• Raj Kumar

      Articles written in Pramana – Journal of Physics

    • An ab-initio derivation of the pi-electron hamiltonian by a nonperturbative open-shell formalism

      Debashis Mukherjee Raj Kumar Moitra Atri Mukhopadhyay

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      A method for generating a pi-electron hamiltonian in an ab-initio manner using the non-perturbative open-shell many-body formalism recently developed by us is presented. The π-hamiltonian thus derived is energy-independent, and is also proved to be spin-independent. A recipe is given with the help of which Goldstone—like matrix-elements ofHπ can be extracted up to three body terms. It has been demonstrated that the use of diagrammatics considerably simplifies the algebra and allows one to keep track of the various quantities involved. Up to a given order of approximation, an explicit form ofHπ containing up to the three body terms has been given, and some of the important physical effects embedded in the hamiltonian are discussed. A comparative analysis of the various formalisms currently in use forms the concluding section of the paper.

    • Operation of a capacitor bank for plasma metal forming

      P Sarkar S Chaturvedi Raj Kumar Rajesh Kumar D Lathi A Shyam J Sonara

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      Previously metal forming has been done using electromagnet in pulsed power mode, better known as magneform [1]. Here we will be presenting a different technique for metal forming. We are using water as a medium for this process. By discharging the stored electrical energy of the capacitor bank in water, we are getting the desired result i.e. to form (expand or compress) a wide range of workpiece to the desired shapes. The advantage of this method over conventional method is that it uses low power (negligible running cost). It does not require any post assembly cleaning degreasing and is hence environmentally ‘friendly’.

    • Interferometric key readable security holograms with secrete-codes

      Raj Kumar D Mohan A K Aggarwal

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      A new method is described to create secrete-codes in the security holograms for enhancing their anti-counterfeiting characteristics. To imitate these codes is difficult as pure phase objects having complex phase distribution function are used to modulate the object beam that is recorded in conjunction with an encoded interferometric reference beam derived from a key hologram. Lloyd's folding mirror interferometer is used to convert phase variations of the reconstructed wave-front into an intensity pattern for hologram authenticity verification. Creating the secrete-codes through an interferometric reference beam from the key hologram facilitates a multi-stage authenticity verification as well as easy repositioning of the security hologram through a specific Moiré pattern generated during the verification process.

    • Phase knife-edge laser Schlieren diffraction interferometry with boundary diffraction wave theory

      Raj Kumar D Mohan Sushil K Kaura D P Chhachhia A K Aggarwal

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      Within the framework of boundary diffraction wave theory it has been shown that the first bright fringe on either side of the central dark fringe of the phase knife-edge Fresnel diffraction pattern could be broadened to cover the whole field of view. Broadening of the first diffraction fringe, instead of conventionally modifying the spatial frequency spectrum, enhances the sensitivity of the Schlieren system. The use of phase knife-edge as viewing diaphragm in Schlieren diffraction interferometry not only enhances the fringe contrast but also avoids the loss in phase information as it lets through light from all parts of the test object and its thin interfacing makes the method suitable even for studying weak disturbances.

    • Comparative study of different Schlieren diffracting elements

      Raj Kumar Sushil K Kaura D P Chhachhia D Mohan A K Aggarwal

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      This paper presents an analysis of diffraction effects taking place at different Schlieren diffracting elements. Two types of diffraction effects are prominent in the Schlieren schemes. One is diffraction of direct light (source image) at the Schlieren element, which limits the sensitivity and resolution of Schlieren systems. The second type is the diffraction of light deflected from the test object at the Schlieren-diffracting element. This second type of diffraction degrades the quality of Schlieren results. Experimental results showing the effect of diffraction of light deflected from the test object at a phase knife-edge, corner of a square phase aperture and an optical fiber tip as Schlieren diffracting elements have been presented and discussed.

    • Modular networks with hierarchical organization: The dynamical implications of complex structure

      Raj Kumar Pan Sitabhra Sinha

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      Several networks occurring in real life have modular structures that are arranged in a hierarchical fashion. In this paper, we have proposed a model for such networks, using a stochastic generation method. Using this model we show that, the scaling relation between the clustering and degree of the nodes is not a necessary property of hierarchical modular networks, as had previously been suggested on the basis of a deterministically constructed model. We also look at dynamics on such networks, in particular, the stability of equilibria of network dynamics and of synchronized activity in the network. For both of these, we find that, increasing modularity or the number of hierarchical levels tends to increase the probability of instability. As both hierarchy and modularity are seen in natural systems, which necessarily have to be robust against environmental fluctuations, we conclude that additional constraints are necessary for the emergence of hierarchical structure, similar to the occurrence of modularity through multi-constraint optimization as shown by us previously.

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