arXiv subjects

L. Mahadevan

Publications and source records attributed to L. Mahadevan.

At least 19 recordsLinked to original sources

arXiv2026

Optimizing diffusion-limited transport, with applications to electrochemical systems

Transport in certain systems fails when diffusion cannot replenish or remove material from a boundary rapidly enough, causing the boundary concentration to reach a critical minimum or maximum. Motivated by experiments in electrochemical systems that demonstrate this diffusion-limited failure of charge transport, we determine dynamic current protocols that maximize charge transfer subject to a prescribed concentration constraint. The optimal protocol has a "bang-ride" structure: the maximum feasible current is used until the boundary concentration reaches its critical value, after which the current is progressively reduced to maintain that value. For semi-infinite domains, we derive the optimal currents analytically and obtain system-independent upper bounds on their improvement over constant-current operation. We also extend the framework to finite and multilayer domains and show that the same formulation applies to both charging and discharging.

cond-mat.soft↗

arXiv2026

LieStoNet: Learning Lie Symmetries from Spatiotemporal Data for Stochastic Dynamical Systems

Symmetry is central to modern machine learning and physics: invariances and equivariances improve sample efficiency, robustness, and out-of-distribution generalization, while symmetry principles guide scientific modeling. Yet for stochastic dynamical systems the relevant continuous symmetries are rarely known, and symmetry discovery for SDEs has remained essentially unexplored. We introduce \textit{LieStoNet}, an end-to-end, \emph{template-free} framework for discovering Lie-point symmetries of SDEs directly from spatiotemporal trajectories, without prespecifying symmetry groups, templates, or canonical coordinates. Building on the seminal SDE Lie-symmetry theory of Gaeta and Quintero (1999), which formalizes Lie-point SDE symmetries and their relation to Fokker-Planck symmetries, LieStoNet learns neural surrogates for drift and diffusion from increments, then learns projectable generators by enforcing the SDE determining equations, separately regularizing for closure under Lie brackets, adherence to the Lie algebra axioms (bilinearity, antisymmetry, Jacobi), and a non-redundant independent basis. The surrogate also defines an associated Fokker-Planck equation, enabling optional discovery of its Lie-point symmetries in parallel. Across multiple canonical SDEs with known analytic symmetries, LieStoNet recovers generators consistent with the ground-truth symmetry algebra, providing interpretable symmetry discovery for noisy dynamics. Code is available at \href{https://github.com/sumit-sinha-seas/LieStoNet_Final.git}{this link}.

cond-mat.stat-mech↗

arXiv2026

Elastohydrodynamic instability of a spinning elastic disk

A soft thin elastic disk spinning in a viscous fluid experiences centrifugal tension generated by rotation together with viscous shear generated by the surrounding flow. While the former stabilizes the flat state, the latter can destabilize it. We combine the linearized F\"{o}ppl-von K\'{a}rm\'{a}n equations for a rotating elastic disk with the shear stresses arising from the classical von K\'{a}rm\'{a}n swirling flow to derive an elastohydrodynamic stability problem. Linear stability analysis identifies the onset of buckling in terms of two dimensionless control parameters measuring centrifugal stiffening and fluid-induced shear. Above threshold the disk buckles into azimuthally periodic saddle-like modes whose wavenumber increases with increasing rotational tension. The buckled configuration also supports retrograde traveling waves that rotate more slowly than the material frame. These results identify a simple mechanism whereby fluid shear destabilizes rotating elastic structures.

physics.flu-dyn↗

arXiv2026

Self-propelled evolution on regenerating landscapes

Evolving populations both respond to and reshape their environments, making fitness landscapes dynamic rather than static. We present a minimal eco-evolutionary model that couples replicator dynamics for a population density with a regenerating resource-driven landscape through a single environmental sensitivity parameter. This allows evolving populations to generate and ride self-induced selection gradients, enabling directed motion in trait space even on initially flat landscapes. Our analysis reveals sustained oscillations, chaotic dynamics, and evolutionary branching. To explain these, we derive reduced dynamical equation that extend Fisher's fundamental theorem to deformable landscapes by incorporating curvature-driven variance dynamics and environmental feedback. Together, these results show how populations actively reshape and self-propel themselves on regenerating landscapes.

q-bio.PE↗

arXiv2026

When proofreading improves both speed and accuracy

Proofreading is generally thought to improve accuracy at the expense of speed. We show that this trade-off can be reversed in stochastic processes with long-lived stalled states. Using a non-Markovian renewal framework, we derive exact expressions for the error rate and completion time under proofreading for arbitrary stall-time distributions. Our analysis reveals that fluctuations in stall durations, rather than their mean alone, determine whether proofreading can simultaneously increase speed and accuracy. In the limit of strong stalling, this regime emerges when the coefficient of variation of the stall time exceeds a threshold set by the intrinsic error rate. These results provide a general criterion for proofreading in systems ranging from self-assembly and polymer replication to immune recognition and other nonequilibrium information-processing systems.

cond-mat.stat-mech↗

arXiv2026

How to grow a straight filament

How can a growing biological filament remain straight despite stochastic fluctuations in growth? Motivated by filamentary structures that develop reproducibly across biological systems, we study the stability of a noisy, growing elastic filament regulated by feedback. We formulate a minimal model in which growth responds to the filament's strain, curvature, and orientation through local or nonlocal spatiotemporal feedback laws. Linear stability analysis identifies the conditions under which these feedback mechanisms stabilize a straight configuration. In the presence of noise, we show that purely local feedback requires orientation sensing to suppress long-wavelength instabilities, whereas nonlocal feedback allows stabilization through proprioceptive (curvature) sensing alone. Coupling to an elastic substrate further suppresses large-scale fluctuations. Our results establish minimal control strategies that ensure robust straight growth and suggest experimental signatures for identifying the feedback mechanisms underlying morphogenesis.

cond-mat.soft↗

arXiv2026

Emergent cohesion via self-caging in maximally entangled rod packings

Random packings of disordered rigid rods exhibit emergent cohesion, as exemplified in a nest of twigs that is self-equilibrated, free-standing structures. We analyze the geometric motif underlying this cohesion using a rod packing that maximizes the average crossing number subject to non-penetration constraints. We show that this protocol leads to self-caging: collective geometric constraints that prevent rod escape even in finite systems with free boundaries, leading to packings that remain mechanically cohesive due to a combination of purely repulsive and frictional interactions. We show that self-caging is controlled by the available free-volume in translational and rotational configuration spaces, which is minimal when $N/(Z\alpha)=1/3$ where $N$ is the number of rods, $\alpha$ is the aspect ratio, and $Z$ is the average coordination number. Our results establish a minimal geometric motif for entanglement-induced cohesion in athermal rod packings, with implications for cohesive granular matter without attractive forces.

cond-mat.soft↗

arXiv2026

How geometry of subduction zones correlates with earthquake dynamics

Subduction zones on the surface of the Earth, where abrupt sliding leads to earthquakes, are generally curved and localized. How does the geometry of these zones influence the occurrence of megathrust earthquakes? Here we use a combination of simple scaling arguments and data analysis using the differential geometry of surfaces to examine the relationship between the earthquake productivity of subduction zones and their shape. A scaling argument suggests how interface curvature changes both the accumulation and release of stress relative to planar interfaces; conformable sliding along relatively flat subduction zones should lead to rare but large events, while curved subduction zones should lead to frequent smaller events. To test this, we leverage global geometry datasets and analyze the correlation between the surface curvatures of the subduction zones and the frequency and magnitude of earthquakes therein. Our analysis shows that weakly curved slab geometries are associated with rarer larger magnitude events, while slab geometries with a larger relative dispersion in curvature are associated with frequent but smaller magnitude events. Using different scale-dependent shape metrics of the subduction zones, we show that the earthquake productivity is influenced by the conformability of the overriding and downgoing plates. More broadly, our results suggest the need to incorporate the large-scale geometry of subduction zones in computational models and predictive frameworks for earthquake risk.

physics.geo-ph↗

arXiv2026

Generative optimal transport via forward-backward HJB matching

Controlling the evolution of a many-body stochastic system from a disordered reference state to a structured target ensemble, characterized empirically through samples, arises naturally in non-equilibrium statistical mechanics and stochastic control. The natural relaxation of such a system - driven by diffusion - runs from the structured target toward the disordered reference. The natural question is then: what is the minimum-work stochastic process that reverses this relaxation, given a pathwise cost functional combining spatial penalties and control effort? Computing this optimal process requires knowledge of trajectories that already sample the target ensemble - precisely the object one is trying to construct. We resolve this by establishing a time-reversal duality: the value function governing the hard backward dynamics satisfies an equivalent forward-in-time HJB equation, whose solution can be read off directly from the tractable forward relaxation trajectories. Via the Cole-Hopf transformation and its associated Feynman-Kac representation, this forward potential is computed as a path-space free energy averaged over these forward trajectories - the same relaxation paths that are easy to simulate - without any backward simulation or knowledge of the target beyond samples. The resulting framework provides a physically interpretable description of stochastic transport in terms of path-space free energy, risk-sensitive control, and spatial cost geometry. We illustrate the theory with numerical examples that visualize the learned value function and the induced controlled diffusions, demonstrating how spatial cost fields shape transport geometry analogously to Fermat's Principle in inhomogeneous media. Our results establish a unifying connection between stochastic optimal control, Schr\"odinger bridge theory, and non-equilibrium statistical mechanics.

cond-mat.stat-mech↗

arXiv2026

Embodied intelligence solves the centipede's dilemma

Although commonly associated with limbless animals like snakes and fish, multi-legged organisms like centipedes also utilize undulatory locomotion. Whether these undulations are actively reinforced or resisted by the axial musculature remains an open question. We present a dynamical model of centipede locomotion that integrates leg-ground interactions, passive body mechanics, and active lateral musculature. By varying stepping rate, actuation, and body stiffness, we examine how locomotor strategies affect speed and an effective energetic efficiency. Coordination emerges only when body stiffness is tuned to stepping frequency: overly flexible bodies lose synchrony, while overly rigid ones move slowly and inefficiently. This leads to the prediction that centipedes utilize speed dependent active stiffness to maintain this coordination. Our results suggest that lateral muscles also have a speed dependent function, revealed by optimizing speed and an effective cost, that resists a phase lag between leg touchdowns and body curvature. Together, we find that centipedes actively modulate body mechanics to achieve rapid, efficient locomotion, highlighting how complex control can emerge from embodied physical properties rather than solely from neural computation.

physics.bio-ph↗

arXiv2026

Rotational 3D printing of active-passive filaments and lattices with programmable shape morphing

Natural filaments, such as proteins, plant tendrils, octopus tentacles, and elephant trunks, can transform into arbitrary three-dimensional shapes that carry out vital functions. Their shape-morphing behavior arises from intricate patterning of active and passive regions, which are difficult to replicate in synthetic matter. Here, we introduce a filament-centric strategy for programmable shape morphing in which intrinsic curvature and twist are directly encoded within multimaterial elastomeric filaments during fabrication. By harnessing rotational multimaterial 3D printing (RM-3DP), we directly prescribe the filament's natural curvature--twist field $\mathbf{k}(s)$ through controlled material distribution and helical liquid crystal mesogen alignment. When heated above their nematic-to-isotropic transition temperature ($T_\mathrm{NI}$), the helically aligned LCE regions contract along their local director field, while passive regions remain essentially unchanged. This approach enables independent control of bending and torsion at every cross-section along the filament centerline: the principal natural curvatures of the filament along two orthogonal axes as well as the local twist. Next, we printed architected lattices composed of unit cells formed by sinusoidal filaments that either reversibly contract, expand, or exhibit out-of-plane deformations. Discrete elastic rod simulations of Janus filaments with different natural curvatures and twist, which are interconnected within the printed lattices, allow accurate prediction of their observed shape-morphing behavior. By integrating active-passive elastomers, additive manufacturing, and computational modeling, we have created shape-morphing matter with complex programmable responses for applications that rely on adaptive, robotic, or deployable architectures.

cond-mat.soft↗

arXiv2026

Evaporation-Induced Pattern Formation and Wetting in Active Microtubule-Kinesin Droplets

Active networks composed of biopolymers and motor proteins provide versatile biomimetic systems that have advanced active matter physics and deepened our understanding of cytoskeletal dynamics and self-organization under diverse stimuli. In these systems, activity arises in aqueous solutions where motor proteins cross-link biopolymers and generate active stress driving the emergent network behavior. Here, we establish the active network in the form of a sessile, multi-component droplet on a substrate and investigate how evaporation influences its dynamics. We focus on how mass loss and compositional changes in the droplet reshape the behavior of the active suspension. We show that capillary and Marangoni flows drive the self-organization of microtubules into a distinctive radial arrangement within the droplet. The cross-linking ability of motor proteins gives rise to a striking non-monotonic wetting behavior, where the extensile stresses generated by the motor proteins strongly affect the characteristic timescale of the contact-line retracting and subsequent expansion. Using a combined experimental and theoretical approach, we demonstrate the crucial role of crosslinking in evaporating microtubule networks, and explain how active stresses together with evaporation-induced flows govern the dynamics of reconstituted microtubule systems and their wetting behavior. Evaporating droplets have recently attracted significant attention in the scientific community, and the findings of the setup presented in this study can have broad implications, ranging from self-organization and mechanical pattern formation in biological systems to questions about the origin of life.

cond-mat.soft↗

arXiv2026

Stigmergic optimal transport

Efficient navigation in swarms often relies on the emergence of decentralized approaches that minimize traversal time or energy. Stigmergy, where agents modify a shared environment that then modifies their behavior, is a classic mechanism that can encode this strategy. We develop a theoretical framework for stigmergic transport by casting it as a stochastic optimal control problem: agents (collectively) lay and (individually) follow trails while minimizing expected traversal time. Simulations and analysis reveal two emergent behaviors: path straightening in homogeneous environments and path refraction at material interfaces, both consistent with experimental observations of insect trails. While reminiscent of Fermat's principle, our results show how local, noisy agent+field interactions can give rise to geodesic trajectories in heterogeneous environments, without centralized coordination or global knowledge, relying instead on an embodied slow fast dynamical mechanism.

q-bio.NC↗

arXiv2025

Surface wakes on ultra-soft solids

We explore the dynamical response of the free surface of an ultra-soft solid driven by a localized moving pressure disturbance. Experiments reveal a steady V-shaped wake analogous to a surface Mach wedge. A simple geometric argument provides a qualitative explanation consistent with observations. A theoretical framework combining elastodynamic, capillary, and gravitational effects yields a generalized dispersion relation that smoothly interpolates between Kelvin's theory of liquid interface wakes and Rayleigh's theory of elastic surface waves. Together, our experiments and theory reveal the existence of a soft wake regime that bridges fluid and solid surface wave physics, offering new routes for probing the dynamics of soft surfaces.

cond-mat.soft↗

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

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

Noise-enabled goal attainment in crowded collectives

In crowded environments, individuals must navigate around other occupants to reach their destinations. Understanding and controlling traffic flows in these spaces is relevant for coordinating robot swarms and designing infrastructure for dense populations. Here, we use simulations, theory, and experiments to study how adding stochasticity to agent motion can reduce traffic jams and help agents travel more quickly to prescribed goals. A computational approach reveals the collective behavior. Above a critical noise level, large jams do not persist. From this observation, we analytically approximate the swarm's goal attainment rate, which allows us to solve for the agent density and noise level that maximize the goals reached. Robotic experiments corroborate the behaviors observed in our simulated and theoretical results. Finally, we compare simple, local navigation approaches with a sophisticated but computationally costly central planner. A simple reactive scheme performs well up to moderate densities and is far more computationally efficient than a planner, motivating further research into robust, decentralized navigation methods for crowded environments. By integrating ideas from physics and engineering using simulations, theory, and experiments, our work identifies new directions for emergent traffic research.

cs.RO↗