Abstract:
Following a solution generating technique introduced recently by one of us, we transform the Einstein static Universe into a two - fold infinity class of physically acceptable exact perfect fluid solutions of Einstein's equations. Whereas the entire class of solutions can be considered as generalizations of the familiar Tolman IV solution, no member of the class can be written explicitly in isotropic coordinates. Further, except for a set of measure zero, no member of the class can be written explicitly in curvature coordinates either.

Abstract:
We describe a new algorithm for finding substructures within dark matter haloes from N-body simulations. The algorithm relies upon the fact that dynamically distinct substructures in a halo will have a {\em local} velocity distribution that differs significantly from the mean, i.e. smooth background halo. We characterize the large-scale mean field using a coarsely grained cell-based approach, while a kernel smoothing process is used to determined the local velocity distribution. Comparing the ratio of these two estimates allows us to identify particles which are strongly cluster in velocity space relative to the background and thus resident in substructure. From this population of outliers, groups are identified using a Friends-of-Friends-like approach. False positives are rejected using Poisson noise arguments. This approach does not require a search of the full phase-space structure of a halo, a non-trivial task, and is thus computationally advantageous. We apply our algorithm to several test cases and show that it identifies not only subhaloes, bound overdensities in phase-space, but can recover tidal streams with a high purity. Our method can even find streams which do not appear significantly overdense in either physical or phase-space.

Abstract:
The first objects to arise in a cold dark matter universe present a daunting challenge for models of structure formation. In the ultra small-scale limit, CDM structures form nearly simultaneously across a wide range of scales. Hierarchical clustering no longer provides a guiding principle for theoretical analyses and the computation time required to carry out credible simulations becomes prohibitively high. To gain insight into this problem, we perform high-resolution (N=720^3 - 1584^3) simulations of an Einstein-de Sitter cosmology where the initial power spectrum is P(k) propto k^n, with -2.5 < n < -1. Self-similar scaling is established for n=-1 and n=-2 more convincingly than in previous, lower-resolution simulations and for the first time, self-similar scaling is established for an n=-2.25 simulation. However, finite box-size effects induce departures from self-similar scaling in our n=-2.5 simulation. We compare our results with the predictions for the power spectrum from (one-loop) perturbation theory and demonstrate that the renormalization group approach suggested by McDonald improves perturbation theory's ability to predict the power spectrum in the quasilinear regime. In the nonlinear regime, our power spectra differ significantly from the widely used fitting formulae of Peacock & Dodds and Smith et al. and a new fitting formula is presented. Implications of our results for the stable clustering hypothesis vs. halo model debate are discussed. Our power spectra are inconsistent with predictions of the stable clustering hypothesis in the high-k limit and lend credence to the halo model. Nevertheless, the fitting formula advocated in this paper is purely empirical and not derived from a specific formulation of the halo model.

Abstract:
We study clusters in Warm Dark Matter (WDM) models of a thermally produced dark matter particle $0.5$ keV in mass. We show that, despite clusters in WDM cosmologies having similar density profiles as their Cold Dark Matter (CDM) counterparts, the internal properties, such as the amount of substructure, shows marked differences. This result is surprising as clusters are at mass scales that are {\em a thousand times greater} than that at which structure formation is suppressed. WDM clusters gain significantly more mass via smooth accretion and contain fewer substructures than their CDM brethren. The higher smooth mass accretion results in subhaloes which are physically more extended and less dense. These fine-scale differences can be probed by strong gravitational lensing. We find, unexpectedly, that WDM clusters have {\em higher} lensing efficiencies than those in CDM cosmologies, contrary to the naive expectation that WDM clusters should be less efficient due to the fewer substructures they contain. Despite being less dense, the larger WDM subhaloes are more likely to have larger lensing cross-sections than CDM ones. Additionally, WDM subhaloes typically reside at larger distances, which radially stretches the critical lines associated with strong gravitational lensing, resulting in excess in the number of clusters with large radial cross-sections at the $\sim2\sigma$ level. Though lensing profile for an individual cluster vary significantly with the line-of-sight, the radial arc distribution based on a sample of $\gtrsim100$ clusters may prove to be the crucial test for the presence of WDM.

Abstract:
The nature of the dark sector of the Universe remains one of the outstanding problems in modern cosmology, with the search for new observational probes guiding the development of the next generation of observational facilities. Clues come from tension between the predictions from {\Lambda}CDM and observations of gravitationally lensed galaxies. Previous studies showed that galaxy clusters in the {\Lambda}CDM are not strong enough to reproduce the observed number of lensed arcs. This work aims to constrain the warm dark matter cosmologies by means of the lensing efficiency of galaxy clusters drawn from these alternative models. The lensing characteristics of two samples of simulated clusters in the warm dark matter ({\Lambda}WDM) and cold dark matter ({\Lambda}CDM) cosmologies have been studied. The results show that even though the CDM clusters are more centrally concentrated and contain more substructures, the WDM clusters have slightly higher lensing efficiency than their CDM counterparts. The key difference is that WDM clusters have more extended and more massive subhaloes than CDM analogues. These massive substructures significantly stretch the critical lines and caustics and hence they boost the lensing efficiency of the host halo. Despite the increase in the lensing efficiency due to the contribution of massive substructures in the WDM clusters, this is not enough to resolve the arc statistics problem.

Abstract:
While various codes exist to systematically and robustly find haloes and subhaloes in cosmological simulations (Knebe et al., 2011, Onions et al., 2012), this is the first work to introduce and rigorously test codes that find tidal debris (streams and other unbound substructure) in fully cosmological simulations of structure formation. We use one tracking and three non-tracking codes to identify substructure (bound and unbound) in a Milky Way type simulation from the Aquarius suite (Springel et al., 2008) and post-process their output with a common pipeline to determine the properties of these substructures in a uniform way. By using output from a fully cosmological simulation, we also take a step beyond previous studies of tidal debris that have used simple toy models. We find that both tracking and non-tracking codes agree well on the identification of subhaloes and more importantly, the {\em unbound tidal features} associated with them. The distributions of basic properties of the total substructure distribution (mass, velocity dispersion, position) are recovered with a scatter of $\sim20%$. Using the tracking code as our reference, we show that the non-tracking codes identify complex tidal debris with purities of $\sim40%$. Analysing the results of the substructure finders, we find that the general distribution of {\em substructures} differ significantly from the distribution of bound {\em subhaloes}. Most importantly, both bound and unbound {\em substructures} together constitute $\sim18%$ of the host halo mass, which is a factor of $\sim2$ higher than the fraction in self-bound {\em subhaloes}. However, this result is restricted by the remaining challenge to cleanly define when an unbound structure has become part of the host halo. Nevertheless, the more general substructure distribution provides a more complete picture of a halo's accretion history.

Abstract:
We investigate the formation, growth, merger history, movement, and destruction of cosmic voids detected via the watershed transform code VIDE in a cosmological N-body dark matter {\Lambda}CDM simulation. By adapting a method used to construct halo merger trees, we are able to trace individual voids back to their initial appearance and record the merging and evolution of their progenitors at high redshift. For the scales of void sizes captured in our simulation, we find that the void formation rate peaks at scale factor 0.3, which coincides with a growth in the void hierarchy and the emergence of dark energy. Voids of all sizes appear at all scale factors, though the median initial void size decreases with time. When voids become detectable they have nearly their present-day volumes. Almost all voids have relatively stable growth rates and suffer only infrequent minor mergers. Dissolution of a void via merging is very rare. Instead, most voids maintain their distinct identity as annexed subvoids of a larger parent. The smallest voids are collapsing at the present epoch, but void destruction ceases after scale factor 0.3. In addition, voids centers tend to move very little, less than 0.01 of their effective radii per ln a, over their lifetimes. Overall, most voids exhibit little radical dynamical evolution; their quiet lives make them pristine probes of cosmological initial conditions and the imprint of dark energy.

Abstract:
In a recent contribution, Bahl \& Baumgardt investigated the incidence of planar alignments of satellite galaxies in the Millennium-II simulation, and concluded that vast thin planes of dwarf galaxies, similar to that observed in the Andromeda galaxy (M31), occur frequently by chance in $\Lambda$-Cold Dark Matter cosmology. However, their analysis did not capture the essential fact that the observed alignment is simultaneously radially extended, yet thin, and kinematically unusual. With the caveat that the Millennium-II simulation may not have sufficient mass resolution to identify confidently simulacra of low-luminosity dwarf galaxies, we re-examine that simulation for planar structures, using the same method as employed by Ibata et al. (2013) on the real M31 satellites. We find that 0.04\% of host galaxies display satellite alignments that are at least as extreme as the observations, when we consider their extent, thickness and number of members rotating in the same sense. We further investigate the angular momentum properties of the co-planar satellites, and find that the median of the specific angular momentum derived from the line of sight velocities in the real M31 structure ($1.3\times10^4$ km/s kpc) is very high compared to systems drawn from the simulations. This analysis confirms that it is highly unlikely that the observed structure around the Andromeda galaxy is due to a chance occurrence. Interestingly, the few extreme systems that are similar to M31 arise from the accretion of a massive sub-halo with its own spatially-concentrated entourage of orphan satellites.

Abstract:
The anatomical and clinical importance of the duodeno pancreatic region has always attracted the attention of anatomists and clinicians, and has given rise, in various countries, to numerous publications. However, to our knowledge, no research work has ever been published on the subject, as applied to the Iranian people. That is why we have been prompted to undertake some research work on the anatomical features peculiar to Iranians."nOur task has been to make some research work on the terminal choledoque of 46 fixed man corpses, in the anatomical laboratory of the University of Tehran. By comparing the ~onclusions we have arrived at,to that of other countries, we have met with some noticeable facts:"n1) The distance between the major duodenal papilla and the pylorus is generally inferior to that which has been obtained in other countries, a fact which could possibly account for the frequency of duodenal ulcers among Iranians."n2) The major duodenal papilla was wanting in none of our subjects, and in the majority of cases, it opened into the posterior wall of the duodenum."n3) In the majority of our subjects, the retroduodenal course of the choledoque remained at a distance of 1 to 1,5 em from the left border of the duodenum."n4) In one of our subjects, we have met with a case of short choledoque, probably acquired, since the wall of the first duodenum looked fibrous and had become thick.

Abstract:
The obturator hernia is extremely uncommon. In 252 years only 521 cases or so, have been reported. It is to be"nfound mostly on aged women (9 women out of ten persons, the average age being 67), rather thin, and in poor health condition, owing to a belated diagnostic. The rate of death is high, and the only possible treatment is surgery, either abdominal J or, in certain cases, inguinal. The case we are dealing with, is an obturator hernia of the bladder, found on the fixed corpse of a man, aged about fifty. There are two currently recognized etio-pathogenic theories. One is based on a hypertrophy of the sub-peritoneal fat, the other one particular anatomical disposition of the region, specially in women; however, both these theories fail to account for all the cases because they do not reckon with the vascular influence. We are suggesting a third theory, which proposes a vascular explanation. The particular disposition of the obturating artery may, by itself and in the long run, bring about an obturator hernia. This seems to be the case with our subj ect .