Cosmic structure sizes in generic dark energy models

The maximum allowable size of a spherical cosmic structure as a function of its mass is determined by the maximum turn around radius $R_{\rm TA,max}$, the distance from its centre where the attraction on a radial test particle due to the spherical mass is balanced with the repulsion due to the ambient dark energy. In this work, we extend the existing results in several directions. (a) We first show that for $w\neq -1$, the expression for $R_{\rm TA, max}$ found earlier using the cosmological perturbation theory, can be derived using a static geometry as well. (b) In the generic dark energy model with arbitrary time dependent state parameter $w(t)$, taking into account the effect of inhomogeneities upon the dark energy as well, where it is shown that the data constrain $w(t={\rm today})>-2.3$, and (c) in the quintessence and the generalized Chaplygin gas models, both of which are shown to predict structure sizes consistent with observations.Comment: v2, 19pp; added references and discussions, improved presentation; accepted in EPJ

Environmental Standards as Strategic Outcomes : A Simple Model

This paper examines the strategic nature of choice of environmental standards under different degrees of openness of countries. It also compares and contrasts equilibrium environmental standards and levels of pollution, local and global, with the world optimum levels. It shows that, in case of open economies, environmental standards can be strategic substitutes or complements. In equilibrium, countries set higher environmental standards in case of open economies compared to that in case of closed economies. It also shows that equilibrium standards in case of open economies are higher than the world optimum in certain situations. In contrast, countries set lower environmental standards, in equilibrium, than the world optimum in absence of international trade.Environmental standards, strategic choice, openness, world optimum

Persistence of a Rouse polymer chain under transverse shear flow

We consider a single Rouse polymer chain in two dimensions in presence of a transverse shear flow along the $x$ direction and calculate the persistence probability $P_0(t)$ that the $x$ coordinate of a bead in the bulk of the chain does not return to its initial position up to time $t$. We show that the persistence decays at late times as a power law, $P_0(t)\sim t^{-\theta}$ with a nontrivial exponent $\theta$. The analytical estimate of $\theta=0.359...$ obtained using an independent interval approximation is in excellent agreement with the numerical value $\theta\approx 0.360\pm 0.001$.Comment: 6 page

Analytical study of level crossings in the Stark-Zeeman spectrum of ground state OH

The ground electronic, vibrational and rotational state of the OH molecule is currently of interest as it can be manipulated by electric and magnetic fields for experimental studies in ultracold chemistry and quantum degeneracy. Based on our recent exact solution of the corresponding effective Stark-Zeeman Hamiltonian, we present an analytical study of the crossings and avoided crossings in the spectrum. These features are relevant to non-adiabatic transitions, conical intersections and Berry phases. Specifically, for an avoided crossing employed in the evaporative cooling of OH, we compare our exact results to those derived earlier from perturbation theory.Comment: 5 figures, to be published in Eur. Phys. J.