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.