Dynamical order and many-body correlations in zebrafish show that three is a crowd.

Zebrafish constitute a convenient laboratory-based biological system for studying collective behavior. It is possible to interpret a group of zebrafish as a system of interacting agents and to apply methods developed for the analysis of systems of active and even passive particles. Here, we consider the effect of group size. We focus on two- and many-body spatial correlations and dynamical order parameters to investigate the multistate behavior. For geometric reasons, the smallest group of fish which can exhibit this multistate behavior consisting of schooling, milling and swarming is three. We find that states exhibited by groups of three fish are similar to those of much larger groups, indicating that there is nothing more than a gradual change in weighting between the different states as the system size changes. Remarkably, when we consider small groups of fish sampled from a larger group, we find very little difference in the occupancy of the state with respect to isolated groups, nor is there much change in the spatial correlations between the fish. This indicates that fish interact predominantly with their nearest neighbors, perceiving the rest of the group as a fluctuating background. Therefore, the behavior of a crowd of fish is already apparent in groups of three fish.

Biaxial nematic order in fundamental measure theory.

Liquid crystals consisting of biaxial particles can exhibit a much richer phase behavior than their uniaxial counterparts. Usually, one has to rely on simulation results to understand the phase diagram of these systems since very few analytical results exist. In this work, we apply fundamental measure theory, which allows us to derive free energy functionals for hard particles from first principles and with high accuracy, to systems of hard cylinders, cones, and spherotriangles. We provide a general recipe for incorporating biaxial liquid crystal order parameters into fundamental measure theory and use this framework to obtain the phase boundaries for the emergence of orientational order in the considered systems. Our results provide insights into the phase behavior of biaxial nematic liquid crystals and, in particular, into methods for their analytical investigation.

Ultrafast entropy production in pump-probe experiments.

The ultrafast control of materials has opened the possibility to investigate non-equilibrium states of matter with striking properties, such as transient superconductivity and ferroelectricity, ultrafast magnetization and demagnetization, as well as Floquet engineering. The characterization of the ultrafast thermodynamic properties within the material is key for their control and design. Here, we develop the ultrafast stochastic thermodynamics for laser-excited phonons. We calculate the entropy production and heat absorbed from experimental data for single phonon modes of driven materials from time-resolved X-ray scattering experiments where the crystal is excited by a laser pulse. The spectral entropy production is calculated for SrTiO3 and KTaO3 for different temperatures and reveals a striking relation with the power spectrum of the displacement-displacement correlation function by inducing a broad peak beside the eigenmode-resonance.

Active smectics on a sphere.

The dynamics of active smectic liquid crystals confined on a spherical surface is explored through an active phase field crystal model. Starting from an initially randomly perturbed isotropic phase, several types of topological defects are spontaneously formed, and then annihilate during a coarsening process until a steady state is achieved. The coarsening process is highly complex involving several scaling laws of defect densities as a function of time where different dynamical exponents can be identified. In general the exponent for the final stage towards the steady state is significantly larger than that in the passive and in the planar case, i.e. the coarsening is getting accelerated both by activity and by the topological and geometrical properties of the sphere. A defect type characteristic for this active system is a rotating spiral of evolving smectic layering lines. On a sphere this defect type also determines the steady state. Our results can in principle be confirmed by dense systems of synthetic or biological active particles.

Interactions between interfaces dictate stimuli-responsive emulsion behaviour.

Stimuli-responsive emulsions offer a dual advantage, combining long-term storage with controlled release triggered by external cues such as pH or temperature changes. This study establishes that thermo-responsive emulsion behaviour is primarily determined by interactions between, rather than within, interfaces. Consequently, the stability of these emulsions is intricately tied to the nature of the stabilizing microgel particles - whether they are more polymeric or colloidal, and the morphology they assume at the liquid interface. The colloidal properties of the microgels provide the foundation for the long-term stability of Pickering emulsions. However, limited deformability can lead to non-responsive emulsions. Conversely, the polymeric properties of the microgels enable them to spread and flatten at the liquid interface, enabling stimuli-responsive behaviour. Furthermore, microgels shared between two emulsion droplets in flocculated emulsions facilitate stimuli-responsiveness, regardless of their internal architecture. This underscores the pivotal role of microgel morphology and the forces they exert on liquid interfaces in the control and design of stimuli-responsive emulsions and interfaces.

Chiral active matter in external potentials.

We investigate the interplay between chirality and confinement induced by the presence of an external potential. For potentials having radial symmetry, the circular character of the trajectories induced by the chiral motion reduces the spatial fluctuations of the particle, thus providing an extra effective confining mechanism, that can be interpreted as a lowering of the effective temperature. In the case of non-radial potentials, for instance, with an elliptic shape, chirality displays a richer scenario. Indeed, the chirality can break the parity symmetry of the potential that is always fulfilled in the non-chiral system. The probability distribution displays a strong non-Maxwell-Boltzmann shape that emerges in cross-correlations between the two Cartesian components of the position, that vanishes in the absence of chirality or when radial symmetry of the potential is restored. These results are obtained by considering two popular models in active matter, i.e. chiral Active Brownian particles and chiral active Ornstein-Uhlenbeck particles.

Entropons as collective excitations in active solids.

The vibrational dynamics of solids is described by phonons constituting basic collective excitations in equilibrium crystals. Here, we consider a non-equilibrium active solid, formed by self-propelled particles, which bring the system into a non-equilibrium steady-state. We identify novel vibrational collective excitations of non-equilibrium (active) origin, which coexist with phonons and dominate over them when the system is far from equilibrium. These vibrational excitations are interpreted in the framework of non-equilibrium physics, in particular, stochastic thermodynamics. We call them "entropons" because they are the modes of spectral entropy production (at a given frequency and wave vector). The existence of entropons could be verified in future experiments on dense self-propelled colloidal Janus particles and granular active matter, as well as in living systems, such as dense cell monolayers.

Statistics of carrier-cargo complexes.

We explore the statistics of assembling soft-matter building blocks to investigate the uptake and encapsulation of cargo particles by carriers engulfing their load. While the such carrier-cargo complexes are important for many applications out of equilibrium, such as drug delivery and synthetic cell encapsulation, we uncover here the basic statistical physics in minimal hard-core-like models for particle uptake. Introducing an exactly solvable equilibrium model in one dimension, we demonstrate that the formation of carrier-cargo complexes can be largely tuned by both the cargo concentration and the carriers' interior size. These findings are intuitively explained by interpreting the internal free space (partition function) of the cargo inside a carrier as its engulfment strength, which can be mapped to an external control parameter (chemical potential) of an additional effective particle species. Assuming a hard carrier membrane, such a mapping can be exactly applied to account for multiple cargo uptake involving various carrier or cargo species and even attractive uptake mechanisms, while soft interactions require certain approximations. We further argue that the Boltzmann occupation law identified within our approach is broken when particle uptake is governed by nonequilibrium forces. Speculating on alternative occupation laws using effective parameters, we put forward a Bose-Einstein-like phase transition associated with polydisperse carrier properties.

Stability of interlocked self-propelled dumbbell clusters.

Combining experimental observations of Quincke roller clusters with computer simulations and a stability analysis, we explore the formation and stability of two interlocked self-propelled dumbbells. For large self-propulsion and significant geometric interlocking, there is a stable joint spinning motion of two dumbbells. The spinning frequency can be tuned by the self-propulsion speed of a single dumbbell, which is controlled by an external electric field for the experiments. For typical experimental parameters the rotating pair is stable with respect to thermal fluctuations but hydrodynamic interactions due to the rolling motion of neighboring dumbbells leads to a breakup of the pair. Our results provide a general insight into the stability of spinning active colloidal molecules, which are geometrically locked.

Motility-induced shear thickening in dense colloidal suspensions.

Phase transitions and collective dynamics of active colloidal suspensions are fascinating topics in soft matter physics, particularly for out-of-equilibrium systems, which can lead to rich rheological behaviours in the presence of steady shear flow. Here the role of self-propulsion in the rheological response of a dense colloidal suspension is investigated by using particle-resolved Brownian dynamics simulations. First, the combined effect of activity and shear in the solid on the disordering transition of the suspension is analyzed. While both self-propulsion and shear destroy order and melt the system if critical values are exceeded, self-propulsion largely lowers the stress barrier needed to be overcome during the transition. We further explore the rheological response of the active sheared system once a steady state is reached. While passive suspensions show a solid-like behaviour, turning on particle motility fluidises the system. At low self-propulsion, the active suspension behaves in the steady state as a shear-thinning fluid. Increasing the self-propulsion changes the behaviour of the liquid from shear-thinning to shear-thickening. We attribute this to clustering in the sheared suspensions induced by motility. This new phenomenon of motility-induced shear thickening (MIST) can be used to tailor the rheological response of colloidal suspensions.

Network topology of interlocked chiral particles.

Self-assembly of chiral particles with an L-shape is explored by Monte-Carlo computer simulations in two spatial dimensions. For sufficiently high packing densities in confinement, a carpet-like texture emerges due to the interlocking of L-shaped particles, resembling a distorted smectic liquid crystalline layer pattern. From the positions of either of the two axes of the particles, two different types of layers can be extracted, which form distinct but complementary entangled networks. These coarse-grained network structures are then analyzed from a topological point of view. We propose a global charge conservation law by using an analogy to uniaxial smectics and show that the individual network topology can be steered by both confinement and particle geometry. Our topological analysis provides a general classification framework for applications to other intertwined dual networks.

Dynamics of active particles with translational and rotational inertia.

Inertial effects affecting both the translational and rotational dynamics are inherent to a broad range of active systems at the macroscopic scale. Thus, there is a pivotal need for proper models in the framework of active matter to correctly reproduce experimental results, hopefully achieving theoretical insights. For this purpose, we propose an inertial version of the active Ornstein-Uhlenbeck particle (AOUP) model accounting for particle mass (translational inertia) as well as its moment of inertia (rotational inertia) and derive the full expression for its steady-state properties. The inertial AOUP dynamics introduced in this paper is designed to capture the basic features of the well-established inertial active Brownian particle model, i.e. the persistence time of the active motion and the long-time diffusion coefficient. For a small or moderate rotational inertia, these two models predict similar dynamics at all timescales and, in general, our inertial AOUP model consistently yields the same trend upon changing the moment of inertia for various dynamical correlation functions.

Glassy Dynamics in Chiral Fluids.

Chiral active matter is enjoying a rapid increase of interest, spurred by the rich variety of asymmetries that can be attained in, e.g., the shape or self-propulsion mechanism of active particles. Though this has already led to the observance of so-called chiral crystals, active chiral glasses remain largely unexplored. A possible reason for this could be the naive expectation that interactions dominate the glassy dynamics and the details of the active motion become increasingly less relevant. Here, we show that quite the opposite is true by studying the glassy dynamics of interacting chiral active Brownian particles. We demonstrate that when our chiral fluid is pushed to glassy conditions, it exhibits highly nontrivial dynamics, especially compared to a standard linear active fluid such as common active Brownian particles. Despite the added complexity, we are still able to present a full rationalization for all identified dynamical regimes. Most notably, we introduce a new "hammering" mechanism, unique to rapidly spinning particles in high-density conditions, that can fluidize a chiral active solid.

Steering self-organisation through confinement.

Self-organisation is the spontaneous emergence of spatio-temporal structures and patterns from the interaction of smaller individual units. Examples are found across many scales in very different systems and scientific disciplines, from physics, materials science and robotics to biology, geophysics and astronomy. Recent research has highlighted how self-organisation can be both mediated and controlled by confinement. Confinement is an action over a system that limits its units' translational and rotational degrees of freedom, thus also influencing the system's phase space probability density; it can function as either a catalyst or inhibitor of self-organisation. Confinement can then become a means to actively steer the emergence or suppression of collective phenomena in space and time. Here, to provide a common framework and perspective for future research, we examine the role of confinement in the self-organisation of soft-matter systems and identify overarching scientific challenges that need to be addressed to harness its full scientific and technological potential in soft matter and related fields. By drawing analogies with other disciplines, this framework will accelerate a common deeper understanding of self-organisation and trigger the development of innovative strategies to steer it using confinement, with impact on, e.g., the design of smarter materials, tissue engineering for biomedicine and in guiding active matter.

Density functional approach to elastic properties of three-dimensional dipole-spring models for magnetic gels.

Magnetic gels are composite materials consisting of a polymer matrix and embedded magnetic particles. Those are mechanically coupled to each other, giving rise to the magnetostrictive effects as well as to a controllable overall elasticity responsive to external magnetic fields. Due to their inherent composite and thereby multiscale nature, a theoretical framework bridging different levels of description is indispensable for understanding the magnetomechanical properties of magnetic gels. In this study, we extend a recently developed density functional approach from two spatial dimensions to more realistic three-dimensional systems. Along these lines, we connect a mesoscopic characterization resolving the discrete structure of the magnetic particles to macroscopic continuum parameters of magnetic gels. In particular, we incorporate the long-range nature of the magnetic dipole-dipole interaction and consider the approximate incompressibility of the embedding media and relative rotations with respect to an external magnetic field breaking rotational symmetry. We then probe the shape of the model system in its reference state, confirming the dependence of magnetostrictive effects on the configuration of the magnetic particles and on the shape of the considered sample. Moreover, calculating the elastic and rotational coefficients on the basis of our mesoscopic approach, we examine how the macroscopic types of behavior are related to the mesoscopic properties. Implications for real systems of random particle configurations are also discussed.

Acoustic Crystallization of 2D Colloidal Crystals.

2D colloidal crystallization provides a simple strategy to produce defined nanostructure arrays over macroscopic areas. Regularity and long-range order of such crystals is essential to ensure functionality, but difficult to achieve in self-assembling systems. Here, a simple loudspeaker setup for the acoustic crystallization of 2D colloidal crystals (ACDC) of polystyrene, microgels, and core-shell particles at liquid interfaces is introduced. This setup anneals an interfacial colloidal monolayer and affords an increase in average grain size by almost two orders of magnitude. The order is characterized via the structural color of the colloidal crystal, the acoustic annealing process is optimized via the frequency and the amplitude of the applied sound wave, and its efficiency is rationalized via the surface coverage-dependent interactions within the interfacial colloidal monolayer. Computer simulations show that multiple rearrangement mechanisms at different length scales, from the local motion around voids to grain boundary movements via consecutive particle rotations around common centers, collude to remove defects. The experimentally simple ACDC process, paired with the demonstrated applicability toward complex particle systems, provides access to highly defined nanostructure arrays for a wide range of research communities.

Fitting an active Brownian particle's mean-squared displacement with improved parameter estimation.

The active Brownian particle (ABP) model is widely used to describe the dynamics of active matter systems, such as Janus microswimmers. In particular, the analytical expression for an ABP's mean-squared displacement (MSD) is useful as it provides a means to describe the essential physics of a self-propelled, spherical Brownian particle. However, the truncated or "short-time" form of the MSD equation is typically fitted, which can lead to significant problems in parameter estimation. Furthermore, heteroscedasticity and the often statistically dependent observations of an ABP's MSD lead to a situation where standard ordinary least-squares regression leads to biased estimates and unreliable confidence intervals. Instead, we propose here to revert to always fitting the full expression of an ABP's MSD at short timescales, using bootstrapping to construct confidence intervals of the fitted parameters. Additionally, after comparison between different fitting strategies, we propose to extract the physical parameters of an ABP using its mean logarithmic squared displacement. These steps improve the estimation of an ABP's physical properties and provide more reliable confidence intervals, which are critical in the context of a growing interest in the interactions of microswimmers with confining boundaries and the influence on their motion.

Structural correlations and phase separation in binary mixtures of charged and neutral colloids.

Structural correlations between colloids in a binary mixture of charged and neutral spheres are calculated using computer simulations of the primitive model with explicit microions. For aqueous suspensions in a solvent of large dielectric constant, the traditional Derjaguin-Landau-Vervey-Overbeek (DLVO) theory of linear screening, supplemented with hard core interactions, reproduces the structural correlations obtained in the full primitive model quantitatively. However, for lower dielectric contrast, the increasing Coulomb coupling between the counterions and charged colloids results in strong deviations. We find a fluid-fluid phase separation into two regions either rich in charged or rich in neutral colloids, which is not reproduced by DLVO theory. Our results are verifiable in scattering or real-space experiments on charged-neutral mixtures of colloids or nanoparticles.

Active matter in space.

In the last 20 years, active matter has been a highly dynamic field of research, bridging fundamental aspects of non-equilibrium thermodynamics with applications to biology, robotics, and nano-medicine. Active matter systems are composed of units that can harvest and harness energy and information from their environment to generate complex collective behaviours and forms of self-organisation. On Earth, gravity-driven phenomena (such as sedimentation and convection) often dominate or conceal the emergence of these dynamics, especially for soft active matter systems where typical interactions are of the order of the thermal energy. In this review, we explore the ongoing and future efforts to study active matter in space, where low-gravity and microgravity conditions can lift some of these limitations. We envision that these studies will help unify our understanding of active matter systems and, more generally, of far-from-equilibrium physics both on Earth and in space. Furthermore, they will also provide guidance on how to use, process and manufacture active materials for space exploration and colonisation.