Akanksha Srivastava

Numerical simulation of singularly perturbed non-linear elliptic boundary value problems using finite element method

The present paper presents the finite element solution of two-dimensional non-linear singularly perturbed elliptic partial differential equation subject to appropriate Dirichlet boundary conditions. A new fifth order convergent Newton type iterative method has been described and used to linearize the non-linear problem. The inclusion of this Newtons method of fifth order convergence in finite element method for solving non-linear system of equations reduces the number of iterations and hence the cost of computation. To demonstrate the usefulness of the proposed scheme, a non-convex variational Ginzburg-Landau equation is considered.

Geraniol Based Side Chain Liquid Crystalline Polymer: Synthesis and Characterization

Side chain liquid crystalline (SCLC) polysiloxane polymer with a geraniol mesogenic group and polymethylene spacers were prepared, and their properties were compared with those of an equivalent SCLC polymer, SCLCPs, with phenyl benzoate mesogenic group. The phase behavior was studied by differential scanning calorimetry (DSC) and optical polarizing microscopy (OPM). The DSC curve showed a clear melting temperature and isotropization at 72 and 148°C, respectively, with a glass transition at 25°C. The observation of a fan‐shaped texture confirms the presence Smectic A phase under an optical polarized microscope.

A finite element approach for finding positive solutions of a logistic equation with a sign-changing weight function

In this article, we describe the mathematical modeling and use finite element approximation to study the existence and multiplicity of numerical positive solutions of well-known generalized logistic equation with sign-changing weight function. We investigate the range of the real parameter involved in this problem to achieve the numerical solutions and discuss the behavior of the branch of the solutions using MATLAB 7.0.

Synthesis and characterization of side-chain liquid crystalline polysiloxanes containing α-terpineol in mesogenic group

The synthesis and characterization of polysiloxanes containing α-terpineol in mesogenic group is described. Their phase behaviour was studied by differential scanning calorimetry and optical polarizing microscopy, and compared with the phase behaviour of the corresponding cyclohexane-based polysiloxane. The monomer containing an undecenyl(-11-oxy) flexible spacer and α-terpineol shows a nematic and smectic-A mesophase. The synthesized polymers display a smectic mesophase without undergoing side-chain crystallization.

An Elementary Introduction to Recently Developed Computational Methods for Solving Singularly Perturbed Partial Differential Equations Arising in Science and Engineering

This paper presents a survey of innovative approaches of the most effective computational techniques for solving singular perturbed partial differential equations, which are useful because of their numerical and computer realizations. Many applied problems appearing in semiconductors theory, biochemistry, kinetics, theory of electrical chains, economics, solid mechanics, fluid dynamics, quantum mechanics, and many others can be modelled as singularly perturbed systems. Here, we summarize a wide range of research articles published by numerous researchers during the last ten years to get a better view of the present scenario in this area of research.