Sourav Dutta

Solution of the Duffing–van der Pol oscillator equation by a differential transform method

In this paper, we have tried to implement a relatively new exact series method of solution, known as the differential transform method, for solving one of the widely studied and challenging equations in nonlinear dynamics, the Duffing–van der Pol oscillator equation. Chandrasekar et al (2004 J. Phys. A 37 4527) showed that the force-free Duffing–van der Pol oscillator is completely integrable for a specific parametric choice, and they derived a general solution for this parametric choice. The results of this paper are in sufficient agreement with those of Chandrasekar et al.

A study of phantom scalar field cosmology using Lie and Noether symmetries

The paper deals with phantom scalar field cosmology in Einstein gravity. At first, using Lie symmetry, the coupling function to the kinetic term and the potential function of the scalar field and the equation of state parameter of the matter field are determined and a simple solution is obtained. Subsequently, Noether symmetry is imposed on the Lagrangian of the system. The symmetry vector is obtained and the potential takes a very general form from which potential using Lie symmetry can be obtained as a particular case. Then, we choose a point transformation (a,ϕ) → (u,v) such that one of the transformed variables (say u) is a cyclic for the Lagrangian. Using conserved charge (corresponding to the cyclic coordinate) and the constant of motion, solutions are obtained.

An Attempt for an Emergent Scenario with Modified Chaplygin Gas

The present work is an attempt for emergent universe scenario with modified Chaplygin gas. The universe is chosen as spatially flat FRW space-time with modified Chaplygin gas as the only cosmic substratum. It is found that emergent scenario is possible for some specific (unrealistic) choice of the parameters in the equation of state for modified Chaplygin gas.

Research note: Capacity assignment in computer communication networks with unreliable links

This paper considers the problem of selecting the optimum capacities of the links in a computer communication network which employs unreliable links. Given the nodes, links, link probabilities, grade of service and cost functions of the network, the objective of this problem is to find the optimum link capacities that minimize the network design cost, subject to the constraint equation involving the grade of service. This is essentially a combinatorial optimization problem. A general methematical model for this problem is formulated and a set of feasible solutions is obtained using Lagrangean relaxation and subgradient optimization techniques. A simulation study has been performed to verify the model, and favourable results obtained for a variety of nontrivial networks.

Does fractal universe describe a complete cosmic scenario

The present work deals with evolution of the fractal model of the universe in the background of homogeneous and isotropic FLRW space-time geometry. The cosmic substrum is taken as perfect fluid with barotropic equation of state. A general prescription for the deceleration parameter is determined and it is examined whether the deceleration parameter may have more than one transition during the evolution of the fractal universe for monomial form of the fractal function as a function of the scale factor. Finally, the model has been examined by making comparison with the observed data.

Cosmological consequences in the framework of generalized Rastall theory of gravity

The paper deals with generalized Rastall theory of gravity and its cosmological consequences in the background of homogeneous and isotropic flat FLRW model with perfect fluid as the matter context. The model shows a non singular era (emergent scenario) at the early phase of expansion for a particular choice of the Rastall parameter. Also the model finds to be equivalent to the particle creation mechanism in Einstein gravity in the framework of non-equilibrium thermodynamics. Universal thermodynamics is briefly presented and it is found that the entropy function in Rastall theory is the usual Bekenstein entropy and there is no correction to it. Finally, a complete cosmic history starting from inflation to late time acceleration is presented for suitable choices of the Rastall parameter.

A study of dynamical equations for non-minimally coupled scalar field using Noether symmetric approach

Non-minimally coupled scalar field cosmology has been studied in this work within the framework of Einstein gravity. In the background of homogeneous and isotropic Friedmann–Lemaitre–Robertson–Walker (FLRW) spacetime non-minimally coupled scalar field having self-interacting potential is taken as the source of the matter content. The constraint of imposing Noether symmetry on the Lagrangian of the system not only determines the infinitesimal generator (the symmetry vector) but also the coupling function and the self-interacting potential for the scalar field. By choosing appropriately a point transformation in the augmented space, one of the transformed variables is cyclic for the Lagrangian. Finally, using constants of motion, the solutions are analyzed.

Answer to the Comments on the paper “A study of phantom scalar field cosmology using Lie and Noether symmetries” by A. Paliathanasis et al., arXiv:1605.05147

This is a short communication in reference to the comments in (arXiv: 1605.05147) of our paper in Int. J. Mod. Phys. D 25, 1650051 (2016). We have tried to answer to the comments or criticism in the paper.

Quintom cosmological model and some possible solutions using Lie and Noether symmetries

The present work deals with a quintom model of dark energy in the framework of a spatially flat isotropic and homogeneous Friedmann–Lemaitre–Robertson–Walker (FLRW) universe. At first, Lie point symmetry is imposed to the system and the unknown coupled potential of the model is determined. Then Noether symmetry, which is also a point like symmetry of the Lagrangian, is imposed on the physical system and the potential takes a general form. It is shown that the Lie algebra of Noether symmetry is a sub-algebra of the corresponding Lie algebra of the Lie symmetry. Finally, a point transformation in the three-dimensional augmented space is performed suitably so that one of the variables become cyclic and as a result there is considerable simplification to the physical system. Hence, conserved quantities (i.e. constants of motion) are expressed in a compact form and cosmological solutions are evaluated and analyzed in the present context.

Integrability of the discretization of the controlled Euler Top

The Euler equations with two controls are discretized by using the bilinear transformation method. The discrete equations are explicit and exhibit a sufficient number of conserved quantities for integrability. The explicit solution to the discrete controlled Euler top are deduced in terms of elliptic functions.