Nonlinear Dynamics

One of my areas of interest is nonlinear dynamics. Here is a list of some of my works in this area.

Here is a model of an induction motor with quasiperiodic drive. I did this together with PRANAV, who was my junior in IITK. We completed this in June 2015. The journal reference is Journal of Applied Nonlinear Dynamics 6 (1), 57-77 (2017).
Motor with quasiperiodic

Here is a work done with MATTHEW DAVIDOW under Professor RICHARD RAND's supervision. It deals with a singularity in a delayed differential equation. We completed this in January 2017. It has been accepted for publication in Nonlinear Dynamics.
Delay

Here is a basic but general model of shock wave propagation in linear medium with a travelling disturbance. A calculation of the appropriate GREEN's function leads to an exact formula for the wavefront in the cases where the disturbance is subsonic and supersonic. It also shows a phase reversal of the wave across the sound barrier. Unfortunately, a similar situation had already been considered by PHILIP MORSE and UNO INGARD in their book "Theoretical Acoustics," a fact which was brought to my attention by a reviewer for EPL. The technique that MORSE et. al. had used is completely different so this document still has some archival value.
Shock wave

Here is a first-principles model of the motion of a violin string which yields Helmholtz type limit cycles as a solution and also gives the regions of parameter space where this cycle exists and is stable. The small size of this region explains why the instrument is difficult to play. The journal reference is AIP Chaos 28 (8), 083116 (2018). See also Tutorial 125 in DELTA (my differential equations book) for a version with larger number of calculational steps but no literature review.
Violin

Here is a detailed analysis of bifurcations in a pair of MEMS oscillators. The work is done with ADITYA BHASKAR under the supervision of Professors RAND and ALAN ZEHNDER. We completed this in late 2018. It has been published in Nonlinear Dynamics.
MEMS

Here is a dynamic model for the spreading of COVID-19, the disease caused by the Wuhan Coronavirus. We are a team of five here - MOHIT SHARMA, RICHARD RAND, AAWADHESH KUMAR SINGH, ANOOP MISRA and myself. Our model is the first which accounts for the delays on account of the latency period of the virus and the waiting times for tests. The paper dates from 25/03/2020. We find that as a result of these delays, (a) the disease peaks in society a few days before the peak in test results is reached, (b) the optimal interval for imposing a limited duration lockdown is one which straddles the peak in the absence of the lockdown and (c) the effects of lockdown may not be apparent from a naive interpretation of the time hisotry of cases. As time progresses, we shall continue to revise this draft to make it more clear etc. but during revision we shall NOT update it to reflect newer case figures etc. Those shall be in follow-up works.
Corona