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  • 1
    Electronic Resource
    Electronic Resource
    Properties of Standard n-Ideals of a Lattice (2000)
    Springer
    Southeast Asian bulletin of mathematics 24 (2000), S. 403-409 
    Details
    ISSN: 0219-175X
    Keywords: convex sublattice ; standard n-ideal ; neutral element ; homomorphism n-kernel ; boolean algebra
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An n-ideal of a lattice L is a convex sublattice containing a fixed element n ∈ L and it is called standard if it is a standard element of the lattice of n-ideals In(L). In this paper we have shown that, for a neutral element n of a lattice L, the principal n-ideal 〈a〉n of a lattice L is a standard n-ideal if and only if a ∨ n is standard and a ∧ n is dual standard. We have also shown that if n is a neutral element and (n] and [n) are relatively complemented, then every homomorphism n-kernels of L is a standard n-ideal and every standard n-ideal is the n-kernel of precisely one congruence relation. Finally, we have shown that, for a relatively complemented lattice L with 0 and 1, C(L) is a Boolean algebra if and only if every standard n-ideal of L is a principal n-ideal.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s10012-000-0403-0
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  • 2
    Electronic Resource
    Electronic Resource
    Effects of legumes on soil physical quality in a maize crop (1992)
    Springer
    Plant and soil 140 (1992), S. 15-23 
    Details
    ISSN: 1573-5036
    Keywords: continuous maize ; intercropped legumes ; N fertilization ; soil physical quality ; soil management
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract The effect of intercropped legumes and three N fertilizer rates in a continuous maize (Zea mays L.) cropping system on the physical properties of two soils were investigated for three years. The legumes, being a mixture of alfalfa, clover and hairy vetch, had a significant cumulative effect on some physical properties of both soil. The lowest stability and smallest mean weight diameter of soil aggregates were associated with monoculture maize plots. Aggregate size and stability were not affected by N fertilization at any of the rates of 0, 70, and 140 kg ha-1 in intercropped plots, except that aggregate stability was actually reduced by N fertilization in one soil, the Ste. Rosalie clay. In maize plots in both soils, stability and size of soil aggregates were significantly increased with increased added N. Intercropped legumes significantly decreased dry bulk density and soil penetration resistance. Added N had no measurable influence on these compaction factors. Soil water properties were not significantly affected by either intercropping or N fertilization. Positive effects noted on soil aggregation and other physical properties in intercropped plots are the result of enhanced root activity, or incorporation of legumes as green manure, or both. Improvement of soil structure in maize plots associated with increasing N application was the result of increased maize-root residues.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00012802
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  • 3
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    Witnessing the birth of a supermassive protostar (2016)
    Oxford University Press
    Details
    Publication Date: 2016-03-06
    Description: The detection of z 〉 6 quasars reveals the existence of supermassive black holes of a few 10 9 M . One of the potential pathways to explain their formation in the infant universe is the so-called direct collapse model which provides massive seeds of 10 5 –10 6 M . An isothermal direct collapse mandates that haloes should be of a primordial composition and the formation of molecular hydrogen remains suppressed in the presence of a strong Lyman Werner flux. In this study, we perform high resolution cosmological simulations for two massive primordial haloes employing a detailed chemical model which includes H – cooling as well as realistic opacities for both the bound–free H – emission and the Rayleigh scattering of hydrogen atoms. We are able to resolve the collapse up to unprecedentedly high densities of ~10 –3 g cm –3 and to scales of about 10 –4 au. Our results show that the gas cools down to ~5000 K in the presence of H – cooling, and induces fragmentation at scales of about 8000 au in one of the two simulated haloes, which may lead to the formation of a binary. In addition, fragmentation also occurs on the au scale in one of the haloes but the clumps are expected to merge on short time-scales. Our results confirm that H – cooling does not prevent the formation of a supermassive star and the trapping of cooling radiation stabilizes the collapse on small scales.
    Print ISSN: 0035-8711
    Electronic ISSN: 1365-2966
    Topics: Physics
    Published by Oxford University Press
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  • 4
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    How an improved implementation of H2 self-shielding influences the formation of massive stars and black holes (2015)
    Oxford University Press
    Details
    Publication Date: 2015-07-16
    Description: High-redshift quasars at z  〉 6 have masses up to ~10 9 M . One of the pathways to their formation includes direct collapse of gas, forming a supermassive star, precursor of the black hole seed. The conditions for direct collapse are more easily achievable in metal-free haloes, where atomic hydrogen cooling operates and molecular hydrogen (H 2 ) formation is inhibited by a strong external (ultraviolet) UV flux. Above a certain value of UV flux ( J crit ), the gas in a halo collapses isothermally at ~10 4 K and provides the conditions for supermassive star formation. However, H 2  can self-shield, reducing the effect of photodissociation. So far, most numerical studies used the local Jeans length to calculate the column densities for self-shielding. We implement an improved method for the determination of column densities in 3D simulations and analyse its effect on the value of J crit . This new method captures the gas geometry and velocity field and enables us to properly determine the direction-dependent self-shielding factor of H 2  against photodissociating radiation. We find a value of J crit that is a factor of 2 smaller than with the Jeans approach (~2000 J 21 versus ~4000 J 21 ). The main reason for this difference is the strong directional dependence of the H 2  column density. With this lower value of J crit , the number of haloes exposed to a flux 〉 J crit is larger by more than an order of magnitude compared to previous studies. This may translate into a similar enhancement in the predicted number density of black hole seeds.
    Print ISSN: 0035-8711
    Electronic ISSN: 1365-2966
    Topics: Physics
    Published by Oxford University Press
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  • 5
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    Assessing inflow rates in atomic cooling haloes: implications for direct collapse black holes (2015)
    Oxford University Press
    Details
    Publication Date: 2015-07-12
    Description: Supermassive black holes are not only common in the present-day galaxies, but billion solar masses black holes also powered z  ≥ 6 quasars. One efficient way to form such black holes is the collapse of a massive primordial gas cloud into a so-called direct collapse black hole. The main requirement for this scenario is the presence of large accretion rates of ≥ 0.1 M yr – 1 to form a supermassive star. It is not yet clear how and under what conditions such accretion rates can be obtained. The prime aim of this work is to determine the mass accretion rates under non-isothermal collapse conditions. We perform high-resolution cosmological simulations for three primordial haloes of a few times 10 7 M illuminated by an external UV flux, J 21  = 100–1000. We find that a rotationally supported structure of about parsec size is assembled, with an aspect ratio between 0.25 and 1 depending upon the thermodynamical properties. Rotational support, however, does not halt collapse, and mass inflow rates of ~ 0.1 M yr – 1 can be obtained in the presence of even a moderate UV background flux of strength J 21  ≥ 100. To assess whether such large accretion rates can be maintained over longer time-scales, we employed sink particles, confirming the persistence of accretion rates of ~ 0.1 M yr – 1 . We propose that complete isothermal collapse and molecular hydrogen suppression may not always be necessary to form supermassive stars, precursors of black hole seeds. Sufficiently high inflow rates can be obtained for UV flux J 21  = 500–1000, at least for some cases. This value brings the estimate of the abundance of direct collapse black hole seeds closer to that high-redshift quasars.
    Print ISSN: 0035-8711
    Electronic ISSN: 1365-2966
    Topics: Physics
    Published by Oxford University Press
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  • 6
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    High-resolution studies of massive primordial haloes (2013)
    Oxford University Press
    Details
    Publication Date: 2013-02-28
    Description: Atomic cooling haloes with virial temperatures T vir ≥ 10 4  K are the most plausible sites for the formation of the first galaxies and the first intermediate-mass black holes. It is therefore important to assess whether one can obtain robust results concerning their main properties from numerical simulations. A major uncertainty is the presence of turbulence, which is barely resolved in cosmological simulations. We explore the latter both by pursuing high-resolution simulations with up to 64 cells per Jeans length and by incorporating a subgrid-scale turbulence model to account for turbulent pressure and viscosity on unresolved scales. We find that the main physical quantities in the halo, in particular the density, temperature and energy density profile, are approximately converged. However, the morphologies in the central 500 au change significantly with increasing resolution and appear considerably more turbulent. In a systematic comparison of three different haloes, we further found that the turbulence subgrid-scale model gives rise to more compact central structures and decreases the amount of vorticity. Such compact morphologies may in particular favour the accretion on to the central object.
    Print ISSN: 0035-8711
    Electronic ISSN: 1365-2966
    Topics: Physics
    Published by Oxford University Press
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  • 7
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    How realistic UV spectra and X-rays suppress the abundance of direct collapse black holes (2014)
    Oxford University Press
    Details
    Publication Date: 2014-12-07
    Description: Observations of high-redshift quasars at z  〉 6 indicate that they harbour supermassive black holes (SMBHs) of a billion solar masses. The direct collapse scenario has emerged as the most plausible way to assemble SMBHs. The nurseries for the direct collapse black holes are massive primordial haloes illuminated with an intense UV flux emitted by Population II (Pop II) stars. In this study, we compute the critical value of such a flux ( $J_{21}^{\rm crit}$ ) for realistic spectra of Pop II stars through three-dimensional cosmological simulations. We derive the dependence of $J_{21}^{\rm crit}$ on the radiation spectra, on variations from halo to halo, and on the impact of X-ray ionization. Our findings show that the value of $J_{21}^{\rm crit}$ is a few times 10 4 and only weakly depends on the adopted radiation spectra in the range between T rad  = 2 x 10 4 and10 5  K. For three simulated haloes of a few times 10 7 M , $J_{21}^{\rm crit}$ varies from 2 x 10 4 to 5 x 10 4 . The impact of X-ray ionization is almost negligible and within the expected scatter of $J_{21}^{\rm crit}$ for background fluxes of J X, 21 ≤ 0.1. The computed estimates of $J_{21}^{\rm crit}$ have profound implications for the quasar abundance at z  = 10 as it lowers the number density of black holes forming through an isothermal direct collapse by a few orders of magnitude below the observed black hole density. However, the sites with moderate amounts of H 2 cooling may still form massive objects sufficient to be compatible with observations.
    Print ISSN: 0035-8711
    Electronic ISSN: 1365-2966
    Topics: Physics
    Published by Oxford University Press
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  • 8
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    Magnetic fields during the formation of supermassive black holes (2014)
    Oxford University Press
    Details
    Publication Date: 2014-04-15
    Description: Observations of quasars at z 〉 6 report the existence of a billion solar mass black holes. Comprehending their formation in such a short time-scale is a matter of ongoing research. One of the most promising scenarios to assemble supermassive black holes is a monolithic collapse of protogalactic gas clouds in atomic cooling haloes with T vir ≥ 10 4 K. In this paper, we study the amplification and impact of magnetic fields during the formation of seed black holes in massive primordial haloes. We perform high-resolution cosmological magnetohydrodynamic simulations for four distinct haloes and follow their collapse for a few free-fall times until the simulations reach a peak density of 7 x 10 –10 g cm –3 . Our findings show that irrespective of the initial seed field, the magnetic field strength reaches a saturated state in the presence of strong accretion shocks. Under such conditions, the growth time becomes very short and amplification occurs rapidly within a small fraction of the free-fall time. We find that the presence of such strong magnetic fields provides additional support against gravity and helps in suppressing fragmentation. Massive clumps of a few hundred solar masses are formed at the end of our simulations and high accretion rates of 1 M yr –1 are observed. We expect that in the presence of such accretion rates, the clumps will grow to form supermassive stars of ~10 5 M . Overall, the role of the magnetic fields seems supportive for the formation of massive black holes.
    Print ISSN: 0035-8711
    Electronic ISSN: 1365-2966
    Topics: Physics
    Published by Oxford University Press
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  • 9
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    Impact of baryonic streaming velocities on the formation of supermassive black holes via direct collapse (2014)
    Oxford University Press
    Details
    Publication Date: 2014-04-19
    Description: Baryonic streaming motions produced prior to the epoch of recombination became supersonic during the cosmic dark ages. Various studies suggest that such streaming velocities change the halo statistics and also influence the formation of Population III stars. In this study, we aim to explore the impact of streaming velocities on the formation of supermassive black holes at z 〉10 via the direct collapse scenario. To accomplish this goal, we perform cosmological large eddy simulations for two haloes of a few times 10 7 M with initial streaming velocities of 3, 6 and 9 km s –1 . These massive primordial haloes illuminated by the strong Lyman–Werner flux are the potential cradles for the formation of direct collapse seed black holes. To study the evolution for longer times, we employ sink particles and track the accretion for 10 000 years. Our findings show that higher streaming velocities increase the circular velocities from about 14 to 16 km s –1 . They also delay the collapse of haloes for a few million years, but do not have any significant impact on the halo properties such as turbulent energy, radial velocity, density and accretion rates. Sink particles of about ~10 5 M are formed at the end of our simulations and no clear distribution of sink masses is observed in the presence of streaming motions. It is further found that the impact of streaming velocities is less severe in massive haloes compared to the minihaloes as reported in the previous studies.
    Print ISSN: 0035-8711
    Electronic ISSN: 1365-2966
    Topics: Physics
    Published by Oxford University Press
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  • 10
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    The small-scale dynamo and the amplification of magnetic fields in massive primordial haloes (2013)
    Oxford University Press
    Details
    Publication Date: 2013-05-21
    Description: While the present standard model of cosmology yields no clear prediction for the initial magnetic field strength, efficient dynamo action may compensate for initially weak seed fields via rapid amplification. In particular, the small-scale dynamo is expected to exponentially amplify any weak magnetic field in the presence of turbulence. We explore whether this scenario is viable using cosmological magneto-hydrodynamics simulations modelling the formation of the first galaxies, which are expected to form in so-called atomic cooling haloes with virial temperatures T vir  ≥ 10 4  K. As previous calculations have shown that a high Jeans resolution is needed to resolve turbulent structures and dynamo effects, our calculations employ resolutions of up to 128 cells per Jeans length. The presence of the dynamo can be clearly confirmed for resolutions of at least 64 cells per Jeans length, while saturation occurs at approximate equipartition with turbulent energy. As a result of the large Reynolds numbers in primordial galaxies, we expect saturation to occur at early stages, implying magnetic field strengths of ~0.1 μG at densities of 10 4  cm –3 .
    Print ISSN: 0035-8711
    Electronic ISSN: 1365-2966
    Topics: Physics
    Published by Oxford University Press
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