Interpenetration of two chains different in sizes: Some Exact Results

A model of two interacting polymer chains has been proposed to study the effect of penetration of one chain in to the other. We show that small chain penetrates more in comparison to the long chain. We also find a condition in which both chains cannot grow on their own (or polymerize) but can grow (polymerize) in zipped form.Comment: RevTex, 2 postscript figures; Accepted in Physica

On dynamics of composite entire functions and singularities

We consider the dynamical properties of transcendental entire functions and their compositions. We give several conditions under which Fatou set of a transcendental entire function $f$ coincide with that of $f\circ g,$ where $g$ is another transcendental entire function. We also prove some result giving relationship between singular values of transcendental entire functions and their compositions.Comment: 7 pages, accepted for publication in Bull. Cal. Math. So

Semigroups of transcendental entire functions and their dynamics

We study the dynamics of an arbitrary semigroup of transcendental entire functions using Fatou-Julia theory. Several results of the dynamics associated with iteration of a transcendental entire function have been extended to transcendental semigroups. We provide some conditions for connectivity of the Julia set of the transcendental semigroups. We also study finitely generated transcendental semigroups, abelian transcendental semigroups and limit functions of transcendental semigroups on its invariant Fatou components.Comment: 12 pages, accepted for publication in Proc. Indian Acad. Sci. (Math. Sci.). arXiv admin note: text overlap with arXiv:1302.724

A note on Schwarzian derivatives and normal families

We establish a criterion for local boundedness and hence normality of a family \F of analytic functions on a domain $D$ in the complex plane whose corresponding family of derivatives is locally bounded. Furthermore we investigate the relation between domains of normality of a family \F of meromorphic functions and its corresponding Schwarzian derivative family. We also establish some criterion for the Schwarzian derivative family of a family \F of analytic functions on a domain $D$ in the complex plane to be a normal family.Comment: 5 page

The dynamics of semigroups of transcendental entire functions I

We consider the dynamics associated with an arbitrary semigroup of transcendental entire functions. Fatou-Julia theory is used to investigate the dynamics of these semigroups. Several results of the dynamics associated with iteration of a transcendental entire function have been extended to transcendental semigroup case. We also investigate the dynamics of conjugate semigroups, Abelian transcendental semigroups and wandering and Baker domains of transcendental semigroups.Comment: 12 pages, accepted for publication in Indian J. Pure Appl. Mat

The dynamics of semigroups of transcendental entire functions II

We introduce the concept of escaping set for semigroups of transcendental entire functions using Fatou-Julia theory. Several results of the escaping set associated with the iteration of one transcendental entire function have been extended to transcendental semigroups. We also investigate the properties of escaping sets for conjugate semigroups and abelian transcendental semigroups. Several classes of transcendental semigroups for which Eremenko's conjectures hold have been provided.Comment: 14 pages. Accepted for publication in Indian J. Pure Appl. Math.(2015). arXiv admin note: text overlap with arXiv:1405.0224, arXiv:1406.245

Adaptive Quadrilateral Mesh in Curved Domains

Nonlinear elliptic system for generating adaptive quadrilateral meshes in curved domains is presented. Presented technique has been implemented in the C++ language. The included software package can write the converged meshes in the GMV and Matlab formats. Since, grid adaptation is required for numerically capturing important characteristics of a process such as boundary layers. So, the presented technique and the software package can be a useful tool.Comment: 16 Page

Grid Generation and Adaptation by Functionals

Accuracy of a simulation is strongly depend on the grid quality. Here, quality means orthogonality at the boundaries and quasi-orthogonality within the critical regions, smoothness, bounded aspect ratios, solution adaptive behaviour, etc. We review various functionals for generating high quality structured quadrilateral meshes in two dimensional domains. Analysis of Winslow and Modified Liao functionals are presented. Numerical examples are also presented to support our theoretical analysis. We will demonstrate the use of the Area functional for generating adaptive quadrilateral meshes.Comment: 1

Multiblock Grid Generation for Simulations in Geological Formations

Simulating fluid flow in geological formations requires mesh generation, lithology mapping to the cells, and computing geometric properties such as normal vectors and volume of cells. The purpose of this research work is to compute and process the geometrical information required for performing numerical simulations in geological formations. We present algebraic techniques, named Transfinite Interpolation, for mesh generation. Various transfinite interpolation techniques are derived from 1D projection operators. Many geological formations such as the Utsira formation (Torp and Gale, 2004; Khattri, Hellevang, Fladmark and Kvamme, 2006) and the Snohvit gas field (Maldal and Tappel, 2004) can be divided into layers or blocks based on the geometrical or lithological properties of the layers. We present the concept of block structured mesh generation for handling such formations.Comment: 1

Periodically driven DNA: Theory and simulation

We propose a generic model of driven DNA under the influence of an oscillatory force of amplitude $F$ and frequency $\nu$ and show the existence of a dynamical transition for a chain of finite length. We find that the area of the hysteresis loop, $A_{\rm loop}$, scales with the same exponents as observed in a recent study based on a much more detailed model. However, towards the true thermodynamic limit, the high-frequency scaling regime extends to lower frequencies for larger chain length $L$ and the system has only one scaling ($A_{\rm loop} \approx \nu^{-1}F^2)$. Expansion of an analytical expression for $A_{\rm loop}$ obtained for the model system in the low-force regime revealed that there is a new scaling exponent associated with force ($A_{\rm loop} \approx \nu^{-1}F^{2.5}$), which has been validated by high-precision numerical calculation. By a combination of analytical and numerical arguments, we also deduce that for large but finite $L$, the exponents are robust and independent of temperature and friction coefficient.Comment: 6 pages, 5 figures Physical Review E (2016) (R) (Accepted