Constraints on the warm dark matter model from gravitational lensing

Formation of sub-galactic halos is suppressed in warm dark matter (WDM) model due to thermal motion of WDM particles. This may provide a natural resolution to some puzzles in standard cold dark matter (CDM) theory such as the cusped density profiles of virialized dark halos and the overabundance of low mass satellites. One of the observational tests of the WDM model is to measure the gravitationally lensed images of distant quasars below sub-arcsecond scales. In this Letter, we report a comparison of the lensing probabilities of multiple images between CDM and WDM models using a singular isothermal sphere model for the mass density profiles of dark halos and the Press-Schechter mass function for their distribution and cosmic evolution. It is shown that the differential probability of multiple images with small angular separations down to 10 milliarcseconds should allow one to set useful constraints on the WDM particle mass. We discuss briefly the feasibility and uncertainties of this method in future radio surveys (e.g. VLBI) for gravitational lensing.Comment: 3 pages, 1 figure, accepted for publication in ApJ Let

Basis-conjugating automorphisms of a free group and associated Lie algebras

Let F_n = denote the free group with generators {x_1,...,x_n}. Nielsen and Magnus described generators for the kernel of the canonical epimorphism from the automorphism group of F_n to the general linear group over the integers. In particular among them are the automorphisms chi_{k,i} which conjugate the generator x_k by the generator x_i leaving the x_j fixed for j not k. A computation of the cohomology ring as well as the Lie algebra obtained from the descending central series of the group generated by chi_{k,i} for i<k is given here. Partial results are obtained for the group generated by all chi_{k,i}.Comment: This is the version published by Geometry & Topology Monographs on 22 February 200

Correlation Between the Halo Concentration (c) and the Virial Mass (Mvir) Determined from X-ray Clusters

Numerical simulations of structure formation have suggested that there exists a good correlation between the halo concentration c (or the characteristic density delta_c) and the virial mass Mvir for any virialized dark halo described by the Navarro, Frenk & White (1995) density profile. In this Letter, we present an observational determination of the c-Mvir (or delta_c-Mvir) relation in the mass range of 10^14< Mvir <10^16 (solar mass) using a sample of 63 X-ray luminous clusters. The best-fit power law relation, which is roughly independent of the values of Omega_M and Lambda, is c propto Mvir^(-0.5) or delta_c propto Mvir^(-1.2), indicating n=-0.7 for a scale-free power spectrum of the primordial density fluctuations. We discuss the possible reasons for the conflict with the predictions by typical CDM models such as SCDM, LCDM and OCDM.Comment: 13 pages, 1 figure, two tables. Accepted for publication in ApJ

Structure-based Discovery of Novel Small Molecule Wnt Signaling Inhibitors by Targeting the Cysteine-rich Domain of Frizzled.

Frizzled is the earliest discovered glycosylated Wnt protein receptor and is critical for the initiation of Wnt signaling. Antagonizing Frizzled is effective in inhibiting the growth of multiple tumor types. The extracellular N terminus of Frizzled contains a conserved cysteine-rich domain that directly interacts with Wnt ligands. Structure-based virtual screening and cell-based assays were used to identify five small molecules that can inhibit canonical Wnt signaling and have low IC50 values in the micromolar range. NMR experiments confirmed that these compounds specifically bind to the Wnt binding site on the Frizzled8 cysteine-rich domain with submicromolar dissociation constants. Our study confirms the feasibility of targeting the Frizzled cysteine-rich domain as an effective way of regulating canonical Wnt signaling. These small molecules can be further optimized into more potent therapeutic agents for regulating abnormal Wnt signaling by targeting Frizzled

Adiabatic Geometric Phase for a General Quantum States

A geometric phase is found for a general quantum state that undergoes adiabatic evolution. For the case of eigenstates, it reduces to the original Berry's phase. Such a phase is applicable in both linear and nonlinear quantum systems. Furthermore, this new phase is related to Hannay's angles as we find that these angles, a classical concept, can arise naturally in quantum systems. The results are demonstrated with a two-level model.Comment: 4 pages, 2 figure

Adiabatic Theory of Nonlinear Evolution of Quantum States

We present a general theory for adiabatic evolution of quantum states as governed by the nonlinear Schrodinger equation, and provide examples of applications with a nonlinear tunneling model for Bose-Einstein condensates. Our theory not only spells out conditions for adiabatic evolution of eigenstates, but also characterizes the motion of non-eigenstates which cannot be obtained from the former in the absence of the superposition principle. We find that in the adiabatic evolution of non-eigenstates, the Aharonov-Anandan phases play the role of classical canonical actions.Comment: substantial revision, 5 pages and 3 figure

Controlled Generation of Dark Solitons with Phase Imprinting

The generation of dark solitons in Bose-Einstein condensates with phase imprinting is studied by mapping it into the classic problem of a damped driven pendulum. We provide simple but powerful schemes of designing the phase imprint for various desired outcomes. We derive a formula for the number of dark solitons generated by a given phase step, and also obtain results which explain experimental observations.Comment: 4pages, 4 figure

Reexamination of the galaxy formation-regulated gas evolution model in groups and clusters

As an alternative explanation of the entropy excess and the steepening of the X-ray luminosity-temperature relation in groups and clusters, the galaxy formation-regulated gas evolution (GG) model proposed recently by Bryan makes an attempt to incorporate the formation of galaxies into the evolution of gas without additional heating by nongravitational processes. This seems to provide a unified scheme for our understanding of the structures and evolution of both galaxies and gas in groups and clusters. In this paper, we present an extensive comparison of the X-ray properties of groups and clusters predicted by the GG model and those revealed by current X-ray observations, using various large data sources in the literature and also taking the observational selection effects into account. These include an independent check of the fundamental working hypothesis of the GG model, i.e., galaxy formation was less efficient in rich clusters than in groups, a new test of the radial gas distributions revealed by both the gas mass fraction and the X-ray surface brightness profiles, and an reexamination of the X-ray luminosity-temperature and entropy-temperature relations. In particular, it shows that the overall X-ray surface brightness profiles predicted by the GG model are very similar in shape, insensitive to the X-ray temperature, and the shallower X-ray surface brightness profiles seen at low-temperature systems may arise from the current observational selection effect. This can be used as the simplest approach to distinguishing between the GG model and the preheating scenario. The latter yields an intrinsically shallower gas distribution in groups than in rich clusters.Comment: 30 pages, 10 figures, accepted for publication in Ap