Papers

Active Brownian particles (ABPs) in viscoelastic (VE) media exhibit fascinating dynamical phenomena set by self-propulsion, thermal fluctuations, and fluid viscoelasticity. We extend our model, in which the Brownian dynamics within a slowly diffusing harmonic well emulates that in a single-relaxation VE fluid, to study active Brownian motion in such media. Consequently, the resultant dynamics is governed by the interplay of the characteristic timescales of the systems: the crossover and equilibration times of the VE fluid, $\tau_k$ and $\lambda$, respectively, and the persistence time of the ABP, $\tau_{\mathrm{R}}$. Following analytical predictions and simulations, we study two practically relevant regimes where the dynamics is dominated by the persistence of active motion and the elastic confinement of the VE fluid, with a phoretically active Pt-coated Janus colloid in a dynamic optical trap, and show quantitative agreement with the simulations. This approach provides a VE environment with tunable VE properties that remain unaffected by the strength of self-propulsion, allowing us to systematically investigate active Brownian motion in VE media in ways that are not otherwise possible with physical VE fluids.

Dense-liquid relaxation evolves from local particle collisions to cooperative structural rearrangements. While hard-sphere kinetics determines an early $t^{3/2}$ fractional decay in density correlation functions, collective theories describe the subsequent structural relaxation. A central open question has been how short-time contact physics supplies an exact starting point for the memory kernel governing later times without being modified by subsequent many-body rearrangements. Here we resolve this problem for a broad class of reversible Brownian systems. We prove that hard particle contacts act as reflecting boundaries in configuration space, uniquely dictating the amplitude of the leading $t^{3/2}$ density relaxation. Mechanistically, diffusion samples a contact boundary layer of thickness $O(\sqrt{t})$, which combines with the local density response to produce the fractional signal. We derive an explicit surface formula expressing this amplitude in terms of equilibrium contact probability, normal mobility, and density sensitivity. For monodisperse hard spheres, this yields an exact, fit-free prediction determined entirely by static structure $S(k)$, radial contact value $g(\sigma^+)$, and short-time diffusion $D_0$. Extending the construction, we determine the corresponding normalization for soft interfaces and prove via a Gram–Schur projection hierarchy that regular collective variables leave the leading contact amplitude strictly invariant. The resulting formulation connects microscopic collision kinetics directly to caging and glass-like structural relaxation, providing an exact microscopic boundary condition for scattering experiments, molecular simulations, and memory-kernel reconstructions.

We systematically investigate the different coefficients of restitution of a dissipative, frictional disc as a function of the impact angle $\theta$, the friction coefficient $\mu$ and initial rotation $\omega_{\mathrm{in}}$. We observe a non-monotonic, non-linear behaviour of $e_{\mathrm{T}}$ and $e_{\mathrm{kin}}$ with a clear minimum at $\mu$-dependent values of $\theta$ and a convergence for all $\mu$ at large $\theta$, bounded by the cases of pure rolling and pure sliding. Changing the dissipative normal interaction affects the $\mu$ convergence at large $\theta$ and leads to a convergence at low $\theta$. The presence of initial angular velocity $\omega_{\mathrm{in}}$ can significantly alter the functional behaviour of $e_{\mathrm{T}}$ at steep impacts and slightly change the magnitude of $e_{\mathrm{kin}}$, with friction playing only a minor role. Overall, our results indicate that any specific value of $e_{\mathrm{T}}$ or $e_{\mathrm{kin}}$ is highly situational and can simultaneously describe entirely different contact configurations.

Erosion-induced landslide mobility is a prominent phenomenon in nature. However, this topic remains poorly understood, even though erosion greatly alters nearly every aspect of landslide mechanics, dynamics, run-out, mobility, deposition structure and the enormous destructive power carried by such catastrophic events. Here, I present a simple, elegant, and exact analytical model describing the kinematics of erosion-induced landslide mobility in terms of a newly constructed mobility controller containing essential forcing mechanisms in erosion. In contrast to the classical perspective, I formally prove that, irrespective of how large the erosion rate is, the erosion rate alone is not sufficient to determine enhanced or reduced mobility; mobility is also greatly regulated by the volume bulking rate, erosion drag or thrust, and flow depth. With this mechanical mobility controller, it is now possible to explain precisely when the mobility of an erodible landslide is enhanced or reduced. I demonstrate that, a mechanically valid, physically founded erosion model must be able to explain both the enhanced and reduced mobility of erosive landslides.

In order to determine the structural relaxation time of a polymer glass during deformation, a strain rate switching experiment is performed in the steady-state plastic flow regime. A lightly cross-linked poly (methyl methacrylate) (PMMA) glass was utilized, and simultaneously the segmental motion in the glass was quantified using an optical probe reorientation method. After the strain rate switch, a non-monotonic stress response is observed, consistent with previous work. The correlation time for segmental motion, in contrast, monotonically evolves towards a new steady-state, providing an unambiguous measurement of the structural relaxation time during deformation, which is found to be approximately equal to the segmental correlation time. The Chen-Schweizer model qualitatively predicts the changes in the segmental correlation time and the observed non-monotonic stress response. In addition, our experiments are reasonably consistent with the material time assumption used in polymer deformation modeling; in this approach, the response of a polymer glass to a large deformation is described by combining a linear-response model with a time-dependent segmental correlation time.

Living matter undergoes continuous turnover. The hydrodynamic theory of Malthusian flocks describes polar active matter with turnover, but its phase diagram and nonlinear scaling behavior is not well understood. Using a nonperturbative renormalization group approach, rotationally invariant to second order in derivatives, and without defects, we explicitly obtain the strong-coupling fixed point governing true long-range order, uncover a quasi long-range ordered phase, and identify a critical point similar to, but distinct from the Berezinskii-Kosterlitz-Thouless universality class at the transition.

Novel phases, beyond long-range order in two dimensions, have continued to be discovered within flocking models, establishing flocking as one of the pivotal paradigms in active matter. However, much of the discussion around “Malthusian” (constant density) flocks, an analytically more tractable alternative to the Vicsek model, has centred around the scaling exponents governing the intermediate regime prior to the proliferation of asters, leaving open the question of what other phases the model might display. Here, we study the two-dimensional dynamics of Malthusian flocks and identify a previously unnoticed phase, where the dynamics is that of the equilibrium XY Model. By identifying the symmetries of the model, we derive the effective equations of motion for the Goldstone modes and analyse the spin-wave fluctuations. We identify a novel critical point separating two distinct phases and, using a perturbative RG procedure, determine the RG flows in its vicinity. This allows us to calculate the universal scaling behaviour at the critical point, along with its logarithmic corrections. The novel phase transition here is due to the interaction of activity and spin-waves, unlike the equilibrium counterpart, which undergoes a phase transition in effective degrees of freedom, namely vortices. Nevertheless, the RG flows are similar to those of the Berezinskii-Kosterlitz-Thouless transition, and we show that for sufficiently strong noise, the activity becomes irrelevant and the system crosses over to the equilibrium XY universality class.

Spatial confinement profoundly impacts the transport and self-organization of active matter across diverse biological systems. While the collective orders in confined active matter have been extensively characterized, how geometric constraints reshape near-field flows and the resulting inter-particle correlations remains largely unexplored. In this study, we combine experiments and hydrodynamic simulations to investigate inter-particle correlations within quasi-two-dimensional Chlamydomonas reinhardtii suspensions. We reveal two disentangled modes characterizing cell pairs: a dipolar mode and an entrainment mode, which exhibit a density- and distance-dependent competition. Combining single-cell flow field analysis, hydrodynamic simulations, and active-passive mixtures, we link these two modes to singular hydrodynamics and lubrication-induced entrainment. Our results demonstrate that spatiotemporal correlations in confined active matter are fundamentally rooted in the interplay of these two hydrodynamic mechanisms.

Reported maxima of the advancing contact angle scatter from $87^\circ$ to $147^\circ$ in a single systematic study, and liquids on surfaces with static angles as low as $5^\circ$ reach dynamic maxima near $90^\circ$. We show that both observations follow from the hinged motion of the free surface near a moving contact line. The local Stokes solution for a wedge rotating about its contact line has two singular angles of opposite character: at $90^\circ$ the hinged motion generates no wall shear and the rotation is free, and at $\theta_h = 128.73^\circ$, where $\tan 2\alpha = 2\alpha$, a resonance with the $r^2$ eigensolution arrests the rotation through an $r^2 \ln r$ term. Between the two angles lies a band that a transient advancing angle cannot leave while the interface near the contact line remains a quasi-steady wedge. A compilation of 68 liquid-solid systems from nine sources and five configurations confirms the band and its two exits: systems not limited by the apparatus, with $\theta_s \le 40^\circ$, reach $87^\circ$ to $119^\circ$ regardless of chemistry, and every exceedance of $\theta_h$ occurs either where chemistry places the static angle above the band or where the flow leaves the quasi-steady regime. The record of a waterline on a vertical wall exhibits the band within a single unsteady experiment, together with a distinct quieting of the local contact angle at the crossing of $90^\circ$.

Antifreeze materials prevent ice-formation by disrupting the ice-formation by binding to certain ice-planes. Cellulose, the most abundant biopolymer, has shown the ability to bind to ice-planes but the exact mechanism of this binding is far from being understood. Molecular dynamics simulations are used to investigate the hydration water of chains of cellulose-type glycans and its significance in the expression of the antifreeze behavior of sugar-derivatives found in some antifreeze materials. We find that glycans are able to prevent water from freezing near its surface by preventing their rearrangement to achieve a highly tetrahedral structure at temperatures well-below the freezing point of water. This validates our hypothesis on the role of tetrahedral coordination based on previous $\textit{ab initio}$ calculations that demonstrated cellulose prefers to bind to ice basal and prismatic planes using a tetrahedral geometry. Our findings suggest that the tetrahedral ordering of water around glycans is the key to understanding and designing cellulose-based antifreeze materials.

The mechanisms governing triboelectric charging between insulating particles of the same material remain an open question in nonequilibrium physics, with several competing models proposed to explain observed charging behaviour. Here, we investigate charge evolution in a minimal system consisting of two acoustically levitated particles undergoing repeated binary collisions. To quantify particle charge transfer, purpose-built Faraday cage picoammeters were developed and calibrated. The MultiLev acoustic levitation system was used alongside Ultraino simulations to generate transducer control signals, enabling controlled collision and separation of polystyrene (PS) particles. Although individual collision events exhibit stochastic charge transfer, described by skew-normal distributions, we demonstrate for the first time that the cumulative charge evolution of an individual acoustically levitated particle pair follows the saturation behaviour predicted by the condenser model of triboelectric charging, with fits achieving $R^2 > 0.99$. Under identical conditions, conductive graphite-coated PS particles also undergo charge transfer, but accumulate substantially less charge, consistent with the distinct charging behaviour expected for conductive materials.

In recent years, non-reciprocity has been explored as a ubiquitous manifestation of non-equilibrium activity at the microscopic scales for various active matter systems, from mixtures of chemically active enzymes, colloids, and droplets, to engineered light-controlled active colloids and robotic meta-materials. A commonly used minimal model to describe the dynamics of a binary mixture of conserved species with non-reciprocal interactions is the non-reciprocal Cahn-Hilliard (NRCH) model. The model is characterized by a temperature-like tuning parameter, which can trigger phase separation, and a non-reciprocal coupling, which can lead to the formation of spatio-temporal patterns, as it represents an intrinsic source of non-equilibrium activity and breaks parity and time-reversal symmetries. Here, we study the scaling behavior of the NRCH model near the critical point using perturbative dynamical renormalization group techniques. We find that structural and dynamical correlations are controlled by different correlation lengths, both of which diverge at the critical point, but governed by different scaling laws. In particular, while the structural correlations are always controlled by temperature and the classical Wilson-Fisher critical exponent, the dynamical correlation length exhibits multiple scaling regimes in which either temperature or non-reciprocal coupling can dominate as the key tuning parameter, with a new critical exponent characterizing the divergence. The critical point corresponds to a conserved equilibrium-like dynamics with odd mobility, which we denote as the odd Cahn-Hilliard (OCH) model. Our findings may have important implications on how living systems can control phase separation and spatio-temporal pattern formation using the rates of catalytic reactions, and in general metabolism, as control parameters.

We study the prediction of plastic activity in the confined channel flow of two-dimensional amor- phous soft particles around a circular obstacle. Using datasets generated with a particle-based bubble model, we formulate the prediction problem within two supervised-learning frameworks: re- gression of the non-affine displacement and binary classification of neighbor change events. A key technical challenge is that the obstacle and the confining walls explicitly break translational and rotational symmetries. We address this issue by introducing additional structural descriptors that encode the positions of particles relative to these boundaries. Starting from simple linear models, we systematically increase the complexity of the learning framework by considering a logarithmic transformation of the target variable, the incorporation of particle-size information, the addition of symmetry-breaking obstacle and wall descriptors, the coarse-graining of local structural descrip- tors, and nonlinear neural-network models. We find that the obstacle and wall descriptors provide the largest improvement in predictive performance. Nevertheless, the models considered here cap- ture mainly the overall localization of plastic activity near the obstacle and do not fully reproduce its detailed heterogeneous pattern in individual configurations. A perturbation analysis indicates that this heterogeneity is robustly encoded in the initial structure, suggesting that further progress requires more expressive structural representations and machine-learning architectures.

We investigate the structural and dynamical behavior of methane water systems under nanoconfinement using molecular dynamics simulations across pore widths from 1 to 5 nm. Structural analysis reveals a strong and nonmonotonic dependence on confinement: while tetrahedral ordering partially recovers as confinement is reduced, cubic like order associated with clathrate precursors is maximized at intermediate pore sizes. Radial distribution functions show that three dimensional correlations are suppressed under strong confinement, whereas lateral ordering persists, indicating a reduction in the effective dimensionality of structural organization. Transport properties reflect the same structural competition. Parallel diffusion is nonmonotonic with pore size, while perpendicular motion is subdiffusive due to confinement induced trapping and heterogeneity. Methane exhibits stronger subdiffusion and remains dynamically coupled to the water matrix. A characteristic confinement length scale emerges at which structural ordering, dynamical heterogeneity, and solvent solute decoupling are simultaneously maximized. At strong confinement, three dimensional correlations are suppressed, leading to dimensional reduction, frustrated ordering, and inhibited nucleation.

Data-driven discovery of governing equations from spatiotemporal data offers a promising route to obtaining coarse-grained descriptions of complex dynamical systems. Here, we investigate the performance of PDE-SINDy for discovering phase-ordering dynamics using the Allen–Cahn equation as a benchmark and the Ising model with Glauber spin-flip dynamics as a microscopic system. We systematically analyze the effects of data availability, size of the candidate library, and noise on the efficiency of the equation discovery. We find that stability-selection PDE-SINDy can robustly identify the relevant terms in the governing dynamics even under limited or noisy data, while the recovered coefficient values are substantially more sensitive to these factors. We further show that enlarging the candidate library can strongly affect both term identification and coefficient recovery. Incorporating library bagging with stability selection reduces this sensitivity and improves the efficiency of equation discovery. For the Glauber spin flip Ising model dynamics, the resulting coarse-grained equation reproduces the characteristic phase-separation and coarsening dynamics of the underlying microscopic system. Overall, our results demonstrate the potential of PDE-SINDy for phase-ordering systems while highlighting the importance of carefully assessing the factors that influence the efficiency of equation discovery.

> Dense non-Brownian suspensions exhibit complex resuspension dynamics governed by hydrodynamic interactions, particle microstructure, and gravity. While viscous resuspension in spherical suspensions is known to be strain-controlled, its applicability to anisotropic particles remains unclear. Here, we investigate dense suspensions of spherical and rod-shaped particles under steady and oscillatory shear. The results reveal two strain-controlled transitions: particle detachment from the sediment bed and the transition to a fully suspended state. Both particle shapes exhibit the same critical strain for detachment, approximately 6, indicating that resuspension onset is largely independent of particle morphology. In contrast, complete resuspension requires a critical strain of approximately 120 for spheres and 180 for rods, demonstrating a strong effect of particle anisotropy. A fluid-strain scaling collapses the onset of resuspension across particle concentrations and shapes while highlighting the distinct influence of particle shape on complete suspension. These findings establish a unified strain-based framework for viscous resuspension and clarify the role of particle anisotropy in dense suspension dynamics.

Stress relaxation in transient polymer networks often shows extended power-law behavior, $G(t) \sim t^{-\beta}$, where the exponent $\beta$ frequently departs from the value $1/2$ predicted by the sticky Rouse model and its variants. We introduce the fractional inhomogeneous Rouse model (FIRM), which uses a generalized Langevin equation driven by fractional Gaussian noise of exponent $\alpha$, while retaining heterogeneous bead friction to represent sticky cross-links. Thus, FIRM unifies subdiffusive sticker dynamics and chain heterogeneity within a single framework. We show that the relaxation modulus $G(t)$ can be represented as a linear combination of Mittag-Leffler functions. For homogeneous chains, it recovers two power-law regimes, $t^{-\alpha/2}$ and $t^{-2\alpha}$, on either side of the terminal relaxation time. Fitting FIRM to stress relaxation data for an imine-based polystyrene vitrimer shows that $\alpha < 1$ is required to capture the shape of the terminal relaxation. It also accommodates both Arrhenius and non-Arrhenius temperature dependence in the rheological activation energy. We derive expressions for dynamic properties such as mean-squared displacement and dielectric response and outline how generalized memory kernels extend the framework to real materials. Together, these results suggest novel ways in which data from rheology, dielectric spectroscopy, scattering, and other experimental methods may be incorporated into a chemistry-specific molecular model.

The centre-mode elastic instability, prevalent in rectilinear flows of dilute polymer solutions, allows dynamic states to emerge even in the absence of inertia. Here, we show that this instability can be significantly enhanced when the base flow has a nonuniform spatial-distribution of polymers. In such a flow, the polymeric stress not only depends on the conformation tensor (determined here by the Oldroyd-B equation) but also varies proportionally with the polymer concentration field, which satisfies a scalar transport equation. Focusing on the inertialess Stokes limit, we first consider the simple setting of periodic Kolmogorov flow. A linear stability analysis shows that a nonuniform polymer concentration either promotes or suppresses the centre-mode instability, depending on whether the polymers are localised near or away from the maximum of the base-velocity profile. We then focus on a base flow with a distinct polymer-laden stream overlying the base-velocity maximum, and sandwiched between polymer-free streams. We find that the critical Weissenberg number (product of the elastic relaxation time and the typical strain-rate) at the onset of instability undergoes a sudden decrease as the total polymer loading is increased. An energy analysis attributes this destabilisation to elastic feedback forces that arise from concentration gradients near the interfaces between the polymer-laden and polymer-free streams. The insights from Kolmogorov flow are shown to carry over to channel flow, where localising polymers about the centreline strongly promotes the centre-mode instability.

Local detailed balance restricts transport by self-propulsion in static activity landscapes. We show that a delayed speed adaptation (“delayed motility/kinesis”) generically breaks this symme try, inducing directed transport in asymmetric periodic motility profiles and enhancing diffusion in symmetric ones. Both effects occur for run-and-tumble, active Brownian, and inertial active particles, without requiring potential interactions, walls, imposed gradients, higher dimensions, or translational diffusion. Their magnitudes, and even current reversals, are conveniently tuned via the delay time, which establishes delayed motility as a versatile generic and experimentally accessible mechanism for autonomous self-steering and transport control in motile-active-matter circuity.

The motility of microswimmers in confined environments is a fundamental problem in active matter physics, with direct implications for microfluidic applications and the understanding of microorganism behavior in complex natural habitats. Although the run-and-tumble dynamics of flagellated microalgae such as Chlamydomonas Reinhardtii (CR) are well characterized in bulk suspension, the extent to which elementary geometric confinements alter their swimming remains insufficiently understood, particularly regarding the relative contributions of steric contact versus hydrodynamic interactions. Here, we experimentally investigate the trajectories of individual CR cells in a diversity of PDMS microfluidic geometries of growing complexity using single-particle tracking and statistical analysis. We show that cells in straight channels accumulate near walls and align along the channel axis, a behavior qualitatively reproduced by steric Active Brownian Particle simulations, yet showing a confinement-dependent velocity enhancement consistent with hydrodynamic wall coupling. In circular cavities with diameter below the persistence length L_0 ~350 microns, cells transition from bulk active Brownian exploration to quasi-circular wall-following trajectories. In dumbbell geometries, inter-compartment dwell length reflect purely geometric predictions, evidencing no measurable hydrodynamic contributions even for strong confinements. Together, these results demonstrate that environmental geometry can selectively amplify or suppress motility modes in active biological suspensions, opening avenues for the passive control of microswimmer transport in engineered microfluidic networks.

A finite density of mutually avoiding directed polymers in a quenched random medium is a minimal model of glassy line matter. The dilute theory, solved by replica Bethe ansatz, predicts an interaction free energy proportional to $\rho^2$ and disorder cumulants with distinct power-law dependences on the density $\rho$, but direct numerical tests have been hindered by the combinatorially large many-polymer transfer matrix. We recast the problem as filling logarithmic eigenvalues of a single-polymer transfer-matrix product, obtaining the quenched free energy, its cumulants, and a disorder-induced linear spectral edge consistent with the replica prediction.

Developing synthetic materials that exhibit life-like behavior, such as internally driven cycles, remains a central challenge in active matter. Here, we introduce a minimal colloidal model of chemical signaling in which particles produce diffusing signaling molecules that selectively promote or inhibit attractive interactions among neighboring particles. This bio-inspired, paracrine-like signaling mechanism generates context- and history-dependent many-body interactions that break time-reversal symmetry and drive the system far from equilibrium, leading to the spontaneous emergence of autonomous, internally sustained limit cycles in the composition of particle clusters. Using computer simulations, we map the resulting nonequilibrium phase behavior and identify distinct dynamical regimes controlled by the rates of signal production and degradation, together with the diffusion range of the signaling molecules. Among these, we find a robust oscillatory state in which particle clusters autonomously assemble in a cyclic fashion, driven entirely by internal feedback loops. Our results establish paracrine-signaling colloids as a minimal, physically realizable platform for programmable nonequilibrium materials with life-like functionality and provide a general route toward synthetic active matter with self-regulated collective dynamics.

Helices are among the most common ordered structures in biological and synthetic polymers, but their formation involves more than local conformational preference. A finite helix must nucleate, grow, resist breaking, and maintain a selected handedness against thermal fluctuations. We develop a three-state Ising-like transfer-matrix theory in which each segment is coil-like, right-handed helical, or left-handed helical. This formulation separates ordinary helix–coil cooperativity from the persistence of handedness. The right–left symmetric problem decomposes into symmetric and antisymmetric sectors, giving two characteristic lengths: the helical correlation length $\xi_H$ and the chiral persistence length $\xi_\chi$. In the strongly helical rare-wall limit, $\xi_\chi\simeq (1/2)\exp[\beta(K+J)]$. A local chiral bias, motivated by the Ramachandran landscape, is then amplified over finite helical domains.

Motility-induced phase separation occurs in assemblies of self-propelled units when activity is coupled negatively to density. In contrast, the consequences of a positive coupling between density and activity on the collective behaviour of active matter remain unexplored. Here, we show that collective activity can emerge from such a positive coupling among non-motile building blocks. We perform experiments with self-sustained oscillators powered by contact-charge electrophoresis. Although the oscillators are non-motile by design, they spontaneously form an active gas when confined together. The super-elastic nature of collisions constitutes a positive density-activity coupling and underlies the active gas properties. Elucidating the origin of binary collisions allows us to precisely control the structure of the active gas and its eventual crystallization. Beyond considering the overlooked positive coupling between density and activity, our work suggests that rich collective properties can emerge not only from the symmetry of interactions between active building blocks, but also from their adaptable and responsive behaviour.

Cell adhesion to viscoelastic substrates is mediated by focal adhesions (FAs), which dynamically couple actomyosin contractility to the extracellular matrix. Although substrate stress relaxation is known to regulate adhesion stability and cell migration, a predictive physical framework linking viscoelasticity to force transmission and adhesion dynamics remains lacking. Here we review briefly what is known about the active wetting and de-wetting of FAs on viscoelastic substrates and synthesize existing experimental and theoretical work into a two-timescale physical framework to describe the phenomena reported. At short timescales, oscillatory actomyosin-driven displacements are transmitted through molecular clutches, leading to frequency-dependent energy transfer to the substrate. We show that this transfer is maximized at an optimal frequency set by a balance between elastic energy storage and viscous dissipation, establishing a resonance-like mechanism that selects both the effective FA stiffness and traction force amplitude. At longer timescales, this mechanically optimal state couples to adhesion remodelling through an effective surface tension, enabling FA growth and disassembly to be interpreted as active wetting and de-wetting processes. The model predicts that adhesion stability and steady-state size are controlled by substrate stiffness and viscoelastic timescales, as well as mechanosensitive feedback mediated by Piezo1-dependent calcium signalling.

We develop a continuum theory for proliferating active matter starting from a microscopic stochastic model of self-propelled particles undergoing birth, death, and nonlocal competition. Beginning from the master equation, we derive mean-field evolution equations for the particle density and polarization fields and close the resulting hierarchy through a von Mises ansatz, providing a coupled hydrodynamic description applicable to a broad class of proliferating active systems. As an application, we study the recently introduced Active Brownian Bug model, in which the form of flocking emerges despite the absence of explicit alignment interactions. Linear stability analysis predicts both Turing and Hopf instabilities, whose analytical thresholds agree with numerical simulations. The continuum model reproduces the principal dynamical regimes of the underlying particle system, including homogeneous states, stationary periodic clusters, and coherently propagating flocking states. These results establish a general continuum framework for proliferating active matter and provide a physical interpretation of collective motion driven by the interplay between activity and population dynamics.

We develop a thermodynamic theory of electric double layers in binary liquid mixtures by allowing the Stern-layer capacitance to depend on the local solvent composition. This coupling produces an additional negative contribution to the inverse differential capacitance. As a result, the surface potential can become a nonmonotonic function of the surface charge density, leading to negative differential capacitance and a voltage-induced first-order transition between two electric-double-layer states. We determine the coexistence condition using a common-tangent construction for the surface-charge-controlled grand potential and obtain phase diagrams in terms of the Stern-capacitance contrast, surface charge density, bulk composition, and surface potential. We also compare the theory with capacitance data for tetrabutylammonium chloride in water/1-propanol mixtures, finding semi-quantitative agreement in the continuous-response regime. These results suggest that solvent exchange inside the Stern layer can strongly control the capacitance and interfacial phase behavior of binary mixtures.

Exotic nanoparticle superstructures can be accessed by harnessing nanoparticle softness and charge regulation, features often viewed as obstacles to structural control. Here, we show that regulated charge mismatch in polymer-grafted nanoparticles enables the assembly of high-stoichiometry cubic superlattices. By co-tuning grafting density, particle size, and bulk composition, we realize ionic-lattice analogues such as CaF2 and Th3P4, as well as single-component A3 and A7 superlattices without atomic counterparts. The A3 lattice has recently been identified theoretically as a photonic band-gap lattice. These phases emerge from a 1:1 "parent" lattice when local charge neutrality cannot be satisfied, driving either progressive interstitial filling or reorganization into a larger basis. For instance, the systematic occupation of ZnS tetrahedral sites yields CaF2, while ligand-swapping symmetry breaking converts CsCl into Th3P4. Upon heating, the assemblies exhibit reversible lattice contraction and pronounced negative thermal expansion. Furthermore, the energetic penalty for defects increases with nanoparticle size, facilitating the scalable production of high-quality, open superlattices for photonic applications.

The synchronization and phase-locking behavior of oscillators with smooth dynamics is well captured by continuous phase-models à la Kuramoto. However, these models do not apply seamlessly for hybrid oscillators, where discrete events occur along their otherwise smooth dynamics. Consequently, the synchronization and phase-locking mechanisms of hybrid oscillators remain overlooked. Here, we combine experiments, theory, and simulations, to investigate and rationalize the coherent motion of pairs of hybrid oscillator. Using contact-charge electrophoretic (CCEP) oscillators as an experimental realization, we show that in-phase oscillations can occur, despite oscillators repelling each other. We rationalize this behavior by introducing a discrete-time framework that explicitly accounts for discrete events and elucidates the origin of phase-locking. Our model highlights the roles played by inertia and the decay of interaction strength along the oscillation cycle in promoting phase-locking of CCEP oscillators. More generally, it provides a phase-locking criterion that holds for a broader class of coupled hybrid oscillators, and reveals that various mechanisms can lead to their coherence.

This book has one primary goal: To get you moving quickly from learning basic principles of colloid science, to designing colloidal systems for function or motion in the lab. It is not intended to provide encyclopedic knowledge about all aspects of colloid and surface science; rather, I have chosen not to include many topics of genuine importance. In reaching the intended goal, I use two parallel strategies. First, I give practical results that can be used immediately. If there is a cumbersome calculation, I have worked to reframe it into a table or figure. This is the case for Hamaker constants and hydrodynamics of spheroids, for instance. Second, I describe the physics of various colloidal phenomena, so that you as a researcher can think about alternative strategies. In balancing algorithms with explanations, I provide plug-and-chug example problems to familiarize you with units, constants, and typical values. The practice problems provide extensions to the most basic theory that open new possibilities, while also giving results that are useful in practical and research studies. Throughout the book, I provide data we commonly use for viscosities, zeta potentials, ionic phenomena, and other parameters. Rather than providing every reference and every technique, I have provided those references and techniques that we most often use in our lab. In the end, this book aims not to be an exhaustive study of colloids, but rather to be a doorway to producing desired colloidal systems as quickly as possible.