Grant-Funded Researcher (A)
School of Computer and Mathematical Sciences
Faculty of Sciences, Engineering and Technology
I am an ARC Grant Funded Researcher in Applied Mathematics in the School of Mathematical Sciences at the University of Adelaide. I completed a Bachelor of Aerospace Engineering (Hons) and a Bachelor of Science (Mathematics and Physics) in 2016 from Monash University. I then completed a PhD in Physics from Monash University in 2020. During my PhD, my research focused on investigating, both experimentally and theoretically, a hydrodynamic system of self-propelled droplets on a vibrating fluid bath.
I have a broad interest in applying mathematics to understand various physical and biological phenomena. My specific interests are in dynamical systems & chaos, fluid dynamics and active matter.
- Inertial particle focusing in curved microfluidic ducts - Particles suspended in a fluid flow through a curved duct can focus to equilibrium locations within the duct cross-section. Such particle focusing is exploited in various medical and industrial technologies aimed at separating particles by size. We are using mathematical models to understand particle dynamics as the system parameters are varied. Understanding of particle dynamics and their equilibria will assist in the design of inertial microfluidic devices that can separate particles efficiently.
- Superwalking droplets - Vertically vibrating a bath of silicone oil can give rise to a millimeter-sized classical wave-particle entity in the form of a walking droplet on the free surface of the liquid. These walking droplets have been shown to mimic several features from the quantum regime. By vibrating the bath at two frequencies, a new class of walking droplets emerge, coined superwalkers. Two-frequency driven superwalkers are typically bigger and faster than single-frequency driven walkers and interactions of many superwalkers give rise to novel multidroplet behaviors.
- Attractor-driven matter - Murmurations of birds, schooling of fish, insect swarms, bacterial suspensions, human crowd and swarming of robots/drones are all examples of complex and dynamical collective behaviours that result from complex interactions among individuals. We have explored a collection of particles, coined attractor-driven matter, where we model each particle’s internal complexity by attributing to it an internal state space that is represented by a point on an attracting set of a chaotic dynamical system. We illustrate the rich dynamical and emergent behaviors that can arise from such particles. The formalism provides a flexible means to generate complex dynamical and collective behaviors that may be broadly applied in various contexts.
- Dynamics of active wave-particle entities - A classical wave-particle entity in the form of a millimetric walking droplet can emerge on the free surface of a vertically vibrating liquid bath. Such wave-particle entities have been shown to exhibit hydrodynamic analogs of quantum systems. We are exploring, theoretically and numerically, the rich dynamical behaviours emerging for a single as well as a pair of interacting wave-particle entities. In some situations, the dynamics of the wave-particle entity reduces to the classic Lorenz dynamical system.
Date Position Institution name 2019 - 2020 Teaching Professional Monash College 2017 - 2019 Teaching Assistant Monash University 2015 - 2017 Research Assistant Monash University
Awards and Achievements
Date Type Title Institution Name Country Amount 2021 Research Award Robert Street Doctoral Prize 2020 Monash University Australia - 2021 Scholarship Australian Government RTP Scholarship Australian Government Australia - 2021 Award T.M. Cherry award ANZIAM Australia - 2020 Research Award 2020 Norris Family Award for Outstanding Research Output by a Graduate Research Student Monash University Australia - 2018 Award Best student presentation award Brown University United States - 2017 Scholarship J L William Postgraduate Top Up Scholarship Monah University Australia - 2016 Award Best in School Award Monash University Australia -
Language Competency English Can read, write, speak, understand spoken and peer review Gujarati Can read, speak and understand spoken Hindi Can read, speak and understand spoken
Date Institution name Country Title 2017 - 2020 Monash University Australia PhD 2012 - 2017 Monash University Australia Bachelor of Science 2012 - 2016 Monash University Australia Bachelor of Aerospace Engineering (Hons)
Year Citation 2020 Valani, R. (2020). Superwalking Droplets and Generalised Pilot-Wave Dynamics. (PhD Thesis).
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