• Vinayak

      Articles written in Pramana – Journal of Physics

    • Transition from Poisson to circular unitary ensemble

      Vinayak Akhilesh Pandey

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      Transitions to universality classes of random matrix ensembles have been useful in the study of weakly-broken symmetries in quantum chaotic systems. Transitions involving Poisson as the initial ensemble have been particularly interesting. The exact two-point correlation function was derived by one of the present authors for the Poisson to circular unitary ensemble (CUE) transition with uniform initial density. This is given in terms of a rescaled symmetry breaking parameter Λ. The same result was obtained for Poisson to Gaussian unitary ensemble (GUE) transition by Kunz and Shapiro, using the contour-integral method of Brezin and Hikami. We show that their method is applicable to Poisson to CUE transition with arbitrary initial density. Their method is also applicable to the more general $\ell$CUE to CUE transition where CUE refers to the superposition of $\ell$ independent CUE spectra in arbitrary ratio.

    • Chaotic travelling rolls in Rayleigh–Bénard convection

      Supriyo Paul Krishna Kumar Mahendra K Verma Daniele Carati Arnab K De Vinayak Eswaran

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      In this paper we investigate two-dimensional (2D) Rayleigh–B ́enard convection using direct numerical simulation in Boussinesq fluids with Prandtl number $P = 6.8$ confined between thermally conducting plates. We show through the simulation that in a small range of reduced Rayleigh number $r (770 < r < 890)$ the 2D rolls move chaotically in a direction normal to the roll axis. The lateral shift of the rolls may lead to a global flow reversal of the convective motion. The chaotic travelling rolls are observed in simulations with free-slip as well as no-slip boundary conditions on the velocity field. We show that the travelling rolls and the flow reversal are due to an interplay between the real and imaginary parts of the critical modes.

    • Impact of density-dependent symmetry energy and Coulomb interactions on the evolution of intermediate mass fragments

      Karan Singh Vinayak Suneel Kumar

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      Within the framework of isospin-dependent quantum molecular dynamics (IQMD) model, we demonstrate the evolution of intermediate mass fragments in heavy-ion collisions. In this paper, we study the time evolution, impact parameter, and excitation energy dependence of IMF production for the different forms of density-dependent symmetry energy. The IMF production and charge distribution show a minor but considerable sensitivity towards various forms of densitydependent symmetry energy. The Coulomb interactions affect the IMF production significantly at peripheral collisions. The IMF production increases with the stiffness of symmetry energy.

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