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Anupam Bhandari

Publications and source records attributed to Anupam Bhandari.

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Theoretical development in the viscosity of ferrofluid

The viscosity of ferrofluid has an important role in liquid sealing of the hard disk drives, biomedical applications as drug delivery, hyperthermia, and magnetic resonance imaging. In the absence of a magnetic field, the viscosity of ferrofluid depends on the volume concentration of magnetic nanoparticles including surfactant layers. However, under the influence of a stationary magnetic field, the viscosity of ferrofluid depends on the angle between the applied magnetic field and vorticity in the flow. If this angle is 90o, then there is a maximum increase in the viscosity. If the magnetic field and the vorticity in the flow are parallel to each other, then there is no change in the viscosity since the applied magnetic field does not change the speed of the rotation of magnetic nanoparticles in the fluid. The viscosity of ferrofluid in the presence of an alternating magnetic field demonstrates interesting behavior. When field frequency matches with the relaxation time, known as resonance condition, then there is no impact of an alternating magnetic field in the viscosity of ferrofluid. If the frequency of an alternating magnetic field is less than resonance frequency, then an alternating magnetic field increases the viscosity of ferrofluid. Using higher frequency than resonance condition reduces the viscosity of ferrofluid and researchers reported this incident as the negative viscosity effect. If the frequency of an alternating magnetic field tends to infinite, then ferrofluid ceases to feel a magnetic field. In this case, there is no impact of an alternating magnetic field on the viscosity of ferrofluid.

physics.flu-dyn

Complex Dynamics of a Second Order Rational Difference Equation

The dynamics of the second order rational difference equation $\displaystyle{z_{n+1}=\frac{α+ z_{n-1}}{βz_n + z_{n-1}}}$ with the real parameter $α$, $β$ and arbitrary non-negative real initial conditions is investigated a decade ago. In the present manuscript, the same has been revisited considering the parameters $α$ and $β$ as complex numbers and the initial values as arbitrary complex numbers. It is found that some of the results which are valid in real line but does not valid in complex plane. The chaotic solutions of the difference equation with complex parameters are achieved, however there does not exists such solutions in the case of real parameters.

math.DS