Inversion of the star transform

We define the star transform as a generalization of the broken ray transform introduced by us in previous work. The advantages of using the star transform include the possibility to reconstruct the absorption and the scattering coefficients of the medium separately and simultaneously (from the same data) and the possibility to utilize scattered radiation which, in the case of the conventional X-ray tomography, is discarded. In this paper, we derive the star transform from physical principles, discuss its mathematical properties and analyze numerical stability of inversion. In particular, it is shown that stable inversion of the star transform can be obtained only for configurations involving odd number of rays. Several computationally-efficient inversion algorithms are derived and tested numerically.Comment: Accepted to Inverse Problems in this for

Thick fireballs and the steep decay in the early X-ray afterglow of gamma-ray bursts

We study the early afterglows of gamma-ray bursts produced by geometrically thick fireballs, following the development of the external shock as energy is continually supplied to the shocked material. We study the dependence of the early afterglow slope on the luminosity history of the central engine. The resulting light curves are modeled with power-law functions and the importance of a correct choice of the reference time t_0 is investigated. We find that deviations from a simple power-law are observed only if a large majority of the energy is released at late times. The light curve in this case can be described as a simple power-law if the reference time is set to be close to the end of the burst. We applied our analysis to the cases of GRB 050219a and GRB 050315. We show that the early steep decay of the afterglow cannot result from the interaction of the fireball with the ambient medium. We conclude that the early X-ray afterglow emission is associated with the prompt phase and we derive limits on the radius at which the prompt radiation is produced.Comment: Minor revisions, accepted for publication in Ap

Solar Modulation of the Galactic Helium Spectrum Above 30 Mev Per Nucleon

Time measurements of differential energy spectra and flux of primary helium nuclei by use of charged particle telescope

Acceleration of particles in the earth's shock transition region and beyond

Acceleration of particles in earth shock transition region and beyon

Predicting rare events in chemical reactions: application to skin cell proliferation

In a well-stirred system undergoing chemical reactions, fluctuations in the reaction propensities are approximately captured by the corresponding chemical Langevin equation. Within this context, we discuss in this work how the Kramers escape theory can be used to predict rare events in chemical reactions. As an example, we apply our approach to a recently proposed model on cell proliferation with relevance to skin cancer [P.B. Warren, Phys. Rev. E {\bf 80}, 030903 (2009)]. In particular, we provide an analytical explanation for the form of the exponential exponent observed in the onset rate of uncontrolled cell proliferation.Comment: New materials and references added. To appear in Physical Review

Standard Model couplings and collider signatures of a light scalar

The electroweak symmetry breaking (EWSB) sector of the Standard Model can be far richer and more interesting than the usual single scalar doublet model. We explore scenarios where the EWSB sector is nearly scale invariant and consequently gives rise to a light CP even scalar particle. The one-doublet SM is in that category, as are many other models with either weakly or strongly coupled sectors that trigger EWSB. We study the couplings of the light scalar to the SM particles that can arise from the explicit breaking of scale invariance focusing on the possible differences with the minimal SM. The couplings of the light scalar to light fermions, as well as to the massless gauge bosons, can be significantly enhanced. We find possible new discovery channels due to the decays of the conformal scalar into e^+e^- and mu^+mu^- pairs as well as new production channels via light quark annihilation.Comment: 10 pages, 7 figure

Bacteria Use Type IV Pili to Walk Upright and Detach from Surfaces

1. Department of Bioengineering, California Nano Systems Institute,University of California, Los Angeles, CA 90024, USA. 2. Department of Chemical and Biomolecular Engineering, University of Houston, Houston, TX 77204, USA. 3. Department of Materials Science and Engineering, University of Illinois, Urbana-Champaign, IL 61801, USA. 4. Department of Civil Engineering and Geological Sciences, University of Notre Dame, Notre Dame, IN 46556, USA.Bacterial biofilms are structured multicellular communities involved in a broad range of infections. Knowing how free-swimming bacteria adapt their motility mechanisms near surfaces is crucial for understanding the transition between planktonic and biofilm phenotypes. By translating microscopy movies into searchable databases of bacterial behavior, we identified fundamental type IV pili–driven mechanisms for Pseudomonas aeruginosa surface motility involved in distinct foraging strategies. Bacteria stood upright and “walked” with trajectories optimized for two-dimensional surface exploration. Vertical orientation facilitated surface detachment and could influence biofilm morphology.Center for Nonlinear Dynamic

Quantum Cluster Variables via Serre Polynomials

For skew-symmetric acyclic quantum cluster algebras, we express the quantum $F$-polynomials and the quantum cluster monomials in terms of Serre polynomials of quiver Grassmannians of rigid modules. As byproducts, we obtain the existence of counting polynomials for these varieties and the positivity conjecture with respect to acyclic seeds. These results complete previous work by Caldero and Reineke and confirm a recent conjecture by Rupel.Comment: minor corrections, reference added, example 4.3 added, 38 page