Rajesh Singh

Spatial confinement and chemical screening fundamentally reshape the non-equilibrium phase behavior of autophoretic active particles. Here, we present a systematic study mapping the collective dynamics of self-propelled particles governed by chemo-attractive translational forces ($\mu_{t}<0$) and chemo-repulsive rotational torques ($\mu_{r}>0$) across varying screening parameters $\kappa$, torque magnitudes $\mu_{r}$, and boundary condition coefficients $\Lambda^{c}$. Beyond standard chemotactic macro-phase separation and dynamic clustering, we report the emergence of novel boundary- and screening-induced bubbly phases, classified into boiling and bursting bubbles. Using a metric triad of steady-state cluster fraction $\langle S\rangle$, temporal fluctuation magnitude $\sigma_{S}$, and coordination number $\langle Q\rangle$, we draw phase diagrams to demarcate phases for no-flux boundaries ($\Lambda^{c}=1$) and chemically permeable interfaces ($\Lambda^{c}=0$). Increasing chemical screening ($\kappa$) systematically suppresses long-range attraction, driving sequential phase transitions from macro-scale collapse toward bubbly states, dynamic micro-clusters, and homogeneous gas phases, while simultaneously inducing aggregate shape anisotropy. These findings provide predictive design rules for controlling active assembly and transport in microfluidic environments.

Equilibrium statistical mechanics owes much of its analytical tractability to symmetry: detailed balance, gradient dynamics, and the resulting vanishing of steady-state entropy production are properties that follow directly from the structure of the underlying dynamics, not from any smallness of the perturbation. Exact solutions of this kind are rare away from equilibrium. Here we identify and characterize a class of far-from-equilibrium colloidal chains – coupled through roto-translational and autophoretic interactions – that, for a specified set of bilaterally-symmetric initial conditions, nevertheless admit an exact description. For fixed chain geometries, the monomer orientational dynamics map directly onto a scalar potential. Detailed balance holds strictly within the orientational sector, causing its steady-state entropy production rate (EPR) to vanish identically despite the system being manifestly driven and dissipative. We solve these reduced dynamics exactly for dimers and semi-analytically for general 𝑁-mers, deriving closed-form expressions for mean-squared orientational fluctuations and total EPR. Crucially, this exact mapping demonstrates that, at fixed chain geometry, all non-equilibrium entropy production is strictly partitioned into the translational (center-of-mass) sector. Extending the framework to incorporate dipolar chemical emission reveals that while dimers retain this quasi-equilibrium structure, longer chains (𝑁>2) break it completely—generating a genuinely non-equilibrium state whose EPR fails to reach a steady state. Monopolar coupling is thus both necessary and sufficient to sustain the polarized quasi-equilibrium state, establishing explicit physical boundaries for exact thermodynamic descriptions of active colloidal chains.

We report a study of the emergent dynamics arising in two-dimensional suspensions of semi-flexible chains whose tip is chemically active, generating a phoretic field. By varying the chain length (number of monomers per chain Npc), the area fraction ϕ , and the sign of the phoretic coupling J 0 , we map out a rich non-equilibrium phase diagram in the presence of phoretic interactions. For repulsive phoretic interactions (J0>0) between the chains, we find that short chains (Npc=2) develop a transient chaotic flow state that crosses over at long times to a global polar flock with super-diffusive mean-squared displacement and long-ranged velocity correlations. Surprisingly, we find this state to have suppressed density fluctuations, indicating the emergence of hyperuniformity. At intermediate chain lengths (Npc ∼ 4 – 8 ), the repulsive chemical field drives chaotic mesoscale flows — a dry route to active turbulence without the need to hydrodynamic interactions or steric alignment interactions. For attractive phoretic interactions (J0<0), chains self-organise into hedgehog-like micellar aggregates with heads forming the core and flexible tails radiating outward, in structural analogy with amphiphile micellisation but driven entirely by non-equilibrium self-propulsion. A coarse-grained theory of a tip-emitting active rod predicts the onset of the flocking of dimers, though overestimates the presence of polar order for longer chains. Our results establish phoretic tip activity as a minimal, experimentally realisable mechanism for a spectrum of collective states hitherto attributed to hydrodynamic interactions or steric alignment.

Active matter systems are driven out of thermodynamic equilibrium by localized, microscale energy dissipation. While active field theories are highly successful at simulating these non-equilibrium phenomena (the forward problem), characterizing real-world active materials is fundamentally bottle-necked by the difficulty of measuring active stresses directly. This paper addresses the inverse problem using deep learning: model inference and model selection from observable flow field data of active fluids. We formulate an inversion framework applied to two cornerstone paradigms of active continuum physics: Active Model H (representing scalar active matter) and Active Nematics (representing active systems with orientational order). We demonstrate that the kinetic energy spectrum obtained from the fluid flow field preserves a high-fidelity signature of activity to infer parameters of active model H and active nematics. The classification of the models requires comparison using conventional numerical work against predicted parameters. Our deep learning method presents a principled way to bear upon questions of model inference and selection given the flow field data in continuum models of active matter.

The collective behavior of passive particles within chiral active matter has emerged as a significant area of soft matter research. However, most existing studies focus on systems where chirality is imposed by external torques rather than intrinsic activity. In this work, we study emergent dynamics in a suspension of active spinners and passive colloids by computing many-body hydrodynamic interactions via Ewald summation. By systematically exploring a broad range of area fractions and rotational velocities, we identify distinct phase-separation regimes sensitive to the system's kinematic parameters. Specifically, we report the emergence of unique structural morphologies, including the formation of passive particle vortices surrounding phase-separated active spinners and the development of large-scale active-passive bands. We characterize the underlying dynamics by analyzing the temporal evolution of characteristic length scales and the non-equilibrium velocity distributions of the passive particles. Our findings provide new insights into the role of long-range hydrodynamic couplings in governing the self-organization of non-equilibrium condensed matter.

Recent studies of active colloidal matter have revealed that a global polar order can arise from chemorepulsive interactions among particles without any explicit alignment interaction between them. In this work, we investigate such chemically interacting active colloids in the presence of quenched disorder, where a fraction of particles are randomly pinned in space. These pinned particles are restricted to rotational motion while remaining chemically coupled to the mobile population. In addition, angular noise is incorporated into the rotational dynamics to capture stochastic effects. To elucidate the interplay of quenched disorder and noise, we construct phase diagrams based on polar order and its fluctuations, and systematically analyze the associated disorder- and noise-driven phase transitions. Surprisingly, we find that the phase transition driven by the noise is significantly dependent on the density of the particles, whereas such a density-dependence is not present when the control parameter is the pinning fraction. The finite-size effects on these transitions are also examined. An effective interaction range, governed by the coefficient related to screening of the chemorepulsive interaction, plays a crucial role in collective behavior. When the effective interaction range is much smaller than the system size, the system exhibits density band formation, a feature absent in the long-range interaction regime. Moreover, near the transition point, the order parameter distribution becomes bimodal for the case of short-range interaction.

The control of active colloidal particles via optical traps is a cornerstone for research of matter at the micron and nanometer scale. A central challenge in this domain is the derivation of optimal transport protocols that minimize the mean work required to move a particle over a finite-time interval. Here we present a Ritz method in which open-loop protocols are constructed from a global basis of Chebyshev polynomials and optimised by a genetic algorithm. We apply the method to study optimal transport of an active particle, which is modelled as a force-dipole (or a stresslet) near a no-slip wall. The methodology is validated in the limits of zero activity and infinite wall separation, where it successfully recovers the known analytical protocols and the theoretical minimum work. Crucially, we demonstrate that the presence of the boundary breaks the time-reversal symmetry of the optimal protocol found in bulk solutions. This symmetry breaking is shown to be a complex function of the transport direction and the particle's intrinsic activity. Because the presented approach requires only the capability to simulate stochastic trajectories, it offers a robust, principled framework for optimizing transport protocols in complex fluid environments that remain inaccessible to exact analytical treatment.

Recent studies in the collective behavior of active colloids have shown that a global polar order may emerge due to long-ranged chemo-repulsive interactions between them. Here, we report the role of pinning disorder in the flocking transition for such a system. To this end, we study the problem of chemically interacting active colloids with some fraction of the colloids randomly pinned over space such that they can only rotate while phoretically interacting with other particles. Using this model, we investigate the sustenance of global polar order in the presence of quenched spatial disorder. We quantify the flocking transition by studying the global polarization, and the role of finite-size effects. We find that in the crystallite flocking phase, even a small fraction of pinning can destroy spatial crystalline order, although polar order in the form of a liquid phase is maintained. It is observed that polar order is sustained in a system with a higher pinning fraction if the long-ranged repulsive force is subsequently increased. However, in absence of chemo-repulsive forces between particles, polar order drastically decreases even with a smaller pinning fraction. Our work suggests that the flocking transition of active colloids can be controlled via "translationally inert" obstacles, that rotate but do not translate whilst interacting with the bulk.

Motivated by a recently synthesizable class of active interfaces formed by linked self--propelled colloids, we investigate the dynamics and fluctuations of a phoretically (chemically) interacting active interface with roto--translational coupling. We enumerate all steady--state shapes of the interface across parameter space and identify a regime where the interface acquires a finite curvature, leading to a characteristic ''C--shaped'' topology, along with persistent self--propulsion. In this phase, the interface height fluctuations obey Family--Vicsek scaling but with novel exponents: a dynamic exponent z_h≈0.5, a roughness exponent α_h≈0.9 and a super--ballistic growth exponent β_h≈1.7. In contrast, the orientational fluctuations of the colloidal monomers exhibit a negative roughness exponent, reflecting a surprising smoothness law, where steady--state fluctuations diminish with increasing system size. Together, these findings point towards a unique non--equilibrium universality class associated with self--propelled interfaces of non--standard shape.

Coherent collective motion is a widely observed phenomenon in active matter systems. Here, we report a flocking transition mechanism in a system of chemically interacting active colloidal particles sustained purely by chemo-repulsive torques at low to medium densities. The basic requirements to maintain the global polar order are excluded volume repulsions and long-ranged repulsive torques. This mechanism requires that the time scale for individual colloids to move a unit length be dominant with respect to the time they deterministically respond to chemical gradients, or equivalently, pair colloids slide together a minimal unit length before deterministically rotating away from each other. Switching on the translational repulsive forces renders the flock a crystalline structure. Furthermore, liquid flocks are observed for a range of chemo-attractive inter-particle forces. Various properties of these two distinct flocking phases are contrasted and discussed. We complement these results with stability analysis of a hydrodynamic model, which reveals the transition corresponding to destabilization of the flocking state observed in particle-based simulations.

Intracellular phagosomes have a lipid bilayer-encapsulated fluidic shell outside the particle, on the outer side of which, molecular motors are attached. An optically trapped spherical birefringent particle phagosome provides an ideal platform to probe fluidity of the shell, as the inner particle is optically confined both in translation and in rotation. Using a recently reported method to calibrate the translation and pitch rotations - yielding a spatial resolution of about 2 nm and angular resolution of 0.1 degrees - we report novel roto-translational coupled dynamics. We also suggest a new technique where we explore the correlation between the translation and pitch rotation to study extent of activity. Given that a spherical birefringent particle phagosome is almost a sphere, the fact that it turns due to the activity of the motors is not obvious, even implying high rigidity of shell. Applying a minimal model for the roto-translational coupling, we further show that this coupling manifests itself as sustained fluxes in phase space, a signature of broken detailed balance.

The dynamics of self-propelled colloidal particles is strongly influenced by their environment through hydrodynamic and, in many cases, chemical interactions. We develop a theoretical framework to describe the motion of confined active particles by combining the Lorentz reciprocal theorem with a Galerkin discretisation of surface fields, yielding an equation of motion that efficiently captures self-propulsion without requiring an explicit solution for the bulk fluid flow. Applying this framework, we identify and characterise the long-time behaviours of a Janus particle near rigid, permeable and fluid–fluid interfaces, revealing distinct motility regimes, including surface-bound skating, stable hovering and chemo-hydrodynamic reflection. Our results demonstrate how the solute permeability and the viscosity contrast of the surface influence a particle’s dynamics, providing valuable insights into experimentally relevant guidance mechanisms for autophoretic particles. The computational efficiency of our method makes it particularly well suited for systematic parameter sweeps, offering a powerful tool for mapping the phase space of confined active particles and informing high-fidelity numerical simulations.

Active colloidal particles create flow around them due to non-equilibrium process on their surfaces. In this paper, we infer the activity of such colloidal particles from the flow field created by them via deep learning. We first explain our method for one active particle, inferring the 2s mode (or the stresslet) and the 3t mode (or the source dipole) from the flow field data, along with the position and orientation of the particle. We then apply the method to a system of many active particles. We find excellent agreements between the predictions and the true values of activity. Our method presents a principled way to predict arbitrary activity from the flow field created by active particles.

We present a method to compute the Ewald summation for the irreducible components of flow around active particles to study hydrodynamic interactions in active colloidal suspensions. An active particle is modeled as a colloidal sphere with a surface slip velocity. Using this model, we obtain an irreducible representation of the fluid flow produced by an active particle in the periodic geometry of Stokes flow for an arbitrary surface slip. The solution of the active flow is obtained in terms of the lattice sum of the Oseen tensor and its derivatives. The lattice sum is accelerated using the Ewald summation technique. We apply the method to compute explicit expressions for the rigid body motion of hydrodynamically interacting active particles. Our method presents a way for the dynamic simulation of active particles due to arbitrary modes of active slip in the periodic geometry of Stokes flow.