Cosmic Reionisation by Stellar Sources: Population II Stars

We study the reionisation of the Universe by stellar sources using a numerical approach that combines fast 3D radiative transfer calculations with high resolution hydrodynamical simulations. Ionising fluxes for the sources are derived from intrinsic star formation rates computed in the underlying hydrodynamical simulations. Our mass resolution limit for sources is M~ 4.0 x 10^7 h^-1 M_sol, which is roughly an order of magnitude smaller than in previous studies of this kind. Our calculations reveal that the reionisation process is sensitive to the inclusion of dim sources with masses below ~10^9 h^-1 M_sol. We present the results of our reionisation simulation assuming a range of escape fractions for ionising photons and make statistical comparisons with observational constraints on the neutral fraction of hydrogen at z~6 derived from the z=6.28 SDSS quasar of Becker and coworkers. Our best fitting model has an escape fraction of ~20% and causes reionisation to occur by z~8, although the IGM remains fairly opaque until z~6. In order to simultaneously match the observations from the z=6.28 SDSS quasar and the optical depth measurement from WMAP with the sources modeled here, we require an evolving escape fraction that rises from f_esc=0.20 near z~6 to f_esc>~10 at z~18.Comment: 42 pages, 13 figure

Conflict-Free Coloring of Planar Graphs

A conflict-free k-coloring of a graph assigns one of k different colors to some of the vertices such that, for every vertex v, there is a color that is assigned to exactly one vertex among v and v's neighbors. Such colorings have applications in wireless networking, robotics, and geometry, and are well-studied in graph theory. Here we study the natural problem of the conflict-free chromatic number chi_CF(G) (the smallest k for which conflict-free k-colorings exist). We provide results both for closed neighborhoods N[v], for which a vertex v is a member of its neighborhood, and for open neighborhoods N(v), for which vertex v is not a member of its neighborhood. For closed neighborhoods, we prove the conflict-free variant of the famous Hadwiger Conjecture: If an arbitrary graph G does not contain K_{k+1} as a minor, then chi_CF(G) <= k. For planar graphs, we obtain a tight worst-case bound: three colors are sometimes necessary and always sufficient. We also give a complete characterization of the computational complexity of conflict-free coloring. Deciding whether chi_CF(G)<= 1 is NP-complete for planar graphs G, but polynomial for outerplanar graphs. Furthermore, deciding whether chi_CF(G)<= 2 is NP-complete for planar graphs G, but always true for outerplanar graphs. For the bicriteria problem of minimizing the number of colored vertices subject to a given bound k on the number of colors, we give a full algorithmic characterization in terms of complexity and approximation for outerplanar and planar graphs. For open neighborhoods, we show that every planar bipartite graph has a conflict-free coloring with at most four colors; on the other hand, we prove that for k in {1,2,3}, it is NP-complete to decide whether a planar bipartite graph has a conflict-free k-coloring. Moreover, we establish that any general} planar graph has a conflict-free coloring with at most eight colors.Comment: 30 pages, 17 figures; full version (to appear in SIAM Journal on Discrete Mathematics) of extended abstract that appears in Proceeedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017), pp. 1951-196

A Study For Efficiently Solving Optimisation Problems With An Increasing Number Of Design Variables

Coupling optimisation algorithms to Finite Element Methods (FEM) is a very promising way to achieve optimal metal forming processes. However, many optimisation algorithms exist and it is not clear which of these algorithms to use. This paper investigates the sensitivity of a Sequential Approximate Optimisation algorithm (SAO) proposed in [1-4] to an increasing number of design variables and compares it with two other algorithms: an Evolutionary Strategy (ES) and an Evolutionary version of the SAO (ESAO). In addition, it observes the influence of different Designs Of Experiments used with the SAO. It is concluded that the SAO is very capable and efficient and its combination with an ES is not beneficial. Moreover, the use of SAO with Fractional Factorial Design is the most efficient method, rather than Full Factorial Design as proposed in [1-4]

Flame Enhancement and Quenching in Fluid Flows

We perform direct numerical simulations (DNS) of an advected scalar field which diffuses and reacts according to a nonlinear reaction law. The objective is to study how the bulk burning rate of the reaction is affected by an imposed flow. In particular, we are interested in comparing the numerical results with recently predicted analytical upper and lower bounds. We focus on reaction enhancement and quenching phenomena for two classes of imposed model flows with different geometries: periodic shear flow and cellular flow. We are primarily interested in the fast advection regime. We find that the bulk burning rate v in a shear flow satisfies v ~ a*U+b where U is the typical flow velocity and a is a constant depending on the relationship between the oscillation length scale of the flow and laminar front thickness. For cellular flow, we obtain v ~ U^{1/4}. We also study flame extinction (quenching) for an ignition-type reaction law and compactly supported initial data for the scalar field. We find that in a shear flow the flame of the size W can be typically quenched by a flow with amplitude U ~ alpha*W. The constant alpha depends on the geometry of the flow and tends to infinity if the flow profile has a plateau larger than a critical size. In a cellular flow, we find that the advection strength required for quenching is U ~ W^4 if the cell size is smaller than a critical value.Comment: 14 pages, 20 figures, revtex4, submitted to Combustion Theory and Modellin

Role of the Bcl-2 gene family in prostate cancer progression and its implications for therapeutic intervention.

Prostate cancer (PC) is an escalating health burden in the western world. A large number of patients still present with extraprostatic (i.e., T3/T4, N0, M0/M1 or any T category and M1 disease or involved lymph nodes) and therefore incurable disease. Since the work of Huggins in 1940, there have been no major therapeutic advances and androgen ablation remains the best treatment option for extraprostatic androgen-responsive PC. Eighty to ninety percent of PC patients respond well to this form of treatment initially. After a median time of approximately 2 years, however, relapse to an androgen-independent (AI) state occurs, followed by death after a further median 6 months. Androgen ablation is rarely curative. The major molecular defect in extraprostatic and AI PC is the inability of PC cells to initiate apoptosis in response to a variety of stimuli, including different forms of androgen ablation and cytotoxic agents. The balance between cellular proliferation and cell death is regulated by multiple genes or families of genes through the cell cycle. The exact mechanisms governing this intricate and complex process are as yet not fully understood. One family of genes involved in cell survival/death control is the Bcl-2 gene family, which consists of homologous proteins that function to regulate distal and crucial commitment steps of the apoptotic pathway. The Bcl-2 family constitutes both agonists and antagonists of apoptosis that function at least in part through protein-protein interactions between various members of the family. The final outcome depends on the relative ratio of death agonists and antagonists. Bcl-2 expression has been closely associated with the AI phenotype of PC. Cytotoxic chemotherapy may be used as palliative therapy in AI PC but has not been found effective. Most chemotherapeutic cytotoxic agents induce apoptosis in cancer cells by direct and indirect action on the cell cycle. In vitro and in vivo studies have established that Bcl-2 expression confers an antiapoptotic activity against androgen withdrawal and cytotoxic chemotherapy. It thus offers a tempting potential target for therapeutic manipulations of PC

Resolving the Formation of Protogalaxies. III. Feedback from the First Stars

The first stars form in dark matter halos of masses ~10^6 M_sun as suggested by an increasing number of numerical simulations. Radiation feedback from these stars expels most of the gas from their shallow potential well of their surrounding dark matter halos. We use cosmological adaptive mesh refinement simulations that include self-consistent Population III star formation and feedback to examine the properties of assembling early dwarf galaxies. Accurate radiative transport is modeled with adaptive ray tracing. We include supernova explosions and follow the metal enrichment of the intergalactic medium. The calculations focus on the formation of several dwarf galaxies and their progenitors. In these halos, baryon fractions in 10^8 solar mass halos decrease by a factor of 2 with stellar feedback and by a factor of 3 with supernova explosions. We find that radiation feedback and supernova explosions increase gaseous spin parameters up to a factor of 4 and vary with time. Stellar feedback, supernova explosions, and H_2 cooling create a complex, multi-phase interstellar medium whose densities and temperatures can span up to 6 orders of magnitude at a given radius. The pair-instability supernovae of Population III stars alone enrich the halos with virial temperatures of 10^4 K to approximately 10^{-3} of solar metallicity. We find that 40% of the heavy elements resides in the intergalactic medium (IGM) at the end of our calculations. The highest metallicity gas exists in supernova remnants and very dilute regions of the IGM.Comment: 15 pages, 16 figures, accepted to ApJ. Many changes, including estimates of metal line cooling. High resolution images and movies available at http://www.slac.stanford.edu/~jwise/research/PGalaxies3

Spitzer Uncovers Active Galactic Nuclei Missed by Optical Surveys in 7 Late-type Galaxies

We report the discovery using Spitzers high resolution spectrograph of 7 Active Galactic Nuclei (AGN) in a sample of 32 late-type galaxies that show no definitive signatures of AGN in their optical spectra. Our observations suggest that the AGN detection rate in late-type galaxies is possibly 4 times larger than what optical spectroscopic observations alone suggest. We demonstrate using photoionization models with an input AGN and an extreme EUV-bright starburst ionizing radiation field that the observed mid-infrared line ratios cannot be replicated unless an AGN contribution, in some cases as little as 10% of the total galaxy luminosity, is included. These models show that when the fraction of the total luminosity due to the AGN is low, optical diagnostics are insensitive to the presence of the AGN. In this regime of parameter space, the mid-infrared diagnostics offer a powerful tool for uncovering AGN missed by optical spectroscopy. The AGN bolometric luminosities in our sample range from ~3 X 10^41 - ~2 X 10^43 ergs s^-1, which, based on the Eddington limit, corresponds to a lower mass limit for the black hole that ranges from ~3 X 10^3Mdot to as high as ~1.5 X 10^5Mdot. These lower mass limits however do not put a strain on the well-known relationship between the black hole mass and the host galaxy's stellar velocity dispersion established in predominantly early-type galaxies. Our findings add to the growing evidence that black holes do form and grow in low-bulge environments and that they are significantly more common than optical studies indicate.Comment: 8 figures, 17 pages, astro-ph\0801.2766 (Abel & Satyapal 2008; ApJ accepted) and this posting designed to form a two-part investigatio

Initial Ionization of Compressible Turbulence

We study the effects of the initial conditions of turbulent molecular clouds on the ionization structure in newly formed H_{ii} regions, using three-dimensional, photon-conserving radiative transfer in a pre-computed density field from three-dimensional compressible turbulence. Our results show that the initial density structure of the gas cloud can play an important role in the resulting structure of the H_{ii} region. The propagation of the ionization fronts, the shape of the resulting H_{ii} region, and the total mass ionized depend on the properties of the turbulent density field. Cuts through the ionized regions generally show ``butterfly'' shapes rather than spherical ones, while emission measure maps are more spherical if the turbulence is driven on scales small compared to the size of the H_{ii} region. The ionization structure can be described by an effective clumping factor $\zeta=< n > \cdot /^2$, where $n$ is number density of the gas. The larger the value of $\zeta$, the less mass is ionized, and the more irregular the H_{ii} region shapes. Because we do not follow dynamics, our results apply only to the early stage of ionization when the speed of the ionization fronts remains much larger than the sound speed of the ionized gas, or Alfv\'en speed in magnetized clouds if it is larger, so that the dynamical effects can be negligible.Comment: 9 pages, 10 figures, version with high quality color images can be found in http://research.amnh.org/~yuexing/astro-ph/0407249.pd

Radio Foregrounds for the 21cm Tomography of the Neutral Intergalactic Medium at High Redshifts

Absorption or emission against the cosmic microwave background radiation (CMB) may be observed in the redshifted 21cm line if the spin temperature of the neutral intergalactic medium prior to reionization differs from the CMB temperature. This so-called 21cm tomography should reveal important information on the physical state of the intergalactic medium at high redshifts. The fluctuations in the redshifted 21 cm, due to gas density inhomogeneities at early times, should be observed at meter wavelengths by the next generation radio telescopes such as the proposed {\it Square Kilometer Array (SKA)}. Here we show that the extra-galactic radio sources provide a serious contamination to the brightness temperature fluctuations expected in the redshifted 21 cm emission from the IGM at high redshifts. Unless the radio source population cuts off at flux levels above the planned sensitivity of SKA, its clustering noise component will dominate the angular fluctuations in the 21 cm signal. The integrated foreground signal is smooth in frequency space and it should nonetheless be possible to identify the sharp spectral feature arising from the non-uniformities in the neutral hydrogen density during the epoch when the first UV sources reionize the intergalactic medium.Comment: 5 pages emulateapj with 1 figure, accepted to Ap