Scaling Relations for Gravitational Collapse in Two Dimensions

It is known that radial collapse around density peaks can explain the key features of evolution of correlation function in gravitational clustering in three dimensions. The same model also makes specific predictions for two dimensions. In this paper we test these predictions in two dimensions with the help of N-Body simulations. We find that there is no stable clustering in the extremely non-linear regime, but a nonlinear scaling relation does exist and can be used to relate the linear and the non-linear correlation function. In the intermediate regime, the simulations agree with the model.Comment: Revised version, To appear in Ap

Nonlinear density evolution from an improved spherical collapse model

We investigate the evolution of non-linear density perturbations by taking into account the effects of deviations from spherical symmetry of a system. Starting from the standard spherical top hat model in which these effects are ignored, we introduce a physically motivated closure condition which specifies the dependence of the additional terms on the density contrast, $\delta$. The modified equation can be used to model the behaviour of an overdense region over a sufficiently large range of $\delta$. The key new idea is a Taylor series expansion in ($1/\delta$) to model the non-linear epoch. We show that the modified equations quite generically lead to the formation of stable structures in which the gravitational collapse is halted at around the virial radius. The analysis also allows us to connect up the behaviour of individual overdense regions with the non-linear scaling relations satisfied by the two point correlation function.Comment: 11 pages, 6 figures. Final version, contains added discussion and modified figures to match the accepted versio

Spherical collapse with dark energy

I discuss the work of Maor and Lahav [1], in which the inclusion of dark energy into the spherical collapse formalism is reviewed. Adopting a phenomenological approach, I consider the consequences of - a) allowing the dark energy to cluster, and, b) including the dark energy in the virialization process. Both of these issues affect the final state of the system in a fundamental way. The results suggest a potentially differentiating signature between a true cosmological constant and a dynamic form of dark energy. This signature is unique in the sense that it does not depend on a measurement of the value of the equation of state of dark energy.Comment: To appear in the proceedings of the ``Peyresq Physics 10" Workshop, 19 - 24 June 2005, Peyresq, Franc

Aerospace components made by Polymer material

The aerospace and aviation industry have fasted growing industries on a global scale. Reliable aircraft demands many top rubber components. These rubber components must-have high performance and endurance properties, since they will be exposed to a range of extreme weather conditions, such as excessively hot or cold temperatures, and different types of oils and gases. Rubber products are becoming more famous because of their durability under extreme environmental conditions and cost-effectiveness. The rubber used for aircraft must be of high quality, and this factor is most important in the production of the necessary parts. To study the effect of all compounding ingredients while optimizing compound design and conforming to the various specification requirements and to study the effect of aging, generally, rubber is tested at three different stages viz. Unvulcanised rubber, vulcanized rubber, and finished product

On the physical origin of dark matter density profiles

The radial mass distribution of dark matter haloes is investigated within the framework of the spherical infall model. We present a new formulation of spherical collapse including non-radial motions, and compare the analytical profiles with a set of high-resolution N-body simulations ranging from galactic to cluster scales. We argue that the dark matter density profile is entirely determined by the initial conditions, which are described by only two parameters: the height of the primordial peak and the smoothing scale. These are physically meaningful quantities in our model, related to the mass and formation time of the halo. Angular momentum is dominated by velocity dispersion, and it is responsible for the shape of the density profile near the centre. The phase-space density of our simulated haloes is well described by a power-law profile, rho/sigma^3 = 10^{1.46\pm0.04} (rho_c/Vvir^3) (r/Rvir)^{-1.90\pm0.05}. Setting the eccentricity of particle orbits according to the numerical results, our model is able to reproduce the mass distribution of individual haloes.Comment: 12 pages, 13 figures, submitted to MNRA

Dark Energy and Gravity

I review the problem of dark energy focusing on the cosmological constant as the candidate and discuss its implications for the nature of gravity. Part 1 briefly overviews the currently popular `concordance cosmology' and summarises the evidence for dark energy. It also provides the observational and theoretical arguments in favour of the cosmological constant as the candidate and emphasises why no other approach really solves the conceptual problems usually attributed to the cosmological constant. Part 2 describes some of the approaches to understand the nature of the cosmological constant and attempts to extract the key ingredients which must be present in any viable solution. I argue that (i)the cosmological constant problem cannot be satisfactorily solved until gravitational action is made invariant under the shift of the matter lagrangian by a constant and (ii) this cannot happen if the metric is the dynamical variable. Hence the cosmological constant problem essentially has to do with our (mis)understanding of the nature of gravity. Part 3 discusses an alternative perspective on gravity in which the action is explicitly invariant under the above transformation. Extremizing this action leads to an equation determining the background geometry which gives Einstein's theory at the lowest order with Lanczos-Lovelock type corrections. (Condensed abstract).Comment: Invited Review for a special Gen.Rel.Grav. issue on Dark Energy, edited by G.F.R.Ellis, R.Maartens and H.Nicolai; revtex; 22 pages; 2 figure

Dickey-Lincoln School Lakes Project at Dickey, Maine : Final Environmental Statement, Volume 1-4

The proposed Dickey-Lincoln School Lakes Project in northern Maine is a multipurpose installation on the St.John River. The combination hydroelectric power and flood control project is located in Aroostook County, Maine, near the Canadian border. The two proposed earth fill dams located at Dickey are 10,200 feet in length with a maximum height of 335 feet. They would impound 7.7 million acre feet of water at a maximum pool elevation 910 feet mean sea level. A second earth filled dam located 11 miles downstream at Lincoln School would serve as a regulatory dam. It would be 2100 feet in lenqth, 90 feet above the existing streambed

Review of Flywheel based Internal Combustion Engine Hybrid Vehicles

Hybrid vehicles of different configurations and utilizing different energy storage systems have existed in development for many decades and more recently in limited production. They can be grouped as parallel, series or complex hybrids. Another classification is micro, mild and full hybrids which makes the distinction on the basis of functionality. The common energy storage systems in hybrid vehicles are batteries, supercapacitors and high speed flywheels. This paper aims to review a specific type of hybrid vehicle which involves the internal combustion engine (ICE) as the prime mover and the high speed flywheel as an energy storage device. Such hybrids are now attracting considerable interest given their potential for low cost. It is hence timely to produce a review of research and development in this subject. The flywheel is coupled to the drive line with a continuous variable transmission (CVT). The CVT can be of various types such as electrical, hydraulic or mechanical but usually in this case it is a non-electrical one. Different configurations are possible and the paper provides a timeline of the development of such powertrains with various examples. These types of hybrid vehicles have existed as prototypes for many decades and the authors believe that their development has reached levels where they can be considered serious contenders for production vehicles