On Jacobi Sums in Q(ζp)\mathbb Q(\zeta_p)

We study the p-adic behavior of Jacobi Sums for $\mathbb Q(\zeta_p)$ and link this study to the p-Sylow subgroup of the ideal class group of $\mathbb Q(\zeta_p\`a^+

On the shape of the mass-function of dense clumps in the Hi-GAL fields. II. Using Bayesian inference to study the clump mass function

Context. Stars form in dense, dusty clumps of molecular clouds, but little is known about their origin, their evolution and their detailed physical properties. In particular, the relationship between the mass distribution of these clumps (also known as the "clump mass function", or CMF) and the stellar initial mass function (IMF), is still poorly understood. Aims. In order to better understand how the CMF evolve toward the IMF, and to discern the "true" shape of the CMF, large samples of bona-fide pre- and proto-stellar clumps are required. Two such datasets obtained from the Herschel infrared GALactic Plane Survey (Hi-GAL) have been described in paper I. Robust statistical methods are needed in order to infer the parameters describing the models used to fit the CMF, and to compare the competing models themselves. Methods. In this paper we apply Bayesian inference to the analysis of the CMF of the two regions discussed in Paper I. First, we determine the Bayesian posterior probability distribution for each of the fitted parameters. Then, we carry out a quantitative comparison of the models used to fit the CMF. Results. We have compared the results from several methods implementing Bayesian inference, and we have also analyzed the impact of the choice of priors and the influence of various constraints on the statistical conclusions for the preferred values of the parameters. We find that both parameter estimation and model comparison depend on the choice of parameter priors. Conclusions. Our results confirm our earlier conclusion that the CMFs of the two Hi-GAL regions studied here have very similar shapes but different mass scales. Furthermore, the lognormal model appears to better describe the CMF measured in the two Hi-GAL regions studied here. However, this preliminary conclusion is dependent on the choice of parameters priors.Comment: Submitted for publication to A&A on November 12, 2013. This paper contains 11 pages and 7 figure

A DFT plus U study of the structural, electronic, magnetic, and mechanical properties of cubic and orthorhombic SmCoO3

SmCoO3 is a perovskite material that has gained attention as a potential substitute for La1−xSrxMnO3−d as a solid oxide fuel cell cathode. However, a number of properties have remained unknown due to the complexity of the material. For example, we know from experimental evidence that this perovskite exists in two different crystal structures, cubic and orthorhombic, and that the cobalt ion changes its spin state at high temperatures, leading to a semiconductor-to-metal transition. However, little is known about the precise magnetic structure that causes the metallic behavior or the spin state of the Co centers at high temperature. Here, we therefore present a systematic DFT+U study of the magnetic properties of SmCoO3 in order to determine what magnetic ordering is the one exhibited by the metallic phase at different temperatures. Similarly, mechanical properties are difficult to measure experimentally, which is why there is a lack of data for the two different phases of SmCoO3. Taking advantage of our DFT calculations, we have determined the mechanical properties from our calculated elastic constants, finding that both polymorphs exhibit similar ductility and brittleness, but that the cubic structure is harder than the orthorhombic phase

Ground state numerical study of the three-dimensional random field Ising model

The random field Ising model in three dimensions with Gaussian random fields is studied at zero temperature for system sizes up to 60^3. For each realization of the normalized random fields, the strength of the random field, Delta and a uniform external, H is adjusted to find the finite-size critical point. The finite-size critical point is identified as the point in the H-Delta plane where three degenerate ground states have the largest discontinuities in the magnetization. The discontinuities in the magnetization and bond energy between these ground states are used to calculate the magnetization and specific heat critical exponents and both exponents are found to be near zero.Comment: 10 pages, 6 figures; new references and small changes to tex

The role of bacterial and algal exopolymeric substances in iron chemistry

© 2015 Elsevier B.V. It is widely accepted that the complexation of iron (Fe) with organic compounds is the primary factor that regulates Fe reactivity and its bioavailability to phytoplankton in the open ocean. Despite considerable efforts to unravel the provenance of the many organic ligands present in the 'ligand soup' and their contribution to Fe chemistry, much of this pool remains largely unresolved. Bacteria and phytoplankton are known to release exopolymeric substances (EPS) for a variety of functions and it is known that this material has metal binding properties. However, the contribution that bacterial and algal EPS makes to Fe biogeochemistry is not well documented. This study revealed that both bacterial and algal EPS contain functional components known to bind Fe (uronic acid, saccharides) and details the molecular weight distribution of the EPS. It is also demonstrated that components of the EPS have a high affinity for Fe-binding, in some cases similar to that of bacterial siderophores (~KFe'L 1012) and that this material greatly enhances Fe solubility (and, possibly, Fe oxyhydroxide reactivity via prevention of aggregation) in seawater. However, EPS may also accelerate Fe(II) oxidation and thus Fe(II) removal from the system. Our findings indicate that, in remote ocean regions, bacterial and algal EPS could play a significant role in the biogeochemical cycling of Fe and their contribution should be considered to further our understanding of the dynamics of Fe-limited oceans

Multifractals of Normalized First Passage Time in Sierpinski Gasket

The multifractal behavior of the normalized first passage time is investigated on the two dimensional Sierpinski gasket with both absorbing and reflecting barriers. The normalized first passage time for Sinai model and the logistic model to arrive at the absorbing barrier after starting from an arbitrary site, especially obtained by the calculation via the Monte Carlo simulation, is discussed numerically. The generalized dimension and the spectrum are also estimated from the distribution of the normalized first passage time, and compared with the results on the finitely square lattice.Comment: 10 pages, Latex, with 3 figures and 1 table. to be published in J. Phys. Soc. Jpn. Vol.67(1998

The Computational Complexity of Generating Random Fractals

In this paper we examine a number of models that generate random fractals. The models are studied using the tools of computational complexity theory from the perspective of parallel computation. Diffusion limited aggregation and several widely used algorithms for equilibrating the Ising model are shown to be highly sequential; it is unlikely they can be simulated efficiently in parallel. This is in contrast to Mandelbrot percolation that can be simulated in constant parallel time. Our research helps shed light on the intrinsic complexity of these models relative to each other and to different growth processes that have been recently studied using complexity theory. In addition, the results may serve as a guide to simulation physics.Comment: 28 pages, LATEX, 8 Postscript figures available from [email protected]

On the nature of the phase transition in the three-dimensional random field Ising model

A brief survey of the theoretical, numerical and experimental studies of the random field Ising model during last three decades is given. Nature of the phase transition in the three-dimensional RFIM with Gaussian random fields is discussed. Using simple scaling arguments it is shown that if the strength of the random fields is not too small (bigger than a certain threshold value) the finite temperature phase transition in this system is equivalent to the low-temperature order-disorder transition which takes place at variations of the strength of the random fields. Detailed study of the zero-temperature phase transition in terms of simple probabilistic arguments and modified mean-field approach (which take into account nearest-neighbors spin-spin correlations) is given. It is shown that if all thermally activated processes are suppressed the ferromagnetic order parameter m(h) as the function of the strength $h$ of the random fields becomes history dependent. In particular, the behavior of the magnetization curves m(h) for increasing and for decreasing $h$ reveals the hysteresis loop.Comment: 22 pages, 12 figure

Disorder, Order, and Domain Wall Roughening in the 2d Random Field Ising Model

Ground states and domain walls are investigated with exact combinatorial optimization in two-dimensional random field Ising magnets. The ground states break into domains above a length scale that depends exponentially on the random field strength squared. For weak disorder, this paramagnetic structure has remnant long-range order of the percolation type. The domain walls are super-rough in ordered systems with a roughness exponent $\zeta$ close to 6/5. The interfaces exhibit rare fluctuations and multiscaling reminiscent of some models of kinetic roughening and hydrodynamic turbulence.Comment: to be published in Phys.Rev.E/Rapid.Com