Science and engineering of collective phenomena
From a scientific perspective, we are interested in studying this emergence, which involves understanding the relationship between the agent-interactions and the group-level phenomena, either as a forward problem where we build connections across scales from agents, all the way to the group or as an inverse problem where given data or any information about the group, we infer the characteristics of the agents and discover micro/macroscopic governing equations. At the same time, from an engineering perspective, we are interested in solving design problems where we are tasked in finding out if the agent-interactions or behavior can be altered, surroundings carefully designed, to orchestrate a particular collective behavior depending on the application at hand.
We employ a complex-systems approach, where a system is modeled as a collection of interacting agents. In this approach, the agents are not studied in isolation, but considered in relation to other agents and the environment with and through which they interact. Using an Agent Based Model (ABM) a bottom-up framework is built which integrates the domain specific agent-level information to explain the observations at the level of the collective. We also employ formalism from Network Science to understand how interactions at agent-level ultimately lead to interesting functionality at the level of the collective. We like to work at the interface of the physics of collectives and data-science research, where we combine ABMs with techniques from systems engineering and data science like optimization (sparse, evolutionary, etc.), classification, neural-networks, model-based feedback control, etc., to understand how dynamics of collectives affects the enterprise of inferring properties, gov equations, etc. from data. When it is difficult to derive simple models for interactions between agents, we develop data-physics hybrid models that integrates what we know of the physics of interactions to the data-based discovery of these rules. Some of the work we do involves performing data collection and analysis. Most often, the data collected is in the form of videos which have to be analysed; i.e. agents have to be detected and tracked to get the movement information. This data is essential for a number of reasons: 1) To test the predictions of the ABMs and improve the models and, 2) To develop methods to reliably discover the governing physics in the system and also build physics-data hybrid models.
DROPLET MICROFLUIDICS RESEARCH
Droplets interact nonlinearly with other droplets, the surrounding walls, fluid etc. to produce phenomena that are collective in nature. To engineer the motion of these droplets as desired, one has to first understand how a phenomenon at the droplet-level gives rise to the dynamics at the device-level. For this purpose we develop an agent based model (ABM) for droplet motion—where the hydrodynamics of the droplet-interactions are modeled using simple rules. The primary challenge, however, lies in identifying these rules that sufficiently explain the physics at hand while being computationally inexpensive. We studied how droplets self-organize in 2D microchannels using ABMs which were then incorporated into optimsation frameworks to identify non-trivial operating and design conditions to assemble droplets as desired. We discovered that the nature of the hydrodynamic interactions between droplets was directly associated with the design features of the microfluidic device such as the functionality and robustness. When these droplets self organise to form tightly packed assemblies in a 2D microchannel they exhibit coalescence avalanches; a phenomenon where coalescence of a pair of droplets triggers an avalanche of similar events that destabilizes the assembly. We studied the dynamic (and probabilistic) propagation of these avalanches using a stochastic verison of the ABM which housed a measure of the local propensity for coalescence propagation. The model captures the autocatalytic nature of avalanche growth, the dynamics of multiple interacting avalanches and explores the link between the observed ‘emergent’ features and the anisotropy in the propagation.
M Danny Raj and R. Rengaswamy, “Understanding drop-pattern formation in 2-D microchannels: a multi-agent approach”, Microfluid. Nanofluidics, vol. 17, no. 3, pp. 527–537, Jan. 2014.
M. Danny Raj and R. Rengaswamy, “Coalescence of drops in a 2D microchannel: critical transitions to autocatalytic behavior”, Soft Matter, vol. 12, no. 1, pp. 115-122, 2016.
M. Danny Raj, A. Gnanasekaran and R. Rengaswamy, “On the role of hydrodynamic interactions in the engineered assembly of droplet ensembles”, Soft Matter, 2019.
COLLECTIVE BEHAVIOUR IN SOCIAL ORGANISMS
Individual organisms are typically unaware of the group’s collective state and are only capable of limited cognition, and exhibit very simple rules of interaction and yet they exhibit remarkably robust global coordination that offers them advantages in foraging and protection against predator attack. Hence, it is interesting to understand how local interactions translate to useful functionality at the level of the group. Real fish are brought to a lab (expts done in TEELAB, IISc) and allowed to school in a large tank, where they are imaged and their motion is analyzed. Investigating the stochastic dynamics of an order parameter that characterizes how well a school is aligned, we find that interactions between fish are quite simple in nature: each fish interacts with only one neighboring fish at a time. This raises an interesting question, how do fish schools manage to stay cohesive (as a tight-knit group) and polarized (move together in a common direction) when interacting with just one fish from its local neighborhood? In a school with small number of fish, we find that when a fish copies the direction of another, it affects the overall order of a disordered school much more than that of an already ordered one. This results in the school residing in an ordered state for more time than in a disordered state—a classic example of state-dependent noise induced order. This feature manifests as a multiplicative noise term in a stochastic differential equation model of schooling. Interestingly, even when disorganized, we find the school to be cohesive. To understand how cohesion is achieved we turn to ex- plore which of its neighbors a fish interacts with§. Using a novel data-inspired spatial model for schooling fish, we probe into the conditions necessary to achieve cohesion. We find that fish interacting with just their nearest neighbor does not guarantee cohesion. However, if fish chose its neighbor randomly from a small set of nearby fish, the school was able to achieve cohesion—uncertainty in choice of neighbor gives rise to cohesion. Using a graph-theoretic framework, we show how the interactions between fish give rise to a well connected network when fish choose their neighbors randomly.
Jitesh Jhawar, Richard G. Morris, U. R. Amith-Kumar, M. Danny Raj, Tim Rogers, Harikrishnan R., Vishwesha Guttal, ‘Noise-Induced Schooling of Fish’, Nature Physics, vol 16, 2020.
Vivek Jadhav, Vishwesha Guttal and M Danny Raj*, “Randomness in the choice of neighbours promotes cohesion in mobile animal groups”, Royal Society Open Science, vol 9 issue 3, 2022.
INVERSE PROBLEMS IN TRAFFIC SYSTEMS
We take advantage of the similarities between traffic and granular flows, to solve a complex problem in one field using the existing knowledge in another. We explore the traffic problem of moving through a crowd, where an elite agent with priority for motion tries to maneuver through a dense crowd of agents that are otherwise inert: similar to the movement of an ambulance through a dense assembly of vehicles. The challenge here is to find out how a group of inert agents can make small coordinated movements that facilitate or shepherd the movement of the elite agent. In the study of granular flows, an intruder is forced through the medium and its motion is analyzed to understand the microrheology of the granular medium. The flow of grains typically follows a source-sink like pattern around the intruder. Here, since we are interested in the inverse microrheology problem where we want to find out how grains should move, we allow them to move based on a dipole traffic rule that has a source-sink like feature. We test the efficacy of the traffic rule using an agent based model. We find that the traffic rule, in general, increases the mobility of the elite. At intermediately high densities, motion is effected via ‘local melting’ of the crystallized agents—a phenomenon observed in the microrheological experiments of colloidal systems. At even higher densities, the traffic rule gives rise to a collective migration of the agents, despite being frozen. In another study, we explore the possibility of identifying the characteristics of agents from data of the collective. In the context of a composite crowd with two groups of agents, we explore how accurately an observer can classify agents according to their groups, using the data of the collective motion of the crowd. We find that collective effects affect the classification problem in interesting ways. When agents aggregate into clusters, they move faster and are more likely to be classified correctly. In contrast, in certain cases, we observe misclassifications to increase with increasing intrinsic speeds—a phenomenon reminiscent of the faster-is-slower effect. We trace its origins to a transition from a frozen state to a mobile state. Based on our understanding of these collective effects, we propose a new observer algorithm that incorporates information about inter-agent interactions, quantifying how the local neighborhood of an agent aids or hinders agent movement. This new observer, derived purely from phenomenology, is a data-agnostic classifier that is able to differentiate agents belonging to different groups even when their motion is identical
M Danny Raj* and Kumaran V, “Moving efficiently through a crowd: a nature inspired traffic rule”, Physical Review E, 104, 054609.
Arshed Nabeel and M Danny Raj*, “Disentangling intrinsic motion from neighbourhood effects in heterogeneous collective motion”, Chaos, 32, 063119 (2022).