arXiv subjects

L. Mahadevan

Publications and source records attributed to L. Mahadevan.

At least 37 records · Page 2Linked to original sources

arXiv2025

Hovering of an actively driven fluid-lubricated foil

Inspired by recent experimental observations of a harmonically excited elastic foil hovering near a wall while supporting substantial weight, we develop a theoretical framework that describes the underlying physical effects. Using elastohydrodynamic lubrication theory, we quantify how the dynamic deformation of the soft foil couples to the viscous fluid flow in the intervening gap. Our analysis shows that the soft foil rectifies the reversible forcing, breaking time-reversal symmetry; the relative spatial support of the forcing determines whether the sheet is attracted to or repelled from the wall. A simple scaling law predicts the time-averaged equilibrium hovering height and the maximum weight the sheet can sustain before detaching from the surface. Numerical simulations of the governing equation corroborate our theoretical predictions, are in qualitative agreement with experiments, and might explain the behavior of organisms while providing design principles for soft robotics.

physics.flu-dyn↗

arXiv2025

Self-organized adaptive branching in frangible matter

Soft and frangible materials that remodel under flow can give rise to branched patterns shaped by material properties, boundary conditions, and the time scales of forcing. We present a general theoretical framework for emergent branching in these frangible (or threshold) materials that switch abruptly from resisting flow to permitting flow once local stresses exceed a threshold, relevant for examples as varied as dielectric breakdown of insulators and the erosion of soft materials. Simulations in 2D and 3D show that branching is adaptive and tunable via boundary conditions and domain geometry, offering a foundation for self-organized engineering of functional transport architectures.

cond-mat.soft↗

arXiv2025

Optimal switching strategies for navigation in stochastic settings

When navigating complex environments, animals often combine multiple strategies to mitigate the effects of external disturbances. These modalities often correspond to different sources of information, leading to speed-accuracy trade-offs. Inspired by the intermittent reorientation strategy seen in the behavior of the dung beetle, we consider the problem of the navigation strategy of a correlated random walker moving in two dimensions. We assume that the heading of the walker can be reoriented to the preferred direction by paying a fixed cost as it tries to maximize its total displacement in a fixed direction. Using optimal control theory, we derive analytically and confirm numerically the strategy that maximizes the walker's speed, and show that the average time between reorientations scales inversely with the magnitude of the environmental noise. We then extend our framework to describe execution errors and sensory acquisition noise. As a result, we provide a range of testable predictions and suggest new experimental directions. Our approach may be amenable to other navigation problems involving multiple sensory modalities that require switching between egocentric and geocentric strategies.

cond-mat.stat-mech↗

arXiv2025

Viscous adhesion in vibrated sheets: elastohydrodynamics with inertia and compressibility effects

Inspired by recent experiments demonstrating that vibrating elastic sheets can function as seemingly contactless suction cups, we investigate the elastohydrodynamic hovering of a thin elastic sheet vibrating near a rigid substrate. Previous theoretical work suggests that the hovering height results from a balance between the active forcing that triggers the vibrations, the bending forces associated with the sheet's deformation, the viscous lubrication flow between the sheet and the substrate, and the sheet's weight. Here, we extend this analysis beyond the asymptotic regime of weak forcing and explore the regime of strong forcing through numerical simulations. We further quantify the influence of fluid inertia and compressibility on the equilibrium hovering height and the maximum load that can be supported. Both effects are found to introduce repulsive contributions to the net force on the sheet, which can significantly reduce its adhesive strength. Beyond providing insights into soft contactless grippers and swimming near surfaces, our analysis is relevant to the elastohydrodynamics of squeeze films and near-field acoustic levitation.

physics.flu-dyn↗

arXiv2025

Collective synchrony in confluent, pulsatile epithelia

Collective cell migration lies at the intersection of developmental biology and non-equilibrium physics, where active processes give rise to emergent patterns that are biologically relevant. Here, we investigate dilatational modes--cycles of expansion and contraction--in epithelial monolayers, and show that the divergence of the velocity field exhibits robust, large-scale temporal oscillations. These oscillatory patterns, reminiscent of excitable media and their biological analogs, emerge spontaneously from the coupled dynamics of actively pulsing cells. We find that the temporal persistence of these oscillations varies non-monotonically with cell density: synchrony initially increases with density, reaches a maximum at intermediate densities and is lost at higher values. This trend mirrors changes in the spatial correlation length of cell-cell interactions, and the density of topological defects in the system, suggesting a shared physical origin. We develop a continuum model in which a complex-valued Ginzburg-Landau-type field that governs the amplitude and phase of oscillations is coupled to local cell density. Simulations reproduce the observed behavior, revealing that local density adapts to phase patterns, reinforcing temporal coherence up to a critical density, and variations in the density of topological defects as a function of cell density. Extending our analysis to breast cancer cell lines with increasing invasiveness, we find that malignant cells exhibit longer phase persistence and fewer topological defects, suggesting a mechanistic link between temporal coherence and metastatic potential. Together, these results highlight the role of density-dependent synchrony dynamics as a fundamental, quantifiable mode of collective behavior in active epithelial matter, with implications for morphogenesis, cancer progression, and tissue diagnostics.

cond-mat.soft↗

arXiv2025

Thin active nematohydrodynamic layers: asymptotic theories and instabilities

Starting from a three-dimensional description of an active nematic layer, we employ an asymptotic theory to derive a series of low-dimensional continuum models that capture the coupled dynamics of flat and curved films, including variations in film thickness, shape deformations, internal velocity fields, and the dynamics of orientational order. Using this asymptotic theory, we investigate instabilities driven by activity in both the nematic and isotropic phases for cylindrical and flat films. In the flat case, we demonstrate that incorporating shape and thickness variations fundamentally alters the bend and splay nature of instabilities compared to conventional two dimensional nematic instabilities. In the isotropic phase, we find that both extensile and contractile activity can induce nematic order, in contrast with active nematics on fixed surfaces, where only extensile activity leads to ordering. For the case of curved geometries such as a cylindrical film, we reveal that thickness and shape instabilities are inherently coupled. In the isotropic phase, the emergence of nematic order triggers both thickness and shape instabilities. In the nematic phase, contractile activity induces thickness instabilities, which in turn drive geometric deformations. Our results highlight the crucial interplay between activity, thickness variations, and curvature, providing new insights into the behavior of active nematic films beyond the conventional two dimensional paradigm that has been studied to date.

cond-mat.soft↗

arXiv2025

Stochastic elastohydrodynamics of soft valves

Soft valves serve to modulate and rectify flows in complex vasculatures across the tree of life, e.g. in the heart of every human reading this. Here we consider a minimal physical model of the heart mitral valve modeled as a flexible conical shell capable of flow rectification via collapse and coaptation in an impinging (reverse) flow. Our experiments show that the complex elastohydrodynamics of closure features a noise-activated rectification mechanism. A minimal theoretical model allows us to rationalize our observations while illuminating a dynamical bifurcation driven by stochastic hydrodynamic forces. Our theory also suggests a way to trigger the coaptation of soft valves on demand, which we corroborate using experiments, suggesting a design principle for their efficient operation.

cond-mat.soft↗

arXiv2025

Orientational ordering in active nematic solids

In vivo and in vitro systems of cells and extra-cellular matrix (ECM) systems are well known to form ordered patterns of orientationally aligned fibers. Here, we interpret them as active analogs of the (disordered) isotropic to the (ordered) nematic phase transition seen in passive liquid crystalline elastomers. A minimal theoretical framework that couples cellular activity (embodied as mechanical stress) and the finite deformation elasticity of liquid crystal elastomers sets the stage to explain these patterns. Linear stability analysis of the governing equations about simple homogeneous isotropic base states shows how the onset of periodic morphologies depends on the activity, elasticity, and applied strain, provides an expression for the wavelength of the instability, and is qualitatively consistent with observations of cell-ECM experiments. Finite element simulations of the nonlinear problem corroborate the results of linear analysis. These results provide quantitative insights into the onset and evolution of nematic order in cell-matrix composites.

cond-mat.soft↗

arXiv2025

Image Reconstruction from an Elastically Distorted Scan

We consider the problem of inverting the artifacts associated with scanning a page from an open book, i.e. "xeroxing." The process typically leads to a non-uniform combination of distortion, blurring and darkening owing to the fact that the page is bound to a stiff spine that causes the sheet of paper to be bent inhomogeneously. Complementing purely data-driven approaches, we use knowledge about the geometry and elasticity of the curved sheet to pose and solve a minimal physically consistent inverse problem to reconstruct the image. Our results rely on 3 dimensionless parameters, all of which can be measured for a scanner, and show that we can improve on the data-driven approaches. More broadly, our results might serve as a "textbook" example and a tutorial of how knowledge of generative mechanisms can speed up the solution of inverse problems.

eess.IV↗

arXiv2025

Lyapunov-Schmidt bifurcation analysis of a supported compressible elastic beam

The archetypal instability of a structure is associated with the eponymous Euler beam, modeled as an inextensible curve which exhibits a supercritical bifurcation at a critical compressive load. In contrast, a soft compressible beam is capable of a subcritical instability, a problem that is far less studied, even though it is increasingly relevant in the context of soft materials and structures. Here, we study the stability of a soft extensible elastic beam on an elastic foundation under the action of a compressive axial force, using the Lyapunov-Schmidt reduction method which we corroborate with numerical calculations. Our calculated bifurcation diagram differs from those associated with the classical Euler-Bernoulli beam, and shows two critical loads, $p^\pm_{\text{cr}}(n)$, for each buckling mode $n$. The beam undergoes a supercritical pitchfork bifurcation at $p^+_{\text{cr}}(n)$ for all $n$ and slenderness. Due to the elastic foundation, the lower order modes at $p^-_{\text{cr}}(n)$ exhibit subcritical pitchfork bifurcations, and perhaps surprisingly, the first supercritical pitchfork bifurcation point occurs at a higher critical load. The presence of the foundation makes it harder to buckle the elastic beam, but when it does so, it tends to buckle into a more undulated shape. Overall, we find that an elastic support can lead to a myraid of buckled shapes for the classical elastica and one can tune the substrate stiffness to control desired buckled modes -- an experimentally testable prediction.

physics.class-ph↗

arXiv2024

Kinetically arrested clusters in active filament arrays

We use Brownian dynamics simulations and theory to study the over-damped spatiotemporal dynamics and pattern formation in a fluid-permeated array of equally spaced, active, elastic filaments that are pinned at one end and free at the other. The filaments are modeled as connected colloidal chains with activity incorporated via compressive follower forces acting along the filament backbone. The length of the chains is smaller than the thermal persistence length. For a range of filament separation and activity values, we find that the filament array eventually self-assembles into a series of regularly spaced, kinetically arrested, compact clusters. Filament activity, geometry, elasticity, and grafting density are each seen to crucially influence the size, shape, and spacing of emergent clusters. Furthermore, cluster shapes for different grafting densities can be rescaled into self-similar forms with activity-dependent scaling exponents. We derive theoretical expressions that relate the number of filaments in a cluster and the spacing between clusters, to filament activity, filament elasticity, and grafting density. Our results provide insight into the physical mechanisms involved in the initiation of clustering and suggest that steric contact forces and friction balance active forces and filament elasticity to stabilize the clusters. Our simulations suggest design principles to realize filament-based clusters and similar self-assembling biomimetic materials using active colloids or synthetic microtubule-motor systems.

cond-mat.soft↗

arXiv2024

Exploitation-exploration transition in the physics of fluid-driven branching

Self-organized branching structures can emerge spontaneously as interfacial instabilities in both simple and complex fluids, driven by the interplay between bulk material rheology, boundary constraints, and interfacial forcing. In our experiments, injecting dye between a source and a sink in a Hele-Shaw cell filled with a yield-stress fluid reveals an abrupt transition in morphologies as a function of injection rate. Slow injection leads to a direct path connecting the source to the sink, while fast injection leads to a rapid branching morphology that eventually converges to the sink. This shift from an exploitative (direct) to an exploratory (branched) strategy resembles search strategies in living systems; however, here it emerges in a simple physical system from a combination of global constraints (fluid conservation) and a switch-like local material response. We show that the amount of fluid needed to achieve breakthrough is minimal at the transition, and that there is a trade-off between speed and accuracy in these arborization patterns. Altogether, our study provides an embodied paradigm for fluidic computation driven by a combination of local material response (body) and global boundary conditions (environment).

cond-mat.soft↗

arXiv2024

Emergent functional dynamics of link-bots

Synthetic active collectives, composed of many nonliving individuals capable of cooperative changes in group shape and dynamics, hold promise for practical applications and for the elucidation of guiding principles of natural collectives. However, the design of collective robotic systems that operate effectively without intelligence or complex control at either the individual or group level is challenging. We investigate how simple steric interaction constraints between active individuals produce a versatile active system with promising functionality. Here we introduce the link-bot: a V-shape-based, single-stranded chain composed of active bots whose dynamics are defined by its geometric link constraints, allowing it to possess scale- and processing-free programmable collective behaviors. A variety of emergent properties arise from this dynamic system, including locomotion, navigation, transportation, and competitive or cooperative interactions. Through the control of a few link parameters, link-bots show rich usefulness by performing a variety of divergent tasks, including traversing or obstructing narrow spaces, passing by or enclosing objects, and propelling loads in both forward and backward directions. The reconfigurable nature of the link-bot suggests that our approach may significantly contribute to the development of programmable soft robotic systems with minimal information and materials at any scale.

cond-mat.soft↗

arXiv2024

Hamiltonian bridge: A physics-driven generative framework for targeted pattern control

Patterns arise spontaneously in a range of systems spanning the sciences, and their study typically focuses on mechanisms to understand their evolution in space-time. Increasingly, there has been a transition towards controlling these patterns in various functional settings, with implications for engineering. Here, we combine our knowledge of a general class of dynamical laws for pattern formation in non-equilibrium systems, and the power of stochastic optimal control approaches to present a framework that allows us to control patterns at multiple scales, which we dub the "Hamiltonian bridge". We use a mapping between stochastic many-body Lagrangian physics and deterministic Eulerian pattern forming PDEs to leverage our recent approach utilizing the Feynman-Kac-based adjoint path integral formulation for the control of interacting particles and generalize this to the active control of patterning fields. We demonstrate the applicability of our computational framework via numerical experiments on the control of phase separation with and without a conserved order parameter, self-assembly of fluid droplets, coupled reaction-diffusion equations and finally a phenomenological model for spatio-temporal tissue differentiation. We interpret our numerical experiments in terms of a theoretical understanding of how the underlying physics shapes the geometry of the pattern manifold, altering the transport paths of patterns and the nature of pattern interpolation. We finally conclude by showing how optimal control can be utilized to generate complex patterns via an iterative control protocol over pattern forming pdes which can be casted as gradient flows. All together, our study shows how we can systematically build in physical priors into a generative framework for pattern control in non-equilibrium systems across multiple length and time scales.

cond-mat.soft↗

arXiv2024

Emergent Strategies for Shepherding a Flock

We investigate how a shepherd should move to effectively herd a flock towards a target. Using an agent-based (ABM) and a coarse-grained (ODE) model for the flock, we pose and solve for the optimal strategy of a shepherd that must keep the flock cohesive and coerce it towards a target. Three distinct strategies emerge naturally as a function of the scaled herd size {and} the scaled shepherd speed: (i) mustering, where the shepherd circles the herd to ensure compactness, (ii) droving, where the shepherd chases the herd in a desired direction while sweeping back and forth, and (iii) driving, where the flock surrounds a shepherd that drives it from within. A minimal dynamical model for the size, shape, and position of the herd captures the effective behavior of the ABM and further allows us to characterize the different herding strategies in terms of the behavior of the shepherd that librates (mustering), oscillates (droving), or moves steadily (driving).

cond-mat.soft↗

arXiv2024

Entanglement transition in random rod packings

Random packings of stiff rods are self-supporting mechanical structures stabilized by long range interactions induced by contacts. To understand the geometrical and topological complexity of the packings, we first deploy X-ray computerized tomography to unveil the structure of the packing. This allows us to directly visualize the spatial variations in density, orientational order and the entanglement, a mesoscopic field that we define in terms of a local average crossing number, a measure of the topological complexity of the packing. We find that increasing the aspect ratio of the constituent rods in a packing leads to a proliferation of regions of strong entanglement that eventually percolate through the system, and correlated with a sharp transition in the mechanical stability of the packing. To corroborate our experimental findings, we use numerical simulations of contacting elastic rods and characterize their stability to static and dynamic loadings. Our experiments and computations lead us to an entanglement phase diagram which we also populate using published experimental data from pneumatically tangled filaments, worm blobs, and bird nests along with additional numerical simulations using these data sets. Together, these show the regimes associated with mechanically stable entanglement as a function of the statistics of the packings and loading, with lessons for a range of systems from reconfigurable architectures and textiles to active morphable filamentous assemblies.

cond-mat.soft↗

arXiv2024

Textile hinges enable extreme properties of mechanical metamaterials

Mechanical metamaterials -- structures with unusual properties that emerge from their internal architecture -- that are designed to undergo large deformations typically exploit large internal rotations, and therefore, necessitate the incorporation of flexible hinges. In the mechanism limit, these metamaterials consist of rigid bodies connected by ideal hinges that deform at zero energy cost. However, fabrication of structures in this limit has remained elusive. Here, we demonstrate that the fabrication and integration of textile hinges provides a scalable platform for creating large structured metamaterials with mechanism-like behaviors. Further, leveraging recently introduced kinematic optimization tools, we demonstrate that textile hinges enable extreme shape-morphing responses, paving the way for the development of the next generation of mechanism-based metamaterials.

cond-mat.soft↗

arXiv2024

Controlling moving interfaces in solid state batteries

Safe, all-solid-state lithium metal batteries enable high energy density applications, but suffer from instabilities during operation that lead to rough interfaces between the metal and electrolyte and subsequently cause void formation and dendrite growth that degrades performance and safety. Inspired by the morphogenetic control of thin lamina such as tree leaves that robustly grow into flat shapes -- we propose a range of approaches to control lithium metal stripping and plating. To guide discovery of materials that will implement these feedback mechanisms, we develop a reduced order model that captures couplings between mechanics, interface growth, temperature, and electrochemical variables. We find that long-range feedback is required to achieve true interface stability, while approaches based on local feedback always eventually grow into rough interfaces. All together, our study provides the beginning of a practical framework for analyzing and designing stable electrochemical interfaces in terms of the mechanical properties and the physical chemistry that underlie their dynamics.

cond-mat.mtrl-sci↗