Papers

On cooling liquids towards their glass-transition temperature, the dramatic increase of their relaxation times is accompanied by changes in particle dynamics at two distinct temperatures: A high-T crossover, where particles become temporarily caged by their neighbors, and a low-T crossover, where the cage escape mechanism changes. While there is some evidence that the former is associated with a change in local particle arrangement, no structural modification has so far been detected across the low-T crossover, fueling scepticism about the relevance of structure for glassy dynamics. Here, we introduce a novel four-point correlation function which allows to determine a structural length scale characterizing cage anisotropy. Extensive molecular dynamics simulations reveal that this scale, as well as the mean structural length scale of the glass-former, extends into the medium range, i.e., significantly exceeds the particle size. Strikingly, the difference between these two scales - a measure of the degree of cage anisotropy - peaks at both crossover temperatures. We discuss how the presence of these peaks enables understanding the nature of the change in the microscopic transport mechanism at the two temperatures, thereby linking both dynamical crossovers to a single structural observable, the anisotropic medium-range order. This fundamental insight demonstrates that structure, extending well-beyond the local cage, is an essential ingredient for understanding the relaxation dynamics of deeply supercooled liquids.

We investigated the nucleation, growth, and solid-to-solid phase transition processes of spherical six-fold symmetric crystals (C6) and ten-fold symmetric quasicrystals (DQC) using the Lifshitz-Petrich model. By combining the spherical-harmonic pseudospectral method with a nullspace-preserving saddle-point search technique, we resolved the critical nucleus structures and phase transition pathways. Although both transitions from the homogeneous state to the ordered state involve the formation of localized critical nuclei, their subsequent growth processes exhibit distinct modes of accommodating geometric mismatch: C6 forms branched domain structures and persistent line defects associated with orientation and phase mismatches, whereas DQC relaxes collision-induced defects through local coordination rearrangements. The resolved DQC-to-C6 pathway proceeds through a series of metastable intermediates that progressively connect these distinct modes of mismatch accommodation. Its multi-step character reflects the coupled adjustment of local coordination and compatibility between the emerging C6 domains. These results reveal the intrinsic link between the multi-step nature of the phase transition and the distinct structural requirements for accommodating geometric mismatch.

We propose a deviatoric-stress constitutive equation derived from orientational kinetics, while implicitly retaining contributions from conformational stretch. Starting from the dumbbell model, we show that conformational stretch affects orientational dynamics through an effective stress scale and rotational diffusivity, which determine an effective relaxation time. The orientation-based equation is derived by assuming an approximate relation between orientational anisotropy and the stretch state. Within the proposed framework, constant effective coefficients yield steady-oscillatory shear correspondences closely related to the empirical Cox-Merz and Gleissle-Osaki relations. For model-specific effective coefficients, the upper-convected Maxwell model is characterized by a constant relaxation time and an increasing modulus under steady shear, whereas finite extensibility with Peterlin preaveraging shortens the relaxation time and suppresses the modulus increase. With coefficients determined from steady-shear states, the proposed equation successfully reproduces stress responses under transient shear, large-amplitude oscillatory shear, and uniaxial extension. These results show that the effects of conformational stretch on orientational kinetics can be retained implicitly, providing a constitutive description based on a deviatoric-stress state reconstructable from standard rheometry and a physical interpretation of how stretch enters polymer viscoelasticity.

Gas bubbles impose large penalties in water electrolysis at industrially relevant rates. Capillary-fed electrolyzers greatly mitigate them by wicking electrolyte to electrodes and venting gas from the backside, but only below a threshold current density. We show that the separator pore size sets this threshold through two opposing effects: smaller pores raise the supersaturation required for nucleation but reduce the permeability for electrolyte replenishment. A coupled electrochemical-transport model, anchored to a single measured onset, quantifies both mechanisms across 0.1-8 $\mu$m pores. Experimentally, reducing pore size from 8 to 1.2 ${\mu}$m raises the bubble onset limit from 0.18 to 1.73 A cm$^{-2}$ and lowers cell voltage by 0.11 V at 1 A cm$^{-2}$, primarily by suppressing bubble-induced overpotential. At 0.45 ${\mu}$m and below, the replenishment limit takes over and the cells dry out before bubbles form. Our findings establish the bubble-free operation limit as designable rather than purely empirical.

We investigate fatigue failure in two-dimensional (2D) model glasses under cyclic shear deformation using atomistic simulations. We find that the number of cycles to failure diverges as a power law as the strain amplitude approaches the fatigue limit, with an exponent close to $-1$, in contrast to the exponent of $-2$ reported in three dimensions (3D). A failure exponent of $-1$ has also recently been observed in a 2D elastoplastic model, suggesting an interesting dependence on spatial dimensionality that needs to be rationalized. Measures of accumulated plastic activity, including dissipated work and non-affine displacements, exhibit scaling with the failure time that is consistent with results in 3D, and indicate a robust connection between damage accumulation and failure. To probe the origins of the variability of failure times, we perform isoconfigurational seeded simulations in which a localized soft region is introduced. While such seeding constrains the spatial location of failure, the distribution of failure times remains broad. These findings extend recent results in 3D concerning fatigue failure times to 2D glasses, including their relation to accumulated plasticity and apparent stochasticity, while also revealing a key difference, namely the exponent describing the divergence of the failure times.

Activity can enhance the long-wavelength density fluctuations of a solid beyond the equilibrium fluctuations predicted by the Mermin-Wagner-Hohenberg theorem, but the microscopic origin of this enhancement remains unclear. We study a two-dimensional active Brownian crystal whose longitudinal and transverse displacement covariances scale as $C^u_\lambda(q)\sim q^{-3}$ as compared to the passive counterpart with $q^{-2}$ law. This spectrum predicts an MSD-plateau divergence proportional to $L$ in two dimensions, logarithmic in three dimensions, and finite in four dimensions, in close correspondence with recent results reported in Dey et al. [Nat. Commun. 16, 5498 (2025)]. Inverse of the Covariance gives $H^{\mathrm{cov}}_\lambda\sim |q|^3$ with the corresponding dispersion $\omega_{\mathrm{cov},\lambda}\sim q^{3/2}$, whereas direct mechanical response gives $K_{\mathrm{resp},\lambda}\sim q^2$ and acoustic modes with $\omega_{0,\lambda}\sim q$. The nonlinear dispersion is therefore covariance-defined rather than mechanical. The mobility and integrated active-force correlations remain non-singular, although a finite-persistence crossover cannot be ruled out completely with the existing data. Microscopically, the longitudinal and transverse Irving-Kirkwood interaction-stress spectra scale as $q^{-1}$. The transverse stress-stress correlation connects well with the anomalous displacement field, indicating that activity anomalously populates ordinary acoustic modes, while the conservative interaction network transmits the resulting fluctuations as long-ranged stress. A three-dimensional active FCC crystal exhibits the same paired low-$q$ trends.

We report measurements of the surface tension of aqueous sodium dodecyl sulfate solutions at sixteen concentrations from 0.17 to 43$\,$mM, spanning 0.02 to 5 times the room-temperature critical micelle concentration (cmc), and at temperatures from 26 to 83$\,$$^\circ{\rm C}$, using the Wilhelmy plate method. At the lowest concentration the surface tension decreases with temperature, as it does for pure water. Above about 0.4$\,$mM, however, it increases: the temperature coefficient changes sign at a concentration of 0.3 to 0.8$\,$mM, roughly a tenth of the cmc, and reaches $+0.53\,\rm mN\,m^{-1}\,K^{-1}$ near 3$\,$mM, three times the magnitude of that of pure water and of the opposite sign. Above the cmc the surface tension is nearly independent of temperature, saturating at $35.2\pm0.3\,\rm mN\,m^{-1}$. The behavior cannot be attributed to the temperature dependence of the cmc, which is an order of magnitude too weak. It is instead consistent with a surfactant layer that thins as the temperature rises. The results imply that the sign and magnitude of thermocapillary stresses in SDS solutions can be selected through the concentration.

Harnessing active matter to power functional devices has attracted growing interest. We propose a minimal battery model for storing energy extracted from active matter and derive its charging and discharging characteristics analytically. When the energetic cost of sustaining activity is included, the charging power-efficiency trade-off becomes loop-like and the efficiency attains a finite-time maximum, in sharp contrast to passive energy devices.

In this article, we explore how transport at a solid–electrolyte interface is affected by the internal fluctuations of the solid and quantify the role of solid excitations on ionic friction. Combining molecular dynamics simulations with theoretical modeling, we show that the presence of ions enhances the dynamical response of the electrolyte compared to pure water. This leads to an ionic contribution to the fluctuation-induced interfacial friction. We show that collective ionic modes dominate the dissipation, such that ionic friction arises from many-body effects rather than from individual drag forces. Furthermore, high-frequency molecular modes are found to be ion-specific, suggesting possible routes toward spectral separation of ions, with implications for desalination, filtration, and energy conversion.

Dynamic approaches to minimize the classical curvature-elasticity free energy for a fluid lipid membrane, are extended towards a Surface Beris–Edwards–Helfrich model. This extension explicitly treats the liquid crystal structure of the membrane, which results from the lipid molecules, that are, on average, oriented normal to the surface. Locally varying liquid crystal order leads to local variations in bending rigidities and surface viscosity and thus influences the shape evolution. This provides a multiscale coupling between the local membrane mechanics on the level of the lipids and the mesoscopic length and time scales of biological functions. The model is derived using the Lagrange–d'Alembert principle. We provide a numerical algorithm to solve the equations in the one-constant approximation and demonstrate the impact on the emerging equilibrium shapes, which not only depend on the specified conserved surface area and enclosed volume, as for the classical curvature-elasticity free energy, but also the elastic parameter. Exploring the dynamic evolution shows a tight coupling of tangential flow, shape evolution and liquid crystalline order. We further point to extensions towards lipid phase separation and asymmetric lipid bilayers.

A variety of disordered materials, including jammed particulate systems and crumpled paper, can be trained to exhibit memory of a cyclic strain amplitude. Only recently, however, have questions emerged around the whether random driving can impart similar training. Here, we employ x-ray photon correlation spectroscopy to study a fractal nanoparticle gel trained via either deterministic cyclic shear or random shear bounded by strain amplitudes $-\gamma_t$ and $+\gamma_t$. Both types of training lead to microstructural reversibility, with a slower and more irregular training for the random protocol. In both cases, the shear induces redistribution of internal stress in the gel with corresponding irreversible strain displacements whose magnitudes decrease during training. Finally, we show that memory of the random driving can be read out and quantified using a standard protocol.

Beyond a critical Toner–Tu drive, bacterial turbulence exhibits universal statistics, including a parameter-independent energy spectrum $E(k)\sim k^{-3/2}$. We show that the same universal state can be reached not only by increasing activity, but also by strengthening nonlinear advection, weakening nonlinear saturation, or tuning the Swift–Hohenberg instability. Motivated by the competition between these processes, we identify the independent dimensionless groups governing the dynamics and construct a Reynolds-like control parameter from them. A single critical value, calibrated from the known activity-controlled transition, predicts the onset of universality along the other parameter routes and collapses them onto a common threshold. These results identify a dynamical organizing parameter for the onset of universal active turbulence and provide a Reynolds-like measure for the Toner–Tu–Swift–Hohenberg universality class.

Membrane curvature has been shown to bias the location of lipid or protein domains, but the roles of bending rigidity, spontaneous curvature, Gaussian bending modulus, and line tension are difficult to separate in general. We develop a small-domain description for a membrane whose shape is held fixed, e.g. by strong adhesion to a curved substrate. Combining a local Helfrich energy with the small-area isoperimetric expansion gives a position-dependent energy determined by the local mean and Gaussian curvatures. We identify four generic regimes of curvature preference whose boundaries depend on only two dimensionless parameters. On specific membrane shapes with complex curvature, we show that this curvature preference determines the energy landscapes experienced by small domains, which are strongly dependent on the size of the domain through the line tension contribution. For example, on an oblate-shaped membrane, very small domains tend to localize at the poles, whereas larger domains prefer to localize at the equator. Whether this transition is continuous or discontinuous is found to strongly depend on the spontaneous curvature of the domain. This ordering suggests a mechanism by which small domains can collect and coalesce at one location before relocating as they grow.

Inferring the entropy production rate $\sigma$ from recorded trajectories is a key challenge in stochastic thermodynamics. In experiments, the forces governing the dynamics are usually unknown and often only some of the system's degrees of freedom can be observed. Building on a recently introduced method [I. Di Terlizzi, Phys. Rev. Lett. 135, 237101 (2025)], we develop and validate CYNAR (computation yields nonequilibrium analysis and reconstruction), a pipeline that estimates $\sigma$ from trajectories. It exploits a kinetic decomposition of $\sigma$ into a traffic term ${\cal T}$, inferred from the short-time curvature of correlation functions, and an inflow rate ${\cal G}$, computed from the steady-state score, i.e., the gradient of the log-density. We show that the same decomposition, evaluated on any subset of observed coordinates, always bounds $\sigma$ from below, for any diffusion tensor and without knowledge of the hidden degrees of freedom. We then compare CYNAR with a more standard approach that estimates $\sigma$ from steady-state probability currents, on four systems of increasing complexity. CYNAR proves to be more reliable, with no detectable bias close to equilibrium, weak dependence on spatial discretization, and marked robustness to measurement noise. It is also readily applicable to high-dimensional systems, where the traffic alone provides a lower bound close to $\sigma$, and remains informative under partial observation, including cases where the flux-based estimate vanishes identically. CYNAR is provided as an open-source Python package.

The regular bending waves of cilia and flagella provide an iconic model system for the collective dynamics of molecular motors. The known regular arrangement of dynein motors in a cilium's axoneme allows us to connect mesoscopic cilia properties, such as axonemal bending stiffness, to microscopic motor properties, such as the force exerted by an individual motor. We estimate the active force generated by the collection of dynein molecular motors in $\mathit{Chlamydomonas}$ axonemes using previous estimates of its bending stiffness. Divided by the maximal possible number of active motor heads, this provides a lower bound of ${>}10\,\mathrm{pN}$ for the peak force generated by a motor head, which exceeds typical stall forces ${<}5\,\mathrm{pN}$ of molecular motors. This discrepancy suggests that either the bending stiffness of microtubules and axonemes was previously overestimated, or that collective force generation in dense motor arrays can surpass the sum of expected contributions of individual motors.

Active spinners inject angular momentum into their surroundings without persistent translation, providing a route to chiral active matter distinct from self-propelled particles moving along curved trajectories. Recent studies have shown that spinner fluids can self-organize into rotating clusters with circulating edge currents characteristic of odd-viscous fluids. Whether angular-momentum injection alone can transmit chirality and edge-current dynamics to ordinary passive matter - and thus serve as a generic mechanism for imparting chiral functionality to undriven material components - remains an open question. Here, we show experimentally and numerically that purely rotational magnetic spinners can transfer chirality and edge-current dynamics to passive colloidal matter. At high passive-particle fraction, active spinners assemble into rotating clusters surrounded by passive matter. Remarkably, upon changing composition and spinner attraction, this organization turns inside out: passive colloids form rotating clusters surrounded by a chiral spinner fluid. These passive rotors exhibit edge currents and the same angular-velocity scaling, $|\Omega|\sim R^{-2}$, as their active counterparts. A minimal model shows that spinner-mediated transverse and non-reciprocal interactions are sufficient to reproduce these complementary chiral states and their boundary-driven dynamics. Our results establish angular-momentum injection by active spinners as a route to endow otherwise passive matter with chirality, collective rotation and boundary transport.

Since prehistoric times, painters have used brush-like tools made from animal and plant materials to apply pigments to rock surfaces. Over time, techniques for creating brushes evolved, and converged towards optimized shapes. Our study performed over hundreds of brushes reveals universal scaling laws. In particular, we uncover a relation between bristle length and diameter linked to the shape of the bristle ends, which governs their mechanical response with and without paint. For round brushes, we found that the size of the paint stain scales with the compression distance, meaning it only depends on the force applied by the painter and not on the mechanical responses of the brushes. These results shed light on the underlying universal physical principles governing brush design and their impact on artistic techniques.

Non-equilibrium systems challenge the standard definitions of phases and phase transitions from equilibrium statistical physics. For example, in active fluids continuous energy injection at the microscale drives the system intrinsically out of equilibrium. This process gives rise to collective turbulent-like flows whose onset remains poorly defined. Here we show that the onset corresponds to an activity-driven phase transition, marked by the emergence of a system-spanning critical backbone of vorticity nodal lines. Combining two independent experiments, microtubule kinesin active nematics and dense suspensions of swimming bacteria, with large-scale simulations of active nematics and fluctuating nematohydrodynamics, we show that this transition occurs at a critical activity threshold. Below this threshold, vorticity structures are fragmented and vortex centres form only finite, mechanically floppy networks. Above this threshold, the nodal lines of the vorticity field percolate and the vortex centres form a rigid, system-spanning cluster. The geometric transition is characterised by the emergence of critical percolation statistics for the vorticity nodal lines, while the mechanical transition reflects the emergence of a vortex configuration that shows rigidity percolation statistics for vortex centres. We show that both transitions are absent in equilibrium systems that obey detailed balance, demonstrating that the transition is intrinsically non-equilibrium. These results establish an experimentally accessible definition of fully developed active turbulence, linking microscopic activity to macroscopic geometry, and mechanics of living systems.

We develop a theory of phase separation in fluids conserving higher-order multipole moments of a scalar density, and investigate the resulting coarsening dynamics, nucleation, and interfacial fluctuations. We find that higher-order conservation laws slow the relaxation of all phenomena investigated, whereas nonequilibrium violations of the fluctuation–dissipation theorem suppress density and interfacial fluctuations while hindering nucleation. Simulations support these predictions.

We show that periodically modulating the self-propulsion of active particles in an asymmetric potential can both enhance rectified transport and reverse its direction, even when the propulsion speed itself never changes sign. Current enhancement results from the nonlinear response of active transport to propulsion strength, whereas current reversal emerges from the interplay between activity-induced spreading and passive relaxation. Our theoretical analysis identifies the regimes governed by these distinct rectification mechanisms and predicts the finite range of driving periods over which current reversal occurs. These results establish cyclic activity as a means of dynamically controlling rectified active transport, with potential applications to the selective sorting of active particles.

The effective Hamiltonian (EH), also referred to as the potential of mean force or free-energy landscape, is widely used to describe equilibrium properties and slow dynamics in chemical and soft-matter systems. However, the conventional EH has been argued to be ill-defined because it does not transform as a scalar under coordinate transformations. We identify an implicit change of reference measure (gauge), rather than the coordinate transformation itself, as the origin of this apparent problem. We formulate the EH as a scalar relative to a chosen gauge and derive the intrinsic, gauge-independent Fokker–Planck equation (FPE) on the manifold of slow variables. The conventional EH and the diffusion-dependent EH introduced in a Riemannian formulation, together with their corresponding FPEs, are thus different gauge representations of the same equilibrium measure and intrinsic stochastic dynamics. We further demonstrate that the gauge choice has an operational meaning: different restraint protocols select different reference measures. In the macroscopic limit, the leading EH becomes gauge independent within a class of subleading gauges and is determined by the large-deviation rate function. In the same limit, the stochastic dynamics reduces to gauge-independent deterministic dynamics.

Soap films afford gentle production of air-water interfaces and underlie numerous practical applications. Recently these interfaces have been shown to exhibit unexpected redox capability, wherein Triton X soap films formed with water or HAuCl4 solutions (i) oxidize water up to 1.67 mM H2O2 and (ii) reduce aqueous Au3+ ions into gold nanoparticles, without external energy or catalyst. These reports tend to align with the broader claims of the redox nature of the air-water interface, which has been intensely debated. Here, we re-examine these claims via complementary application of a broad range of techniques, including NMR spectroscopy, fluorescence, colorimetric, TEM, DLS, ICP-OES. Experimental results reveal no evidence for H2O2 formation despite repeated formation of over 300 cycles of soap films, were probed via NMR spectroscopy and other analytical methods. Next, we interrogated soap films for their ability to spontaneously reduce Au3+ ions. TEM and time-resolved DLS revealed that the formation of Au nanoparticles was already formed spontaneous in bulk solutions, and casting soap films (300 cycles) had no measurable effect on particle size or density. This observation was confirmed via complementary quantitative ICP-OES. Our investigations showed that Au nanoparticles formation in bulk HAuCl4 solution without or with triton soap was accompanied by H2O2 generation, and we provide mechanistic insights into these processes. Collectively, these results demonstrate that amplification of the air-water interfacial area through soap-film formation is insufficient, by itself, to induce detectable H2O2 generation or enhance Au-ion reduction. More broadly, our findings highlight the need to distinguish reactions that are driven by purely air-water interfacial effects from those that originate from bulk-solution chemistry and at the solid-water interface

Soft tactile sensors elevate robotic touch through enhanced flexibility and adaptability, yet most existing designs depend on embedded electronics that are susceptible to interference and environmental limitations. In this work, we leverage fluid-solid interactions to develop a class of soft tactile sensors that operate entirely without electronics at the sensing site. The sensor comprises a fluid-filled elastomeric channel connected to only two external pressure sensors. Touching different regions of the elastomeric surface displaces the viscous fluid, producing distinct pressure patterns that encode both touch position and force. These signals are decoded through a machine learning framework that integrates feature extraction, soft clustering, and adaptive neuro-fuzzy inference to achieve accurate localization and force estimation. We validate this concept through single-point touch localization and force estimation in a linear (1D) sensor and extend the same sensing principle to 2D tactile mapping by routing the channel across the surface using space-filling curves, while maintaining the same minimal hardware setup. This simple approach remains effective in environments where conventional electronic sensors often fail, such as underwater or in the presence of magnetic interference.

Tetrahymena calcium-binding protein (Tcb2) forms Ca$^{2+}$-responsive networks that exhibit contractile behavior, yet how Ca$^{2+}$ concentration controls their local mechanical response remains poorly understood. Here, we use optical tweezers to perform active microrheology on reconstituted Tcb2 networks inside a microfluidic device that enables precise control of Ca$^{2+}$ concentration, allowing systematic tuning of network structure and mechanics. We find that increasing Ca$^{2+}$ from 1 to 100~mM enhances the effective stiffness by nearly two orders of magnitude, from $\sim$1$\times$10$^{-3}$ to $\sim$7$\times$10$^{-2}$~pN/nm, corresponding to a transition from a viscosity-dominated to a more elastic and mechanically robust network. Recoil assays further reveal rapid release of stored elastic energy following deformation. After two orthogonal pulls, the bead recoils along the diagonal rather than retracing the loading path, indicating that stresses from different directions combine to produce a resultant restoring response. These results establish Tcb2 networks as a minimal, tunable system for probing chemomechanical coupling and viscoelasticity in Ca$^{2+}$-regulated protein networks.

We explore new methods for inducing the movement of water droplets on elastomeric substrates, such as polydimethylsiloxane (PDMS). Our approach builds upon the well-known phenomenon that water droplets move easily across these substrates when swelled w,ith silicone oil. While designing shallow open channels and traps on a PDMS film offers a simple way to control a droplet's trajectory by tilting the substrate in two orthogonal directions, this method is poorly suited for manipulating multiple droplets simultaneously. To address this limitation, we introduce two new methods. The first method utilizes a plano-concave PDMS platform with a radius of curvature significantly larger than the size of the droplet and its translation distance. When the system's configuration is altered, this curved substrate consistently guides the droplet along a curved geodesic. The second method incorporates diode-like gates on the PDMS. These gates are created on either flat or plano-concave PDMS films by embedding thin, rigid plates into the elastomer prior to crosslinking, followed by swelling in silicone oil. This process generates sigmoidal steps that restrict droplet motion to a single direction. Finally, we demonstrate how combining these two strategies enables various forms of directed motion for both single and multiple droplets.

A dense two-dimensional layer of aligned microtubules (MTs), powered by molecular motors, is a canonical laboratory model of active materials and a synthetic analog of biological systems such as bacterial turbulence, mitotic spindles, and morphogenesis. This material exhibits nematic ordering and associated topological defects, which display complex emergent dynamics, including the creation and annihilation of defects and the braiding of defects around one another in a complicated chaotic dance. Despite its prominent role in research, the MT-based active nematic material lacks a well established theoretical model that accurately captures the rich density variations prominently seen in experiments—density variations that are, in fact, the experimental signature of the nematic structure itself. The MT-system is typically modeled using two fields: the Q-tensor (encoding the order and orientation of the nematic phase) and the fluid velocity; critically, the microtubule density is assumed to be constant. This traditional model is adopted from classical Landau-de Gennes liquid crystal theory. Here, we present a fundamentally different approach to modeling MT-based active nematics that explicitly incorporates density variations, producing simulations that strongly resemble experimental videos, including the characteristic striation patterns. It also reproduces important behavior of the system confined to a circular well—behavior seen experimentally, but not captured by current theory. In crafting our model, we present an alternative to Landau-de Gennes theory for the creation and annihilation of topological defects that does not rely on the classic isotropic-nematic phase transition.

Active nematics are non-equilibrium fluids composed of rod-like self-propelled units that collectively generate large-scale coherent flows. Here, we focus on a canonical experimental system: an active nematic fluid in $2D$ driven by ATP, composed of densely packed, extended microtubule (MT) bundles cross-linked by kinesin motors. An intriguing feature of this system is the creation and annihilation of topological defects with topological charge $\pm1/2$, due to the fracturing of the material. Experiments confirm that the positive ($+1/2$) defects serve as "virtual stirring rods" that move around each other in a complex braiding pattern. This collective braiding motion of positive defects stretches and folds the fluid itself, i.e., produces macroscale chaotic advection. The degree of self-mixing due to the chaotic advection can be measured using topological entropy and the Lyapunov exponent. Our goal is to determine whether continuum models of MT-based active nematic fluid can reproduce these measurements. To this end, we use two continuum models: the traditional Beris-Edwards (BE) model and the more recently developed Beris-Edwards model with enhanced nematic locking (BENL). The difference between the two models is the adoption of the "nematic locking principle", which states that an individual MT bundle cannot rotate independently of its neighbors due to steric interactions among elongated dense MT bundles. This principle holds in the BENL model except in small localized areas of the material domain where the material fractures, specifically near the creation and annihilation of topological defects. We employ several numerical methods to estimate measures of chaotic advection using both models. Our study shows that the BENL model more accurately reproduces experimental measures of self-mixing driven by chaotic advection in MT-based active nematic fluids.

The Rheological Universal Differential Equation (RUDE) framework embeds neural networks within a frame-indifferent tensorial constitutive backbone and so enables data-driven discovery of complex material rheological behavior. However, the flexibility that makes the RUDE framework attractive also makes it difficult to deploy: the learned neural network correction can make the constitutive equation numerically stiff during training, distribute corrections across non-unique combinations of tensor-basis terms, and extrapolate poorly with increasing nonlinearity, especially for industrially relevant materials with broad relaxation spectra. We develop a stability- and reliability-focused multi-mode RUDE framework that addresses three key challenges: thermodynamic admissibility, out-of-distribution prediction, and interpretability. Logarithmic compression of the input invariants and a split-network architecture improve numerical conditioning during training, while a differentiable projection layer enforces the Clausius–Duhem inequality at every time step. We illustrate the framework with both synthetic (a multi-mode Giesekus model) and experimental data on an entangled silicone polymer melt. Both models were trained on LAOS; they remain stable and accurate under unseen flow conditions, including steady shear, transient stress growth, and extensional flows, for which the unconstrained models may diverge numerically. To aid in interpretation of the contributions of each learned correction to the rheological behavior, we introduce the rheome, a compact way of representing the dominant weighted tensor-basis contributions to the overall rheological behavior. These improvements to the RUDE framework lead to stable and interpretable trained models, paving the way for implementation in computational fluid dynamics simulations and for guiding the rational design of soft material processing operations.

We investigate the dynamics of spherical lipid vesicles subjected to an osmotic shock using continuum simulations of a permeable, area-incompressible fluid membrane with bending elasticity and surface viscosity. The dynamics are governed by a single dimensionless parameter $\varGamma$, which measures the relative strength of osmotic pressure and bending forces. Osmotic forcing drives a three-stage evolution comprising rapid buckling and collapse, smoothing of the resulting wrinkles and ridges, and slow folding into an invaginated morphology resembling the precursor to experimentally observed vesicle-in-vesicle structures. Linear stability analysis predicts the wavelength and growth rate of the initial buckling instability and shows that the dimensionless buckling time scales as $\varGamma^{-2}$, in quantitative agreement with simulations. At longer times, the energy budget reveals a reversal in elastic energy transfer: bending energy accumulated during buckling is released during relaxation and dissipated by membrane viscosity. A scaling analysis of the folding dynamics predicts that the dimensionless folding time scales as $\varGamma^{-2/3}$, again in excellent agreement with simulations. These results provide a continuum description of the mechanisms and widely separated timescales governing osmotically driven membrane collapse and invagination.

Viruses are among the most highly charged objects in biology, and electrostatic interactions permeate nearly every stage of their life cycle. At the same time, an empty icosahedral capsid is almost isotropic as far as the surrounding electrolyte is concerned—its charge distribution is anisotropic only at high multipole order, and electrostatic screening removes such anisotropy long before it can be probed at a distance. Here, we show that the packaged genome of a filled virus imparts a long-range electrostatic anisotropy that extends throughout the surrounding medium, which is not present for empty capsids. We support these findings with a novel Poisson–Boltzmann continuum theory where the orientational order of dsDNA enters through an anisotropic dielectric tensor and an inhomogeneous volume-charge distribution, which is coupled to a charge-regulating shell containing ionizable amino acid residues of the capsid proteins. The resulting electrostatic potential profiles show that DNA packed in an inverse-spool geometry imprints a highly inhomogeneous potential distribution on the outer capsid surface, whose angular structure is a direct result of the DNA-free axial void. At high salinity, the multipole spectrum of this distribution persists at large distances, whereas at low salt concentration, higher-order multipoles decay more rapidly away from the surface. The surviving quadrupole renders virus–wall and virus–virus interactions orientation dependent at the $k_\mathrm{B}T$ level, with a preferred orientation controlled by the sign of the external charge and the pH. Using phage $\lambda$ as a model system and checking robustness of our results on two other phages, we find the same behavior across a range of pH and ionic strengths. This identifies the packaged genome, rather than the symmetry of the capsid, as the origin of the long-range electrostatic anisotropy of a filled virus.