Bifurcation From Infinity For Reaction–Diffusion Equations Under Nonlinear Boundary Conditions

We consider reaction–diffusion equations under nonlinear boundary conditions where the nonlinearities are asymptotically linear at infinity and depend on a parameter. We prove that, as the parameter crosses some critical values, a resonance-type phenomenon provides solutions that bifurcate from infinity. We characterize the bifurcated branches when they are sub- or supercritical. We obtain both Landesman–Lazer-type conditions that guarantee the existence of solutions in the resonant case and an anti-maximum principle

A Priori Bounds And Existence Of Positive Solutions For Semilinear Elliptic Systems

We provide a-priori L∞ bounds for classical positive solutions of semilinear elliptic systems in bounded convex domains when the nonlinearities are below the power functions v^p and u^q for any (p,q) lying on the critical Sobolev hyperbola. Our proof combines moving planes method and Rellich–Pohozaev type identities for systems. Our analysis widens the known ranges of nonlinearities for which classical positive solutions of semilinear elliptic systems are a priori bounded. Using these a priori bounds, and local and global bifurcation techniques, we prove the existence of positive solutions for a corresponding parametrized semilinear elliptic system

Star Formation in the Trifid Nebula

We have obtained maps of the 1.25mm thermal dust emission and the molecular gas emission over a region of 20' by 10' arcmin around the Trifid Nebula (M20), with the IRAM 30m and the CSO telescopes as well as in the mid-infrared wavelength with ISO and SPITZER. Our survey is sensitive to features down to N(H2) \sim 10^{22} cm-2 in column density. The cloud material is distributed in fragmented dense gas filaments (n(H2) \sim 1000 cm-3) with sizes ranging from 1 to 10 pc. A massive filament, WF, with properties typical of Infra Red Dark Clouds, connects M20 to the W28 supernova remnant. These filaments pre-exist the formation of the Trifid and were originally self-gravitating. The fragments produced are very massive (100 Msun or more) and are the progenitors of the cometary globules observed at the border of the HII region. We could identify 33 cores, 16 of which are currently forming stars. They are usually gravitationally unbound and have low masses of a few Msun. The densest starless cores (several 10^5 cm-3) may be the site for the next generation of stars. The physical gas and dust properties of the cometary globules have been studied in detail and have been found very similar. They all are forming stars. Several intermediate-mass protostars have been detected in the cometary globules and in the deeply embedded cores. Evidence of clustering has been found in the shocked massive cores TC3-TC4-TC5. M20 is a good example of massive-star forming region in a turbulent, filamentary molecular cloud. Photoionization appears to play a minor role in the formation of the cores. The observed fragmentation is well explained by MHD-driven instabilities and is usually not related to M20. We propose that the nearby supernova remnant W28 could have triggered the formation of protostellar clusters in nearby dense cores of the Trifid.Comment: 16 pages, 24 figures, 5 Tables To appear in Astronomy and Astrophysic

Theoretical and experimental study of AC loss in HTS single pancake coils

The electromagnetic properties of a pancake coil in AC regime as a function of the number of turns is studied theoretically and experimentally. Specifically, the AC loss, the coil critical current and the voltage signal are discussed. The coils are made of Bi2Sr2Ca2Cu3O10/Ag (BiSCCO) tape, although the main qualitative results are also applicable to other kinds of superconducting tapes, such as coated conductors. The AC loss and the voltage signal are electrically measured using different pick up coils with the help of a transformer. One of them avoids dealing with the huge coil inductance. Besides, the critical current of the coils is experimentally determined by conventional DC measurements. Furthermore, the critical current, the AC loss and the voltage signal are simulated, showing a good agreement with the experiments. For all simulations, the field dependent critical current density inferred from DC measurements on a short tape sample is taken into account.Comment: 22 pages, 15 figures; contents extended (sections 3.2 and 4); one new figure (figure 5) and two figures replaced (figures 3 and 8); typos corrected; title change

The extended hypergeometric class of L\'evy processes

With a view to computing fluctuation identities related to stable processes, we review and extend the class of hypergeometric L\'evy processes explored in Kuznetsov and Pardo (arXiv:1012.0817). We give the Wiener-Hopf factorisation of a process in the extended class, and characterise its exponential functional. Finally, we give three concrete examples arising from transformations of stable processes.Comment: 22 page

High-J v=0 SiS Maser Emission in IRC+10216: A New Case of Infrared Overlaps

We report on the first detection of maser emission in the J=11-10, J=14-13 and J=15-14 transitions of the v=0 vibrational state of SiS toward the C-rich star IRC+10216. These masers seem to be produced in the very inhomogeneous region between the star and the inner dust formation zone, placed at 5-7 R*, with expansion velocities below 10 km/s. We interpret the pumping mechanism as due to overlaps between v=1-0 ro-vibrational lines of SiS and mid-IR lines of C2H2, HCN and their 13C isotopologues. The large number of overlaps found suggests the existence of strong masers for high-J v=0 and v=1 SiS transitions, located in the submillimeter range. In addition, it could be possible to find several rotational lines of the SiS isotopologues displaying maser emission.Comment: 4 pages, 1 figure, published in the ApJ Letter

A methodology for unified hardware-software design

Unified hardware-software design for digital computer