• Prasanta K Panigrahi

      Articles written in Pramana – Journal of Physics

    • Characterizing and modelling cyclic behaviour in non-stationary time series through multi-resolution analysis

      Dilip P Ahalpara Amit Verma Jiterndra C Parikh Prasanta K Panigrahi

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      A method based on wavelet transform is developed to characterize variations at multiple scales in non-stationary time series. We consider two different financial time series, S&P CNX Nifty closing index of the National Stock Exchange (India) and Dow Jones industrial average closing values. These time series are chosen since they are known to comprise of stochastic fluctuations as well as cyclic variations at different scales. The wavelet transform isolates cyclic variations at higher scales when random fluctuations are averaged out; this corroborates correlated behaviour observed earlier in financial time series through random matrix studies. Analysis is carried out through Haar, Daubechies-4 and continuous Morlet wavelets for studying the character of fluctuations at different scales and show that cyclic variations emerge at intermediate time scales. It is found that Daubechies family of wavelets can be effectively used to capture cyclic variations since these are local in nature. To get an insight into the occurrence of cyclic variations, we then proceed to model these wavelet coefficients using genetic programming (GP) approach and using the standard embedding technique in the reconstructed phase space. It is found that the standard methods (GP as well as artificial neural networks) fail to model these variations because of poor convergence. A novel interpolation approach is developed that overcomes this difficulty. The dynamical model equations have, primarily, linear terms with additive Padé-type terms. It is seen that the emergence of cyclic variations is due to an interplay of a few important terms in the model. Very interestingly GP model captures smooth variations as well as bursty behaviour quite nicely.

    • Polarized spectral features of human breast tissues through wavelet transform and principal component analysis

      Anita Gharekhan Ashok N Oza M B Sureshkumar Asima Pradhan Prasanta K Panigrahi

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      Fluorescence characteristics of human breast tissues are investigated through wavelet transform and principal component analysis (PCA). Wavelet transform of polarized fluorescence spectra of human breast tissues is found to localize spectral features that can reliably differentiate different tissue types. The emission range in the visible wavelength regime of 500–700 nm is analysed, with the excitation wavelength at 488 nm using laser as an excitation source, where flavin and porphyrin are some of the active fluorophores. A number of global and local parameters from principal component analysis of both high- and low-pass coefficients extracted in the wavelet domain, capturing spectral variations and subtle changes in the diseased tissues are clearly identifiable.

    • Compacton-like solutions for modified KdV and nonlinear Schrödinger equation with external sources

      Thokala Soloman Raju C Nagaraja Kumar Prasanta K Panigrahi

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      We present new types of compacton-like solutions for modified KdV and nonlinear Schrödinger equation with external sources, using a recently developed fractional transformation. In particular, we explicate these novel compactons for the trigonometric case, and compare their properties with those of the compactons and solitons in the case of modified KdV equation. Keeping in mind the significance of nonlinear Schrödinger equation with external source, for pulse propagation through asymmetric twin-core fibres, we hope that the newly found compacton may be launched in a long-haul telecommunication network utilizing asymmetric twin-core fibres.

    • Exceptional polynomials and SUSY quantum mechanics

      K V S Shiv Chaitanya S Sree Ranjani Prasanta K Panigrahi R Radhakrishnan V Srinivasan

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      We show that for the quantum mechanical problem which admit classical Laguerre/Jacobi polynomials as solutions for the Schrödinger equations (SE), will also admit exceptional Laguerre/Jacobi polynomials as solutions having the same eigenvalues but with the ground state missing after a modification of the potential. Then, we claim that the existence of these exceptional polynomials leads to the presence of non-trivial supersymmetry.

    • Solitons and spin transport in graphene boundary

      Kumar Abhinav Vivek M Vyas Prasanta K Panigrahi

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      It is shown that in (2+1)-dimensional condensed matter systems, induced gravitational Chern–Simons (CS) action can play a crucial role for coherent spin transport in a finite geometry, provided zero-curvature condition is satisfied on the boundary. The role of the resultant KdV solitons is explicated. The fact that KdV solitons can pass through each other without interference, represent `resistanceless' spin transport.

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