S Ganga Prasath’s research while affiliated with Harvard University and other places

Posture and its control are fundamental aspects of animal behavior that capture the complex interplay between sensorimotor activity driven by muscular forces and mediated by environmental feedback. An extreme example of this is seen in brown tree snakes and juvenile pythons, which can stand almost upright, with 70% of their body length in the air. We quantify experimental observations of this behavior and present a minimal theoretical framework for postural stability by modeling the snake as an active elastic filament whose shape is controlled by muscular forces. We explore two approaches to characterize the musculature needed to achieve a specific posture: proprioceptive feedback (whereby the snake senses and reacts to its own shape) and a control-theoretic optimization approach (whereby the snake minimizes the expended energy to stand up), and also analyze the dynamic stability of the snake in its upright pose. Our results lead to a three-dimensional postural stability diagram in terms of muscle extent and strength, and gravity, consistent with experimental observations. In addition to general predictions about posture control in animals, our study suggests design principles for robotic mimics.

Particle-laden flows are ubiquitous, ranging across systems such as platelets in blood, dust storms, marine snow, and cloud droplets. The dynamics of a small particle in such non-uniform flows, under the idealization of being rigid and spherical, is described by the Maxey–Riley–Gatignol equation, which includes the Basset–Boussinesq history force among other better-understood forces. The history force, which is an integral over time with a weakly singular kernel, is often neglected, not because such neglect is known to be justified, but because it is difficult to be included in general scenarios. It is becoming increasingly evident that there are situations where neglecting this force might not be valid. In this review, after introducing classical knowledge about the history force, we outline recent studies that suggest alternative forms for it and discuss the range of validity of each, and describe recent numerical methods that have been developed to efficiently compute the history force. The question of whether the history force matters requires careful consideration and can be settled only with its accurate inclusion. We hope this review will help researchers addressing the multitude of open questions related to particulate flows to account for this effect.

Recent studies of elastocapillary phenomena have triggered interest in a basic variant of the classical Young-Laplace-Dupré (YLD) problem: the capillary interaction between a liquid drop and a thin solid sheet of low bending stiffness. Here we consider a two-dimensional model where the sheet is subjected to an external tensile load and the drop is characterized by a well-defined Young's contact angle θY. Using a combination of numerical, variational, and asymptotic techniques, we discuss wetting as a function of the applied tension. We find that, for wettable surfaces with 0<θY<π/2, complete wetting is possible below a critical applied tension due to the deformation of the sheet in contrast with rigid substrates requiring θY=0. Conversely, for very large applied tensions, the sheet becomes flat and the classical YLD situation of partial wetting is recovered. At intermediate tensions, a vesicle forms in the sheet, which encloses most of the fluid, and we provide an accurate asymptotic description of this wetting state in the limit of small bending stiffness. We show that bending stiffness, however small, affects the entire shape of the vesicle. Rich bifurcation diagrams involving partial wetting and “vesicle” solution are found. For moderately small bending stiffnesses, partial wetting can coexist with both the vesicle solution and complete wetting. Finally, we identify a tension-dependent bendocapillary length, λBC, and find that the shape of the drop is determined by the ratio A/λBC2, where A is the area of the drop.

The physics of signal propagation in a collection of organisms that communicate with each other both enables and limits how active excitations at the individual level reach, recruit and lead to collective patterning. Inspired by the spatio-temporal patterns in a planar swarm of bees that use pheromones and fanning flows to recruit additional bees, we develop a theoretical framework for patterning via active flow-based recruitment. Our model generalizes the well-known Patlak–Keller–Segel model of diffusion dominated aggregation and leads to an enhanced phase space of patterns spanned by two dimensionless parameters that measure the scaled stimulus/activity and the scaled chemotactic response. Together these determine the efficacy of signal communication via fluid flow (which we dub rheomergy ) that leads to a variety of migration and aggregation patterns, consistent with observations.

The solution of complex problems by the collective action of simple agents in both biologically evolved and synthetically engineered systems involves cooperative action. Understanding the resulting emergent solutions requires integrating across the organismal behaviors of many individuals. Here we investigate an ecologically relevant collective task in black carpenter ants Camponotus pennsylvanicus: excavation of a soft, erodible confining corral. Individual ants show a transition from individual exploratory excavation at random locations to spatially localized collective exploitative excavation and eventual excavate out from the corral. An agent minimal continuum theory that coarse-grains over individual actions and considers their integrated influence on the environment leads to the emergence of an effective phase space of behaviors in terms of excavation strength and cooperation intensity. To test the theory over the range of both observed and predicted behaviors, we used custom-built robots (RAnts) that respond to stimuli to characterize the phase space of emergence (and failure) of cooperative excavation. By tuning the amount of cooperation between RAnts, we found that we could vary the efficiency of excavation and synthetically generate the other macroscopic phases predicted by our theory. Overall, our approach shows how the cooperative completion of tasks can arise from simple rules that involve the interaction of agents with a dynamically changing environment that serves as both an enabler and a modulator of behavior.

Cooperative task execution, a hallmark of eusociality, is enabled by local interactions between the agents and the environment through a dynamically evolving communication signal. Inspired by the collective behavior of social insects whose dynamics is modulated by interactions with the environment, we show that a robot collective can successfully nucleate a construction site via a trapping instability and cooperatively build organized structures. The same robot collective can also perform de-construction with a simple change in the behavioral parameter. These behaviors belong to a two-dimensional phase space of cooperative behaviors defined by agent-agent interaction (cooperation) along one axis and the agent-environment interaction (collection and deposition) on the other. Our behavior-based approach to robot design combined with a principled derivation of local rules enables the collective to solve tasks with robustness to a dynamically changing environment and a wealth of complex behaviors.

There have been a number of pharmaceutical and non-pharmaceutical interventions associated with COVID-19 over the past two years. Various non-pharmaceutical interventions were proposed and implemented to control the spread of the COVID-19 pandemic. Most common of these were partial and complete lockdowns that were used in an attempt to minimize the costs associated with mortality, economic losses and social factors, while being subject to constraints such as finite hospital capacity. Here, we use a minimal model posed in terms of optimal control theory to understand the costs and benefits of such strategies. This allows us to determine top-down policies for how to restrict social contact rates given an age-structured model for the dynamics of the disease. Depending on the relative weights allocated to mortality and socioeconomic losses, we see that the optimal strategies range from long-term social-distancing only for the most vulnerable, partial lockdown to ensure not over-running hospitals, and alternating-shifts, all of which lead to significant reduction in mortality and/or socioeconomic losses. Crucially, commonly used strategies that involve long periods of broad lockdown are almost never optimal, as they are highly unstable to reopening and entail high socioeconomic costs. Using parameter estimates from data available for Germany and the USA early in the pandemic, we quantify these policies and use sensitivity analysis in the relevant model parameters and initial conditions to determine the range of robustness of our policies. Finally we also discuss how bottom-up behavioral changes affect the dynamics of the pandemic and show how they can work in tandem with top-down control policies to mitigate pandemic costs even more effectively.

The physics of signal propagation in a collection of organisms that communicate with each other both enables and limits how active excitations at the individual level reach, recruit and lead to collective patterning. Inspired by the patterns in a planar swarm of bees that release pheromones, and use fanning flows to recruit additional bees, we develop a theoretical framework for patterning via active flow-based recruitment. Our model generalizes the well-known Patlak-Keller-Segel model of diffusion-dominated aggregation and leads to more complex phase space of patterns spanned by two dimensionless parameters that measure the scaled stimulus/activity and the scaled chemotactic response. Together these determine the efficacy of signal communication that leads to a variety of migration and aggregation patterns consistent with observations.

Recent studies of elasto-capillary phenomena have triggered interest in a basic variant of the classical Young-Laplace-Dupr\'e (YLD) problem: The interaction between a liquid drop and a thin solid sheet of low bending stiffness. Here we consider a two-dimensional model where the sheet is subjected to an external tensile load and assume that the solid surface is characterised by a well-defined Young's contact angle $\theta_Y$. Using a combination of numerical, variational, and asymptotic techniques, we discuss wetting as a function of the applied tension. We find that, for wettable surfaces, with $0<\theta_Y<\pi/2$, complete wetting is possible below a critical applied tension thanks to the deformation of the sheet. Conversely, for very large applied tensions, the sheet becomes flat and the classical YLD situation of partial wetting is recovered. At intermediate tensions, a vesicle forms in the sheet, which encloses most of the fluid and we provide an accurate asymptotic description of this vesicle. We show that bending stiffness, however small, affects the entire shape of the vesicle. Rich bifurcation diagrams involving partial wetting and "vesicle" solution are found. For moderately small bending stiffnesses, partial wetting can coexist both with the vesicle solution and complete wetting.

Significance Existing shape-morphing materials and structures are limited in their ability to transition between a few stable configurations. Here we show how to create structural materials that have an arbitrary range of shape-morphing capabilities using the idea of neutral stability, as embedded in a unit cell with a range of energetically equivalent configurations. These structures allow for a decoupling of the local and global geometry from the local and global mechanical response and thus allow for independent control of the structure and mechanics, laying the foundation for engineering functional shapes using a new type of morphable unit cell.