Anisotropic rod-like particles form liquid crystalline phases with varying degrees of orientational and translational order. When confined geometrically, these phases can give rise to topological defects, which can be selected and controlled by tuning how the rods align near boundaries, known as anchoring. While anchoring in molecular liquid crystals can be controlled through surface functionalization, this approach is not easily applicable to microscale colloidal systems, which have so far been limited to planar anchoring. Here, using particle-based simulations, Landau-de Gennes theory, and experiments on colloidal rods, we demonstrate that topographical patterning of the boundary can effectively control the anchoring type and, in turn, the defect state in two-dimensional confined nematics. Building on this, we numerically predict that dynamically shape-shifting the boundaries can transform and transport topological defects.

Knotted fields in classical and quantum systems have long been recognized for their nontrivial topologies and particlelike behavior, but practical applications have been limited by the difficulty of stabilizing them. Recently, stable knotted solitonic textures—heliknotons—were discovered in chiral liquid crystals, forming adaptive crystal assemblies via elastic distortion-mediated interactions. We use machine learning to develop single-site coarse-grained potentials that accurately capture these chiral anisotropic effective interactions. The resulting potentials accurately reproduce experimentally observed heliknoton assemblies and enable simulations at length scales and timescales far beyond the range of fine-grained continuum models. This general framework is readily transferable to other topological solitons, providing a powerful route to understand, predict, and ultimately control their collective behavior and dynamics.

We investigate the dynamical behavior and vibrational properties of three structurally distinct two-dimensional systems: a supercooled binary liquid, a dodecagonal quasicrystal (DDQC), and a hexagonal crystal. Using molecular dynamics simulations, we find that all three systems exhibit transient caging in the mean-squared displacement and non-Gaussian single-particle displacement statistics. However, the temperature dependence of the dynamics differs markedly among them. In the supercooled liquid, the peak of the non-Gaussian parameter increases upon cooling, reflecting the growth of dynamical heterogeneity. In contrast, in the DDQC, the peak decreases as temperature is lowered, consistent with the progressive suppression of thermally activated, localized rearrangements. For the DDQC, this behavior is confirmed by the cage-relative self part of the van Hove function, which shows a systematic suppression of large single-particle displacements upon cooling. At the same time, the DDQC exhibits a large dynamical susceptibility, indicating that many-body dynamical correlations remain strong despite the reduction of large particle displacements upon cooling. A real-space cluster analysis reveals that mobile particles remain organized into extended, spatially correlated, dynamical clusters, with temperature primarily affecting the cluster-size distribution rather than the intrinsic cluster morphology. The vibrational spectra further differentiate the three systems: the crystal exhibits van Hove singularities, the supercooled liquid shows a boson peak, and the DDQC displays additional low-frequency contributions associated with quasiperiodic order. These results establish the DDQC as an intermediate state, combining glass-like caging dynamics with vibrational signatures strongly influenced by quasiperiodic order.

The exponential growth in energy consumption of artificial intelligence systems has spurred interest in physical computing paradigms that exploit the relaxation of physical systems toward steady states. However, many existing physical networks are fundamentally linear and incapable of performing nonlinear operations crucial for meaningful machine learning tasks. Here we use simulations to show that nonlinearity alone is insufficient; physical learning systems must also support signal amplification and suppression to perform nontrivial computations. We present physically plausible circuit designs that incorporate these essential features, enabling effective nonlinear information processing. Our findings clarify the limitations of linear physical networks and provide guidance for developing energy-efficient physical learning architectures capable of general machine learning tasks.

Attractive three-body interactions have been reported for like-charged colloids in low-salt suspensions, based on both finite-element Poisson-Boltzmann calculations and direct experimental measurements, and have been proposed as a mechanism to drive colloidal clustering. However, these Poisson-Boltzmann calculations typically neglect charge regulation and higher-order many-body effects. Here, we construct machine-learned (ML) many-body interaction potentials for charge-regulating colloids, trained on finite-element Poisson-Boltzmann calculations, to accurately capture three-body and higher-order contributions. We find that the three-body contribution to the many-body potential as obtained from Poisson-Boltzmann calculations on isolated colloid triplets is strongly attractive, consistent with previous work, whereas the four-body contribution for an equilateral pyramid configuration of four colloids is repulsive. We then construct ML many-body potentials for charged colloids using finite-element Poisson-Boltzmann calculations on clusters of 13 colloids, and find that the incorporation of higher-body interactions weakens the cohesive nature of the interactions. We identify a parameter regime exhibiting gas-liquid or gas-solid phase separation using the ML potentials in molecular dynamics simulations. However, when we include clusters of 48 colloids in the training data, the cohesion diminishes further, and molecular dynamics simulations using these potentials no longer include broad phase separation in aqueous dispersions of charged colloids. Finally, we compute the potential of mean force of pairs and triplets of colloids using primitive model simulations. We find that the resulting potentials are in good agreement with those obtained from the Poisson-Boltzmann calculations, thereby supporting the validity of the Poisson-Boltzmann approach for determining many-body interactions.

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.

Grain boundaries are complex defects in polycrystalline systems and their migration has a key role in determining the properties of such solids. Understanding grain boundary motion in terms of both particle and dislocation dynamics remains a central problem. Here we establish a fundamental geometric principle governing grain boundary migration at the microscopic level: particles preferentially transition between grains at specific lattice equivalence points identified through a refined O-lattice construction. We validate this principle using loop-shaped grain boundaries in two-dimensional colloidal crystals created with holographic optical tweezers and computer simulations. Building on this principle, we develop a geometric framework that accurately predicts the microscopic dynamics of both particles and dislocations during grain boundary migration. Our results shed light on the microscopic mechanism of grain boundary migration and reveal the intrinsic connection between the dynamics of particles and dislocations.

The ordering of rod-like particles in soft, deformable containers emerges from the interplay of anisotropic interactions, geometric confinement, and boundary compliance. This competition couples internal particle organization to container morphology, producing behavior distinct from both rigid confinement and bulk systems. Such coupling is also relevant to biological contexts in which filamentous structures are confined by deformable membranes. Using a minimal model combining experiments and simulations of colloidal rods encapsulated in lipid vesicles, we show that soft confinement drives a bidirectional coupling between internal order and vesicle shape. This interplay gives rise to a phase diagram in which elongated vesicles promote nematic alignment at lower packing fractions, whereas higher packing fractions induce smectic-like ordering that reshapes vesicles into plate-like morphologies with increased bending energy. Furthermore, by controlling vesicle volume and membrane area, we demonstrate that boundary conditions enable reversible tuning of both vesicle shape and internal rod organization. These results establish a framework for dynamically controlling colloidal self-assembly in soft containers and provide insight into the organization of anisotropic building blocks in deformable, cell-like, confinements.

Past experimental observations of gas-liquid and gas-crystal coexistence in low-salinity suspensions of highly charged colloids have suggested the existence of like charge attraction. Evidence for this phenomenon was also observed in primitive-model simulations of (asymmetric) electrolytes and of low-charge nanoparticle dispersions. These results from low-valency simulations have often been extrapolated to experimental parameter regimes of high colloid valency where like-charge attraction between colloids has been reported. However, direct simulations of highly charged colloids remain computationally demanding. To circumvent slow equilibration, we employ a machine-learning (ML) framework to construct ML potentials that accurately describe the effective colloid interactions. Our ML potentials enable fast simulations of dispersions and successfully reproduce the gas-liquid and gas-solid phase separation observed in primitive-model simulations at low charge numbers. Extending the ML-based simulations to higher valencies, where primitive-model simulations become prohibitively slow, also reveals like-charge attractions and gas-liquid spinodal instabilities, however only in the regime of strongly coupled electrostatic interactions and not in the weakly coupled Poisson-Boltzmann regime of the experimental observations of colloidal like-charge attractions.

Artificial intelligence is rapidly permeating modern technology, but its growth is increasingly constrained by the costs of delivering power and removing heat. Neural computation offers a striking counterpoint, for it achieves sophisticated information processing at exceptionally low energy by exploiting ionic flows and adaptive conductance. Inspired by the Hodgkin-Huxley view that function emerges from ion-transport dynamics, recent work has begun to implement memory and learning directly in fluids, where ions simultaneously carry signals and encode the internal device state. This Review charts the emerging landscape of fluidic ionic memristors, from soft, bioinspired materials to manufacturable solid-state nanofluidic architectures. In lipid bilayers, droplet networks, tissues and ionic polymers, electrical activity is intrinsically coupled to chemistry and mechanics, enabling plasticity across multiple timescales. In rigid nanopores, nanochannels and angstrom-scale slits, the softness is transferred from the scaffold to the ionic degrees of freedom, where electric double-layer dynamics, concentration polarization and confinement-driven effects produce history-dependent transport in robust inorganic frameworks. Hybrid approaches integrate gels, brushes, particles, or biomolecules within microfabricated structures to combine stability with rich analogue dynamics. We conclude by outlining the key requirements for translation from reproducibility to scalable integration towards ionic intelligence technologies.

Many active particles are embedded in environments that exhibit viscoelastic properties. An important class of such media lacks a single characteristic relaxation timescale when subjected to a time-dependent stress. Rather, the stress response spans a broad continuum of timescales, a behavior naturally described by a scale-free, fractal-like power-law relaxation modulus. Using a generalization of the fractional Langevin equation, we investigate an active Brownian particle embedded in a power-law viscoelastic environment with translational and rotational dynamics governed by independent fractional orders. We solve the model analytically, develop a numerical scheme to validate the theoretical predictions, and provide tools that can be used in further studies. A rich variety of diffusion regimes emerges, which modify the intermediate-time behavior of the mean squared displacement. Notably, we find that the competition between translational and rotational contributions favors a superdiffusive persistence over the standard ballistic motion, and over-stretches its characteristic timescale, fundamentally altering the standard relation between persistence and propulsion in active matter.

Quasicrystals occupy a unique middle ground between periodically ordered crystals and disordered glasses, making them an ideal platform for examining the interplay between disorder and the emergence of mechanical memory. Using athermal quasistatic shear simulations, we show that two-dimensional dodecagonal quasicrystals encode and recover memory under cyclic driving. Above the yielding transition, the response becomes irreversible, characterized by persistent shear bands and locally transformed regions. Below yielding, cyclic shear with varying amplitudes produces a hierarchy of nested hysteresis loops in the stress-strain response characteristic of loop-return point memory. By resolving the underlying reversible plastic events, we reveal localized phason-like tile rearrangements as the elementary switching units and identify tile-switch hysterons responsible for memory in the quasicrystal. Such a microscopic identification of the fundamental switching units is considerably more challenging, and often impossible, in amorphous solids. Despite their structural diversity, these rearrangements share a compact core, sharp bistability, and an Eshelby-compatible elastic far field. In contrast, a periodic approximant of the quasicrystal lacks both the structural disorder and the bistable tile-switch rearrangements required for cyclic-shear memory, linking phason degrees of freedom to bistable hysterons.

Many living systems, such as birds and fish, exhibit collective behaviors like flocking and swarming. Recently, an experimental system of active colloidal particles has been developed, where the motility of each particle is adjusted based on its visual detection of surrounding particles. These particles with visual-perception-dependent motility exhibit group formation and cohesion. Inspired by these behaviors, we investigate intelligent active Brownian particles (iABPs) equipped with visual perception and velocity alignment in three dimensions using computer simulations. The visual-perception-based self-steering describes the tendency of iABPs to move toward the center of mass of particles within their visual cones, while velocity alignment encourages alignment with neighboring particles. We examine how the behavior varies with the visual cone angle theta, self-propulsion speed (Peclet number Pe), and the interaction strengths of velocity alignment (Omega_a) and visual-based self-steering (Omega_v). Our findings show that spherical iABPs form clusters, worm-like clusters, milling behaviors, and dilute-gas phases, consistent with 2D studies. By reducing the simulation box size, we observe additional structures like band-like clusters and dense baitball formations. Additionally, rod-like iABPs form band-like, worm-like, radiating, and helical structures, while iABP worms exhibit streamlined and blob-like structures. Many of these patterns resemble collective behaviors in nature, such as ant milling, fish baitballs, and worm clusters. Advances in synthetic techniques could enable nanorobots with similar capabilities, offering insights into multicellular systems through active matter.

Optimizing the design and synthesis of complex crystal structures presents pivotal opportunities and challenges in materials design. While recent computational advances in inverse design have proven effective for simpler crystals, their extension to intricate structures such as zeolites remains challenging. In this work, we introduce an efficient and robust inverse design workflow specifically tailored for the predictive design of a broad range of complex phases. By integrating an evolutionary parameter optimization strategy with enhanced sampling molecular dynamics simulations, this approach effectively surmounts the high energy barriers that typically hinder self-assembly in these complex structures. We apply this inverse design workflow to facilitate the efficient self-assembly of target zeolite frameworks in an efficient coarse-grained model of a tetrahedral network-forming component and a structure-directing agent. Using this method, we not only successfully reproduce the self-assembly of known structures like the Z1 and SGT zeolites and Type-I clathrates but also uncover previously unknown optimal design parameters for SOD and CFI zeolites. Remarkably, our approach also leads to the discovery of an uncatalogued framework, which we designate as Z5. Our methodology not only enables the screening and optimization of self-assembly protocols but also expands the possibilities for discovering hypothetical structures, driving innovation in materials design and offering a robust tool for advancing crystal engineering in complex systems.

Curved cylinders, if rigid, cannot roll on a surface like straight cylinders, but soft cylinders bent by specific stimuli can! Studying the autonomous locomotion of these soft robots and their interactions with the environment using finite element analysis is challenging due to the complex multiphysics of stimuli-responsive soft materials and nonlinear contact mechanics. In this pioneering work, we simulate the rolling of stimuli-bent cylinders on a surface using contact finite elements and introduce a simple yet effective pseudo-thermal field method. Our approach successfully reproduces several modes of autonomous locomotion observed experimentally, including phototropic locomotion, phototropic climbing on a slanted surface, steering under partial illumination, and backward rolling under alternating heat-light stimuli. Parametric analysis demonstrates strong agreement between the experiments and our numerical results, validating the effectiveness of our approach. This study reveals the intriguing and highly nonintuitive dynamics of photo- or thermally bent cylindrical soft robots, and serves as a paradigm for modelling and simulating such rolling robots.

We employ molecular dynamics simulations to investigate ion and water transport driven by an electric field through quasi-two-dimensional nanoslits with a tapered geometry. Despite the absence of surface charge on the (non-polarizable) channel walls and the associated electric double layer, we do observe robust ion selectivity. This selectivity favors the transport of cations from base to tip when the electric field is directed from base to tip, and anions from base to tip when the field direction is reversed. In addition, we observe a corresponding electro-osmotic water flow from base to tip, regardless of the electric field direction. Intriguingly, ion selectivity and electro-osmotic flow are conventionally associated with surface charge and electric double layers. Here, however, we uncover a novel mechanism for these phenomena in uncharged tapered nanoslits, where ion selectivity arises from the divergence of the heterogeneous water polarization.

Intelligent soft matter stands at the intersection of materials science, physics, and cognitive science, promising to change how we design and interact with materials. This transformative field seeks to create materials that possess life-like capabilities, such as perception, learning, memory, and adaptive behavior. Unlike traditional materials, which typically perform static or predefined functions, intelligent soft matter dynamically interacts with its environment. It integrates multiple sensory inputs, retains experiences, and makes decisions to optimize its responses. Inspired by biological systems, these materials intend to leverage the inherent properties of soft matter: flexibility, self-evolving, and responsiveness to perform functions that mimic cognitive processes. By synthesizing current research trends and projecting their evolution, we present a forward-looking perspective on how intelligent soft matter could be constructed, with the aim of inspiring innovations in fields such as biomedical devices, adaptive robotics, and beyond. We highlight new pathways for integrating design of sensing, memory and action with internal low-power operations and discuss challenges for practical implementation of materials with "intelligent behavior". These approaches outline a path towards to more robust, versatile and scalable materials that can potentially act, compute, and "think" by their inherent intrinsic material behaviour beyond traditional smart technologies relying on external control.

Since the influential work of ten Wolde, Ruiz-Montero, and Frenkel [Phys. Rev. Lett. 75, 2714 (1995)], crystal nucleation from a Lennard-Jones fluid has been regarded as a paradigmatic example of metastable crystal ordering at the surface of a critical nucleus. We apply seven commonly used local structure detection algorithms to characterize crystal nuclei obtained from transition path sampling simulations. The polymorph composition of these nuclei varies significantly depending on the algorithm used. Our results indicate that one should be very careful when characterizing the local structure near solid-solid and solid-fluid interfaces. Particles near such interfaces exhibit a local structure distinct from that of bulk fluid or bulk crystal phases. We argue that incorporating outlier detection into the local structure detection method is beneficial, leading to greater confidence in the classification results. Interestingly, the bcc coating nearly disappears when adopting a machine learning method with outlier detection.

The intrinsic Helmholtz free-energy functional, the centerpiece of classical density functional theory, is at best only known approximately for 3D systems. Here we introduce a method for learning a neural-network approximation of this functional by exclusively training on a dataset of radial distribution functions, circumventing the need to sample costly heterogeneous density profiles in a wide variety of external potentials. For a supercritical Lennard-Jones system with planar symmetry, we demonstrate that the learned neural free-energy functional accurately predicts inhomogeneous density profiles under various complex external potentials obtained from simulations.