Triggering the Formation of Halo Globular Clusters with Galaxy Outflows

We investigate the interactions of high-redshift galaxy outflows with low-mass virialized (Tvir < 10,000K) clouds of primordial composition. While atomic cooling allows star formation in larger primordial objects, such "minihalos" are generally unable to form stars by themselves. However, the large population of high-redshift starburst galaxies may have induced widespread star formation in these objects, via shocks that caused intense cooling both through nonequilibrium H2 formation and metal-line emission. Using a simple analytic model, we show that the resulting star clusters naturally reproduce three key features of the observed population of halo globular clusters (GCs). First, the 10,000 K maximum virial temperature corresponds to the ~ 10^6 solar mass upper limit on the stellar mass of GCs. Secondly, the momentum imparted in such interactions is sufficient to strip the gas from its associated dark matter halo, explaining why GCs do not reside in dark matter potential wells. Finally, the mixing of ejected metals into the primordial gas is able to explain the ~ 0.1 dex homogeneity of stellar metallicities within a given GC, while at the same time allowing for a large spread in metallicity between different clusters. To study this possibility in detail, we use a simple 1D numerical model of turbulence transport to simulate mixing in cloud-outflow interactions. We find that as the shock shears across the side of the cloud, Kelvin-Helmholtz instabilities arise, which cause mixing of enriched material into > 20% of the cloud. Such estimates ignore the likely presence of large-scale vortices, however, which would further enhance turbulence generation. Thus quantitative mixing predictions must await more detailed numerical studies.Comment: 21 pages, 11 figures, Apj in pres

Toward an Improved Analytical Description of Lagrangian Bias

We carry out a detailed numerical investigation of the spatial correlation function of the initial positions of cosmological dark matter halos. In this Lagrangian coordinate system, which is especially useful for analytic studies of cosmological feedback, we are able to construct cross-correlation functions of objects with varying masses and formation redshifts and compare them with a variety of analytical approaches. For the case in which both formation redshifts are equal, we find good agreement between our numerical results and the bivariate model of Scannapieco & Barkana (2002; SB02) at all masses, redshifts, and separations, while the model of Porciani et al. (1998) does well for all parameters except for objects with different masses at small separations. We find that the standard mapping between Lagrangian and Eulerian bias performs well for rare objects at all separations, but fails if the objects are highly-nonlinear (low-sigma) peaks. In the Lagrangian case in which the formation redshifts differ, the SB02 model does well for all separations and combinations of masses, apart from a discrepancy at small separations in situations in which the smaller object is formed earlier and the difference between redshifts or masses is large. As this same limitation arises in the standard approach to the single-point progenitor distribution developed by Lacey & Cole (1993), we conclude that a more complete understanding of the progenitor distribution is the most important outstanding issue in the analytic modeling of Lagrangian bias.Comment: 22 pages, 8 figures, ApJ, in pres

Heating of the IGM

Using the cosmic virial theorem, Press-Schechter analysis and numerical simulations, we compute the expected X-ray background (XRB) from the diffuse IGM with the clumping factor expected from gravitational shock heating. The predicted fluxes and temperatures are excluded from the observed XRB. The predicted clumping can be reduced by entropy injection. The required energy is computed from the two-point correlation function, as well as from Press-Schechter formalisms. The minimal energy injection of 1 keV/nucleon excludes radiative or gravitational heating as a primary energy source. We argue that the intergalactic medium (IGM) must have been heated through violent processes such as massive supernova bursts. If the heating proceeded through supernova explosions, it likely proceeded in bursts which may be observable in high redshift supernova searches. Within our model we reproduce the observed cluster luminosity-temperature relation with energy injection of 1 keV/nucleon if this injection is assumed to be uncorrelated with the local density. These parameters predict that the diffuse IGM soft XRB has a temperature of ~1 keV with a flux near 10 keV/cm^2 s str keV, which may be detectable in the near future.Comment: to appear in ApJ Lett., 11 pages incl 1 figur

Common fixed point theorems for non-self mappings of nonlinear contractive maps in convex metric spaces

In this paper, we introduce a class of nonlinear contractive mappings in metric space. We also establish common fixed point theorems for these pair of non-self mappings satisfying the new contractive conditions in the convex metric space . An example is given to validate our results. The results generalize and extend some results in literature

Common Fixed Point Theorems for Four Maps in G-Partial Metric Spaces

The common fixed point principle for two set of maps satisfying specified contractive conditions in cone metric spaces is proved in the context of G-partial metric space and none of the maps involved therein is continuous. Our research outcome extends well known similar results available in the literature

Theoretical And Artificial Neural Network Computation and Analysis Of Global Solar Radiation At Enugu with Atmospheric Parameter

Records of measured sunshine hour’s data for a period of seventeen years (1991-2007) at Enugu 7.550N, 6.470E and 141.50m within the south-east zone of Nigeria were used to compute the global solar radiation of the same location with theoretical and artificial neural network models. The first part of the results (ie January to May )  has similar values with the third part (October to December). This indicate that weather conditions of the location  of study is of two periods, rainy and dry seasons. The values of the results also shows that global solar radiation is directly proportional to sunshine hours both for measured, theoretical and artificial neural network computations. Again Correlation of the two models show high performance of neural network over theoretical computation, as the neural network coefficent of determination R2 = 0.96 while coefficent of determination of theoretical computation  is R2 = 0.91 respectively. The above result shows that the two models has the ability of computing global solar radiation with sunshine hours, but the artificial neural network computation is  more accurate.   Keywords: Atmospheric parameters, theoretical, neural network, Global solar radiation and sunshine hours

Acute Lymphoblastic Leukaemia presenting as Juvenile Idiopathic Arthritis in a Nigerian boy

Background: Acute Lymphoblastic Leukaemia in children commonly presents with osteo articular manifestations that may mimic Juvenile Idiopathic Arthritis. This may create considerable diagnostic difficulty andlead to delay in commencing appropriate treatment.Case: An eight year old boy who presented with multiple joint pains and swellings of two months duration, had an elevated Rheumatoid factor and X-ray findings suggestive of Juvenile Idiopathic Arthritis. A blood film and bone marrow aspirate however, confirmed the diagnosis of Acute Lymphoblastic Leukaemia for which he was managed.Conclusion: This report emphasizes the need for a high index of suspicion in children presenting with osteo articular manifestations of Acute Lymphoblastic Leukaemia in order to make a prompt diagnosis and institute treatment.Key words: Acute Lymphoblastic Leukaemia, Juvenile Idiopathic Arthritis

Programming codes of block-Milne's device for solving fourth-order ODEs

Block-Milne’s device is an extension of block-predictor-corrector method and specifically developed to design a worthy step size, resolve the convergence criteria and maximize error. In this study, programming codes of block- Milne’s device (P-CB-MD) for solving fourth order ODEs are considered. Collocation and interpolation with power series as the basic solution are used to devise P-CB-MD. Analysing the P-CB-MD will give rise to the principal local truncation error (PLTE) after determining the order. The P-CB-MD for solving fourth order ODEs is written using Mathematica which can be utilized to evaluate and produce the mathematical results. The P-CB-MD is very useful to demonstrate speed, efficiency and accuracy compare to manual computation applied. Some selected problems were solved and compared with existing methods. This was made realizable with the support of the named computational benefit

Predictions of the causal entropic principle for environmental conditions of the universe

The causal entropic principle has been proposed as a superior alternative to the anthropic principle for understanding the magnitude of the cosmological constant. In this approach, the probability to create observers is assumed to be proportional to the entropy production \Delta S in a maximal causally connected region -- the causal diamond. We improve on the original treatment by better quantifying the entropy production due to stars, using an analytic model for the star formation history which accurately accounts for changes in cosmological parameters. We calculate the dependence of \Delta S on the density contrast Q=\delta\rho/\rho, and find that our universe is much closer to the most probable value of Q than in the usual anthropic approach and that probabilities are relatively weakly dependent on this amplitude. In addition, we make first estimates of the dependence of \Delta S on the baryon fraction and overall matter abundance. Finally, we also explore the possibility that decays of dark matter, suggested by various observed gamma ray excesses, might produce a comparable amount of entropy to stars.Comment: RevTeX4, 13pp, 10 figures; v2. clarified introduction, added ref

Tidal Effects in Clusters of Galaxies

High-redshift clusters of galaxies show an over-abundance of spirals by a factor of 2-3, and the corresponding under-abundance of S0 galaxies, relative to the nearby clusters. This morphological evolution can be explained by tidal interactions with neighboring galaxies and with the hierarchically growing cluster halo. The efficiency of tidal interactions depends on the size and structure of the cluster, as well as on the epoch of its formation. I simulate the formation and evolution of Virgo-type clusters in three cosmologies: a critical density model Omega_0=1, an open model Omega_0=0.4, and a flat model Omega_0=0.4 with a cosmological constant. The orbits of identified halos are traced with a high temporal resolution (~10^7 yr). Halos with low relative velocities merge only shortly after entering the cluster; after virialization mergers are suppressed. The dynamical evolution of galaxies is determined by the tidal field along their trajectories. The maxima of the tidal force do not always correspond to closest approach to the cluster center. They are produced to a large extent by the local density structures, such as the massive galaxies and the unvirialized remnants of infalling groups of galaxies. Collisions of galaxies are intensified by the substructure, with about 10 encounters within 10 kpc per galaxy in the Hubble time. These very close encounters add an important amount (10-50%) of the total heating rate. The integrated effect of tidal interactions is insufficient to transform a spiral galaxy into an elliptical, but can produce an S0 galaxy. Overall, tidal heating is stronger in the low Omega_0 clusters