The critical dimension for a 4th order problem with singular nonlinearity

We study the regularity of the extremal solution of the semilinear biharmonic equation \bi u=\f{\lambda}{(1-u)^2}, which models a simple Micro-Electromechanical System (MEMS) device on a ball B\subset\IR^N, under Dirichlet boundary conditions $u=\partial_\nu u=0$ on $\partial B$. We complete here the results of F.H. Lin and Y.S. Yang \cite{LY} regarding the identification of a "pull-in voltage" \la^*>0 such that a stable classical solution u_\la with 0 exists for \la\in (0,\la^*), while there is none of any kind when \la>\la^*. Our main result asserts that the extremal solution $u_{\lambda^*}$ is regular $(\sup_B u_{\lambda^*} <1)$ provided $N \le 8$ while $u_{\lambda^*}$ is singular ($\sup_B u_{\lambda^*} =1$) for $N \ge 9$, in which case $1-C_0|x|^{4/3}\leq u_{\lambda^*} (x) \leq 1-|x|^{4/3}$ on the unit ball, where $C_0:= (\frac{\lambda^*}{\overline{\lambda}})^{1/3}$ and $\bar{\lambda}:= {8/9} (N-{2/3}) (N- {8/3})$.Comment: 19 pages. This paper completes and replaces a paper (with a similar title) which appeared in arXiv:0810.5380. Updated versions --if any-- of this author's papers can be downloaded at this http://www.birs.ca/~nassif

The Science of Sungrazers, Sunskirters, and Other Near-Sun Comets

This review addresses our current understanding of comets that venture close to the Sun, and are hence exposed to much more extreme conditions than comets that are typically studied from Earth. The extreme solar heating and plasma environments that these objects encounter change many aspects of their behaviour, thus yielding valuable information on both the comets themselves that complements other data we have on primitive solar system bodies, as well as on the near-solar environment which they traverse. We propose clear definitions for these comets: We use the term near-Sun comets to encompass all objects that pass sunward of the perihelion distance of planet Mercury (0.307 AU). Sunskirters are defined as objects that pass within 33 solar radii of the Sun’s centre, equal to half of Mercury’s perihelion distance, and the commonly-used phrase sungrazers to be objects that reach perihelion within 3.45 solar radii, i.e. the fluid Roche limit. Finally, comets with orbits that intersect the solar photosphere are termed sundivers. We summarize past studies of these objects, as well as the instruments and facilities used to study them, including space-based platforms that have led to a recent revolution in the quantity and quality of relevant observations. Relevant comet populations are described, including the Kreutz, Marsden, Kracht, and Meyer groups, near-Sun asteroids, and a brief discussion of their origins. The importance of light curves and the clues they provide on cometary composition are emphasized, together with what information has been gleaned about nucleus parameters, including the sizes and masses of objects and their families, and their tensile strengths. The physical processes occurring at these objects are considered in some detail, including the disruption of nuclei, sublimation, and ionisation, and we consider the mass, momentum, and energy loss of comets in the corona and those that venture to lower altitudes. The different components of comae and tails are described, including dust, neutral and ionised gases, their chemical reactions, and their contributions to the near-Sun environment. Comet-solar wind interactions are discussed, including the use of comets as probes of solar wind and coronal conditions in their vicinities. We address the relevance of work on comets near the Sun to similar objects orbiting other stars, and conclude with a discussion of future directions for the field and the planned ground- and space-based facilities that will allow us to address those science topics

Fungal Planet description sheets: 1284–1382

Novel species of fungi described in this study include those from various countries as follows: Antartica, Cladosporium austrolitorale from coastal sea sand. Australia, Austroboletus yourkae on soil, Crepidotus innuopurpureus on dead wood, Curvularia stenotaphri from roots and leaves of Stenotaphrum secundatum and Thecaphora stajsicii from capsules of Oxalis radicosa. Belgium, Paraxerochrysium coryli (incl. Paraxerochrysium gen. nov.) from Corylus avellana. Brazil, Calvatia nordestina on soil, Didymella tabebuiicola from leaf spots on Tabebuia aurea, Fusarium subflagellisporum from hypertrophied floral and vegetative branches of Mangifera indica and Microdochium maculosum from living leaves of Digitaria insularis. Canada, Cuphophyllus bondii fromagrassland. Croatia, Mollisia inferiseptata from a rotten Laurus nobilis trunk. Cyprus, Amanita exilis oncalcareoussoil. Czech Republic, Cytospora hippophaicola from wood of symptomatic Vaccinium corymbosum. Denmark, Lasiosphaeria deviata on pieces of wood and herbaceousdebris. Dominican Republic, Calocybella goethei among grass on a lawn. France (Corsica) , Inocybe corsica onwetground. France (French Guiana) , Trechispora patawaensis on decayed branch of unknown angiosperm tree and Trechispora subregularis on decayed log of unknown angiosperm tree. Germany, Paramicrothecium sambuci (incl. Paramicrothecium gen. nov.)ondeadstemsof Sambucus nigra. India, Aureobasidium microtermitis from the gut of a Microtermes sp. termite, Laccaria diospyricola on soil and Phylloporia tamilnadensis on branches of Catunaregam spinosa. Iran, Pythium serotinoosporum from soil under Prunus dulcis. Italy, Pluteus brunneovenosus on twigs of broad leaved trees on the ground. Japan, Heterophoma rehmanniae on leaves of Rehmannia glutinosa f. hueichingensis. Kazakhstan, Murispora kazachstanica from healthy roots of Triticum aestivum. Namibia, Caespitomonium euphorbiae (incl. Caespitomonium gen. nov.)from stems of an Euphorbia sp. Netherlands, Alfaria junci, Myrmecridium junci, Myrmecridium juncicola, Myrmecridium juncigenum, Ophioceras junci, Paradinemasporium junci (incl. Paradinemasporium gen. nov.), Phialoseptomonium junci, Sporidesmiella juncicola, Xenopyricularia junci and Zaanenomyces quadripartis (incl. Zaanenomyces gen. nov.), fromdeadculmsof Juncus effusus, Cylindromonium everniae and Rhodoveronaea everniae from Evernia prunastri, Cyphellophora sambuci and Myrmecridium sambuci from Sambucus nigra, Kiflimonium junci, Saro cladium junci, Zaanenomyces moderatricis academiae and Zaanenomyces versatilis from dead culms of Juncus inflexus, Microcera physciae from Physcia tenella, Myrmecridium dactylidis from dead culms of Dactylis glomerata, Neochalara spiraeae and Sporidesmium spiraeae from leaves of Spiraea japonica, Neofabraea salicina from Salix sp., Paradissoconium narthecii (incl. Paradissoconium gen. nov.)from dead leaves of Narthecium ossifragum, Polyscytalum vaccinii from Vaccinium myrtillus, Pseudosoloacrosporiella cryptomeriae (incl. Pseudosoloacrosporiella gen. nov.)fromleavesof Cryptomeria japonica, Ramularia pararhabdospora from Plantago lanceolata, Sporidesmiella pini from needles of Pinus sylvestris and Xenoacrodontium juglandis (incl. Xenoacrodontium gen. nov. and Xenoacrodontiaceae fam. nov.)from Juglans regia. New Zealand, Cryptometrion metrosideri from twigs of Metrosideros sp., Coccomyces pycnophyllocladi from dead leaves of Phyllocladus alpinus, Hypoderma aliforme from fallen leaves Fuscopora solandri and Hypoderma subiculatum from dead leaves Phormium tenax. Norway, Neodevriesia kalakoutskii from permafrost and Variabilispora viridis from driftwood of Picea abies. Portugal, Entomortierella hereditatis from abio film covering adeteriorated limestone wall. Russia, Colpoma junipericola from needles of Juniperus sabina, Entoloma cinnamomeum on soil in grasslands, Entoloma verae on soil in grasslands, Hyphodermella pallidostraminea on a dry dead branch of Actinidia sp., Lepiota sayanensis onlitterinamixedforest, Papiliotrema horticola from Malus communis , Paramacroventuria ribis (incl. Paramacroventuria gen. nov.)fromleaves of Ribes aureum and Paramyrothecium lathyri from leaves of Lathyrus tuberosus. South Africa, Harzia combreti from leaf litter of Combretum collinum ssp. sulvense, Penicillium xyleborini from Xyleborinus saxesenii , Phaeoisaria dalbergiae from bark of Dalbergia armata, Protocreopsis euphorbiae from leaf litter of Euphorbia ingens and Roigiella syzygii from twigs of Syzygium chordatum. Spain, Genea zamorana on sandy soil, Gymnopus nigrescens on Scleropodium touretii, Hesperomyces parexochomi on Parexochomus quadriplagiatus, Paraphoma variabilis from dung, Phaeococcomyces kinklidomatophilus from a blackened metal railing of an industrial warehouse and Tuber suaveolens in soil under Quercus faginea. Svalbard and Jan Mayen, Inocybe nivea associated with Salix polaris. Thailand, Biscogniauxia whalleyi oncorticatedwood. UK, Parasitella quercicola from Quercus robur. USA , Aspergillus arizonicus from indoor air in a hospital, Caeliomyces tampanus (incl. Caeliomyces gen. nov.)fromoffice dust, Cippumomyces mortalis (incl. Cippumomyces gen. nov.)fromatombstone, Cylindrium desperesense from air in a store, Tetracoccosporium pseudoaerium from air sample in house, Toxicocladosporium glendoranum from air in a brick room, Toxicocladosporium losalamitosense from air in a classroom, Valsonectria portsmouthensis from airinmen'slockerroomand Varicosporellopsis americana from sludge in a water reservoir. Vietnam, Entoloma kovalenkoi on rotten wood, Fusarium chuoi inside seed of Musa itinerans , Micropsalliota albofelina on soil in tropical evergreen mixed forest sand Phytophthora docyniae from soil and roots of Docynia indica. Morphological and culture characteristics are supported by DNA barcodes

Search for gravitational waves from Scorpius X-1 in the second Advanced LIGO observing run with an improved hidden Markov model

We present results from a semicoherent search for continuous gravitational waves from the low-mass x-ray binary Scorpius X-1, using a hidden Markov model (HMM) to track spin wandering. This search improves on previous HMM-based searches of LIGO data by using an improved frequency domain matched filter, the J-statistic, and by analyzing data from Advanced LIGO's second observing run. In the frequency range searched, from 60 to 650 Hz, we find no evidence of gravitational radiation. At 194.6 Hz, the most sensitive search frequency, we report an upper limit on gravitational wave strain (at 95% confidence) of h095%=3.47×10-25 when marginalizing over source inclination angle. This is the most sensitive search for Scorpius X-1, to date, that is specifically designed to be robust in the presence of spin wandering. © 2019 American Physical Society

Search for Tensor, Vector, and Scalar Polarizations in the Stochastic Gravitational-Wave Background

The detection of gravitational waves with Advanced LIGO and Advanced Virgo has enabled novel tests of general relativity, including direct study of the polarization of gravitational waves. While general relativity allows for only two tensor gravitational-wave polarizations, general metric theories can additionally predict two vector and two scalar polarizations. The polarization of gravitational waves is encoded in the spectral shape of the stochastic gravitational-wave background, formed by the superposition of cosmological and individually unresolved astrophysical sources. Using data recorded by Advanced LIGO during its first observing run, we search for a stochastic background of generically polarized gravitational waves. We find no evidence for a background of any polarization, and place the first direct bounds on the contributions of vector and scalar polarizations to the stochastic background. Under log-uniform priors for the energy in each polarization, we limit the energy densities of tensor, vector, and scalar modes at 95% credibility to Ω0T<5.58×10-8, Ω0V<6.35×10-8, and Ω0S<1.08×10-7 at a reference frequency f0=25 Hz. © 2018 American Physical Society

Erratum: "A Gravitational-wave Measurement of the Hubble Constant Following the Second Observing Run of Advanced LIGO and Virgo" (2021, ApJ, 909, 218)

[no abstract available

On the progenitor of binary neutron star merger GW170817

On 2017 August 17 the merger of two compact objects with masses consistent with two neutron stars was discovered through gravitational-wave (GW170817), gamma-ray (GRB 170817A), and optical (SSS17a/AT 2017gfo) observations. The optical source was associated with the early-type galaxy NGC 4993 at a distance of just ∼40 Mpc, consistent with the gravitational-wave measurement, and the merger was localized to be at a projected distance of ∼2 kpc away from the galaxy's center. We use this minimal set of facts and the mass posteriors of the two neutron stars to derive the first constraints on the progenitor of GW170817 at the time of the second supernova (SN). We generate simulated progenitor populations and follow the three-dimensional kinematic evolution from binary neutron star (BNS) birth to the merger time, accounting for pre-SN galactic motion, for considerably different input distributions of the progenitor mass, pre-SN semimajor axis, and SN-kick velocity. Though not considerably tight, we find these constraints to be comparable to those for Galactic BNS progenitors. The derived constraints are very strongly influenced by the requirement of keeping the binary bound after the second SN and having the merger occur relatively close to the center of the galaxy. These constraints are insensitive to the galaxy's star formation history, provided the stellar populations are older than 1 Gyr