P. C. Ray

The dark energy equation of state

We perform a study of cosmic evolution with an equation of state parameter

Discrete breathers in nonlinear LiNbO3-type ferroelectrics

\omega(t)=\omega_0+\omega_1(t\dot H/H)

Dynamical systems analysis for polarization in ferroelectrics

by selecting a phenomenological

Importance of damping on nanoswitching in LiNbO3-type ferroelectrics

\Lambda

Scenario of Inflationary Cosmology from the Phenomenological Λ Models

model of the form,

Large Amplitude Free Vibration of a Rotating Nonhomogeneous Beam With Nonlinear Spring and Mass System

\dot\Lambda\sim H^3

GENERALIZED MODEL FOR Λ DARK ENERGY

. This simple proposition explains both linearly expanding and inflationary Universes with a single set of equations. We notice that the inflation leads to a scaling in the equation of state parameter,

Analytical approaches for the approximate solution of a nonlinear fractional ordinary differential equation

\omega(t)

Exact Analytical Solution of Fractional Relaxation-Oscillation Equation by Adomian Decomposition and He’s Variational Technique

, and hence in equation of state. In this approach, one of its two parameters have been pin pointed and the other have been delineated. It has been possible to show a connection between dark energy and Higgs-Boson.

Solution of non-linear Klein–Gordon equation with a quadratic non-linear term by Adomian decomposition method

Ferroelectric materials, such as lithium niobate, show interesting nonlinear hysteresis behavior that can be explained by a dynamical system analysis by using a nonlinear Klein- Gordon equation previously constructed from the Hamiltonian with Landau-Ginzburg two-well potential. In the discrete case [Phys. Rev. B 81, 064104 (2010)], the intrinsic localized modes were shown to exist above the linear modes. Nonlinearity and discreteness of domain structures in ferroelectrics slab domains arrayed in the x-direction lead to breather solutions under different values of controlling parameters, such as interaction between the domains and damping term mainly due to pinning effect. Different types of classical breather solution, namely Hamiltonian, dissipative and moving breather solutions are shown by numerical simulation with data on actual ferroelectric materials.