A physiologically based model of arousal dynamics is improved to incorporate the effects of the light spectrum on circadian phase resetting, melatonin suppression, and subjective sleepiness. To account for these nonvisual effects of light, melanopic irradiance replaces photopic illuminance that was used previously in the model. The dynamic circadian oscillator is revised according to the melanopic irradiance definition and tested against experimental circadian phase resetting dose‐response and phase response data. Melatonin suppression function is recalibrated against melatonin dose‐response data for monochromatic and polychromatic light sources. A new light‐dependent term is introduced into the homeostatic weight component of subjective sleepiness to represent the direct alerting effect of light; the new term responds to light change in a time‐dependent manner and is calibrated against experimental data. The model predictions are compared to a total of 14 experimental studies containing 26 data sets for 14 different spectral light profiles. The revised melanopic model shows on average 1.4 times lower prediction error for circadian phase resetting compared to the photopic‐based model, 3.2 times lower error for melatonin suppression, and 2.1 times lower error for subjective sleepiness. Overall, incorporating melanopic irradiance allowed simulation of wavelength‐dependent responses to light and could explain the majority of the observations. Moving forward, models of circadian phase resetting and the direct effects of light on alertness and sleep need to use nonvisual photoreception‐based measures of light, for example, melanopic irradiance, instead of the traditionally used illuminance based on the visual system.

A theoretical investigation has been made of the nonlinear propagation of ion-acoustic waves associated with a dense plasma system consisting degenerate electron and ion fluids. This fluid model, which is valid for both the non-relativistic and ultra-relativistic limits, has been employed with the reductive perturbation method. The K-dV and modified K-dV (mK-dV) equations have been derived and numerically analyzed. The basic features of solitons have been observed. It has been shown that the plasma system under consideration supports the propagation of solitons (electrostatic solitary structures) obtained from the solutions of K-dV and mK-dV equations. The implications of our results obtained from this investigation in compact astrophysical objects have been briefly discussed.

A theoretical investigation on the nonlinear propagation of ion-acoustic waves in a degenerate dense plasma has been made by employing the reductive perturbation method. The Burger's equation has been derived, and numerically analyzed. The basic features of electrostatic shock structures have been examined. It has been shown that the plasma system under consideration supports the propagation of electrostatic shock structures. The implications of our results (obtained from this investigation) in compact astrophysical objects have been briefly discussed.

A rigorous theoretical investigation has been made of basic characteristics of the nonplanar dust-ion-acoustic shock and solitary waves in electronegative dusty plasma containing Boltzmann electrons, Boltzmann negative ions, inertial positive ions, and charge fluctuating (negatively charged) stationary dust. The Burgers' and Korteweg–de Vries (K-dV) equations, which is derived by reductive perturbation technique, is numerically solved to examine the effects of nonplanar geometry on the basic features of the DIA shock and solitary waves formed in the electronegative dusty plasma. The implications of the results (obtained from this investigation) in space and laboratory experiments are briefly discussed.