Cosmological perturbation theory and the spherical collapse model — III. The velocity divergence field and the Ω dependence

Cosmological perturbation theory (PT) is a useful tool to study the cumulants of the density and velocity fields in the large-scale structure of the Universe. In Papers I and II of this series we saw that the spherical collapse (SC) model provides the exact solution to PT at tree-level and gives a good approximation to the loop corrections (next-to-leading orders), indicating negligible tidal effects. Here, we derive predictions for the (smoothed) cumulants of the velocity divergence field θ ≡ ▽ ⊙  v for an irrotational fluid in the SC model. By comparing these with the exact analytic results of Scoccimarro &38; Frieman, it is shown that, at least for the unsmoothed case, the loop corrections to the cumulants of θ are dominated by tidal effects. However, most of the tidal contribution seems to cancel out when computing the hierarchical ratios, T _J  = 〈θ ^J 〉 / 〈θ²〉  ^{J −1}. We also extend the work presented in Papers I and II to give predictions for the cumulants of the density and velocity divergence fields in non-flat spaces. In particular, we show the equivalence between the spherically symmetric solution to the equations of motion in the SC model (given in terms of the density) and that of the Lagrangian PT approach (given in terms of the displacement field). It is shown that the Ω dependence is very weak for both cosmic fields even at one loop (a 10 per cent effect at most), except for the overall factor f (Ω) that couples to the velocity divergence.     

An excursion set model for the distribution of dark matter and dark matter haloes

A model of the gravitationally evolved dark matter distribution, in the Eulerian space, is developed. It is a simple extension of the excursion set model that is commonly used to estimate the mass function of collapsed dark matter haloes. In addition to describing the evolution of the Eulerian space distribution of the haloes, the model allows one to describe the evolution of the dark matter itself. It can also be used to describe density profiles, on scales larger than the virial radius of these haloes, and to quantify the way in which matter flows in and out of Eulerian cells. When the initial Lagrangian space distribution is white noise Gaussian, the model suggests that the Inverse Gaussian distribution should provide a reasonably good approximation to the evolved Eulerian density field, in agreement with numerical simulations. Application of this model to clustering from more general Gaussian initial conditions is discussed at the end.     

Automated classification of stellar spectra — II. Two-dimensional classification with neural networks and principal components analysis

We investigate the application of neural networks to the automation of MK spectral classification. The data set for this project consists of a set of over 5000 optical (3800–5200 Å) spectra obtained from objective prism plates from the Michigan Spectral Survey. These spectra, along with their two-dimensional MK classifications listed in the Michigan Henry Draper Catalogue, were used to develop supervised neural network classifiers. We show that neural networks can give accurate spectral type classifications (σ₆₈= 0.82 subtypes, σ_rms= 1.09 subtypes) across the full range of spectral types present in the data set (B2–M7). We show also that the networks yield correct luminosity classes for over 95 per cent of both dwarfs and giants with a high degree of confidence.   Stellar spectra generally contain a large amount of redundant information. We investigate the application of principal components analysis (PCA) to the optimal compression of spectra. We show that PCA can compress the spectra by a factor of over 30 while retaining essentially all of the useful information in the data set. Furthermore, it is shown that this compression optimally removes noise and can be used to identify unusual spectra.   This paper is a continuation of the work carried out by von Hippel et al. (Paper I).     

岩体结构面水力学模型及应用

本文提出岩体结构面适应性平行板模型和该模型的参数确定方法——三段压水试验新解释,新的模型有益于克服将结构面圆盘模型应用于地下水模拟中的局限性;基于结构面起伏度对地下水流动的影响,导出了起伏度修正系数解析表达式。     

Thermoelastic stress due to a rectangular heat source in a semi-infinite medium. Presentation of an analytical solution

The thermoelastic response due to a time-dependent rectangular heat source in a semi-infinite medium is analyzed. The problem originates from studies of nuclear waste repositories in rock. Canisters containing heat-emitting nuclear waste are deposited over a large rectangular area deep below the ground surface. The solution for a time-dependent heat source is obtained from the corresponding instantaneous heat source by superposition. The thermoelastic problem for the instantaneous rectangular heat source in a infinite surrounding is solved exactly. An important step is the introduction of so-called quadrantal heat sources. The solution for the rectangle is obtained from four quadrantal solutions. The solution for the quadrantal heat source depends on the three dimelasionless coordinates only. Time occurs in the scale factors only. The condition of zero normal and shear stresses at the ground surface is fulfilled by using a mirror heat source and a boundary solution. The boundary solution accounts for the residual normal stress at the ground surface. Using a Hertzian potential, a surprisingly simple solution is obtained. The final analytical solution is quite tractable considering the complexity of the initial problem. The solution may be used to test numerical models for coupled thermoelastic processes. It may also be used in more detailed numerical simulations of the process near the heat sources as boundary conditions to account for the three-dimensional global process.     

航磁ΔT解析信号确定线性构造隐伏形态的算法及阿尔金的应用

本文研究了模拟线性地质构造具有普遍意义的有限延深薄板状体ΔＴ的解析信号强度与其几何参数之间的超定方程关系,运用奇异值分解和广义逆技术求解超定方程,获得了高精度的理论反演方法,同时给出了定性解释板状体产状的辅助方法。对阿尔金地区隐伏断裂形态的反演结果,为西藏地体的“北推东移”提供了定量化的地球物理解释证据。文章还勾画了阿尔金与塔里木的深部界线。     

Evolution of peaks in weakly non-linear density field and dark halo profiles

Using the two-point Edgeworth series up to second order in the linear rms density fluctuation we construct the weakly non-linear conditional probability distribution function for the density field around an overdense region. This requires calculating the two-point analogues of the skewness parameter S ₃. We test the dependence of the two-point skewness on distance from the peak for scale-free power spectra and Gaussian smoothing. The statistical features of such a conditional distribution are given as the values obtained within linear theory corrected by the terms that arise as a result of weakly non-linear evolution. The expected density around the peak is found to be always below the linear prediction while its dispersion is always larger than in the linear case. For large enough overdensities the weakly non-linear corrections can be more significant than the peak constraint introduced by Bardeen et al. We apply these results to the spherical model of collapse as developed by Hoffman & Shaham and find that in general the effect of weakly non-linear interactions is to decrease the scale from which a peak gathers mass and therefore also the mass itself. In the case of an open universe this results in steepening of the final profile of the virialized proto-object.     

'Stokes imaging' of the accretion region in magnetic cataclysmic variables — I. Conception and realization

Modelling the polarized cyclotron emission from magnetic cataclysmic variables has been a pivotal technique for determining the structure of the accretion zones on the white dwarf. To date, model solutions have been obtained from trial fits to the intensity and polarization data, which have been constructed from emission regions (for example arcs and spots) put in by hand. These models were all inferred indirectly from arguments based on the polarization and X-ray light curves.   We present a more analytical and objective technique using optimization by a genetic algorithm, Tikhonov regularization and Powell's method that robustly models the details of polarized emission.   To demonstrate the success of this technique, we show the results of several simulations in which we calculated the intensity and polarization curves from arbitrarily shaped emission regions on the surface of a sphere and then applied our code to these curves to recover the original test data. We also show how adding artificial noise affects the outcome of the optimization technique.     

A coupled model for prediction of settlement and gas flow in MSW landfills

Prediction of long‐term settlement and control of gas pollution to the environment are two principle concerns during the management of municipal solid waste (MSW) landfills. The behavior of settlement and gas flow in MSW landfills is complicated due to the combined effect of mechanical deformation of the solid skeleton and continuous biodegradation of the waste. A one‐dimensional settlement and gas flow model is presented in this paper, which is capable of predicting time evolution of settlement as well as temporal and spatial distribution of gas pressure within multi‐layered landfills under a variety of operating scenarios. The analytical solution to the novel model is evaluated with numerical simulation and field measurements. The resulting efficiency and accuracy highlight the capability of the proposed model to reproduce the settlement behavior and gas flow in MSW landfills. The influences of operating conditions and waste properties on settlement and gas pressure are examined for typical MSW landfills. Copyright © 2009 John Wiley & Sons, Ltd.