Papers

Mechanical metamaterials exhibit anomalous properties induced from non-trivial mesoscopic constituents. Inspired from architectural and industrial structures, we introduce arrangements of long, narrow ribbons intersecting at prescribed angles as a model thin-sheet metamaterial. These ribbon gridshells are shown to display highly non-linear behavior driven by the geometric constraints, nonetheless unlike most complex mechanical systems, we are able to explicitly write out the coarse-grained governing equations and to classify their solutions in terms of the intersection patterns of the ribbons. It is shown that the structure can assume arbitrary, tunable Gaussian curvature distributions, allowing us to formulate an inverse design problem, solvable under a suitably defined local condition. An analysis of the soft modes, confirmed by experiment and numerics, reveals rich mechanics which may exhibit both a rigid and an anomalously soft behaviors.

Topological phases of matter support edge states protected from random perturbations, and the identification of the discrete non-spatial symmetries and dimensions that support such phases was systematically developed for quantum systems and analogous platforms. While topological phases were also discovered in stochastic systems and posited as mechanisms for key biochemical processes, a classification consistent with their Markovian constraints remains lacking, impeding generalization to new scenarios. To address this, we develop new methods including a new homotopy approach, real-space invariants and a redefinition of the point gap to classify both transient and steady states. We find robust transient states in two symmetry classes, no symmetry and pseudo-Hermiticity respectively, while topological steady states are expected only in systems without symmetry. We identify the dimensions with non-trivial phases and their group structure, creating a rigorous framework for predicting robust behavior in active and living matter.

Pairs of spheres sharing an acoustic trap sometimes spin intermittently despite having no self-propulsion, no obvious power source, and no symmetry-breaking mechanism, switching between rocking and spinning within a single trajectory. Nonreciprocal wave scattering powers this emergent activity, and drag shapes their dynamics by coupling rotations to translations. Mismatched pairs can pass through a supercritical Hopf bifurcation into a quasiperiodic torus on which the pair's orbit reverses regularly and, farther from equilibrium, into deterministic chaos. Experiments motivate this mechanism and share its qualitative signatures; simulations reveal a full noise-free route from passivity to chaos, and suggest how analogous dynamics can emerge in other active-matter systems.

Curvature and topology jointly organize defects in two-dimensional crystals, but their combined role remains unresolved when competing lattice symmetries coexist with spatially varying curvature. We use simulated-annealing Langevin dynamics to study Hertzian particles forming coexisting hexagonal (Hex) and square (Sq) lattices on prolate and oblate ellipsoids. Mapping reduced density and aspect ratio reveals a broad sequence of scar and domain-based morphologies in both Hex-dominant and Sq-dominant backgrounds. Latitude-resolved comparisons show that Gaussian curvature biases defects toward its maxima under weak deformation. Strong prolateness, however, confines high curvature to small polar caps that cannot independently accommodate all defect motifs. Defects then spread toward lower-curvature latitudes to relieve defect crowding and elastic repulsion. In the Hex-dominant regime, this competition drives vertex-contacted domains with neutralized corner contacts, and compensating positive defects locate away from the poles. The Sq-dominant regime features Hex-rich triangular domains, bridged states, and linear or open scars similarly reorganized by curvature anisotropy. On oblate ellipsoids, the extended equatorial high-curvature belt allows defects to separate azimuthally while remaining curvature-localized. This work elucidates that nonuniform curvature can engineer rich defect patterns by selecting the spatial distribution of topological charge and the connectivity of finite defect motifs.

Capsules are attractive platforms for microrobot delivery, combining structural simplicity with protected delivery and rapid release remains challenging. Inspired by the latched spring mechanism of Impatiens balsamina seed dispersal, a magnetothermally triggered capsule integrates a phase-change hydrogel latch, a monostable cover that serves as an elastic spring, and a payload-carrying base. Mechanical analysis guides the cover design to avoid bistability after assembly and premature hydrogel latch rupture before triggering. During transport, the hydrogel constrains the inverted cover. Under an alternating magnetic field, Fe3O4-mediated heating softens the hydrogel and induces cohesive failure, releasing stored energy to drive capsule opening and microrobot ejection. The capsule opens within 50 ms after hydrogel softening and ejects microrobots at an estimated initial velocity of 1.0 m/s. Demonstrations on a three-dimensional platform and ex vivo porcine stomach establish protected delivery, target-site opening, and post-release actuation.

We investigate how particle stiffness governs length-scale-dependent relaxation dynamics in dense suspensions of thermoresponsive PNIPAM microgels subjected to temperature variations and large amplitude oscillatory shear. By combining dielectric spectroscopy with rheometric measurements, we directly correlate microscopic polarization fluctuation dynamics with macroscopic mechanical relaxation. Highly crosslinked, stiffer microgels exhibit longer dielectric relaxation times across a broad temperature range and strain-induced slowing down, whereas softer, open-network microgels exhibit nearly strain-independent dielectric dynamics. Below the volume phase transition temperature (VPTT), macroscopic bulk stress relaxation experiments reveal that suspensions of the softest particles relax most rapidly. For the stiffer microgel suspensions, however, the dynamics decouple: bulk stress relaxation speeds up with increasing stiffness even as dielectric relaxation slows down. Above the VPTT, softer particles undergo greater volume collapse, leading to very rapid bulk stress relaxation. Besides exhibiting slower stress decay, stiffer microgel suspensions also undergo shear-induced structural regeneration during the later stages of deformation. These findings demonstrate that particle stiffness and internal architecture govern relaxation pathways across microscopic and macroscopic length scales, thereby providing a framework for designing adaptive soft metamaterials, stress-dissipative coatings, and self-healing robotic materials.

Plasmas sustain strong energy and momentum flux, yet this activity is typically treated as a dissipative loss channel rather than a usable resource, and its conversion into macroscopic work remains challenging. Here we demonstrate a plasma-powered active engine by coupling self-propelled micromotors to ratchet rectification. Dielectric microspheres in the plasma sheath spontaneously develop asymmetric surface charging and undergo a Quincke rotational instability, forming fast micromotors that extract energy directly from the plasma. Their stochastic impacts are rectified by a sawtooth rotor into a directed angular-momentum flux that drives steady rotation, while an outer asymmetric gear organizes the active bath into coherent circulation to amplify torque transfer. Operating in an inertia-relevant regime, the engine achieves orders-of-magnitude enhancements in both power output and end-to-end efficiency compared with liquid-phase active engines, and remains functional down to the single-micromotor limit. More broadly, our results establish a general route to rectify nonequilibrium plasma activity for macroscopic work.

The orbit selected by a magnetic particle in a viscous liquid under a rotating field is commonly described in the instantaneous Stoner–Wohlfarth limit, in which the magnetic moment always occupies a minimum of the anisotropy energy. In this limit, precession out of the field plane exists only for reduced fields $B_0/B_a<1/\sqrt2$, and stronger fields admit only planar synchronous rotation or libration. We study a macroscopic egg-yolk particle, a printed shell containing two freely rotating permanent magnets in fluid-filled cavities, driven by a compensated rotating field and tracked optically. In addition to synchronous rotation, precession, and libration, the particle exhibits a polar phase: above the instantaneous bound and at high frequency, the shell axis leaves the field plane and locks onto a narrow cone about the rotation axis. We extend the model by a finite viscous friction between the magnets and the shell. The extension introduces a single dimensionless parameter, the ratio $\kappa$ of inner to outer rotational friction, and reduces to the instantaneous theory as $\kappa\to0$. Numerical phase diagrams show that increasing $\kappa$ tilts the bistable band to higher fields at higher frequencies and extends stable precession above $B_0/B_a=1/\sqrt2$, whereas for large $\kappa$ planar libration returns at high frequency. With a calibrated anisotropy field, relaxation rate, and $\kappa$ of order unity, the model reproduces the terminal state of all measured records and their tilt angles, including the polar cone. In the model the polar state is maintained by a steady rotation of the magnets relative to the shell, driven by the field and anisotropy torques and dissipated by the inner friction; it therefore exists only for intermediate $\kappa$.

Using optical tweezers, we demonstrate that the CuAAC click reaction increases the positional fluctuations of a trapped 2 micrometer colloid by at least 20% without altering the trap's corner frequency. This excess variance relaxes to the thermal baseline as reagents are depleted. The additional noise is Gaussian, with a flat power spectrum extending past the corner frequency up to 7 kHz. Notably, the noise amplitude decouples from the macroscale reaction rate, and independent molecular force dipoles are orders of magnitude too small to generate the observed variance. Although the chemical free energy released locally exceeds the energy absorbed by the bead by five orders of magnitude, this energy couples inefficiently. The mechanical action of the reacting bath cannot be represented as a sum of independent molecular events.

The environmental transport of microplastic particles has raised concerns because of their potential ecological and human-health impacts. A particular challenge for experiments on microplastic transport in soils is the fact that soil is a highly complex and non-transparent porous medium. Thus, our knowledge of transport mechanisms of microplastics in soils and related ecological implications is still limited and computational simulations offer an additional possibility to obtain important insights into the physical transport behaviour of microplastics. Yet, direct particle-resolved simulations in realistic soil structures for macroscopic sample sizes remain a computational challenge. We introduce an efficient pore-network model, minD-PNM, that predicts particle breakthrough curves in water-saturated soils using experimental X-ray micro-computed tomography ($\mu$CT) pore geometries as the only input. The model combines an approximately $t^{-3}$ pore-scale transit time distribution with a minimum-dissipation partition of multi-inlet-multi-outlet pores, and propagates these distributions through the pore network to predict breakthrough curves. We benchmark minD-PNM against lattice Boltzmann and immersed boundary simulations for small systems, and against microplastic column experiments in quartz sediments for macroscopic sample sizes. In both cases, the predicted breakthrough curves agree well with the corresponding reference data. Because it requires only geometric information, minD-PNM scales to macroscopic sample volumes offering a practical tool for contaminant-hydrology studies of particulate pollutants.

We introduce frustrated triangular networks that mix two different beam thicknesses. The two thicknesses separate the energetic costs of second-order buckling and angular deformation into four competing contributions. Using scaling arguments and mapping to an effective Ising description, we construct the system's phase diagram in terms of its dimensionless geometric parameters. Selected beam arrangements exhibit local bistability: hexagonal motifs switch independently between opposite twisting states, while linear motifs support independently switchable beam states. In both cases, the number of mechanically stable configurations grows exponentially with system size. Experiments on fabricated silicone metamaterials confirm the predicted bistability and local switching. More generally, the allowed beam arrangements map onto rhombus tilings, producing a large combinatorial space of architectures. The system thus combines multiplicity in both architecture and stable deformation states, establishing beam-thickness patterning as a route for programming frustration, multistability, and extensive degeneracy in triangular mechanical metamaterials.

Odd pressure is a parity-odd transport coefficient that gives an isotropic pressure response to vorticity in compressible two-dimensional fluids. By asymmetrically coupling vortical and compressional modes, it provides a direct mechanism for a nonreciprocal hydrodynamic response reminiscent of several biological systems. Yet microscopic models realizing odd pressure as a transport coefficient are relatively scarce. Here, we construct one such model using a lattice-gas cellular automaton based on the Frisch-Hasslacher-Pomeau II model with rest particles and chiral collisions, whose Chapman-Enskog coarse-graining produces a nonzero odd pressure coefficient. The key ingredient is a local parity-breaking collision that weakly rotates moving particles in the presence of a rest particle. At hydrodynamic scales, this microscopic rule acts as an effective magnetic field, converting the model's bulk viscosity into odd pressure. More generally, we derive expressions relating Hall viscosity, odd pressure, and odd torque to their parity-even counterparts in our model.

An asymptotic analysis of the Landau–de Gennes framework is performed to compute higher-order corrections to the Oseen–Frank limit in a bounded three-dimensional domain under appropriately scaled surface anchoring energy. A systematic decomposition of the $\mathbf{Q}$-tensor into three mutually orthogonal subspaces-the uniaxial scalar, geometric tilt vector, and transverse anisotropy tensor-reveals that the leading $\mathcal{O}(\varepsilon)$ correction to the Oseen–Frank director field $\mathbf{n}_0(\mathbf{x})$ is dominated by a non-vanishing tilt field $\mathbf{p}_1(\mathbf{x})$, where $\varepsilon$ represents the ratio of the nematic coherence length to the characteristic domain size. This macroscopic variation constitutes a soft mode released from the boundary once the surface anchoring energy is retained at its physical scaling rather than driven to an infinite strength. We show that this tilt field is governed by the linear Jacobi equation, $\mathcal{J}_{\mathbf{n}_0}(\mathbf{p}_1)=\mathbf{0}$, subject to a non-trivial, anchoring-driven Dirichlet boundary condition, where $\mathcal{J}_{\mathbf{n}_0}$ is the on-shell Jacobi operator of the harmonic map $\mathbf{n}_0$ on $\mathbb{S}^2$. The two fields are accompanied at $\mathcal{O}(\varepsilon^2)$ by an off-shell correction to both the uniaxial scalar and the transverse anisotropy tensor, passively induced by the elastic non-uniformity $(\nabla\mathbf{n}_0\neq\mathbf{0})$ and the boundary-driven tilt $(\mathbf{p}_1\neq\mathbf{0})$. Through $\mathcal{O}(\varepsilon^2)$, the tilt enters the energy only through surface terms, not the bulk, providing a pathway for the system to lower its energy . Under the conventional benchmark of rigid Dirichlet conditions, this response is annihilated outright, demonstrating that corrections built upon infinite energy barriers obscure the underlying physics of anchoring-driven tilt modes.

Motivated by biological systems and my previous studies of quorum sensing with density-enhanced motility, I study a model of density-enhanced size and motility, in which both particle size and motility increase when the local density (over a distance larger than particle diameter) exceeds the global density. The emergent structures along different size ratios are spots, holes, bands and labyrinths controlled by several distinct observations. First, the characteristic pattern length scale is controlled by the sensing radius and remains approximately independent of the size ratio. Second, the total area occupied by the particles decreases with increasing size ratio. Third, the active fraction barely depends on the size ratio. These results demonstrate how both particle size and motility can couple microscopic regulation to large-scale pattern formation. I conclude by discussing possible extensions of the model.

Confined aqueous electrolytes exhibit strong deviations from bulk behaviour, but it remains unclear which changes arise from genuine confinement-induced modification and which merely reflect the influence of interfaces. Here, we introduce an interfacial deficit-length framework, capable of decomposing density, diffusivity, and conductivity of confined electrolyte solutions into interfacial and confinement contributions. By applying the framework to molecular dynamics simulations of aqueous alkali halides in planar graphene nanoslits coupled to bulk reservoirs at variable electrolyte concentration, we show that genuine confinement effects emerge only for slit heights $H \lesssim 1$ nm; for larger H, deviations from bulk behaviour are quantitatively captured by interfacial deficit lengths. These deficit lengths are strongly ion-specific and generally positive for water and salt densities as well as for conductivities, meaning that graphene interfaces reduce the values of these observables, while diffusivity deficit lengths tend to be negative, corresponding to larger slit self-diffusivities relative to the corresponding bulk reference. Our deficit-length framework is applicable to any observable from experiments or simulations on nanoconfined electrolytes and predicts confined electrolyte properties for variable slit height H and reservoir electrolyte concentrations.

Testing the ergodicity hypothesis through experimentation in real systems is of crucial importance as it challenges a fundamental assumption underlying a wide range of theoretical models of physical and complex systems. High-calibre experiments can demonstrate whether, when and how a real system explores all of its possible states, and serve as a crucial conduit between abstract theoretical frameworks and tangible real-world applications. This approach is intended to guarantee that our descriptions of complex systems remain both physically meaningful and technologically relevant, thereby facilitating a more nuanced and comprehensive understanding. The development of a novel light scattering experiment has enabled us the direct measurement of the full distribution of fluctuations in the particle concentration in colloidal model systems and thus the direct determination of the probability distribution. This, in turn, facilitates the experimental verification of the ergodic hypothesis and the quantification of ergodicity breaking as a function of metastability.

Accurate prediction of avalanche motion is essential for hazard assessment in mountainous terrain. This study develops and evaluates a physics-informed neural network (PINN) framework for the Savage-Hutter model of depth-averaged granular flow, progressing from 1D analytical verification to 2D experimental validation. First, three 1D problems of increasing complexity were verified against the analytical solution: height prediction with prescribed velocity, velocity prediction with prescribed height, and coupled prediction of both fields using the conservative formulation. The decoupled tests accurately reconstructed the spatio-temporal evolution of each field when the other was prescribed. The coupled formulation learned both fields without prescribed data, achieving mean height and velocity RMSEs of 0.043 and 0.079 in non-dimensional units. A hyperparameter sensitivity study evaluated the effects of network depth, width, collocation density, learning rate, and epochs. The framework was then extended to 2D and validated against laboratory experiments of a cylindrical granular pile collapsing on an inclined plane, with TITAN2D providing numerical comparisons. Purely physics-based training converged to the trivial zero solution; augmenting the loss with 10 sparse training points from final deposit profiles produced a physics-informed, data-assisted hybrid framework. Peak flow depth, depth-averaged velocity, RMSE, and wetted-area IoU evaluated global and local agreement. Global height RMSE ranged from 2.7 to 6.7 mm across four experimental cases, while mean wetted-area IoU ranged from 69 to 81 %, demonstrating consistent performance across variations in pile mass and slope angle.

We develop a rational-function approximation for the structural properties of multicomponent fluids with narrow square-well and square-shoulder interactions, together with weakly nonadditive hard-sphere mixtures. The theory is obtained by reformulating the analytical Percus–Yevick solution for additive sticky hard-sphere mixtures so as to account for finite interaction widths, leading to a unified semianalytical framework for these classes of fluids. The approximation satisfies the exact low-density limit and preserves the continuity of the cavity functions; a simple local correction restores the continuity of their first derivatives. Comparison with Monte Carlo simulations for binary mixtures shows that the theory accurately describes both the radial distribution functions and their Fourier transforms for narrow wells and shoulders and for weak nonadditivity. The proposed formulation extends previous sticky-hard-sphere-based approaches while retaining their analytical simplicity.

The Cox-Merz rule is an empirical relation between the magnitude of the complex viscosity, $\lvert\eta^*(\omega)\rvert$, obtained from linear viscoelasticity, and the steady-shear viscosity, $\eta(\dot{\gamma})$. In this study, we performed molecular dynamics simulations of coarse-grained polymer melts using the Kremer-Grest model and systematically examined the validity of the Cox-Merz rule as a function of chain length and chain stiffness for linear and ring polymers. For short chains and, more generally, for flexible chains, $\lvert\eta^*(\omega)\rvert$ and $\eta(\dot{\gamma})$ show good agreement at corresponding values of angular frequency $\omega$ and shear rate $\dot{\gamma}$. For linear polymers, however, the discrepancy between the two viscosities becomes increasingly pronounced with increasing chain length and chain stiffness, with $\lvert\eta^*(\omega)\rvert$ exceeding $\eta(\dot{\gamma})$ at high corresponding values of $\omega$ and $\dot{\gamma}$. This deviation is associated with the pronounced nonlinear response under strong steady shear, where flow-induced chain extension and alignment can modify the entanglement constraints that govern relaxation near equilibrium. In contrast, ring polymers retain substantially better agreement between $\lvert\eta^*(\omega)\rvert$ and $\eta(\dot{\gamma})$ with increasing chain length and stiffness within the range examined here, indicating a weaker breakdown of the Cox-Merz rule. These results demonstrate that the applicability of the Cox-Merz rule depends strongly on chain length, chain stiffness, and molecular architecture. When the molecular response under steady shear deviates substantially from the relaxation behavior characterized by linear viscoelasticity near equilibrium, the complex viscosity can no longer accurately predict the steady-shear viscosity, resulting in a pronounced breakdown of the Cox-Merz rule.

Recent high-resolution (500 bp) Hi-C experiments reported contact maps with unusual patterns around highly expressed bacterial DNA loci. These patterns, described as arched stripes and bundled domains, extend over nearly 100 kbp. We performed Brownian Dynamics simulations with a specially designed coarse-grained model to rationalize these findings. The main feature of the model is that it takes explicitly into account the waves of positive (respectively, negative) supercoiling generated by the translocating polymerase downstream (respectively, upstream) of its position. Contact maps computed from the simulations also display the arched stripe and bundled domain patterns for above-threshold values of the rate of twist injection. Computed DNA conformations indicate that these patterns reflect an extraordinarily entangled DNA geometry, which involves both plectonemic and toroidal supercoiling, with some DNA segments experiencing both of them simultaneously. Moreover, DNA segments located on each side of the polymerase systematically wind around tracts located on the other side, which is a purely out-of-equilibrium effect driven by the continuous injection of twist. The present work therefore reveals that repeated transcription of a DNA locus systematically brings into contact DNA segments separated by several tens of kbp, which may eventually contribute to allosteric modulation and long-range communication.

Collective flows in epithelial tissues contain a geometric backbone of vortical interfaces whose statistics exhibit hallmarks of critical percolation and conformal invariance. Yet how fundamental cellular processes govern the breakdown of such symmetry-rich flow geometry remains unclear. Here we show that cell division plays a central physical role in regulating this universal flow organization by controlling both the geometric and mechanical flexibility of the cell-cell network. Using pharmacological perturbations, we find that when proliferation is suppressed through two independent interventions, coherent flows persist but neighbor exchanges decline and conformally invariant geometry is lost. Blocking apoptosis does not affect universality, isolating division as the key control. A vertex model with tunable division quantitatively reproduces these effects and restores conformal invariance when division is allowed. We further trace this effect to changes in both the geometric and mechanical organization of the cell layer: Divisions act as intermittent topological renewals that loosen constraints, preserving the network's flexibility and capacity to rearrange across scales. Thus, beyond its canonical role in growth, cell division acts as a structural and mechanical regulator of collective self-organization. These findings establish a direct connection between fundamental biological processes and emergent physical symmetries.

Polymer informatics has matured from isolated property-prediction studies into an integrated discipline that couples data, models, and decision-making across the polymer design cycle. Yet it still falls short of a true intelligent system capable of inverse design on demand, causal reasoning across chemistry, processing, and performance, and closed-loop autonomous experimentation. This article traces a roadmap toward that goal, grounded in experience developing two complementary agentic and informatics platforms. Central to this vision is a modular, agent-directed architecture in which a polymer super-intelligence layer interprets a researcher's design question in natural language and coordinates domain-specialized tools, matched to the available data, for neat polymers, composites and formulations, solvents, and synthesis and processing. The resulting system spans the full chain from molecular design through processing to product-level performance and human perception. Orchestrated together, its generative design, synthesis-feasibility reasoning, and practicality assessment already form the decision-making core of a self-driving polymer laboratory, leaving autonomous, closed-loop experimentation as the principal step that remains. We survey emerging capabilities along this roadmap, including automated extraction of property data from the literature, chemistry-aware representation, property prediction for membranes and sustainable plastics, solubility and green-solvent recommendation, and computer-guided retrosynthetic planning, exposing the remaining gaps and the research and infrastructure investments needed to move from today's orchestrated tool ecosystem toward a genuinely super-intelligent polymer design partner.

Does the spatial organization of particle mobility in a glass predict future motion beyond what local structure knows? In leakage-free simulations of an aging Kob–Andersen liquid ($N=2028$; 200 trajectories; three temperatures), mobility-network topology raises the out-of-fold $R^2$ by $\dRtwo=0.0049$–$0.0122$, monotonically with quench depth, retaining $\ge 98\%$ atop softness-class baselines. Giant mobile components are dense hotspots whose members subsequently quiet down: exhaustion zones of cooperative motion — a spatial anticorrelation channel invisible to single-particle descriptors.

Charge regulation refers to the ability of ionizable biomolecules and their counterparts to adjust their ionization state in response to external perturbations, including changes in pH, ionic strength, or electrostatic interactions with neighboring charged species. Here, we use explicit-ion molecular dynamics / charge-regulation Monte Carlo simulations to compute the interaction force between two spherical, charge-regulated nanoparticles as a function of separation, and compare symmetric (chemically identical) and asymmetric (chemically complementary) surface configurations against the constant charge approximation. We find that charge regulation produces up to an order-of-magnitude stronger short-range attraction than constant charge for asymmetric nanoparticle pairs, particularly at low electrolyte concentration, and that charge regulation qualitatively alters the interaction between symmetric, chemically identical nanoparticles, driving a crossover from net repulsion to net weak-attraction as ionic strength decreases. This transition is not observed under the constant charge assumption which shows that charge regulation is not a minor correction but can change both the strength and the sign of nanoscale electrostatic interactions, with implications for the assembly and stability of charge-regulated colloidal systems

Structural observations in polymer chemistry are often rationalized through underlying mechanistic insights. The study of families of mechanisms - and the phenomenology and lawlike behavior that can accompany them - is less common. Here we construct a theory that links a mechanistic feature - the number of nearest neighbors $k$ that influence monomer incorporation - with the accessible copolymer sequence space. We find that the reaction mechanisms can be mapped 1-to-1 to a regular de Bruijn graph of degree $k$. We calculate the periodic copolymer sequences as function of neighbor index $k$, and number of monomers $s$. We show that the number of periodic sequences grows explosively with $s,k$, bounded from below by $s!^{s^{k-1}}/s^k$. We find that periodic k-polymerization is governed by several simple laws describing allowed sequences, number of specific reactions, repeating unit length and the allowed and disallowed sequence coexistence in block copolymers. We formulate Simple Assembly Rules (SAR) that capture commonly observed behavior and design of literature systems, and characterize the possible k-polymerizations they are allowed to access ($k\leq2$) as function of symmetries and illustrate our findings with reported examples from the coordination chemistry and supramolecular chemistry literature. We discuss chemical-structural contributions by which nontrivial ($k>1$) sequences are formed, highlighting the importance steric hindrance, long-range interactions and degrees of freedom.

Non-collinear antiferromagnets offer unconventional routes for controlling magnetic, electrical, and thermoelectric responses through their complex spin configurations and interfacial symmetry. Here, we detect exceptional interfacial properties arising from a non-collinear antiferromagnet by demonstrating a robust and quantitatively consistent exchange-bias response in an IrMn$_3$/Py heterostructure. The system consists of a 10 nm IrMn$_3$ layer coupled to a 5 nm permalloy (Py) film. Longitudinal magneto-optical Kerr effect (MOKE), anisotropic magnetoresistance (AMR), and anomalous Nernst effect (ANE) measurements independently reveal the same unidirectional field shift of approximately 50 Oe, together with a consistent cosine angular dependence. The simultaneous observation of these signatures establishes a direct correspondence between the interfacial magnetic symmetry imposed by the non-collinear antiferromagnet and the responses of the adjacent ferromagnet. This symmetry is manifested consistently in magnetization reversal, charge transport, and thermally driven voltage generation, demonstrating that the exchange-bias imprint is not restricted to a single experimental observable. Our results reveal a coherent multifunctional response of IrMn$_3$/Py and extend the conventional understanding of exchange bias beyond collinear antiferromagnetic systems. More broadly, they demonstrate the potential of non-collinear antiferromagnets as platforms for coupling magnetic, electrical, and thermoelectric functionalities in spintronic and spin-caloritronic devices.

We investigate the growth of a circular domain in a phase-separating lipid membrane and its relation to the budding instability. We describe the in-plane dynamics with a conserved, time-dependent Ginzburg-Landau model under radial symmetry. Numerical solutions show a crossover of the domain size $D$ as a function of time $t$ from $D\sim t^{1/3}$ at early times to $D\sim t^{1/2}$ at later times, followed by saturation due to finite system size. The time-dependent line tension $\sigma(t)$, evaluated from the evolving concentration profile, rises rapidly before approaching the planar-interface value. This behavior distinguishes an early line-tension-dominated regime from a later domain-size-dominated regime. To estimate the budding instability, we combine $D(t)$ and $\sigma(t)$ with a quasistatic criterion for the loss of stability of a partially budded domain. The budding-instability time decreases with increasing membrane spontaneous curvature and increases near the critical point. Thus, the evolution of both domain size and line tension is essential for determining the time required for the budding instability.

We experimentally explore the collective behavior of the nematode T. Aceti inside flexible boundaries showing the emergence of previously unreported states. These nematodes have been previously shown to be able to synchronize their body oscillations in a favorable condition of confined space. In this collective state, they are able to exert a strong pushing force which we exploit to study how their collective motion could deform a pliable boundary. Using a novel experimental technique, we were able to simulate a non-rigid border at a liquid-liquid-gas triple point. We discovered a state with periodic boundary deformations which are due to the synchronized oscillations of the nematodes. More interestingly, we found a novel state where the nematodes are able to form multiple protrusions in the border which oscillate, rotate, merge, and split. We propose a numerical model that is able to reproduce some of the observed parameters of this state as well as offer an analytical insight into protrusions dynamics. Our research opens a pathway for exploring the interaction between active matter and flexible interfaces with a new kinds of active matter agents forming dynamic non-chaotic border deformations.

The craft of weaving, where different materials are interlaced, has tremendous potential for creating active and functional systems for use in soft robots, prosthetics, wearables, exoskeletons, and more. These textile-like systems are flexible and safe for human-machine interaction; however, this inherent flexibility limits their ability to carry loads, which is essential for many robotic functions. In this work, we introduce a general framework for integrating active materials into three-dimensional (3D) woven shells to create robotic structures that combine high axial stiffness for load bearing, low bending stiffness for efficient actuation, and system-level resilience for damage tolerance. These woven robots can be modularly assembled from 'woven corners', a fundamental unit of 3D woven structures. We use eigenvalue calculations to identify load bearing and actuation mechanisms of the 3D woven structures, and use that information to make five different robots capable of locomotion. We demonstrate that these 3D woven robots can locomote carrying loads 70 times their self-weight, and can maintain repeatable performance even after being subjected to extreme compression. This work is a pathway toward the design, manufacturing, and simulation of future 3D woven robotic systems where load bearing, high stiffness, active functional deformation, locomotion, and system-level resilience are all needed.

Stochastic density functional theory (SDFT) provides a powerful framework for studying the dynamics of many-body systems both in and out of equilibrium. In its standard form, it can be viewed as a density-based formulation of coupled Langevin equations with white noise. Here, we extend SDFT to a class of systems, ranging from magnetized electrolytes to chiral active matter, that possess a chiral overdamped limit in which a relaxation timescale and an oscillation period are simultaneously taken to zero. We derive this formulation, which we dub “odd SDFT", by taking the overdamped limit of a fluctuating hydrodynamic description of underdamped particles subject to a Lorentz force. We establish the validity and utility of the resulting framework by calculating the collective mobility tensor of interacting particles using both direct linear response and a Green-Kubo relation. We then apply the theory to the Hall conductivity of electrolytes in magnetic fields. Going beyond mean-field theory and using two distinct Green-Kubo relations, we derive the full conductivity tensor, extending the relaxation part of the Debye-Hückel-Onsager theory to the case of finite magnetic fields.