A necessary condition for a power series to be a formal solution of a singular linear differential equation of order k

AbstractWe obtain a necessary condition on the coefficients of a formal power series, which is a formal solution of a nontrivial singular linear differential equation of order k, with analytic coefficients and prove a “uniqueness” theorem for the differential equation

TRAPHIC - Radiative Transfer for Smoothed Particle Hydrodynamics Simulations

We present TRAPHIC, a novel radiative transfer scheme for Smoothed Particle Hydrodynamics (SPH) simulations. TRAPHIC is designed for use in simulations exhibiting a wide dynamic range in physical length scales and containing a large number of light sources. It is adaptive both in space and in angle and can be employed for application on distributed memory machines. The commonly encountered computationally expensive scaling with the number of light sources in the simulation is avoided by introducing a source merging procedure. The (time-dependent) radiative transfer equation is solved by tracing individual photon packets in an explicitly photon-conserving manner directly on the unstructured grid traced out by the set of SPH particles. To accomplish directed transport of radiation despite the irregular spatial distribution of the SPH particles, photons are guided inside cones. We present and test a parallel numerical implementation of TRAPHIC in the SPH code GADGET-2, specified for the transport of mono-chromatic hydrogen-ionizing radiation. The results of the tests are in excellent agreement with both analytic solutions and results obtained with other state-of-the-art radiative transfer codes.Comment: 31 pages, 20 figures. Accepted for publication in MNRAS. Revised version includes many clarifications and a new time-dependent radiative transfer calculation (fig. 19

Simulation and experimental study of rheological properties of CeO2 – water nanofluid

Open Access. This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.Metal oxide nanoparticles offer great merits over controlling rheological, thermal, chemical and physical properties of solutions. The effectiveness of a nanoparticle to modify the properties of a fluid depends on its diffusive properties with respect to the fluid. In this study, rheological properties of aqueous fluids (i.e. water) were enhanced with the addition of CeO2 nanoparticles. This study was characterized by the outcomes of simulation and experimental results of nanofluids. The movement of nanoparticles in the fluidic media was simulated by a large-scale molecular thermal dynamic program (i.e. LAMMPS). The COMPASS force field was employed with smoothed particle hydrodynamic potential (SPH) and discrete particle dynamics potential (DPD). However, this study develops the understanding of how the rheological properties are affected due to the addition of nanoparticles in a fluid and the way DPD and SPH can be used for accurately estimating the rheological properties with Brownian effect. The rheological results of the simulation were confirmed by the convergence of the stress autocorrelation function, whereas experimental properties were measured using a rheometer. These rheological values of simulation were obtained and agreed within 5 % of the experimental values; they were identified and treated with a number of iterations and experimental tests. The results of the experiment and simulation show that 10 % CeO2 nanoparticles dispersion in water has a viscosity of 2.0–3.3 mPasPeer reviewedFinal Published versio

The mass function

We present the mass functions for different mass estimators for a range of cosmological models. We pay particular attention to how universal the mass function is, and how it depends on the cosmology, halo identification and mass estimator chosen. We investigate quantitatively how well we can relate observed masses to theoretical mass functions.Comment: 14 pages, 12 figures, to appear in ApJ

High-Redshift Galaxies in Cold Dark Matter Models

We use hydrodynamic cosmological simulations to predict the star formation properties of high-redshift galaxies (z=2-6) in five variants of the inflationary cold dark matter scenario, paying particular attention to z=3, the redshift of the largest "Lyman-break galaxy" (LBG) samples. Because we link the star formation timescale to the local gas density, the rate at which a galaxy forms stars is governed mainly by the rate at which it accretes cooled gas from the surrounding medium. At z=3, star formation in most of the simulated galaxies is steady on 200 Myr timescales, and the instantaneous star formation rate (SFR) is correlated with total stellar mass. However, there is enough scatter in this correlation that a sample selected above a given SFR threshold may contain galaxies with a fairly wide range of masses. The redshift history and global density of star formation in the simulations depend mainly on the amplitude of mass fluctuations in the underlying cosmological model. The three models whose mass fluctuation amplitudes agree with recent analyses of the Lyman-alpha forest also reproduce the observed luminosity function of LBGs reasonably well, though the dynamic range of the comparison is small and the theoretical and observational uncertainties are large. The models with higher and lower amplitudes appear to predict too much and too little star formation, respectively, though they are not clearly ruled out. The intermediate amplitude models predict SFR ~ 30-40 Msun/yr for galaxies with a surface density 1 per arcmin^2 per unit redshift at z=3. They predict much higher surface densities at lower SFR, and significant numbers of galaxies with SFR > 10 Msun/yr at z >= 5.Comment: Submitted to ApJ. 31 pages including 10 ps figures. Full resolution version of Fig 2 available at http://www.astronomy.ohio-state.edu/~dhw/Sph/zgal.fig2.ps.g

Solving One Dimensional Scalar Conservation Laws by Particle Management

We present a meshfree numerical solver for scalar conservation laws in one space dimension. Points representing the solution are moved according to their characteristic velocities. Particle interaction is resolved by purely local particle management. Since no global remeshing is required, shocks stay sharp and propagate at the correct speed, while rarefaction waves are created where appropriate. The method is TVD, entropy decreasing, exactly conservative, and has no numerical dissipation. Difficulties involving transonic points do not occur, however inflection points of the flux function pose a slight challenge, which can be overcome by a special treatment. Away from shocks the method is second order accurate, while shocks are resolved with first order accuracy. A postprocessing step can recover the second order accuracy. The method is compared to CLAWPACK in test cases and is found to yield an increase in accuracy for comparable resolutions.Comment: 15 pages, 6 figures. Submitted to proceedings of the Fourth International Workshop Meshfree Methods for Partial Differential Equation

Cooling Radiation and the Lyman-alpha Luminosity of Forming Galaxies

We examine the cooling radiation from forming galaxies in hydrodynamic simulations of the LCDM model (cold dark matter with a cosmological constant), focusing on the Ly-alpha line luminosities of high-redshift systems. Primordial composition gas condenses within dark matter potential wells, forming objects with masses and sizes comparable to the luminous regions of observed galaxies. As expected, the energy radiated in this process is comparable to the gravitational binding energy of the baryons, and the total cooling luminosity of the galaxy population peaks at z ~= 2. However, in contrast to the classical picture of gas cooling from the \sim 10^6 K virial temperature of a typical dark matter halo, we find that most of the cooling radiation is emitted by gas with T < 20,000 K. As a consequence, roughly 50% of this cooling radiation emerges in the Ly-alpha line. While a galaxy's cooling luminosity is usually smaller than the ionizing continuum luminosity of its young stars, the two are comparable in the most massive systems, and the cooling radiation is produced at larger radii, where the Ly-alpha photons are less likely to be extinguished by dust. We suggest, in particular, that cooling radiation could explain the two large (\sim 100 kpc), luminous (L_{Ly-alpha} \sim 10^{44} erg s^{-1}) ``blobs'' of Ly-alpha emission found in Steidel et al.'s (1999) narrow band survey of a z = 3 proto-cluster. Our simulations predict objects of the observed luminosity at about the right space density, and radiative transfer effects can account for the observed sizes and line widths. We discuss observable tests of this hypothesis for the nature of the Ly-alpha blobs, and we present predictions for the contribution of cooling radiation to the Ly-alpha luminosity function of galaxies as a function of redshift.Comment: Submitted to ApJ. 28 pages including 9 PS figures. Version with color figures available at http://donald.astro.umass.edu/~fardal/papers/cooling/cooling.htm

Cosmological Evolution of Supergiant Star-Forming Clouds

In an exploration of the birthplaces of globular clusters, we present a careful examination of the formation of self-gravitating gas clouds within assembling dark matter haloes in a hierarchical cosmological model. Our high-resolution smoothed particle hydrodynamical simulations are designed to determine whether or not hypothesized supergiant molecular clouds (SGMCs) form and, if they do, to determine their physical properties and mass spectra. It was suggested in earlier work that clouds with a median mass of several 10^8 M_sun are expected to assemble during the formation of a galaxy, and that globular clusters form within these SGMCs. Our simulations show that clouds with the predicted properties are indeed produced as smaller clouds collide and agglomerate within the merging dark matter haloes of our cosmological model. We find that the mass spectrum of these clouds obeys the same power-law form observed for globular clusters, molecular clouds, and their internal clumps in galaxies, and predicted for the supergiant clouds in which globular clusters may form. We follow the evolution and physical properties of gas clouds within small dark matter haloes up to z = 1, after which prolific star formation is expected to occur. Finally, we discuss how our results may lead to more physically motivated "rules" for star formation in cosmological simulations of galaxy formation.Comment: Accepted to The Astrophysical Journal; 17 pages, 8 figure

An implicit method for radiative transfer with the diffusion approximation in SPH

An implicit method for radiative transfer in SPH is described. The diffusion approximation is used, and the hydrodynamic calculations are performed by a fully three--dimensional SPH code. Instead of the energy equation of state for an ideal gas, various energy states and the dissociation of hydrogen molecules are considered in the energy calculation for a more realistic temperature and pressure determination. In order to test the implicit code, we have performed non--isothermal collapse simulations of a centrally condensed cloud, and have compared our results with those of finite difference calculations performed by MB93. The results produced by the two completely different numerical methods agree well with each other.Comment: 25 pages, 9 figure