Papers

Thermal escape is governed by the Arrhenius law, where the mean escape time scales exponentially with the barrier height. We show that the non-Markovianity induced by time-delayed feedback in the confining force removes this exponential scaling. Beyond a threshold set by the curvature of the minimum, the delay destabilizes the well, and the thermal noise seeds an instability that is subsequently amplified deterministically to the boundary leading to slingshot escape trajectories. The escape time becomes logarithmic in the barrier, its fluctuations follow a Gumbel law, and an optimal delay enables escape faster than free diffusion. Our results propose time delay as a tunable and experimentally feasible control parameter for accelerating activated processes.

Proteins and many other colloids carry ionizable surface groups that are both spatially inhomogeneous (patchy) and pH-responsive (charge-regulating). In the description of the electrostatic interactions between such particles, these two aspects are often treated separately, especially from a theoretical perspective. We present a unified, closed-form theory that unites charge regulation and patchiness within the linearized Poisson–Boltzmann approximation. For spherical particles with anisotropic distributions of titratable sites, we derive both the leading-order mean-field interaction energy as well as the Kirkwood–Shumaker fluctuation interaction. The theory exposes a qualitatively new effect between two electroneutral anisotropic particles: proximity-induced charge regulation generates a net monopole, and splits orientational branches that are degenerate in any linear fixed-charge model. The accompanying correction to the interaction energy has no fixed sign—it softens like-charge repulsion but can deepen or create attraction away from the isoelectric point. We benchmark three ingredients of the theory against published results; no existing simulation probes their combination, which would capture the central prediction of the theory. Lastly, we apply the theory to two proteins—lysozyme and $\alpha$-chymotrypsinogen A—and show that it not only reproduces the measured second virial coefficients reasonably well but also predicts how charge regulation expands the range of pH and screening strength where the protein–protein interaction is attractive.

In Metamorphosis of Plants (1790), Goethe traced diverse plant organs to transformations of a common leaf-like structure – a principle modern mechanics attributes to two material ingredients: non-uniform in-plane strain from differential growth or shrinkage, and spatially patterned stiffness. Here we translate this principle into a synthetic fabrication framework called Polymer Membrane Tensegrity (PMT). A flat elastomeric film swollen with a second monomer is selectively UV-cured through a liquid-crystal display (LCD) photomask in a single-side digital photopatterning step, producing rigid rods embedded in a soft, shrinkable membrane. After the unreacted monomer is extracted with a solvent and the film is dried, the membrane shrinks far more than the rods, generating a ~50% in-plane strain differential and a ~2,000-fold modulus contrast – conditions under which the contracting membrane is held in tension by mutually unconnected rods, a tensegrity-inspired arrangement within a single film. An origami-based inverse design algorithm computes the rod layout that morphs the film into a prescribed 3D surface. We demonstrate PMT on a dome, a hyperbolic surface, and a gyroid unit cell – positively and negatively curved targets – reproducing all three with mean deviations of 1.0-2.1% of the target size; perimeter curve optimization halves the mean deviation of the gyroid. Because patterning occurs on one side only, PMT eliminates the front-to-back alignment demanded by bilayer methods, offering a scalable route from flat polymer films to freeform 3D surfaces.

Understanding the dehydration mechanism of hydrated salts remains fundamentally important in solid state chemistry, as their behavior affect fields ranging from heat storage to heritage conservation and pharmaceutical crystallization. Combining Raman confocal microscopy, dynamic weight loss measurements, SEM, and micro CT, we show that dehydration kinetics of sodium sulfate decahydrate (mirabilite) unfold through two regimes: an initial nucleation controlled phase, where atomic rearrangement drives two dimensional lateral growth following an exponential law, and a subsequent phase boundary controlled regime, where growth advances into the crystal depth, limited by water vacancy formation at the hydrated dehydrated interface. The resulting thenardite product shows around 35 percent shrinkage and forms a porous, layered dual porosity nanocrystalline structure, with relative humidity directly governing crystal size. Extending this analysis to other sulfate hydrates reveals that crystallographic symmetry changes between hydrate and anhydrous phases dictate surface morphology, linking microstructure to mechanism. This multiscale framework uncovers dynamics hidden from bulk measurements and suggests structural indicators could predict dehydration pathways in other hydrated salt families, and opening route toward designing thermal energy storage materials without exhaustive experimental screening.

Calcium mineralisation underpins processes ranging from biomineralisation to scalable carbon storage, yet the earliest stages of nucleation remain unresolved. Here we investigate calcium-containing solutions under nanoscopic confinement while remaining undersaturated with respect to bulk calcium carbonate precipitation. Using sensitive surface force measurements, we identify a long-range non-DLVO repulsive interaction specific to calcium solutions, which we attribute to hydrated ion networks at mineral interfaces. These interfacial networks exhibit viscoelastic behaviour distinct from the bulk solution, persist across a broad pH range, and can be disrupted by competing ions with strong surface affinity. Our findings provide experimental evidence that stable hydrated ion networks can emerge at mineral interfaces under undersaturated conditions, supporting the possibility that interfaces and confinement stabilise intermediate ion assemblies prior to nucleation. These results bridge classical and nonclassical descriptions of mineral nucleation and highlight the central role of interfaces and confinement in directing crystallisation pathways.

The transport of anisotropic tracers in active fluids exhibits rich dynamical behavior arising from the interplay between particle shape, activity, and steric interactions. We employ Brownian dynamics simulations to investigate the motion of an elliptical tracer immersed in a suspension of active dumbbells. We find that both translational and rotational transport, characterized by the mean-square speed and diffusivity, are enhanced by more than an order of magnitude with increasing area fraction, $\phi$, of active dumbbells. Notably, tracer motion is enhanced along the major axis relative to the minor axis, with $\mathrm{v}_{\parallel}>\mathrm{v}_{\perp}$ and $D_{\parallel}>D_{\perp}$. Remarkably, both translational and rotational transport exhibit an optimum at an intermediate packing fraction of active dumbbells, with the corresponding transport coefficients decreasing at higher densities. We show that this non-monotonic transport arises from the anisotropic accumulation and aggregation of active dumbbells around the tracer, which control the non-equilibrium force and torque fluctuations. Thus, establish a direct connection between the collective organization of active dumbbells at the tracer surface and its emergent translational and rotational transport.

Viscoelastic fluid flows over micro-textured surfaces - densely covered by slender protrusions like cilia lining the body airways or villi covering the intestinal epithelium - underpin essential biological processes including transport, mixing, and absorption. Despite their ubiquity, the dynamics generated by the interplay between fluid elasticity and these complex geometries remain largely unexplored. Here we combine fully resolved numerical simulations with microfluidic experiments to reveal the flow dynamics established above dense arrays of microscopic pillars (canopies) immersed in the low-Reynolds-number flow of a viscoelastic liquid. We observe that the flow above the canopy tips spontaneously develops elastic turbulence. Remarkably, the chaotic state coexists with elastic waves emerging from the coupling between fluid elasticity and the heterogeneous shear induced by the canopy geometry. These ordered fluid motions persist across a broad range of flow conditions and canopy configurations. Our results demonstrate that coherent wave propagation and elastic turbulence are complementary manifestations of viscoelastic fluid flow. Beyond their fundamental significance, these mechanisms have broad implications for transport in biological and engineered environments, and reveal how structured geometries can harness the spontaneous dynamics of viscoelastic liquids to manipulate complex flows.

Granular particles typically feature contact friction, which gives rise to various nontrivial properties of granular materials. In this work, we investigate the linear stability of static packings composed of frictional spheres, whose interactions are modeled using the discrete element method. We discuss a key difficulty in properly modeling static friction and address the problem of identifying rattlers. We also explore the spectrum of the energy matrix, which governs the linear viscoelastic response of the system. The intermediate- and high-frequency regimes of the spectrum remain qualitatively independent of both the friction coefficient and the packing fraction.

We applied a dynamic fluctuation measurement method to liquid water-methanol mixtures over a wide range of compositions and temperatures. This method, which we developed in recent years, combines ultrasonic and inelastic X-ray scattering techniques to detect mesoscopic-level fluctuations - that is, the degree of heterogeneity - in liquids using sound waves. As a result, it was found that dynamic fluctuations exist across a wide range of compositions and temperatures, including pure substances (water and methanol). Furthermore, in the low-methanol composition range (approximately 20% mol or less), the strength of dynamic fluctuation increased toward lower compositions and lower temperatures, suggesting that the origin of the fluctuation lies in the low temperature (supercooled) region of water alone. Conversely, this indicates that in the range below 20% methanol, fluctuations in water alone are dominant rather than the mixed effects of water and methanol. We performed similar dynamic fluctuation measurements on water-ethanol and water-glycerol mixtures at room temperature. We found that dynamic fluctuations exist universally across the entire composition range, and confirmed an increase in the strength of dynamic fluctuations toward lower compositions in the regions approximately below 15% and below 20%, respectively. This revealed that the phenomenon is not unique to methanol systems but is a common behavior shared by water-alcohol mixtures. It has long been known that water-alcohol mixtures exhibit various thermodynamic anomalies, but the mechanisms behind them have not yet been fully elucidated. The present results are expected to provide a new direction for discussion on this issue.

Multistable mechanical systems can store and release elastic energy through snap-through instabilities, but controlling transition pathways between stable states remains challenging when multiple routes are accessible. Here, we introduce a two-mass von Mises truss as a general model for studying pathway selection governed by coupled saddle-node bifurcations. The system consists of two coupled snap-through units with geometric imperfections, giving rise to four stable configurations: a fully inverted state, a fully natural state, and two intermediate mixed states. We show that the coupling stiffness reorganizes the quasi-static bifurcation structure and selects among three transition pathways under release: sequential snapping through one mixed state, direct cooperative snapping, or sequential snapping through the other mixed state. Using pseudo-arclength continuation, we track the relevant saddle-node bifurcations and identify the parameter regimes associated with each quasi-static pathway. We then demonstrate that dynamic bifurcation delay provides an additional rate-dependent mechanism for pathway selection. Even when the quasi-static bifurcation structure favours a unique sequential pathway, finite-rate loading delays snap-through beyond the corresponding static saddle-node points and can reorder the snapping sequence of the two units. A local reduction of the coupled dynamics near each saddle-node yields normal forms with coupling-dependent critical points and coefficients. The resulting theory identifies distinct rate-dependent delay laws in the inertia-dominated and overdamped regimes and predicts the critical rate at which the snapping order reverses. These results establish a general mechanics framework for tuning transition pathways in multistable systems through elastic coupling and loading-rate control.

The chemical potentials of charged multi-component mixtures are central to electrolyte thermodynamics, but remain difficult to compute from atomistic simulations. The S0 method enables computing chemical potentials of mixtures from equilibrium molecular dynamics simulations. Here we extend the S0 method to charged mixtures by combining the composition-space framework developed in Part I: Neutral Multi-component Mixtures with a Coulombic treatment of the small-wavenumber limits of static structure factors. This approach separates thermodynamically relevant neutral composition fluctuations from forbidden macroscopic charge fluctuations, and further accounts for charge-neutrality constraints. We use the method to compute the chemical potentials of multiple-halide aqueous salt solutions, elucidating the ion-specific thermodynamic effects. We also calculate the mixing free energies of molten salt mixtures, demonstrating the importance of correctly describing long-wavelength electrostatic correlations.

In recent years, kirigami metamaterials have been widely studied and applied in science and engineering. While various two- and three-dimensional kirigami design methods have been developed, most of them are only applicable to a limited class of kirigami structures. In this work, we develop a unified framework for kirigami design that encompasses a wide range of 2D-to-2D, 2D-to-3D, and 3D-to-3D shape-morphing effects, as well as additional geometric and physical properties such as compact reconfigurability and rigid deployability. In particular, by reformulating the design task as a length-based constrained optimization problem and solving it simultaneously for multiple target states of the kirigami structure, our unified design framework enables greater design flexibility and stronger theoretical support. Experimental results with a wide range of shape-morphing effects are presented to demonstrate the effectiveness of our framework. We further present a rigorous theoretical analysis of several key aspects of kirigami design, covering inertia transposition, aspect-ratio law, and angle defects, thereby elucidating important design rules and limitations. Altogether, our work paves a new way for the design of shape-morphing mechanical metamaterials.

We investigate directed transport in a one-dimensional Brownian flashing ratchet with a piecewise-linear asymmetric periodic potential. Numerical solutions of the Fokker–Planck equation and Brownian dynamics simulations reveal a nonmonotonic dependence of the stationary current on the switching frequency, with a resonant maximum whose position depends on the potential asymmetry $\delta$ and barrier height $\Delta$. For moderate asymmetry, $|\delta|<0.5$, the current obeys a scaling form that separates the dependence on the potential parameters from a common frequency dependence, resulting in a data collapse upon appropriate scaling of the current and frequency. The current amplitude varies linearly with $\delta$, while the resonance frequency follows $\nu(\delta,\Delta)=\nu_0(\Delta)/ [1-b_0\, \delta^2]$. We interpret the resulting $(1-\delta^2)^{-1}$ scaling in terms of coupled relaxation along the two branches of the asymmetric potential, which provides a physical basis for the observed dependence of the resonant frequency on the potential asymmetry.

Wood slices under a polarized optical microscope show a spectrum of interference colors, such as cyan, blue, magenta, yellow, and bluish gray because of the birefringent cellulose in the microfibrils. An optical model is established to simulate the birefringent-colored micrograph of wood. Five typical cell wall architectures, line, helix, ring, crossed helix, and twisted helix, are considered. With a retardation wave plate to distinguish fibrils of different orientations, each structure displays its unique birefringent-colored texture, presenting its underlying 3D structure with the vivid colors. Cross sections of the trunk and twig of Eucalyptus grandis presented birefringent-colored profiles. Three identification methods were compared: visible fibril trends, birefringent-colored optical textures, and the simulated look-up library. The three methods gave consistent results, proving that the birefringent-color tags are efficient and accurate. Electron and atomic force microscopy are unable to resolve cellulose microfibrils embedded in the lignin and hemicellulose matrix. Polarized optical microscopy overcomes this by selectively detecting birefringent cellulose, enabling accurate identification of complex helical structures. This method enables statistical and spatial analysis of complex biomaterial compositions. Capable of profiling dozens of cells simultaneously, this high-throughput optical method provides a potentially fully automated analysis framework for plant science, biomechanics, and bioinspired cellulose materials.

The order of cellulose microfibrils in xylem cell walls is identified using polarized optical microscopy. The line, helix, ring, crossed helix, and twisted helix organizations in a cylindrical shell are the equilibrium states of balanced elastic deformation and surface anchoring. A computational model of the five organizations is established to simulate their birefringent-colored profiles. These five textures present unique optical textures, which are clearly recognized in the cross sections of Eucalyptus grandis. The libriform fiber cell for support has a twisted helical cell wall. The vessel cell for high-speed water uptake consists of a helical layer covered by a layer of vortex array. The ray cell for radial transportation is crossed helical. The microfibril angles versus the radius of the cell wall were measured utilizing the distribution of birefringence colors. In fiber cell walls, the MFA is significantly correlated with the curvature, bending, and surface anchoring, respectively. In vessel cell walls, the vortex array includes focal conic domains of chiral order and topological defects of nematic order, suggesting that the phase transition of cellulose fibrils leads to pattern formation. Liquid crystal phases and patterns in the cell walls reveal how the cell wall thickens and how cells differentiate. Out of the frustration of long, stiff, twisting fibrils packed in slender tubes, trees generate the helical channel networks, transforming the brittle lamina into an elastic, tear-resistant, self-healing tissue.

The capacity for autonomous structural reconfiguration is a defining trait of living systems, yet it remains elusive in artificial active matter. Here, we report the discovery of active embracement, a non-equilibrium phenomenon where active star polymers, comprising a central core and self-propelled monomeric arms, transition from open configurations to tightly collapsed, “hugging” states. By combining polymer experiments using connected vibrobots with simulations, we demonstrate that internal self-propulsion fundamentally overrides the steric repulsion that keeps passive polymers dispersed. This active drive enables a suite of behaviors unattainable in equilibrium systems: individual star polymers undergo a globular-like self-collapse, multiple star polymers mutually intertwine and mutually embrace, and can spontaneously embrace and capture surrounding passive particles. Our findings reveal that active embracement is a distinct kinetic phase that allows star polymers to function as autonomous tweezers. By bridging the gap between macroscopic robotic collectives and microscopic polymer physics, this work provides a versatile blueprint for the design of smart materials capable of targeted cargo capture and self-directed assembly in complex environments.

A density-functional theory developed for equilibrium freezing also produces a high-density endpoint close to terminal packing. We revisit the nonlinear Ramakrishnan–Yussouff bifurcation framework and distinguish the first crystalline fold, thermodynamic coexistence, and terminal marginality. At the terminal point, the grand-potential curvature vanishes along the principal finite-wavevector density mode, exactly when the nonlinear self-consistency equation loses stiffness. The construction gives exact close packing for one-dimensional hard rods, a terminal hard-disk packing fraction near 0.8407, and a hard-sphere value near 0.629, close to random close packing. These results identify a finite-wavevector thermodynamic marginality of a metastable liquid continuation, rather than equilibrium freezing or mechanical jamming, and expose a persistent puzzle: why should liquid-state correlations encode the approach to terminal disordered packing across different physical dimensions and systems?

We report high-resolution Monte Carlo evidence characterizing the hierarchy of transition strengths in biaxial nematogens. By employing multiple histogram reweighting on large lattices, we demonstrate that while the isotropic-to-uniaxial ($I \to N_U$) transition is symmetry-enforced first-order, the uniaxial-to-biaxial ($N_U \to N_B$) transition in the region between the tricritical point and the triple point ($\lambda = 0.26$) is proximity-driven and more than an order of magnitude smaller for large system sizes. Such a class of ultra-weak first-order transitions could be a new pathway for future investigations.

Structural superlubricity, arising from lattice incommensurability, offers a promising route to eliminate friction and associated energy losses in mechanical systems. In real-world systems, roughness and wear currently pose severe limitations on its robustness and especially the contact size. Here, we consider patterned surfaces as a possible route to overcome some of these limitations. We show that the simplest choice of patterning, contacts made up of two incommensurate triangular-triangular patterns, fails at elevated loads because of the small number of load-bearing contacts, causing the maximum local contact pressure to exceed the strength of the superlubric coating. We introduce a square-triangular patterned interface that increases the number of load-bearing contacts and organizes them into continuous contact lines. When sliding along specific directions relative to these lines, superlubricity is maintained at significantly higher loads by reducing pressure-induced coating failure while also remaining somewhat tolerant to surface imperfections. These findings establish a mechanism for stabilizing structural superlubricity against coating failure and a design principle for engineering low-friction interfaces with enhanced load-bearing capacity and defect tolerance.

Liquid-state theory provides a fundamental connection between microscopic structure and macroscopic thermodynamic behaviour. Here, we develop a framework for predicting thermodynamics and phase behaviour directly from structural correlations, using either radial distribution functions or static structure factors as input. The approach constructs a free-energy functional from structural information obtained at a single thermodynamic state point, without requiring explicit knowledge of the underlying interaction potentials. This circumvents a central difficulty in modelling complex fluids, for which effective interactions are often unknown or rely on approximations. We demonstrate the framework for a range of model fluids, including colloidal and colloid–polymer systems, with predictions in good agreement with molecular simulation data. The results show that structural information at a single state point can provide sufficient information to predict the broader thermodynamic response of a system. This establishes a route toward inferring phase behaviour directly from experimentally measured structure, even when the microscopic interactions are not known a priori.

Flows in random networks are known to exhibit heavy-tailed statistics, giving rise to anomalous transport in a range of biological, environmental and engineered systems. Yet, how structure determines flow remains an open question. Here we derive a dual network approach that relates flow statistics and network properties. Conditional statistics in a range of networks reveal the existence of two interlaced subnetworks with distinct hydraulic behaviors. Based on this hidden structure, we derive a universal analytical approach that predicts heavy-tailed flow statistics based on network topology and disorder distribution across a range of random networks.

Numerous experimental and computational studies have been conducted in the past few decades to understand the swimming performance of fish, and to identify the optimal kinematic strategies for a swimming fish or fish-like robot. Many of these studies model the swimmer in a `tethered' condition, in which the swimmer is held fixed while it is subjected to a free stream. Its performance is then quantified using power expenditure, thrust generation, and efficiency. However, the dynamics of a tethered swimmer are different from those of a self-propelled swimmer, whose performance is best measured using its steady-state swimming speed in still fluid and its efficiency. It is an open question whether the conclusions drawn from studies of tethered swimmers can be directly applied to free swimmers. In this study, we use an unsteady panel method to systematically compare the swimming performance of a tethered fin and that of a self-propelled fin attached to a virtual drag-producing body to investigate how their performance varies over a set of prescribed kinematics. After validating the numerical model against previous experimental results, we show how the pitch amplitude, heave amplitude and the phase offset between them affect the efficiency and thrust generation in the tethered case, and how they affect the speed and efficiency in the self-propelled case. We find that the kinematic strategies that optimize the performance of a tethered swimmer do not necessarily optimize the performance of a self-propelled swimmer.

The extreme persistence of per- and polyfluoroalkyl substances (PFAS) in the environment is rooted in their three-dimensional molecular conformation. The helical twist adopted by perfluoroalkyl chains due to hyperconjugation involving their recalcitrant C-F bonds governs their resistance to degradation, yet a quantitative, continuous metric for helicity has remained absent. Here we introduce a data-driven framework that quantifies backbone helicity using three statistical descriptors: void-state (binary occupancy) spatial autocorrelations, local backbone principal component analysis, and persistent homology. We further validate each statistical descriptor against geometric dihedral benchmarks and DFT-calculated Vibrational Circular Dichroism (VCD) spectra. The framework is initially established on a homologous series of perfluorocarboxylic acids (FC2 through FC16) and their hydrogenated analogues, then extended across perfluorosulfonic acids, fluorotelomer alcohols, polyfluoroalkyl hexanoic acid analogues, and longer-chain PFOA and PFOS analogues. Agreement between statistical, geometric, and spectroscopic definitions of helicity is established for PFCAs and extended to structurally distinct subfamilies, including PFOA analogues of varying fluorine content and perfluorosulfonic acids, demonstrating that the descriptors are robust to changes in headgroup chemistry and fluorine substitution pattern. The framework provides a chemistry-agnostic toolset for incorporating backbone conformation into predictive models of PFAS environmental fate and degradation reactivity.

Magnetically coupled damped rotational degrees of freedom can give rise to tribological loss when excited by a relative sliding motion, linking friction to the dynamics of magnetic moments. We analytically investigate such magnetic friction by studying a recently introduced simplified model for a rigid magnetic rotor array sliding over a commensurate magnetic substrate. Here, the array rotors can rotate about an axis perpendicular to the sliding direction and are damped by microscopic shaft friction, while the substrate magnets have a fixed in-plane orientation. The simplified model reduces the collective rotor dynamics of this setup to a set of coupled nonlinear differential equations, which can be studied by the corresponding energy landscape in the quasi-static regime. We find that the parameter plane spanned by layer separation and time can be divided into distinct chambers, in which the structure of the energy landscape remains invariant. Using these chambers, we identify the layer separation intervals corresponding to different dynamical states and recover the emergence of a regime where the moment alignment alternates globally while exhibiting peak dissipation. Additionally, we derive the leading nontrivial orders of the collective magnetic friction in the regimes of small and large gaps between the array and the substrate. For the alternating regime, we find that friction can be computed by tracking energy jumps from unstable to stable critical points at the chamber boundaries. These results provide an analytical foundation for the observed dynamics and dissipation in sliding rotor arrays. Because the simplified model is scale-free, our conclusions transfer across a broad range of microscopic and macroscopic length scales.

During many biological processes, cell aggregates spread on substrates in a process of active wetting. The existing models of tissue spreading, however, do not explicitly capture the state of partial wetting, in which the cell aggregate reaches a non-zero contact angle. Here, modeling cell aggregates as active polar liquid droplets, we predict a transition between partial and complete wetting. This transition emerges from the competition between tissue surface tension and active traction forces, which is captured in an active Young-Dupré equation. The active wetting transition is discontinuous, and it features a region of parameters in which both partial and complete wetting are possible. Unlike in passive wetting, the transition depends on dynamical parameters such as the tissue viscosity and substrate friction. Finally, adding contractile intercellular active stresses leads to higher contact angles and even full dewetting. Overall, our work predicts an active wetting transition for tissues and it captures the partial wetting states often seen in experiments.

A protein's function follows from the structure it adopts, and in some cases which structure that is depends on the pathway taken. In programmable matter the target is fixed before assembly, and whatever else forms is treated as error. Here we show that pathways themselves form a design space. Using reinforcement learning, we fold model DNA-coated droplet chains into rigid two-dimensional geometries, uncovering two classes of pathways: downhill, in which bonds are only added, and detour, in which bonds are broken and remade before the target is reached: for some the only route that exists. Coarse-graining pathways by interactions gives experimentally realizable protocols. Some produce one geometry, others several: structures sharing a detour route can be cycled between, while those that coexist assemble into superstructures inaccessible to a uniform product. Function emerges from the pathways rather than being designed. Designing the process instead of the components could give colloidal materials that reconfigure on demand.

Carrageenan gels are thermoreversible polysaccharide networks whose mechanical properties emerge from ion-mediated helix association, yet how their molecular organization controls nonlinear deformation remains poorly understood. Here, we investigate the temperature-dependent rheology of $\iota$-carrageenan gels formed in KCl solutions using linear and nonlinear oscillatory rheology combined with normal-force measurements. $\iota$-carrageenan forms homogeneous and mechanically reversible gels whose elastic modulus increases continuously with quench depth. Deep quenches generate pronounced strain stiffening before yielding, associated with the development of internal stresses revealed by negative normal forces. Remarkably, large deformations preserve the small-strain elastic modulus while progressively suppressing strain stiffening, demonstrating a partial mechanical reversibility of the network. We interpret these observations using a hierarchical network picture in which a persistent intermolecular network controls linear elasticity, while a more fragile mesoscale organization enables cooperative alignment and stress amplification under deformation. Our results highlight that nonlinear mechanics of thermoreversible polysaccharide gels are governed not only by molecular connectivity, but also by the reversible formation and eventually destruction of mechanically adaptive hierarchical structures.

We develop a continuum theory for a fluid of elongated particles that advance along their own axes. The same kinematics is ideally shared by flocks of sheep, self-propelled rods, vehicular traffic, and turning flocks of birds. Within the framework of continua with vectorial microstructure, in which each point also carries an orientation, we impose the no-side-slip (skate) condition $\vv=u\,\nn$ as an ideal, non-integrable internal constraint. We derive the pure equations of motion and the equation governing the constraint reaction from the principle of virtual power. Using a constitutive closure provided by the Ericksen-Leslie theory of nematic liquid crystals, we show how the constraint also shapes collective effects. It turns parabolic orientational diffusion into hyperbolic orientation-density waves and forbids any steady simple shear. It fixes the empirical Toner-Tu convective coefficient to the flow-alignment ratio measured in colloidal rollers, thereby providing a mechanical foundation for angular sound in micropolar active hydrodynamics. It also recovers the inertial spin model of bird flocks, with the addition of a banking force and a turn-density coupling. Finally, it recovers the classical macroscopic models of one-dimensional traffic flow, while describing steering, lateral tyre forces, and road geometry in two dimensions.

We experimentally investigate the creeping motion of water droplets sliding along an inclined surface immersed in a viscous oil. The droplet velocity, width, and height are measured over a broad range of droplet sizes and inclination angles. The velocity increases with droplet radius according to a power law, but the corresponding exponent depends strongly on the inclination angle. At small inclinations, the exponent is close to 3/2, whereas at larger inclinations it progressively approaches 9/4. The results therefore reveal a continuous inclination-induced crossover in the velocity-size scaling of lubrication-mediated droplet motion. A scaling analysis based on Landau-Levich-Derjaguin film formation and viscous dissipation in the dynamic meniscus reproduces these limiting behaviors, which correspond to the quasi-spherical and pancake scaling regimes, respectively. Remarkably, the evolution of the velocity scaling is substantially more pronounced than the corresponding evolution of the macroscopic droplet shape. While the velocity data progressively approach the pancake scaling law at large inclinations, the global droplet dimensions evolve in a more complex manner than expected from a simple pancake-shape picture. In particular, the approach to pancake-like velocity scaling occurs even when the measured droplet dimensions remain far from the corresponding pancake-limit geometry. These observations suggest a crossover in the dominant lubrication-dissipation mechanism beneath the droplet that is not directly reflected in the global droplet morphology. The results identify inclination angle as a key control parameter governing lubrication-mediated droplet motion and highlight the distinction between global shape evolution and local dissipation dynamics in liquid-liquid systems.

We use particle-based numerical simulations to address a longstanding question regarding the origins of the linear frequency dependence of attenuation in fluid-saturated granular media. We study both the acoustic modes and wave propagation in damped, disordered particle packings. We calculate the damped vibrational modes of packings as a function of frequency, pressure, and grain-contact dissipation. The spatial structure and dissipation of these modes show a clear transition at a pressure-dependent critical frequency from viscous-like continuum behavior to more localized, scattering modes. We also measure how wavespeed and spatial attenuation rate depend on these same parameters. At the same critical frequency, wave propagation also shifts from coherent motion, where attenuation scales quadratically with frequency and linearly with contact damping, to much more incoherent particle-scale motion, where attenuation scales linearly with frequency and sublinearly with contact damping. All of these features, including the transition frequency, are consistent with a large collection of experimental data, which has not been explained by any framework based on grain-scale physics. We refer to this approach as “Jammed-Network Scattering” (JNS), and propose it as a grain-scale framework for understanding the acoustics of fluid-saturated granular media.