9,608 research outputs found
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 coincide with that of where
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
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
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 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 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 and frequency and show the existence
of a dynamical transition for a chain of finite length. We find that the area
of the hysteresis 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 and the system has only one
scaling (. Expansion of an analytical
expression for obtained for the model system in the low-force
regime revealed that there is a new scaling exponent associated with force
(), 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 , the
exponents are robust and independent of temperature and friction coefficient.Comment: 6 pages, 5 figures Physical Review E (2016) (R) (Accepted
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