periodic actions when the map is analytic on a (m, n)-resonant rotational invariant curve (resonant RIC) and p/q is 'sufficiently close' to m/n. The exponent in this upper bound is closely related to the analyticity strip width of a suitable angular variable. The result is obtained in two steps. First, we prove a Neishtadt-like theorem, in which the n-th power of the twist map is written as an integrable twist map plus an exponentially small remainder on the distance to the RIC. Second, we apply the MacKay-Meiss-Percival action principle. We apply our exponentially small upper bound to several billiard problems. The resonant RIC is a boundary of the phase space in almost all of them. For instance, we show that the lengths (respectively, areas) of all the (1, q)-periodic billiard (respectively, dual billiard) trajectories inside (respectively, outside) analytic strictly convex domains are exponentially close in the period q. This improves some classical results of Marvizi, Melrose, Colin de Verdiere, Tabachnikov, and others about the smooth case.Peer ReviewedPostprint (author's final draft

Progetto e realizzazione di un setup per l’analisi del rolling contact: risultati preliminari

Presso il Dipartimento di Ingegneria Meccanica dell’Università di Cagliari (DIMECA) è attiva, da alcuni anni, una linea di ricerca orientata alla valutazione dei principali parametri di contatto (forma e dimensioni dell’area nominale di contatto, area reale di contatto, distribuzione delle pressioni di contatto) in interfacce metalliche, mediante una tecnica sperimentale basata sull’impiego di onde ultrasoniche. L’applicazione di questo metodo ha consentito di ottenere informazioni su contatti a geometria semplice quali, ad esempio, quelli sfera-piano [1-2] su casi più complessi di rilevante impatto ingegneristico come quello relativo all’interazione tra ruota e rotaia ferroviaria [3-4]. Il principale punto di forza dell’indagine ultrasonica risiede nella sua capacità di fornire informazioni sullo stato del contatto a partire da misure del coefficiente di riflessione all’interfaccia, garantendo in tal modo sia la più completa non-invasività (nessun mezzo viene ad interporsi tra i corpi a contatto) e sia la possibilità di investigare “in process”. In particolare quest’ultima peculiarità permette di monitorare le variazioni del parametri di contatto in tempo reale (ad esempio a seguito di variazioni nel carico applicato o nella configurazione geometrica dell’accoppiamento) senza che sia necessario rimuovere i corpi per esaminare gli effetti che tali modifiche hanno generato. Appare importante sottolineare che, a tutt’oggi, la letteratura riporta esempi di impiego de metodo ultrasonico a problemi di contatto quasi esclusivamente nell’analisi di situazioni statiche. Tuttavia, è facilmente intuibile che la possibilità di estendere il campo di applicazione della tecnica a situazioni dinamiche, aumenterebbe in misura considerevole il range di casi di interesse ingegneristico potenzialmente testabili. In considerazione di ciò, il presente studio si pone come obiettivo principale quello di verificare la validità ed affidabilità del metodo ultrasonico per lo studio di situazioni dinamiche, con particolare riferimento a problemi di “rolling contact”

Optimizing periodicity and polymodality in noise-induced genetic oscillators

Many cellular functions are based on the rhythmic organization of biological processes into self-repeating cascades of events. Some of these periodic processes, such as the cell cycles of several species, exhibit conspicuous irregularities in the form of period skippings, which lead to polymodal distributions of cycle lengths. A recently proposed mechanism that accounts for this quantized behavior is the stabilization of a Hopf-unstable state by molecular noise. Here we investigate the effect of varying noise in a model system, namely an excitable activator-repressor genetic circuit, that displays this noise-induced stabilization effect. Our results show that an optimal noise level enhances the regularity (coherence) of the cycles, in a form of coherence resonance. Similar noise levels also optimize the multimodal nature of the cycle lengths. Together, these results illustrate how molecular noise within a minimal gene regulatory motif confers robust generation of polymodal patterns of periodicity.Comment: 9 pages, 6 figure

Monitoring the Petermann Ice Island with TanDEM-X

This paper presents the processing of TanDEM-X acquisitions for the monitoring of the topography of the Petermann ice island. In this particular case the area under study is continuously moving and the acquisition geometry is changing, so the processing of the iceberg’s DEMs is challenging and additional effects are to be considered. The SAR processing chain used is presented and the results obtained summarized, showing the effects and limitations observed during the process