• Priyanka

      Articles written in Pramana – Journal of Physics

    • Anisotropic cosmological models in $f (R, T)$ theory of gravitation

      Shri Ram Priyanka Manish Kumar Singh

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      A class of non-singular bouncing cosmological models of a general class of Bianchi models filled with perfect fluid in the framework of $f (R, T)$ gravity is presented. The model initially accelerates for a certain period of time and decelerates thereafter. The physical behaviour of the model is also studied.

    • Cluster decay of $^{112−122}$Ba isotopes from ground state and as an excited compound system

      Santhosh K P Subha P V Priyanka B

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      The decay properties of various even-even isotopes of barium in the range $112 \le A \le 122$ is studied by modifying the Coulomb and proximity potential model for both the ground and excited state decays, using recent mass tables. Most of the values predicted for ground state decays are within the experimental limit for measurements $(T_{1/2}$less than $10^{30}$s). The minimum $T_{1/2}$ value refers to doubly magic or nearly doubly magic Sn $(Z = 50)$ as the daughter nuclei. A comparison of log$_{10}(T_{1/2})$ value reveals that the exotic cluster decay process slows down due to the presence of excess neutrons in the parent nuclei. The half-lives are also computed using the Universal formulafor cluster decay (UNIV) of Poenaru et al and the Universal decay law (UDL) of Qi et al, and are compared with CPPM values and found to be in good agreement. A comparison of half-life for ground and excited systems reveals that probability of decay increases with a rise in temperature or otherwise, inclusion of excitation energy decreases the $T_{1/2}$ values.

    • A scheme for designing extreme multistable discrete dynamical systems


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      In this paper, we propose a scheme for designing discrete extreme multistable systems coupling two identical dynamical systems. Existence of infinitely many attractors in the system is obtained via partial synchronization between two systems for a given set of parameters. We give a conjecture that extreme multistable systems can be designed by coupling two m-dimensional dynamical systems in such a way that $i (1 \leq i \leq m − 1)$ number of state variables of the two systems synchronize completely and $(m − i )$ number of state variables keep constant difference. We demonstrate the applicability of our scheme in two-dimensional (2D) as well as threedimensional (3D) discrete dynamical systems. In particular, we discuss our scheme taking coupled 2D Hénon maps, coupled 2D Duffing maps and coupled 3D Hénon maps. We have analytically shown the existence of fixed points and period-2 orbits in the coupled system with the variation of initial conditions. These analytically derived conditions matched very well with the numerical simulation results. Variation of the largest Lyapunov exponent with the initial conditions is shown to confirm the existence of extreme multistability in the model. Our scheme may be useful for designing physically, chemically and biologically useful multistable discrete dynamical systems.

    • Extreme multistable synchronisation in coupled dynamical systems


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      A rule for designing extreme multistable synchronised systems by coupling two identical dynamical systems has been proposed in this paper. The basic idea behind the proposed scheme is the existence of chaos in the coupled system in the presence of initial condition-dependent constants of motion. A new conjecture has been introduced according to which an extreme multistable synchronised system can be designed if all states of one system will synchronise with the corresponding states of the other system (of the two coupled systems) and the basin of the synchronised state depends on the difference between the initial conditions of the corresponding states of the individual systems. The proposed scheme has been illustrated with the help of coupled Rössler systems, coupled Hénon maps and coupled logistic maps. Moreover, the existence of flip bifurcation with the variation of initial conditions has been shown analytically as well as numerically in the case of coupled Hénon maps. Numerical results are reported to show the proficiency of the proposed scheme to design extreme multistable synchronisation behaviour. This work establishes a theoretical foundation for constructing extreme multistable synchronised continuous as well as discrete dynamical systems.

    • Ordered level spacing distribution in embedded random matrix ensembles


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      The probability distributions of the closest neighbour (CN) and farther neighbour (FN) spacings from a given level have been studied for interacting fermion/boson systems with and without spin degree of freedom constructed using an embedded Gaussian orthogonal ensemble (GOE) of one plus random two-body interactions. Our numerical results demonstrate a very good consistency with the recently derived analytical expressions using a 3 × 3 random matrix model and other related quantities by Srivastava et al, J. Phys. A: Math. Theor. 52, 025101 (2019). This establishes conclusively that local level fluctuations generated by embedded ensembles (EE) follow the results of classical Gaussian ensembles.

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