Analytical Solutions of Singular Isothermal Quadrupole Lens

Using analytical method, we study the Singular Isothermal Quadrupole (SIQ) lens system, which is the simplest lens model that can produce four images. In this case, the radial mass distribution is in accord with the profile of the Singular Isothermal Sphere (SIS) lens, and the tangential distribution is given by adding a quadrupole on the monopole component. The basic properties of the SIQ lens have been studied in this paper, including deflection potential, deflection angle, magnification, critical curve, caustic, pseudo-caustic and transition locus. Analytical solutions of the image positions and magnifications for the source on axes are derived. As have been found, naked cusps will appear when the relative intensity $k$ of quadrupole to monopole is larger than 0.6. According to the magnification invariant theory of the SIQ lens, the sum of the signed magnifications of the four images should be equal to unity \citep{dal98}. However, if a source lies in the naked cusp, the summed magnification of the left three images is smaller than the invariant 1. With this simple lens system, we study the situations that a point source infinitely approaches a cusp or a fold. The sum of magnifications of cusp image triplet is usually not equal to 0, and it is usually positive for major cusp while negative for minor cusp. Similarly, the sum of magnifications of fold image pair is usually neither equal to 0. Nevertheless, the cusp and fold relations are still equal to 0, in that the sum values are divided by infinite absolute magnifications by definition.Comment: 12 pages, 2 figures, accepted for publication in ApJ

Tidal Barrier and the Asymptotic Mass of Proto Gas-Giant Planets

Extrasolar planets found with radial velocity surveys have masses ranging from several Earth to several Jupiter masses. While mass accretion onto protoplanetary cores in weak-line T-Tauri disks may eventually be quenched by a global depletion of gas, such a mechanism is unlikely to have stalled the growth of some known planetary systems which contain relatively low-mass and close-in planets along with more massive and longer period companions. Here, we suggest a potential solution for this conundrum. In general, supersonic infall of surrounding gas onto a protoplanet is only possible interior to both of its Bondi and Roche radii. At a critical mass, a protoplanet's Bondi and Roche radii are equal to the disk thickness. Above this mass, the protoplanets' tidal perturbation induces the formation of a gap. Although the disk gas may continue to diffuse into the gap, the azimuthal flux across the protoplanets' Roche lobe is quenched. Using two different schemes, we present the results of numerical simulations and analysis to show that the accretion rate increases rapidly with the ratio of the protoplanet's Roche to Bondi radii or equivalently to the disk thickness. In regions with low geometric aspect ratios, gas accretion is quenched with relatively low protoplanetary masses. This effect is important for determining the gas-giant planets' mass function, the distribution of their masses within multiple planet systems around solar type stars, and for suppressing the emergence of gas-giants around low mass stars

Low Redshift QSO Lyman alpha Absorption Line Systems Associated with Galaxies

In this paper we present Monte-Carlo simulations of Lyman alpha absorption systems which originate in galactic haloes, galaxy discs and dark matter (DM) satellites around big central haloes. It is found that for strong Lyman alpha absorption lines galactic haloes and satellites can explain ~20% and 40% of the line number density of QSO absorption line key project respectively. If big galaxies indeed possess such large numbers of DM satellites and they possess gas, these satellites may play an important role for strong Lyman alpha lines. However the predicted number density of Lyman-limit systems by satellites is \~0.1 (per unit redshift), which is four times smaller than that by halo clouds. Including galactic haloes, satellites and HI discs of spirals, the predicted number density of strong lines can be as much as 60% of the HST result. The models can also predict all of the observed Lyman-limit systems. The average covering factor within 250 kpc/h is estimated to be ~0.36. And the effective absorption radius of a galaxy is estimated to be ~150 kpc/h. The models predict W_r propto rho^{-0.5} L_B^{0.15} (1+z)^{-0.5}. We study the selection effects of selection criteria similar to the imaging and spectroscopic surveys. We simulate mock observations through known QSO lines-of-sight and find that selection effects can statistically tighten the dependence of line width on projected distance. (abridged)Comment: 23 pages, 9 postscript figures; references updated, minor change in section

Cusp Summations and Cusp Relations of Simple Quad Lenses

We review five often used quad lens models, each of which has analytical solutions and can produce four images at most. Each lens model has two parameters, including one that describes the intensity of non-dimensional mass density, and the other one that describes the deviation from the circular lens. In our recent work, we have found that the cusp and the fold summations are not equal to 0, when a point source infinitely approaches a cusp or a fold from inner side of the caustic. Based on the magnification invariant theory, which states that the sum of signed magnifications of the total images of a given source is a constant, we calculate the cusp summations for the five lens models. We find that the cusp summations are always larger than 0 for source on the major cusps, while can be larger or smaller than 0 for source on the minor cusps. We also find that if these lenses tend to the circular lens, the major and minor cusp summations will have infinite values, and with positive and negative signs respectively. The cusp summations do not change significantly if the sources are slightly deviated from the cusps. In addition, through the magnification invariants, we also derive the analytical signed cusp relations on the axes for three lens models. We find that both on the major and the minor axes the larger the lenses deviated from the circular lens, the larger the signed cusp relations. The major cusp relations are usually larger than the absolute minor cusp relations, but for some lens models with very large deviation from circular lens, the minor cusp relations can be larger than the major cusp relations.Comment: 8 pages, 4 figures, accepted for publication in MNRA

Crumpling wires in two dimensions

An energy-minimal simulation is proposed to study the patterns and mechanical properties of elastically crumpled wires in two dimensions. We varied the bending rigidity and stretching modulus to measure the energy allocation, size-mass exponent, and the stiffness exponent. The mass exponent is shown to be universal at value $D_{M}=1.33$. We also found that the stiffness exponent $\alpha =-0.25$ is universal, but varies with the plasticity parameters $s$ and $\theta_{p}$. These numerical findings agree excellently with the experimental results

Antifouling bastadin congeners target blue mussel phenoloxidase and complex copper(II) ions

Synthetically prepared congeners of spongederived bastadin derivatives such as 5,5'-dibromohemibastadin- 1 (DBHB) that suppress the settling of barnacle larvae were identified in this study as strong inhibitors of blue mussel phenoloxidase that is involved in the firm attachment of mussels to a given substrate. The IC50 value of DBHB as the most active enzyme inhibitor encountered in this study amounts to 0.84 mu M. Inhibition of phenoloxidase by DBHB is likely due to complexation of copper(II) ions from the catalytic centre of the enzyme by the a-oxo-oxime moiety of the compound as shown here for the first time by structure activity studies and by X-ray structure determination of a copper(II) complex of DBHB.Biotechnology & Applied MicrobiologyMarine & Freshwater BiologySCI(E)EI0ARTICLE61148-11581