Local Lagrangian Approximations for the Evolution of the Density Distribution Function in Large-Scale Structure

We examine local Lagrangian approximations for the gravitational evolution of the density distribution function. In these approximations, the final density at a Lagrangian point q at a time t is taken to be a function only of t and of the initial density at the same Lagrangian point. A general expression is given for the evolved density distribution function for such approximations, and we show that the vertex generating function for a local Lagrangian mapping applied to an initially Gaussian density field bears a simple relation to the mapping itself. Using this result, we design a local Lagrangian mapping which reproduces nearly exactly the hierarchical amplitudes given by perturbation theory for gravitational evolution. When extended to smoothed density fields and applied to Gaussian initial conditions, this mapping produces a final density distribution function in excellent agreement with full numerical simulations of gravitational clustering. We also examine the application of these local Lagrangian approximations to non-Gaussian initial conditions.Comment: LaTeX, 22 pages, and 11 postscript figure

The Real and Redshift Space Density Distribution Function for Large-Scale Structure in the Spherical Collapse Approximation

We use the spherical collapse (SC) approximation to derive expressions for the smoothed redshift-space probability distribution function (PDF), as well as the $p$-order hierarchical amplitudes $S_p$, in both real and redshift space. We compare our results with numerical simulations, focusing on the $\Omega=1$ standard CDM model, where redshift distortions are strongest. We find good agreement between the SC predictions and the numerical PDF in real space even for \sigma_L \simgt 1, where $\sigma_L$ is the linearly-evolved rms fluctuation on the smoothing scale. In redshift space, reasonable agreement is possible only for \sigma_L \simlt 0.4. Numerical simulations also yield a simple empirical relation between the real-space PDF and redshift-space PDF: we find that for \sigma \simlt 1, the redshift space PDF, P[\delta_z], is, to a good approximation, a simple rescaling of the real space PDF, P[\delta], i.e., P[\delta/\sigma] d[\delta/\sigma] = P[\delta_z/\sigma_z] d[\delta_z/\sigma_z], where $\sigma$ and \sigma_z are the real-space and redshift-space rms fluctuations, respectively. This result applies well beyond the validity of linear perturbation theory, and it is a good fit for both the standard CDM model and the Lambda-CDM model. It breaks down for SCDM at $\sigma \approx 1$, but provides a good fit to the \Lambda-CDM models for $\sigma$ as large as 0.8.Comment: 9 pages, latex, 12 figures added (26 total), minor changes to conclusions, to appear in MNRA

The Topology of Large Scale Structure in the 1.2 Jy IRAS Redshift Survey

We measure the topology (genus) of isodensity contour surfaces in volume limited subsets of the 1.2 Jy IRAS redshift survey, for smoothing scales \lambda=4\hmpc, 7\hmpc, and 12\hmpc. At 12\hmpc, the observed genus curve has a symmetric form similar to that predicted for a Gaussian random field. At the shorter smoothing lengths, the observed genus curve shows a modest shift in the direction of an isolated cluster or ``meatball'' topology. We use mock catalogs drawn from cosmological N-body simulations to investigate the systematic biases that affect topology measurements in samples of this size and to determine the full covariance matrix of the expected random errors. We incorporate the error correlations into our evaluations of theoretical models, obtaining both frequentist assessments of absolute goodness-of-fit and Bayesian assessments of models' relative likelihoods. We compare the observed topology of the 1.2 Jy survey to the predictions of dynamically evolved, unbiased, gravitational instability models that have Gaussian initial conditions. The model with an $n=-1$, power-law initial power spectrum achieves the best overall agreement with the data, though models with a low-density cold dark matter power spectrum and an $n=0$ power-law spectrum are also consistent. The observed topology is inconsistent with an initially Gaussian model that has $n=-2$, and it is strongly inconsistent with a Voronoi foam model, which has a non-Gaussian, bubble topology.Comment: ApJ submitted, 39 pages, LaTeX(aasms4), 12 figures, 1 Tabl

Genus statistics using the Delaunay tessellation field estimation method: (I) tests with the Millennium Simulation and the SDSS DR7

We study the topology of cosmic large-scale structure through the genus statistics, using galaxy catalogues generated from the Millennium Simulation and observational data from the latest Sloan Digital Sky Survey Data Release (SDSS DR7). We introduce a new method for constructing galaxy density fields and for measuring the genus statistics of its isodensity surfaces. It is based on a Delaunay tessellation field estimation (DTFE) technique that allows the definition of a piece-wise continuous density field and the exact computation of the topology of its polygonal isodensity contours, without introducing any free numerical parameter. Besides this new approach, we also employ the traditional approaches of smoothing the galaxy distribution with a Gaussian of fixed width, or by adaptively smoothing with a kernel that encloses a constant number of neighboring galaxies. Our results show that the Delaunay-based method extracts the largest amount of topological information. Unlike the traditional approach for genus statistics, it is able to discriminate between the different theoretical galaxy catalogues analyzed here, both in real space and in redshift space, even though they are based on the same underlying simulation model. In particular, the DTFE approach detects with high confidence a discrepancy of one of the semi-analytic models studied here compared with the SDSS data, while the other models are found to be consistent.Comment: 14 pages, 9 figures, accepted by Ap

Recovering the Primordial Density Fluctuations: A comparison of methods

We present a comparative study of six different methods for reversing the gravitational evolution of a cosmological density field to recover the primordial fluctuations: linear theory, the Gaussianization mapping scheme, two different quasi-linear dynamical schemes based on the Zel'dovich approximation, a Hybrid dynamical-Gaussianization method and the Path Interchange Zel'dovich Approximation (PIZA). The final evolved density field from an N-body simulation constitutes our test case. We use a variety of statistical measures to compare the initial density field recovered from it to the true initial density field, using each of the six different schemes. These include point-by-point comparisons of the density fields in real space, the individual modes in Fourier space, as well as global statistical properties such as the genus, the PDF of the density, and the distribution of peak heights and their shapes. We find linear theory to be the most inaccurate of all the schemes. The Gaussianization scheme is the least accurate after linear theory. The two quasi-linear dynamical schemes are more accurate than Gaussianization, although they break down quite drastically when used outside their range of validity - the quasi-linear regime. The complementary beneficial aspects of the dynamical and the Gaussianization schemes are combined in the Hybrid method. We find this Hybrid scheme to be more accurate and robust than either Gaussianization or the dynamical method alone. The PIZA scheme performs substantially better than the others in all point-by-point comparisons. However, it produces an oversmoothed initial density field, with a smaller number of peaks than expected, but recovers the PDF of the initial density with impressive accuracy on scales as small as 3Mpc/h.Comment: 39 pages, including 13 Figures, submitted to Ap

Quantifying distortions of the Lagrangian dark-matter mesh in cosmology

We examine the Lagrangian divergence of the displacement field, arguably a more natural object than the density in a Lagrangian description of cosmological large-scale structure. This quantity, which we denote \psi, quantifies the stretching and distortion of the initially homogeneous lattice of dark-matter particles in the universe. \psi\ encodes similar information as the density, but the correspondence has subtleties. It corresponds better to the log-density A than the overdensity \delta. A Gaussian distribution in \psi\ produces a distribution in A with slight skewness; in \delta, we find that in many cases the skewness is further increased by 3. A local spherical-collapse-based (SC) fit found by Bernardeau gives a formula for \psi's particle-by-particle behavior that works quite well, better than applying Lagrangian perturbation theory (LPT) at first or second (2LPT) order. In 2LPT, there is a roughly parabolic relation between initial and final \psi\ that can give overdensities in deep voids, so low-redshift, high-resolution 2LPT realizations should be used with caution. The SC fit excels at predicting \psi\ until streams cross; then, for particles forming haloes, \psi\ plummets as in a waterfall to -3. This gives a new method for producing N-particle realizations. Compared to LPT realizations, such SC realizations give reduced stream-crossing, and better visual and 1-point-PDF correspondence to the results of full gravity. LPT, on the other hand, predicts large-scale flows and the large-scale power-spectrum amplitude better, unless an empirical correction is added to the SC formula.Comment: Changes in presentation to match MNRAS-accepted version, 14 pages, 15 figure

Galaxy Clustering Topology in the Sloan Digital Sky Survey Main Galaxy Sample: a Test for Galaxy Formation Models

We measure the topology of the main galaxy distribution using the Seventh Data Release of the Sloan Digital Sky Survey, examining the dependence of galaxy clustering topology on galaxy properties. The observational results are used to test galaxy formation models. A volume-limited sample defined by $M_r<-20.19$ enables us to measure the genus curve with amplitude of $G=378$ at $6h^{-1}$Mpc smoothing scale, with 4.8\% uncertainty including all systematics and cosmic variance. The clustering topology over the smoothing length interval from 6 to $10 h^{-1}$Mpc reveals a mild scale-dependence for the shift ($\Delta\nu$) and void abundance ($A_V$) parameters of the genus curve. We find substantial bias in the topology of galaxy clustering with respect to the predicted topology of the matter distribution, which varies with luminosity, morphology, color, and the smoothing scale of the density field. The distribution of relatively brighter galaxies shows a greater prevalence of isolated clusters and more percolated voids. Even though early (late)-type galaxies show topology similar to that of red (blue) galaxies, the morphology dependence of topology is not identical to the color dependence. In particular, the void abundance parameter $A_V$ depends on morphology more strongly than on color. We test five galaxy assignment schemes applied to cosmological N-body simulations of a $\Lambda$CDM universe to generate mock galaxies: the Halo-Galaxy one-to-one Correspondence model, the Halo Occupation Distribution model, and three implementations of Semi-Analytic Models (SAMs). None of the models reproduces all aspects of the observed clustering topology; the deviations vary from one model to another but include statistically significant discrepancies in the abundance of isolated voids or isolated clusters and the amplitude and overall shift of the genus curve. (Abridged)Comment: 24 pages, 19 figures, 10 tables, submitted to ApJS. Version with full resolution images is available at http://astro.kias.re.kr/~cbp/doc/dr7Topo.pd

TEORIJSKA PITANJA O INFORMACIJSKIM SUSTAVIMA RAČUNOVODSTVA OKOLIŠA U OBRAZOVNIM PROGRAMIMA ZA HOTELIJERSTVO

In a competitive environment the application of Information Technology Systems by tourism companies can increase future prosperity and financial growth. The purpose of this paper is to measure the natural assets and to calculate the environmental benefits, as well as, the associated costs, so as to include all the above in the financial statements (balance sheet and profit & loss account). It is crucial to point out that the installation of a Green Accounting Information System requires evaluation of human assets (students and professors), availability of space, value the benefits, as well as, estimate the necessary installation costs. Literature suggests that although many information systems of environmental management have been developed, no significant progress was made on the growth of green accounting information systems due to the inherent difficulty for the monetary expression of environmental accumulated costs and related natural resources.U konkurentskom okruženju primjenom sustava informacijske tehnologije turistička poduzeća mogu jačati svoj budući prosperitet i financijski rast. Svrha je rada izmjerili prirodne vrijednosti, te izračunati ekološke koristi kao i pripadajuće troškove, a radi uključivanja istih u financijska izvješća (bilanca i račun dobiti i gubitka). Ključno je istaknuti da prilikom uvođenja informacijskih sustava računovodstva okoliša treba procijeniti ljudske potencijale (studenti i profesori) i raspoloži prostor, te utvrditi koristi sustava i odrediti troškove njegovog uvođenja. Iz literature se može zaključiti da, iako su izrađeni brojni informacijski sustavi za menadžment okoliša, nema značajnijeg napretka na širenju informacijskih sustava "zelenog" računovodstva zbog inherentne teškoće monetarnog izražavanja akumuliranih ekoloških troškova i s njima povezanih prirodnih resursa

Multi-scale initial conditions for cosmological simulations

We discuss a new algorithm to generate multi-scale initial conditions with multiple levels of refinements for cosmological "zoom-in" simulations. The method uses an adaptive convolution of Gaussian white noise with a real space transfer function kernel together with an adaptive multi-grid Poisson solver to generate displacements and velocities following first (1LPT) or second order Lagrangian perturbation theory (2LPT). The new algorithm achieves RMS relative errors of order 10^(-4) for displacements and velocities in the refinement region and thus improves in terms of errors by about two orders of magnitude over previous approaches. In addition, errors are localized at coarse-fine boundaries and do not suffer from Fourier-space induced interference ringing. An optional hybrid multi-grid and Fast Fourier Transform (FFT) based scheme is introduced which has identical Fourier space behaviour as traditional approaches. Using a suite of re-simulations of a galaxy cluster halo our real space based approach is found to reproduce correlation functions, density profiles, key halo properties and subhalo abundances with per cent level accuracy. Finally, we generalize our approach for two-component baryon and dark-matter simulations and demonstrate that the power spectrum evolution is in excellent agreement with linear perturbation theory. For initial baryon density fields, it is suggested to use the local Lagrangian approximation in order to generate a density field for mesh based codes that is consistent with Lagrangian perturbation theory instead of the current practice of using the Eulerian linearly scaled densities.Comment: 22 pages, 24 figures. MNRAS in press. Updated affiliation

Skewness of the Large-Scale Velocity Divergence from Non-Gaussian Initial Conditions

We compute the skewness $t_3$ and the corresponding hierarchical amplitude $T_3$ of the divergence of the velocity field for arbitrary non-Gaussian initial conditions. We find that $T_3$ qualitatively resembles the corresponding hierarchical amplitude for the density field, $S_3$, in that it contains a term proportional to the initial skewness, which decays inversely as the linear growth factor, plus a constant term which differs from the corresponding Gaussian term by a complex function of the initial three- and four- point functions. We extend the results for $S_3$ and $T_3$ with non-Gaussian initial conditions to evolved fields smoothed with a spherical tophat window function. We show that certain linear combinations, namely $S_3 + {1 \over 2} T_3$, $S_3 + T_3$, and $s_3 + t_3$, lead to expressions which are much simpler, for non-Gaussian initial conditions, than $S_3$ and $T_3$ (or $s_3$ and $t_3$) considered separately.Comment: 13 pages, latex, no figure