Maximizing Human Development

The Human Development Index (HDI) is widely used as an aggregate measure of overall human well being. We examine the allocations implied by the maximization of this index, using a standard growth model — an extended version of Mankiw, Romer, andWeil’s (1992) model — and compare these with the allocations implied by the golden rule in that model. We find that maximization of the HDI leads to the overaccumulation of both physical and human capital, relative to the golden rule, and consumption is pushed to minimal levels. We then propose an alternative specification of the HDI, which replaces its income component with a consumption component. Maximization of this modified HDI yields a “human development golden rule” which balances consumption, education and health expenditures, and avoids the more extreme implications of the existing HDI.Economic growth, Human Development Index, Planning

A formal analysis of two dimensional gravity

Several investigations in the study of cosmological structure formation use numerical simulations in both two and three dimensions. In this paper we address the subtle question of ambiguities in the nature of two dimensional gravity in an expanding background. We take a detailed and formal approach by deriving the equations describing gravity in (D+1) dimensions using the action principle of Einstein. We then consider the Newtonian limit of these equations and finally obtain the necessary fluid equations required to describe structure formation. These equations are solved for the density perturbation in both the linearised form and in the spherical top hat model of nonlinear growth. We find that, when the special case of D=2 is considered, no structures can grow. We therefore conclude that, within the frame work of Einstein's theory of gravity in (2+1) dimensions, formation of structures cannot take place. Finally, we indicate the different possible ways of getting around this difficulty so that growing structures can be obtained in two dimensional cosmological gravitational simulations and discuss their implications.Comment: 13 Page

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

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

Quasi-spherical collapse with cosmological constant

The junction conditions between static and non-static space-times are studied for analyzing gravitational collapse in the presence of a cosmological constant. We have discussed about the apparent horizon and their physical significance. We also show the effect of cosmological constant in the collapse and it has been shown that cosmological constant slows down the collapse of matter.Comment: 7 pages, No figures, RevTeX styl

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

Computer-aided design of large-scale integrated circuits - A concept

Circuit design and mask development sequence are improved by using general purpose computer with interactive graphics capability establishing efficient two way communications link between design engineer and system. Interactive graphics capability places design engineer in direct control of circuit development

Choosing Longevity with Overlapping Generations

We extend Diamond’s (1965) OLG model to allow agents to choose whether to participate in the second period of life. The valuation of early exit (x) is a key parameter. We characterize competitive equilibria, efficient allocations, and predictions for income and life expectancy over time. We find that, with logarithmic utility, for any value of x, there is a range of initial values of the capital stock for which some agents would prefer to exit in equilibrium. The shape of the transition function and the number of steady state equilibria depend crucially on the value of capital’s share of income.ndogenous longevity, overlapping generations, growth