Nonlinear Cosmological Power Spectra in Real and Redshift--Space

We present an expression for the nonlinear evolution of the cosmological power spectrum based on following Lagrangian trajectories. This is simplified using the Zel'dovich approximation to trace particle displacements, assuming Gaussian initial conditions. The model is found to exhibit the transfer of power from large to small scales expected in self- gravitating fields. We have extended this analysis into redshift-space and found a solution for the nonlinear, anisotropic redshift-space power spectrum in the limit of plane--parallel redshift distortions. The quadrupole-to- monopole ratio is calculated for the case of power-law initial spectra. We find that the shape of this ratio depends on the shape of the initial spectrum, but when scaled to linear theory depends only weakly on the redshift-space distortion parameter, $\beta$. The point of zero-crossing of the quadrupole, $k_0$, is found to obey a scaling relation. This model is found to be in agreement with $N$-body simulations on scales down to the zero-crossing of the quadrupole, although the wavenumber at zero-crossing is underestimated. These results are applied to the quadrupole--monopole ratio found in the merged QDOT+1.2 Jy IRAS redshift survey. We have estimated that the distortion parameter is constrained to be $\beta>0.5$ at the $95 \%$ level. The local primordial spectral slope is not well constrained, but analysis suggests $n \approx -2$ in the translinear regime. The zero-crossing scale of the quadrupole is $k_0=0.5 \pm 0.1 h/Mpc$ and from this we infer the amplitude of clustering is $\sigma_8=0.7 \pm 0.05$. We suggest that the success of this model is due to nonlinear redshift--space effects arising from infall onto caustics and is not dominated by virialised cluster cores.Comment: 13 pages, uufiles, Latex with 6 postscript figures, submitted to MNRA

Wide Angle Redshift Distortions Revisited

We explore linear redshift distortions in wide angle surveys from the point of view of symmetries. We show that the redshift space two-point correlation function can be expanded into tripolar spherical harmonics of zero total angular momentum $S_{l_1 l_2 l_3}(\hat x_1, \hat x_2, \hat x)$. The coefficients of the expansion $B_{l_1 l_2 l_3}$ are analogous to the $C_l$'s of the angular power spectrum, and express the anisotropy of the redshift space correlation function. Moreover, only a handful of $B_{l_1 l_2 l_3}$ are non-zero: the resulting formulae reveal a hidden simplicity comparable to distant observer limit. The $B_{l_1 l_2 l_3}$ depend on spherical Bessel moments of the power spectrum and $f = \Omega^{0.6}/b$. In the plane parallel limit, the results of \cite{Kaiser1987} and \cite{Hamilton1993} are recovered. The general formalism is used to derive useful new expressions. We present a particularly simple trigonometric polynomial expansion, which is arguably the most compact expression of wide angle redshift distortions. These formulae are suitable to inversion due to the orthogonality of the basis functions. An alternative Legendre polynomial expansion was obtained as well. This can be shown to be equivalent to the results of \cite{SzalayEtal1998}. The simplicity of the underlying theory will admit similar calculations for higher order statistics as well.Comment: 6 pages, 1 figure, ApJL submitte

Drivers of Microbial Risk for Direct Potable Reuse and de Facto Reuse Treatment Schemes: The Impacts of Source Water Quality and Blending.

Although reclaimed water for potable applications has many potential benefits, it poses concerns for chemical and microbial risks to consumers. We present a quantitative microbial risk assessment (QMRA) Monte Carlo framework to compare a de facto water reuse scenario (treated wastewater-impacted surface water) with four hypothetical Direct Potable Reuse (DPR) scenarios for Norovirus, Cryptosporidium, and Salmonella. Consumer microbial risks of surface source water quality (impacted by 0-100% treated wastewater effluent) were assessed. Additionally, we assessed risks for different blending ratios (0-100% surface water blended into advanced-treated DPR water) when source surface water consisted of 50% wastewater effluent. De facto reuse risks exceeded the yearly 10-4 infections risk benchmark while all modeled DPR risks were significantly lower. Contamination with 1% or more wastewater effluent in the source water, and blending 1% or more wastewater-impacted surface water into the advanced-treated DPR water drove the risk closer to the 10-4 benchmark. We demonstrate that de facto reuse by itself, or as an input into DPR, drives microbial risks more so than the advanced-treated DPR water. When applied using location-specific inputs, this framework can contribute to project design and public awareness campaigns to build legitimacy for DPR

Determination of the Baryon Density from Large Scale Galaxy Redshift Surveys

We estimate the degree to which the baryon density, $\Omega_{b}$, can be determined from the galaxy power spectrum measured from large scale galaxy redshift surveys, and in particular, the Sloan Digital Sky Survey. A high baryon density will cause wiggles to appear in the power spectrum, which should be observable at the current epoch. We assume linear theory on scales $\geq 20h^{-1}Mpc$ and do not include the effects of redshift distortions, evolution, or biasing. With an optimum estimate of $P(k)$ to $k\sim 2\pi/(20 h^{-1} Mpc)$, the $1 \sigma$ uncertainties in $\Omega_{b}$ are roughly 0.07 and 0.016 in flat and open ($\Omega_{0}=0.3$) cosmological models, respectively. This result suggests that it should be possible to test for consistency with big bang nucleosynthesis estimates of $\Omega_{b}$ if we live in an open universe.Comment: 23 Pages, 10 Postscript figure

The quasi-molecular stage of ternary fission

We developed a three-center phenomenological model,able to explain qualitatively the recently obtained experimental results concerning the quasimolecular stage of a light-particle accompanied fission process. It was derived from the liquid drop model under the assumption that the aligned configuration, with the emitted particle between the light and heavy fragment, is reached by increasing continuously the separation distance, while the radii of the heavy fragment and of the light particle are kept constant. In such a way,a new minimum of a short-lived molecular state appears in the deformation energy at a separation distance very close to the touching point. This minimum allows the existence of a short-lived quasi-molecular state, decaying into the three final fragments.The influence of the shell effects is discussed. The half-lives of some quasimolecular states which could be formed in the $^{10}$Be and $^{12}$C accompanied fission of $^{252}$Cf are roughly estimated to be the order of 1 ns, and 1 ms, respectively

The Many Hats of Sonic Hedgehog Signaling in Nervous System Development and Disease.

Sonic hedgehog (Shh) signaling occurs concurrently with the many processes that constitute nervous system development. Although Shh is mostly known for its proliferative and morphogenic action through its effects on neural stem cells and progenitors, it also contributes to neuronal differentiation, axonal pathfinding and synapse formation and function. To participate in these diverse events, Shh signaling manifests differently depending on the maturational state of the responsive cell, on the other signaling pathways regulating neural cell function and the environmental cues that surround target cells. Shh signaling is particularly dynamic in the nervous system, ranging from canonical transcription-dependent, to non-canonical and localized to axonal growth cones. Here, we review the variety of Shh functions in the developing nervous system and their consequences for neurodevelopmental diseases and neural regeneration, with particular emphasis on the signaling mechanisms underlying Shh action

Going beyond the Kaiser redshift-space distortion formula: a full general relativistic account of the effects and their detectability in galaxy clustering

Kaiser redshift-space distortion formula describes well the clustering of galaxies in redshift surveys on small scales, but there are numerous additional terms that arise on large scales. Some of these terms can be described using Newtonian dynamics and have been discussed in the literature, while the others require proper general relativistic description that was only recently developed. Accounting for these terms in galaxy clustering is the first step toward tests of general relativity on horizon scales. The effects can be classified as two terms that represent the velocity and the gravitational potential contributions. Their amplitude is determined by effects such as the volume and luminosity distance fluctuation effects and the time evolution of galaxy number density and Hubble parameter. We compare the Newtonian approximation often used in the redshift-space distortion literature to the fully general relativistic equation, and show that Newtonian approximation accounts for most of the terms contributing to velocity effect. We perform a Fisher matrix analysis of detectability of these terms and show that in a single tracer survey they are completely undetectable. To detect these terms one must resort to the recently developed methods to reduce sampling variance and shot noise. We show that in an all-sky galaxy redshift survey at low redshift the velocity term can be measured at a few sigma if one can utilize halos of mass M>10^12 Msun (this can increase to 10-sigma or more in some more optimistic scenarios), while the gravitational potential term itself can only be marginally detected. We also demonstrate that the general relativistic effect is not degenerate with the primordial non-Gaussian signature in galaxy bias, and the ability to detect primordial non-Gaussianity is little compromised.Comment: 13 pages, 5 figures, published in PR

Nonlinear surface waves on the plasma-vacuum interface

In this paper we study the propagation of weakly nonlinear surface waves on a plasma-vacuum interface. In the plasma region we consider the equations of incompressible magnetohydrodynamics, while in vacuum the magnetic and electric fields are governed by the Maxwell equations. A surface wave propagate along the plasma-vacuum interface, when it is linearly weakly stable. Following the approach of Ali and Hunter, we measure the amplitude of the surface wave by the normalized displacement of the interface in a reference frame moving with the linearized phase velocity of the wave, and obtain that it satisfies an asymptotic nonlocal, Hamiltonian evolution equation. We show the local-in-time existence of smooth solutions to the Cauchy problem for the amplitude equation in noncanonical variables, and we derive a blow up criterion.Comment: arXiv admin note: text overlap with arXiv:1305.5327 by other author

The 2nd order renormalization group flow for non-linear sigma models in 2 dimensions

We show that for two dimensional manifolds M with negative Euler characteristic there exists subsets of the space of smooth Riemannian metrics which are invariant and either parabolic or backwards-parabolic for the 2nd order RG flow. We also show that solutions exists globally on these sets. Finally, we establish the existence of an eternal solution that has both a UV and IR limit, and passes through regions where the flow is parabolic and backwards-parabolic

Community experiences of organised crime in Scotland

The research explored community experiences of serious organised crime in Scotland (SOC). The report provides information on the nature and extent of the impact of SOC on everyday life in the community, as well as offering suggestions for policy development. The study sought to answer the following questions: 1)What are the relationships that exist between SOC and communities in Scotland? 2)What are the experiences and perceptions of residents, stakeholders and organisations of the scope and nature of SOC within their local area? and 3)How does SOC impact on community wellbeing, and to what extent can the harms associated with SOC be mitigated