Gravitational Microlensing Near Caustics I: Folds

We study the local behavior of gravitational lensing near fold catastrophes. Using a generic form for the lensing map near a fold, we determine the observable properties of the lensed images, focusing on the case when the individual images are unresolved, i.e., microlensing. Allowing for images not associated with the fold, we derive analytic expressions for the photometric and astrometric behavior near a generic fold caustic. We show how this form reduces to the more familiar linear caustic, which lenses a nearby source into two images which have equal magnification, opposite parity, and are equidistant from the critical curve. In this case, the simplicity and high degree of symmetry allows for the derivation of semi-analytic expressions for the photometric and astrometric deviations in the presence of finite sources with arbitrary surface brightness profiles. We use our results to derive some basic properties of astrometric microlensing near folds, in particular we predict for finite sources with uniform and limb darkening profiles, the detailed shape of the astrometric curve as the source crosses a fold. We find that the astrometric effects of limb darkening will be difficult to detect with the currently planned accuracy of the Space Interferometry Mission. We verify our results by numerically calculating the expected astrometric shift for the photometrically well-covered Galactic binary lensing event OGLE-1999-BUL-23, finding excellent agreement with our analytic expressions. Our results can be applied to any lensing system with fold caustics, including Galactic binary lenses and quasar microlensing.Comment: 37 pages, 7 figures. Revised version includes an expanded discussion of applications. Accepted to ApJ, to appear in the August 1, 2002 issue (v574

Lensing by Kerr Black Holes. II: Analytical Study of Quasi-Equatorial Lensing Observables

In this second paper, we develop an analytical theory of quasi-equatorial lensing by Kerr black holes. In this setting we solve perturbatively our general lens equation with displacement given in Paper I, going beyond weak-deflection Kerr lensing to third order in our expansion parameter epsilon, which is the ratio of the angular gravitational radius to the angular Einstein radius. We obtain new formulas and results for the bending angle, image positions, image magnifications, total unsigned magnification, and centroid, all to third order in epsilon and including the displacement. New results on the time delay between images are also given to second order in epsilon, again including displacement. For all lensing observables we show that the displacement begins to appear only at second order in epsilon. When there is no spin, we obtain new results on the lensing observables for Schwarzschild lensing with displacement.Comment: 23 pages; final published versio

Quasi-Equatorial Gravitational Lensing by Spinning Black Holes in the Strong Field Limit

Spherically symmetric black holes produce, by strong field lensing, two infinite series of relativistic images, formed by light rays winding around the black hole at distances comparable to the gravitational radius. In this paper, we address the relevance of the black hole spin for the strong field lensing phenomenology, focusing on trajectories close to the equatorial plane for simplicity. In this approximation, we derive a two-dimensional lens equation and formulae for the position and the magnification of the relativistic images in the strong field limit. The most outstanding effect is the generation of a non trivial caustic structure. Caustics drift away from the optical axis and acquire finite extension. For a high enough black hole spin, depending on the source extension, we can practically observe only one image rather than two infinite series of relativistic images. In this regime, additional non equatorial images may play an important role in the phenomenology.Comment: 13 pages, 9 figures. Improved version with detailed physical discussio

A Mathematical Theory of Stochastic Microlensing I. Random Time-Delay Functions and Lensing Maps

Stochastic microlensing is a central tool in probing dark matter on galactic scales. From first principles, we initiate the development of a mathematical theory of stochastic microlensing. Beginning with the random time delay function and associated lensing map, we determine exact expressions for the mean and variance of these transformations. We characterize the exact p.d.f. of a normalized random time delay function at the origin, showing that it is a shifted gamma distribution, which also holds at leading order in the limit of a large number of point masses at a general point of the lens plane. For the large number of point masses limit, we also prove that the asymptotic p.d.f. of the random lensing map under a specified scaling converges to a bivariate normal distribution. We show analytically that the p.d.f. of the random scaled lensing map at leading order depends on the magnitude of the scaled bending angle due purely to point masses as well as demonstrate explicitly how this radial symmetry is broken at the next order. Interestingly, we found at leading order a formula linking the expectation and variance of the normalized random time delay function to the first Betti number of its domain. We also determine an asymptotic p.d.f. for the random bending angle vector and find an integral expression for the probability of a lens plane point being near a fixed point. Lastly, we show explicitly how the results are affected by location in the lens plane. The results of this paper are relevant to the theory of random fields and provide a platform for further generalizations as well as analytical limits for checking astrophysical studies of stochastic microlensing.Comment: New layout, more details and discussion. To appear, Journal of Mathematical Physic

The Inner Caustics of Cold Dark Matter Halos

We prove that a flow of cold collisionless particles from all directions in and out of a region necessarily forms a caustic. A corollary is that, in cold dark matter cosmology, galactic halos have inner caustics in addition to the more obvious outer caustics. The outer caustics are fold catastrophes located on topological spheres surrounding the galaxy. To obtain the catastrophe structure of the inner caustics, we simulate the infall of cold collisionless particles in a fixed gravitational potential. The structure of inner caustics depends on the angular momentum distribution of the infalling particles. We confirm a previous result that the inner caustic is a "tricusp ring" when the initial velocity field is dominated by net overall rotation. A tricusp ring is a closed tube whose cross section is a section of an elliptic umbilic catastrophe. However, tidal torque theory predicts that the initial velocity field is irrotational. For irrotational initial velocity fields, we find the inner caustic to have a tent-like structure which we describe in detail in terms of the known catastrophes. We also show how the tent caustic transforms into a tricusp ring when a rotational component is added to the initial velocity field.Comment: 35 pages, 20 figure

Gravitational Lensing by Black Holes

We review the theoretical aspects of gravitational lensing by black holes, and discuss the perspectives for realistic observations. We will first treat lensing by spherically symmetric black holes, in which the formation of infinite sequences of higher order images emerges in the clearest way. We will then consider the effects of the spin of the black hole, with the formation of giant higher order caustics and multiple images. Finally, we will consider the perspectives for observations of black hole lensing, from the detection of secondary images of stellar sources and spots on the accretion disk to the interpretation of iron K-lines and direct imaging of the shadow of the black hole.Comment: Invited article for the GRG special issue on lensing (P. Jetzer, Y. Mellier and V. Perlick Eds.). 31 pages, 12 figure

Boolean Dynamics with Random Couplings

This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N Boolean elements at a given time is given a value which depends upon K elements in the previous time step. We review the work of many authors on the behavior of the models, looking particularly at the structure and lengths of their cycles, the sizes of their basins of attraction, and the flow of information through the systems. In the limit of infinite N, there is a phase transition between a chaotic and an ordered phase, with a critical phase in between. We argue that the behavior of this system depends significantly on the topology of the network connections. If the elements are placed upon a lattice with dimension d, the system shows correlations related to the standard percolation or directed percolation phase transition on such a lattice. On the other hand, a very different behavior is seen in the Kauffman net in which all spins are equally likely to be coupled to a given spin. In this situation, coupling loops are mostly suppressed, and the behavior of the system is much more like that of a mean field theory. We also describe possible applications of the models to, for example, genetic networks, cell differentiation, evolution, democracy in social systems and neural networks.Comment: 69 pages, 16 figures, Submitted to Springer Applied Mathematical Sciences Serie

A Minimal Threshold of c-di-GMP Is Essential for Fruiting Body Formation and Sporulation in Myxococcus xanthus

Generally, the second messenger bis-(3’-5’)-cyclic dimeric GMP (c-di-GMP) regulates the switch between motile and sessile lifestyles in bacteria. Here, we show that c-di-GMP is an essential regulator of multicellular development in the social bacterium Myxococcus xanthus. In response to starvation, M. xanthus initiates a developmental program that culminates in formation of spore-filled fruiting bodies. We show that c-di-GMP accumulates at elevated levels during development and that this increase is essential for completion of development whereas excess c-di-GMP does not interfere with development. MXAN3735 (renamed DmxB) is identified as a diguanylate cyclase that only functions during development and is responsible for this increased c-di-GMP accumulation. DmxB synthesis is induced in response to starvation, thereby restricting DmxB activity to development. DmxB is essential for development and functions downstream of the Dif chemosensory system to stimulate exopolysaccharide accumulation by inducing transcription of a subset of the genes encoding proteins involved in exopolysaccharide synthesis. The developmental defects in the dmxB mutant are non-cell autonomous and rescued by co-development with a strain proficient in exopolysaccharide synthesis, suggesting reduced exopolysaccharide accumulation as the causative defect in this mutant. The NtrC-like transcriptional regulator EpsI/Nla24, which is required for exopolysaccharide accumulation, is identified as a c-diGMP receptor, and thus a putative target for DmxB generated c-di-GMP. Because DmxB can be—at least partially—functionally replaced by a heterologous diguanylate cyclase, these results altogether suggest a model in which a minimum threshold level of c-di-GMP is essential for the successful completion of multicellular development in M. xanthus

Gravitational Lensing

Gravitational lensing has developed into one of the most powerful tools for the analysis of the dark universe. This review summarises the theory of gravitational lensing, its main current applications and representative results achieved so far. It has two parts. In the first, starting from the equation of geodesic deviation, the equations of thin and extended gravitational lensing are derived. In the second, gravitational lensing by stars and planets, galaxies, galaxy clusters and large-scale structures is discussed and summarised.Comment: Invited review article to appear in Classical and Quantum Gravity, 85 pages, 15 figure

Fungal planet description sheets: 951–1041

Novel species of fungi described in this study include those from various countries as follows: Antarctica , Apenidiella antarctica from permafrost, Cladosporium fildesense fromanunidentifiedmarinesponge. Argentina , Geastrum wrightii onhumusinmixedforest. Australia , Golovinomyces glandulariae on Glandularia aristigera, Neoanungitea eucalyptorum on leaves of Eucalyptus grandis, Teratosphaeria corymbiicola on leaves of Corymbia ficifolia, Xylaria eucalypti on leaves of Eucalyptus radiata. Brazil, Bovista psammophila on soil, Fusarium awaxy on rotten stalks of Zea mays, Geastrum lanuginosum on leaf litter covered soil, Hermetothecium mikaniae-micranthae (incl. Hermetothecium gen. nov.)on Mikania micrantha, Penicillium reconvexovelosoi in soil, Stagonosporopsis vannaccii from pod of Glycine max. British Virgin Isles , Lactifluus guanensis onsoil. Canada , Sorocybe oblongispora on resin of Picea rubens. Chile, Colletotrichum roseum on leaves of Lapageria rosea. China, Setophoma caverna fromcarbonatiteinKarstcave. Colombia , Lareunionomyces eucalypticola on leaves of Eucalyptus grandis. Costa Rica, Psathyrella pivae onwood. Cyprus , Clavulina iris oncalcareoussubstrate. France , Chromosera ambigua and Clavulina iris var. occidentalis onsoil. French West Indies , Helminthosphaeria hispidissima ondeadwood. Guatemala , Talaromyces guatemalensis insoil. Malaysia , Neotracylla pini (incl. Tracyllales ord. nov. and Neotra- cylla gen. nov.)and Vermiculariopsiella pini on needles of Pinus tecunumanii. New Zealand, Neoconiothyrium viticola on stems of Vitis vinifera, Parafenestella pittospori on Pittosporum tenuifolium, Pilidium novae-zelandiae on Phoenix sp. Pakistan , Russula quercus-floribundae onforestfloor. Portugal , Trichoderma aestuarinum from salinewater. Russia , Pluteus liliputianus on fallen branch of deciduous tree, Pluteus spurius on decaying deciduouswoodorsoil. South Africa , Alloconiothyrium encephalarti, Phyllosticta encephalarticola and Neothyrostroma encephalarti (incl. Neothyrostroma gen. nov.)onleavesof Encephalartos sp., Chalara eucalypticola on leaf spots of Eucalyptus grandis × urophylla, Clypeosphaeria oleae on leaves of Olea capensis, Cylindrocladiella postalofficium on leaf litter of Sideroxylon inerme , Cylindromonium eugeniicola (incl. Cylindromonium gen. nov.)onleaflitterof Eugenia capensis , Cyphellophora goniomatis on leaves of Gonioma kamassi , Nothodactylaria nephrolepidis (incl. Nothodactylaria gen. nov. and Nothodactylariaceae fam. nov.)onleavesof Nephrolepis exaltata , Falcocladium eucalypti and Gyrothrix eucalypti on leaves of Eucalyptus sp., Gyrothrix oleae on leaves of Olea capensis subsp. macrocarpa , Harzia metro sideri on leaf litter of Metrosideros sp., Hippopotamyces phragmitis (incl. Hippopota- myces gen. nov.)onleavesof Phragmites australis , Lectera philenopterae on Philenoptera violacea , Leptosillia mayteni on leaves of Maytenus heterophylla , Lithohypha aloicola and Neoplatysporoides aloes on leaves of Aloe sp., Millesimomyces rhoicissi (incl. Millesimomyces gen. nov.) on leaves of Rhoicissus digitata , Neodevriesia strelitziicola on leaf litter of Strelitzia nicolai , Neokirramyces syzygii (incl. Neokirramyces gen. nov.)onleafspots o