Research

Size-based particle separation for biomedical technologies

We developed a dynamical systems framework for inertial microfluidics, providing a predictive theory for particle focusing, bifurcations, and size-based particle separation in curved microchannels. This work enables the rational design of microfluidic devices for applications such as biomedical diagnostics and industrial particle separators, and connects applied mathematics directly with experimental microfluidic platforms.

Biological active matter: active nematics & tissue mechanics

We study theoretical and computational models of biological active matter, with a focus on active nematics and vertex-based descriptions of tissues. Our research addresses how nonequilibrium forcing, deformability, and internal stresses give rise to emergent order, flow instabilities, and intermittent collective migration. Current work includes modelling tissue-scale dynamics in developing embryos and understanding bifurcations and rheology in confined active nematic systems.

  • M. Stower, F. Zhou, R. N. Valani, J. Rozman, H. Hathrell, J. Godwin, X. Lu, J. Rittscher, J. Yeomans, and S. Srinivas. Quantitative multi-scale morphodynamic analysis reveals ratchetlike collective DVE migration and epiblast retrograde cell flow during anterior patterning in the mouse embryo. (under review) bioRxiv
  • Ioannis Hadjifrangiskou, Sumesh P. Thampi and R. N. Valani, Nematic order from phase synchronization of shape oscillations, Physical Review Letters, 135, 068101 (2025) arXiv
  • R. N. Valani, Sumesh Thampi and Julia M. Yeomans, From Equilibrium Multistability to Spatiotemporal Chaos in Channel Flows of Nematic Fluids. (under review) arXiv

Synthetic active matter: superwalking droplets

Superwalking droplets are self-propelled liquid drops that bounce and walk on a vertically vibrated fluid bath, forming a novel class of synthetic active matter in which each droplet acts as an energy consuming particle powered by its interaction with a self-generated wave field. Unlike many synthetic active systems with constant self-propulsion, superwalking droplets exhibit rich internal-state dynamics, including transitions between stationary, steady, and oscillatory motion, driven by memory effects in the wave–particle coupling. Such active wave-particle entities exhibit hydrodynamic analogs of quantum systems.

Microswimmers in fluid flows

We study the dynamics of microswimmers and active particles in background flows using reduced dynamical systems that admit a Hamiltonian structure. In channel flows, this formalism reveals conserved quantities and phase space organisation, allowing the classification of swimmer trajectories, bifurcations, and crossstream migration mechanisms that govern long-time transport and focusing.

Active matter with individual complexity

Murmurations of birds, schools of fish, insect swarms, bacterial suspensions, human crowds, and robotic swarms are all examples of complex collective behaviours that emerge from interactions among individuals. We introduce a class of active systems, termed attractor-driven matter, in which each particle’s internal complexity is represented by an internal state evolving on an attracting set of a chaotic dynamical system. This framework gives rise to rich individual and collective dynamics, including multistability, anomalous transport, and emergent organisation. The formalism provides a flexible and general approach for generating complex dynamical and collective behaviours across a wide range of physical, biological, and engineered systems.

Dynamical origins of hydrodynamic quantum analogs

We investigate the dynamical foundations of hydrodynamic quantum analogs in walking droplet using minimal dynamical models. Using reduced Lorenz-like dynamical descriptions derived from integrodifferential trajectory equations, we show how quantum-like statistical signatures such as Friedel-like oscillations, quantization, and tunnelling analogs, can emerge from purely local perturbations of the particle’s internal dynamical state. This perspective reveals a generic, attractor-driven route to quantum-like behaviour rooted in nonlinear dynamics, without requiring explicitly nonlocal wave-mediated interactions.

Collaborators

  • Julia Yeomans (University of Oxford, UK)
  • Sumesh Thampi (IIT Madras, India)
  • Tapio Simula (Swinburne University of Technology, Australia)
  • Anja Slim (Monash University, Australia)
  • Mohit Dalwadi (University of Oxford, UK)
  • Benjamin Walker (University College London, UK)
  • Shankar Srinivas (University of Oxford, UK)
  • David Paganin (Monash University, Australia)
  • Álvaro López (Universidad Rey Juan Carlos, Spain)
  • David Müller-Bender (Chemnitz University of Technology, Germany)
  • Yvonne Stokes (Adelaide University, Australia)
  • Brendan Harding (Victoria University of Wellington, New Zealand)
  • Divya Jaganathan (Harvard University, USA)
  • Rainer Klages (Queens Mary University of London, UK)
  • Esa Räsänen (Tampere University, Finland)
  • Aditya S. Khair (Carnegie Mellon University, USA)
  • Bruno S. Dandogbessi (UNSTIM, Benin)
  • Antarip Poddar (IIT Dhanbad, India)
  • Aritra Roy (IIT Bombay, India)
  • Yuanmei Li (Nanjing University, China)
  • Titir Mukherjee (IISER Kolkata, India)
  • Soumitro Banerjee (IISER Kolkata, India)
  • Matthew Durey (University of Glasgow, UK)
  • Diogo Pinto (University of Lisbon, Portugal)