Non-Gaussianity of Inflationary Gravitational Waves from the Field Equation

We demonstrate equivalence of the in-in formalism and Green's function method for calculating the bispectrum of primordial gravitational waves generated by vacuum fluctuations of the metric. The tree-level bispectrum from the field equation, $B_h$, agrees with the results obtained previously using the in-in formalism exactly. Characterising non-Gaussianity of the fluctuations using the ratio $B_h/P^2_h$ in the equilateral configuration, where $P_h$ is the power spectrum of scale-invariant gravitational waves, we show that it is much weaker than in models with spectator gauge fields. We also calculate the tree-level bispectrum of two right-handed and one left-handed gravitational wave using Green's function, reproducing the results from in-in formalism, and show that it can be as large as the bispectrum of three right-handed gravitational waves.Comment: 17 pages, 2 figures; comments welcom

Does Subsidising the Cost of Capital Help the Poorest? An Analysis of Saving Opportunities in Group Lending

This paper shows that subsidising the cost of capital restricts the ability of the poorest to participate in the group lending mechanisms that include saving opportunities. We document the group lending mechanism used by a typical microfinance lender in Haryana, India. Individuals can participate in the group either as a borrower or a saver. The lender requires that the borrower partly self-finance their project with their own cash wealth. Consequently, a borrower requires a minimum amount of cash wealth to borrow. The poorest participate in the group by co-financing the borrower's project with their meagre savings. In return, they obtain higher than market returns on their savings. Subsidising the cost of capital reduces the cash wealth required to participate in the group as a borrower. Conversely, it increases the cash wealth required to participate as a saver, thus curtailing the opportunity for the poorest to enrich themselves.Group Lending, Microfinance, Savings, Outreach

DNA confined in a two-dimensional strip geometry

Semiflexible polymers characterized by the contour length $L$ and persistent length $\ell_p$ confined in a spatial region $D$ have been described as a series of ``{\em spherical blobs}'' and ``{\em deflecting lines}'' by de Gennes and Odjik for $\ell_p < D$ and $\ell_p \gg D$ respectively. Recently new intermediate regimes ({\em extended de Gennes} and {\em Gauss-de Gennes}) have been investigated by Tree {\em et al.} [Phys. Rev. Lett. {\bf 110}, 208103 (2013)]. In this letter we derive scaling relations to characterize these transitions in terms of universal scaled fluctuations in $d$-dimension as a function of $L,\ell_p$, and $D$, and show that the Gauss-de Gennes regime is absent and extended de Gennes regime is vanishingly small for polymers confined in a 2D strip. We validate our claim by extensive Brownian dynamics (BD) simulation which also reveals that the prefactor $A$ used to describe the chain extension in the Odjik limit is independent of physical dimension $d$ and is the same as previously found by Yang {\em et al.}[Y. Yang, T. W. Burkhardt, G. Gompper, Phys. Rev. E {\bf 76}, 011804 (2007)]. Our studies are relevant for optical maps of DNA stretched inside a nano-strip.Comment: 6 pages, 4 figure

Out of Equilibrium Characteristics of a Forced Translocating Chain through a Nanopore

Polymer translocation through a nano-pore in a thin membrane is studied using a coarse-grained bead-spring model and Langevin dynamics simulation with a particular emphasis to explore out of equilibrium characteristics of the translocating chain. We analyze the out of equilibrium chain conformations both at the $cis$ and the $trans$ side separately either as a function of the time during the translocation process or as as function of the monomer index $m$ inside the pore. A detailed picture of translocation emerges by monitoring the center of mass of the translocating chain, longitudinal and transverse components of the gyration radii and the end to end vector. We observe that polymer configurations at the $cis$ side are distinctly different from those at the $trans$ side. During the translocation, and immediately afterwards, the chain is clearly out of equilibrium, as different parts of the chain are characterized by a series of effective Flory exponents. We further notice that immediately after the translocation the last set of beads that have just translocated take a relatively compact structure compared to the first set of beads that translocated earlier, and the chain immediately after translocation is described by an effective Flory exponent $0.45 \pm 0.01$. The analysis of these results is further strengthened by looking at the conformations of chain segments of equal length as they cross from the $cis$ to the $trans$ side, We discuss implications of these results to the theoretical estimates and numerical simulation studies of the translocation exponent reported by various groups.Comment: 35 pages, 16 figures. Submitted to Phys. Rev.