Probabilistic aspects of critical growth-fragmentation equations

The self-similar growth-fragmentation equation describes the evolution of a medium in which particles grow and divide as time proceeds, with the growth and splitting of each particle depending only upon its size. The critical case of the equation, in which the growth and division rates balance one another, was considered by Doumic and Escobedo in the homogeneous case where the rates do not depend on the particle size. Here, we study the general self-similar case, using a probabilistic approach based on L\'evy processes and positive self-similar Markov processes which also permits us to analyse quite general splitting rates. Whereas existence and uniqueness of the solution are rather easy to establish in the homogeneous case, the equation in the non-homogeneous case has some surprising features. In particular, using the fact that certain self-similar Markov processes can enter $(0,\infty)$ continuously from either $0$ or $\infty$, we exhibit unexpected spontaneous generation of mass in the solutions.Comment: 28 pages. v2 adds an expository section 6 and fixes some error

Development of a synthetic aperture radar design approach for wide-swath implementation

The first phase of a study program to develop an advanced synthetic aperture radar design concept is presented. Attributes of particular importance for the system design include wide swath coverage, reduced power requirements, and versatility in the selection of frequency, polarization and incident angle. The multiple beam configuration provides imaging at a nearly constant angle of incidence and offers the potential of realizing a wide range of the attributes desired for an orbital imaging radar for Earth resources applications

Pure emitter dephasing : a resource for advanced solid-state single photon sources

We have computed the spectrum emitted spontaneously by a quantum dot coupled to an arbitrarily detuned single mode cavity, taking into account pure dephasing processes. We show that if the emitter is incoherent, the cavity can efficiently emit photons with its own spectral characteristics. This effect opens unique opportunities for the development of devices exploiting both cavity quantum electrodynamics effects and pure dephasing, such as wavelength stabilized single photon sources robust against spectral diffusion.Comment: 5 pages, 3 figure

The dwarf nova SS Cygni: what is wrong?

Since the Fine Guiding Sensor (FGS) on the Hubble Space Telescope (HST) was used to measure the distance to SS Cyg to be $166\pm12$ pc, it became apparent that at this distance the disc instability model fails to explain the absolute magnitude during outburst. It remained, however, an open question whether the model or the distance have to be revised. Recent observations led to a revision of the system parameters of SS Cyg and seem to be consistent with a distance of d\gta 140 pc. We re-discuss the problem taking into account the new binary and stellar parameters measured for SS Cyg. We confront not only the observations with the predictions of the disc instability model but also compare SS Cyg with other dwarf novae and nova-like systems. We assume the disc during outburst to be in a quasi stationary state and use the black-body approximation to estimate the accretion rate during outburst as a function of distance. Using published analysis of the long term light curve we determine the mean mass transfer rate of SS Cyg as a function of distance and compare the result with mass transfer rates derived for other dwarf novae and nova-like systems. At a distance of d\gta 140 pc, both the accretion rate during outburst as well as the mean mass transfer rate of SS Cyg contradict the disc instability model. More important, at such distances we find the mean mass transfer rate of SS Cyg to be higher or comparable to those derived for nova-like systems. Our findings show that a distance to SS Cyg \gta 140 pc contradicts the main concepts developed for accretion discs in cataclysmic variables during the last 30 years. Either our current picture of disc accretion in these systems must be revised or the distance to SS Cyg is $\sim 100$ pcComment: 6 pages, 3 figures, accepted for publication in Astronomy and Astrophysic