Electrostatic contribution to DNA condensation - application of 'energy minimization' in a simple model in strong Coulomb coupling regime

Bending of DNA from a straight rod to a circular form in presence of any of the mono-, di-, tri- or tetravalent counterions has been simulated in strong Coulomb coupling environment employing a previously developed energy minimization simulation technique. The inherent characteristics of the simulation technique allow monitoring the required electrostatic contribution to the bending. The curvature of the bending has been found to play crucial roles in facilitating electrostatic attractive potential energy. The total electrostatic potential energy has been found to decrease with bending which indicates that bending a straight DNA to a circular form or to a toroidal form in presence of neutralizing counterions is energetically favorable and practically is a spontaneous phenomenon

Hyperscaling violation, quasinormal modes and shear diffusion

We study quasinormal modes of shear gravitational perturbations for hyperscaling violating Lifshitz theories, with Lifshitz and hyperscaling violating exponents $z$ and $\theta$. The lowest quasinormal mode frequency yields a shear diffusion constant which is in agreement with that obtained in previous work by other methods. In particular for theories with $z< d_i+2-\theta$ where $d_i$ is the boundary spatial dimension, the shear diffusion constant exhibits power-law scaling with temperature, while for $z=d_i+2-\theta$, it exhibits logarithmic scaling. We then calculate certain 2-point functions of the dual energy-momentum tensor holographically for $z\leq d_i+2-\theta$, identifying the diffusive poles with the quasinormal modes above. This reveals universal behaviour $\eta/s=1/4\pi$ for the viscosity-to-entropy-density ratio for all $z\leq d_i+2-\theta$.Comment: v2: Latex, 21pgs, more details of analysis, review of shear diffusion from membrane paradigm, references added, matches version to be publishe

On doubly nonlocal pp-fractional coupled elliptic system

\noi We study the following nonlinear system with perturbations involving p-fractional Laplacian \begin{equation*} (P)\left\{ \begin{split} (-\De)^s_p u+ a_1(x)u|u|^{p-2} &= \alpha(|x|^{-\mu}*|u|^q)|u|^{q-2}u+ \beta (|x|^{-\mu}*|v|^q)|u|^{q-2}u+ f_1(x)\; \text{in}\; \mb R^n,\\ (-\De)^s_p v+ a_2(x)v|v|^{p-2} &= \gamma(|x|^{-\mu}*|v|^q)|v|^{q-2}v+ \beta (|x|^{-\mu}*|u|^q)|v|^{q-2}v+ f_2(x)\; \text{in}\; \mb R^n, \end{split} \right. \end{equation*} where $n>sp$, $0<s<1$, $p\geq2$, $\mu \in (0,n)$, $\frac{p}{2}\left( 2-\frac{\mu}{n}\right) < q <\frac{p^*_s}{2}\left( 2-\frac{\mu}{n}\right)$, $\alpha,\beta,\gamma >0$, 0< a_i \in C^1(\mb R^n, \mb R), $i=1,2$ and f_1,f_2: \mb R^n \to \mb R are perturbations. We show existence of atleast two nontrivial solutions for $(P)$ using Nehari manifold and minimax methods.Comment: 26 page