arXiv subjects

Ronojoy Adhikari

Publications and source records attributed to Ronojoy Adhikari.

At least 19 recordsLinked to original sources

arXiv2026

Coupling between Phase Separation and Geometry on a Closed Elastic Curve: Free Energy Minimization and Dynamics

We study the free energy and dynamics of a closed elastic filament (a one-dimensional curve in two dimensions) coupled to a scalar concentration field representing, for example, an absorbed species. The density variable has a tendency to phase-separate whereas the local spontaneous curvature is concentration-dependent. We address analytically and by simulation both the free energy landscape and the dynamics (the latter comprising a coupled Willmore flow and Cahn--Hilliard gradient flow on the full differential geometry of a closed filament), addressing issues that previous work typically sidestepped by restricting to the Monge gauge. Specifically we find that the closure constraint for a deformable filament qualitatively changes the free energy landscape compared with either a rigid closed filament or an open elastic one, admitting metastable and stable states with more than one domain of each type. By numerical global free energy minimization we explore equilibrium morphologies across a wide range of model parameters. For selected parameter values we present fully dynamical results, tracking the time evolution of the various contributions to the free energy and confirming the emergence of both metastable and equilibrium multi-domain morphologies.

cond-mat.soft↗

arXiv2026

Shape-space dynamics and geometric pattern formation in nonreciprocal slender bodies

Nonreciprocal interactions in active solids violate action-reaction symmetry and produce a net response to strain. Assuming invariance under Euclidean symmetries, we derive a shape-space formulation for the elastohydrodynamics of nonreciprocal slender bodies that separates intrinsic deformation from rigid motion. The resulting nonlinear reaction-advection-diffusion system represents a geometric flow whose activity-driven instabilities generate steady, oscillatory, and chaotic patterns. These manifest as rigid, swimming, and chaotic motion, linking nonreciprocal elastohydrodynamics to geometric pattern formation and unifying recent observations in slender active structures.

cond-mat.soft↗

arXiv2025

Geometric Field Theory for Elastohydrodynamics of Cosserat Rods

Slender structures are ubiquitous in biological and physical systems, from bacterial flagella to soft robotic arms. The Cosserat rod provides a mathematical framework for slender bodies that can stretch, shear, twist and bend. In viscous fluid environments at low Reynolds numbers - as encountered in soft matter physics, biophysics, and soft continuum robotics - inertial effects become negligible, and hydrodynamic forces are well approximated by Stokes friction. We demonstrate that the resulting elastohydrodynamic equations of motion, when formulated using Cartan's method of moving frames, possess the structure of a geometric field theory in which the configuration field takes values in SE(3), the Lie group of rigid body motions. This geometric formulation yields coordinate-independent equations that are manifestly invariant under spatial isometries and naturally suited to constitutive modeling based on Curie's principle. We derive integrability conditions that determine when constitutive laws can be derived from an energy functional, thereby distinguishing between passive and active material responses. We also obtain the beam limit for small deformations. Our results establish a unified geometric framework for the nonlinear mechanics of slender structures in slow viscous flow and enable efficient numerical solutions.

cond-mat.soft↗

arXiv2025

Elastohydrodynamic instabilities of a soft robotic arm in a viscous fluid

The design and control of soft robots operating in fluid environments requires a careful understanding of the interplay between large elastic body deformations and hydrodynamic forces. Here we show that this interplay leads to novel elastohydrodynamic instabilities in a clamped soft robotic arm driven terminally by a constant pressure in a viscous fluid. We model the arm as a Cosserat rod that can stretch, shear and bend. We obtain invariant, geometrically exact, non-linear equations of motion by using Cartan's method of moving frames. Stability to small perturbations of a straight rod is governed by a non-Hermitian linear operator. Eigenanalysis shows that stability is lost through a Hopf bifurcation with the increase of pressure above a first threshold. A surprising return to stability is obtained with further increase of pressure beyond a second threshold. Numerical solutions of the non-linear equations, using a geometrically exact spectral method, confirms stable limit-cycle oscillations between these two pressure thresholds. An asymptotic analysis in the beam limit rationalizes these results analytically. This counterintuitive sequence of bifurcations underscores the subtle nature of the elastohydrodynamic coupling in Cosserat rods and emphasizes their importance for the control of the viscous dynamics of soft robots.

cond-mat.soft↗

arXiv2025

Nonreciprocal constitutive laws for oriented active solids

We present an overdamped continuum description of oriented active solids in which interactions respect the symmetries of space but do not obey the principle of action and reaction. Taking position and orientation as kinematic variables, we examine the conservation of the linear and angular momentum variables in an elementary volume. We find that nonreciprocal interactions yield, in addition to the areal stresses and moment stresses of classical elasticity, volumetric forces and torques that act as local sources of momentum and angular momentum. Since, by symmetry, these can only depend on the strains, nonreciprocity requires the extension of constitutive modeling to strain-dependent volumetric forces and torques. Using Cartan's method of moving frames and Curie's principle, we derive the materially linear constitutive law that underpins the nonreciprocal, geometrically nonlinear elasticity of the continuum. We study this constitutive law exhaustively for a one-dimensional active solid and identify striking nonreciprocal effects - traveling waves, linear instabilities, spontaneous motion of and about the center of mass - that are absent in a passive, reciprocally interacting solid. Numerical simulations of a particulate active solid model, consisting of a linear assembly of hydrodynamically interacting active particles, yields long-wavelength behavior that is in excellent agreement with theory. Our study provides the foundation for a principled macroscopic mechanics of oriented active solids with symmetry-invariant, nonreciprocal microscopic interactions.

cond-mat.soft↗

arXiv2025

Paramagnetism in spherically confined charged active matter

The celebrated theorem of Bohr and van Leeuwen guarantees that a classical charged system cannot have a magnetization in thermal equilibrium. Quantum mechanically, however, a diamagnetic response is obtained. In contrast, we show here that a classical charged active system, consisting of a motile particle confined to the surface of a sphere, has a nonzero magnetization and a paramagnetic response. We numerically sample Langevin trajectories of this system and compare with limiting analytical solutions of the Fokker-Planck equation, at small and large temperatures, to find excellent agreement in the magnetic response. Our Letter suggests experimental routes to controlling and extracting work from charged active matter.

cond-mat.soft↗

arXiv2024

Fluctuating hydrodynamics of an autophoretic particle near a permeable interface

We study the autophoretic motion of a spherical active particle interacting chemically and hydrodynamically with its fluctuating environment in the limit of rapid diffusion and slow viscous flow. Then, the chemical and hydrodynamic fields can be expressed in terms of integrals. The resulting boundary-domain integral equations provide a direct way of obtaining the traction on the particle, requiring the solution of linear integral equations. An exact solution for the chemical and hydrodynamic problems is obtained for a particle in an unbounded domain. For motion near boundaries, we provide corrections to the unbounded solutions in terms of chemical and hydrodynamic Green's functions, preserving the dissipative nature of autophoresis in a viscous fluid for all physical configurations. Using this, we give the fully stochastic update equations for the Brownian trajectory of an autophoretic particle in a complex environment. First, we analyse the Brownian dynamics of particles capable of complex motion in the bulk. We then introduce a chemically permeable planar surface of two immiscible liquids in the vicinity of the particle and provide explicit solutions to the chemo-hydrodynamics of this system. Finally, we study the case of an isotropically phoretic particle hovering above an interface as a function of interfacial solute permeability and viscosity contrast.

cond-mat.soft↗

arXiv2024

Intrinsic Langevin dynamics of rigid inclusions on curved surfaces

The stochastic dynamics of a rigid inclusion constrained to move on a curved surface has many applications in biological and soft matter physics, ranging from the diffusion of passive or active membrane proteins to the motion of phoretic particles on liquid-liquid interfaces. Here we construct intrinsic Langevin equations for an oriented rigid inclusion on a curved surface using Cartan's method of moving frames. We first derive the Hamiltonian equations of motion for the translational and rotational momenta in the body frame. Surprisingly, surface curvature couples the linear and angular momenta of the inclusion. We then add to the Hamiltonian equations linear friction, white noise and arbitrary configuration-dependent forces and torques to obtain intrinsic Langevin equations of motion in phase space. We provide the integrability conditions, made non-trivial by surface curvature, for the forces and torques to admit a potential, thus distinguishing between passive and active stochastic motion. We derive the corresponding Fokker-Planck equation in geometric form and obtain fluctuation-dissipation relations that ensure Gibbsian equilibrium. We extract the overdamped equations of motion by adiabatically eliminating the momenta from the Fokker-Planck equation, showing how a peculiar cancellation leads to the naively expected Smoluchowski limit. The overdamped equations can be used for accurate and efficient intrinsic Brownian dynamics simulations of passive, driven and active diffusion processes on curved surfaces. Our work generalises to the collective dynamics of many inclusions on curved surfaces.

cond-mat.soft↗

arXiv2024

Sojourn probabilities in tubes and pathwise irreversibility for Itô processes

The sojourn probability of an Itô diffusion process, i.e. its probability to remain in the tubular neighborhood of a smooth path, is a central quantity in the study of path probabilities. For $N$-dimensional Itô processes with state-dependent full-rank diffusion tensor, we derive a general expression for the sojourn probability in tubes whose radii are small but finite, and fixed by the metric of the ambient Euclidean space. The central quantity in our study is the exit rate at which trajectories leave the tube for the first time. This has an interpretation as a Lagrangian and can be measured directly in experiment, unlike previously defined sojourn probabilities which depend on prior knowledge of the state-dependent diffusivity. We find that while in the limit of vanishing tube radius the ratio of sojourn probabilities for a pair of distinct paths is in general divergent, the same for a path and its time-reversal is always convergent and finite. This provides a pathwise definition of irreversibility for Itô processes that is agnostic to the state-dependence of the diffusivity. For one-dimensional systems we derive an explicit expression for our Lagrangian in terms of the drift and diffusivity, and find that our result differs from previously reported multiplicative-noise Lagrangians. We confirm our result by comparing to numerical simulations, and relate our theory to the Stratonovich Lagrangian for multiplicative noise. For one-dimensional systems, we discuss under which conditions the vanishing-radius limiting ratio of sojourn probabilities for a pair of forward and backward paths recovers the established pathwise entropy production. Finally, we demonstrate for our one-dimensional example system that the most probable tube for a barrier crossing depends sensitively on the tube radius, and hence on the tolerated amount of fluctuations around the smooth reference path.

cond-mat.stat-mech↗

arXiv2024

Resolution dependence of most probable pathways with state-dependent diffusivity

Recent experiments have probed the relative likelihoods of trajectories in stochastic systems by observing survival probabilities within a tube of radius $R$ in spacetime. We measure such probabilities here for a colloidal particle in a corrugated channel, corresponding to a bistable potential with state-dependent diffusivity. In contrast to previous findings for state-independent noise, we find that the most probable pathway changes qualitatively as the tube radius $R$ is altered. We explain this by computing the survival probabilities predicted by overdamped Langevin dynamics. At high enough resolution (small enough $R$), survival probabilities depend solely on diffusivity variations, independent of deterministic forces; finite $R$ corrections yield a generalization of the Onsager-Machlup action. As corollary, ratios of survival probabilities are singular as $R \to 0$, but become regular, and described by the classical Onsager-Machlup action, only in the special case of state-independent noise.

cond-mat.stat-mech↗

arXiv2023

Cartan media: geometric continuum mechanics in homogeneous spaces

We present a geometric formulation of the mechanics of a field that takes values in a homogeneous space \mathbb{X} on which a Lie group G acts transitively. This generalises the mechanics of Cosserat media where \mathbb{X} is the frame bundle of Euclidean space and G is the special Euclidean group. Kinematics is described by a map from a space-time manifold to the homogeneous space. This map is characterised locally by generalised strains (representing spatial deformations) and generalised velocities (representing temporal motions). These are, respectively, the spatial and temporal components of the Maurer-Cartan one-form in the Lie algebra of G. Cartan's equation of structure provides the fundamental kinematic relationship between generalised strains and velocities. Dynamics is derived from a Lagrange-d'Alembert principle in which generalised stresses and momenta, taking values in the dual Lie algebra of G, are paired, respectively, with generalised strains and velocities. For conservative systems, the dynamics can be expressed completely through a generalised Euler-Poincare action principle. The geometric formulation leads to accurate and efficient structure-preserving integrators for numerical simulations. We provide an unified description of the mechanics of Cosserat solids, surfaces and rods using our formulation. We further show that, with suitable choices of \mathbb{X} and G, a variety of systems in soft condensed matter physics and beyond can be understood as instances of a class of materials we provisionally call Cartan media.

cond-mat.soft↗

arXiv2023

A geometric formulation of Schaefer's theory of Cosserat solids

The Cosserat solid is a theoretical model of a continuum whose elementary constituents are notional rigid bodies. Here we present a formulation of the mechanics of a Cosserat solid in the language of modern differential geometry and exterior calculus, motivated by Schaefer's "motor field" theory. The solid is modelled as a principal fibre bundle and configurations are related by translations and rotations of each constituent. This kinematic property is described in a coordinate-independent manner by a bundle map. Configurations are equivalent if this bundle map is a global Euclidean isometry. Inequivalent configurations, representing deformations of the solid, are characterised by the local structure of the bundle map. Using Cartan's magic formula we show that the strain associated with infinitesimal deformations is the Lie derivative of a connection one-form on the bundle, revealing it to be a Lie algebra-valued one-form. Extending Schaefer's theory, we derive the finite strain by integrating the infinitesimal strain along a prescribed path. This is path independent when the curvature of the connection one-form is zero. Path dependence signals the presence of topological defects and the non-zero curvature is then recognised as the density of topological defects. Mechanical stresses are defined by a virtual work principle in which the Lie algebra-valued strain one-form is paired with a dual Lie algebra-valued stress two-form to yield a scalar work volume form. The d'Alembert principle for the work form provides the balance laws, which is shown to be integrable for a hyperelastic Cosserat solid. The breakdown of integrability, relevant to active oriented solids, is briefly examined. Our work elucidates the geometric structure of Cosserat solids, aids in constitutive modelling of active oriented materials, and suggests structure-preserving integration schemes.

math-ph↗

arXiv2022

Diffusivity dependence of the transition path ensemble

Transition pathways of stochastic dynamical systems are typically approximated by instantons. Here we show, using a dynamical system containing two competing pathways, that at low-to-intermediate temperatures, instantons can fail to capture the most likely transition pathways. We construct an approximation which includes fluctuations around the instanton and, by comparing with the results of an accurate and efficient path-space Monte Carlo sampling method, find this approximation to hold for a wide range of temperatures. Our work delimits the applicability of large deviation theory and provides methods to probe these limits numerically.

cond-mat.stat-mech↗

arXiv2022

Stokes traction on an active particle

The mechanics and statistical mechanics of a suspension of active particles are determined by the traction (force per unit area) on their surfaces. Here we present an exact solution of the direct boundary integral equation for the traction on a spherical active particle in an imposed slow viscous flow. Both single- and double-layer integral operators can be simultaneously diagonalised in a basis of irreducible tensorial spherical harmonics and the solution, thus, can be presented as an infinite number of linear relations between the harmonic coefficients of the traction and the velocity at the boundary of the particle. These generalise Stokes laws for the force and torque. Using these relations we obtain simple expressions for physically relevant quantities such as the symmetric-irreducible dipole acting on, or the power dissipated by, an active particle in an arbitrary imposed flow. We further present an explicit expression for the variance of the Brownian contributions to the traction on an active colloid in a thermally fluctuating fluid.

cond-mat.soft↗

arXiv2022

Measurement of irreversibility and entropy production via the tubular ensemble

The appealing theoretical measure of irreversibility in a stochastic process, as the ratio of the probabilities of a trajectory and its time reversal, cannot be accessed directly in experiment since the probability of a single trajectory is zero. We regularize this definition by considering, instead, the limiting ratio of probabilities for trajectories to remain in the tubular neighborhood of a smooth path and its time reversal. The resulting pathwise medium entropy production agrees with the formal expression from stochastic thermodynamics, and can be obtained from measurable tube probabilities. Estimating the latter from numerically sampled trajectories for Langevin dynamics yields excellent agreement with theory. By combining our measurement of pathwise entropy production with a Markov Chain Monte Carlo algorithm, we infer the entropy-production distribution for a transition path ensemble directly from short recorded trajectories. Our work enables the measurement of irreversibility along individual paths, and path ensembles, in a model-free manner.

cond-mat.stat-mech↗

arXiv2022

Overdamped Lattice Dynamics of Sedimenting Active Cosserat Crystals

Micropolar active matter requires for its kinematic description both positional and orientational degrees of freedom. Activity generates dynamic coupling between these kinematic variables that are absent in micropolar passive matter, such as the oriented crystals first studied by the Cosserat brothers. Here we study the effect of uniaxial activity on the dynamics of an initially crystalline state of spheroidal colloids sedimenting slowly in a viscous fluid remote from confining boundaries. Despite frictional overdamping by the fluid, the crystalline lattice admits traveling waves of position and orientation. At long wavelengths these obey a vector wave equation with Lamé constants determined by the activity. We find that at least one polarization mode of these waves is always unstable, leading to the melting of the crystal. These results are elucidated by identifying an odd-dimensional Poisson structure consisting of a Hamiltonian and an associated Casimir invariant, where linear combinations of position and orientation are identified as conjugate variables. Our results suggest that Poisson structures may exist generally for active particles in slow viscous flow and thereby allow equilibrium arguments to be applied in the presence of these dissipative systems.

cond-mat.soft↗

arXiv2021

Efficient and flexible methods for time since infection models

Epidemic models are useful tools in the fight against infectious diseases, as they allow policy makers to test and compare various strategies to limit disease transmission while mitigating collateral damage on the economy. Epidemic models that are more faithful to the microscopic details of disease transmission can offer more reliable projections, which in turn can lead to more reliable control strategies. For example, many epidemic models describe disease progression via a series of artificial 'stages' or 'compartments' (e.g. exposed, activated, infectious, etc.) but an epidemic model that explicitly tracks time since infection (TSI) can provide a more precise description. At present, epidemic models with 'compartments' are more common than TSI models , largely due to higher computational cost and complexity typically associated with TSI models. Here, however, we show that with the right discretization scheme a TSI model is not much more difficult to solve than a comparment model with three or four 'stages' for the infected class. We also provide a new perspective for adding 'stages' to a TSI model in a way that decouples the disease transmission dynamics from the residence time distributions at each stage. These results are also generalized for age-structured TSI models in an appendix. Finally, as proof-of-principle for the efficiency of the proposed numerical methods, we provide calculations for optimal epidemic control by non-pharmaceutical intervention. Many of the tools described in this report are available through the software package 'pyross'

q-bio.PE↗

arXiv2021

Internal friction controls active ciliary oscillations near the instability threshold

Ciliary oscillations driven by molecular motors cause fluid motion at micron scale. Stable oscillations require a substantial source of dissipation to balance the energy input of motors. Conventionally, it stems from external fluid. We show, in contrast, that external fluid friction is negligible compared to internal elastic stress through a simultaneous measurement of motion and flow field of an isolated and active Chlamydomonas cilium beating near the instability threshold. Consequently, internal friction emerges as the sole source of dissipation for ciliary oscillations. We combine these experimental insights with theoretical modeling of active filaments to show that an instability to oscillations takes place when active stresses are strain softening and shear thinning. Together, our results reveal a counterintuitive mechanism of ciliary beating and provide a general experimental and theoretical methodology to analyze other active filaments, both biological and synthetic ones.

cond-mat.soft↗