In this paper, we discuss the emergence of extreme events in a parametrically driven nonpolynomial mechanical system with a velocity-dependent potential. We confirm the occurrence of extreme events from the probability distribution function of the peaks, which exhibits a longtail. We also present the mechanism for the occurrence of extreme events. We found that the probability of occurrence of extreme events alternatively increase and decrease with a brief region where the probability is zero. At the point of highest probability of extreme events, when the system is driven externally, we find that the probability decreases to zero. Our investigation confirms that the external drive can be used as an useful tool to mitigate extreme events in this nonlinear dynamical system. Through two parameter diagrams, we also demonstrate the regions where extreme events gets suppressed. In addition to the above, we show that extreme events persits when the sytem is influenced by noise and even gets transformed to super-extreme events when the state variable is influenced by noise.

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We propose a more conservative, physically-intuitive criterion, namely, the boundary enstrophy flux ( $BEF$ ), to characterise leading-edge-type dynamic stall onset in incompressible flows. Our results are based on wall-resolved large-eddy simulations of pitching aerofoils, with fine spatial and temporal resolution around stall onset. We observe that $|BEF|$ reaches a maximum within the stall onset regime identified. By decomposing the contribution to $BEF$ from the flow field, we find that the dominant contribution arises from the laminar leading edge region, due to the combined effect of large clockwise vorticity and favourable pressure gradient. A relatively small contribution originates from the transitional/turbulent laminar separation bubble (LSB) region, due to LSB-induced counter-clockwise vorticity and adverse pressure gradient. This results in $BEF$ being nearly independent of the integration length as long as the region very close to the leading edge is included. This characteristic of $BEF$ yields a major advantage in that the effect of partial or complete inclusion of the noisy LSB region can be filtered out, without changing the $BEF$ peak location in time significantly. Next, we analytically relate $BEF$ to the net wall shear and show that its critical value ( $=\max (|BEF|)$ ) corresponds to the instant of maximum net shear prevailing at the wall. Finally, we have also compared $BEF$ with the leading edge suction parameter ( $LESP$ ) (Ramesh et al., J. Fluid Mech., vol. 751, 2014, pp. 500–538) and find that the former reaches its maximum value between $0.3^{\circ }$ and $0.8^{\circ }$ of rotation earlier.

In this paper, we proposed a new Fuzzy max-min composition technique to diagnose the symptom of the disease using generalized interval-valued intuitionistic fuzzy relation (GIVIFR).

In this paper, two new Operator defined over IVIFSs were introduced, which will be "Multiplication of an IVIFS ‫ܣ‬ with ݊ and Multiplication of an IVIFS ‫ܣ‬ భ with the natural number ଵ "are proved.