Papers

We study the effect of self-propulsion in the approach to the glassy regime of 2D bidisperse mixtures of frictional discs, confined to a horizontal plane, and fluidized by vertical vibrations. The discs are designed either to be passive, that is, exhibiting isotropic motion in the plane, or active, with a preferred polar mobility. When dynamics in mixtures of large active and small passive discs are compared to mixtures of large and small passive discs, the active system shows faster dynamics at equal area fractions. To explore whether activity merely speeds up motion, we select active and passive mixtures with the same relaxation time and compare their dynamics. Many indicators show that dynamical heterogeneity is much greater in the active glass with longer-ranged spatial velocity correlations, larger temporal variations in displacement, and higher amplitude of the four-point correlator. In this very crowded regime, despite frequent collisions, the activity directions of the discs remain persistent. However, the activity direction of the discs remains spatially uncorrelated, and furthermore, the particle displacements are not aligned with the activity direction, thus presenting a puzzle as to how activity leads to such strong heterogeneity.

The interfacial structure and dynamics around a quenched impurity is far from understood till date. Here we explore the structural and dynamical properties of interface between colloidal fluid film and a quenched impurity by using computer simulation. We tune the size($\sigma_{imp}$) of a quenched pinned impurity and observe that the impurity surface is wetted by a fluid layer, giving rise to a finite-width interfacial region for sufficiently large impurities. Beyond this interfacial region, the host fluid exhibits quasi-long ranged orientational order(QLRO) due to the fluid- crystal phase coexistence. We find that the mean diffusivity becomes very low in the QLRO phase where the self van Hove function shows an exponential tail, signature of dynamic heterogeneity within the system. In the presence of second impurity the orientational order is suppressed if the fluid layers around the impurity particles overlap.

The translational dynamics usually decouples earlier than the rotational in supercooled liquids as the temperature decreases, whereas the inverted scenario remains scarce reported. In this work, starting from the coarse-grained ortho-terphenyl model, we build a rigid tetrahedral structure model. It exhibits an earlier decoupling in rotation than in translation. The Stokes-Einstein-Debye relation breaks down while the Stokes-Einstein relation remains intact. The decoupling happens at approximately 2Tg similar as that observed in supercooled water. The rotation shows more heterogeneous dynamics than the translation at all temperatures. Our results suggest that the steric hindrance plays an important role in determining the decoupling between the translational and rotational dynamics.

A physical learning network is read at a few accessible nodes. Every task and learning rule that uses only the steady voltages and currents there, at a fixed operating point, acts through the boundary response map. Changes in the kernel of its Jacobian are blind to first order. A walk along one fiber ran to a 600-step cap, one edge then at 15.2 times its start. A decomposition theorem splits the response Jacobian over the hidden components. The blind dimension adds over components whose surviving slots are disjoint. A boundary-to-boundary edge adds one parameter and deletes one slot. Exposing a hidden node changes only its component. For one hidden node the contribution counts the bipartite components of the non-adjacency graph of its neighbors. For a pocket of h hidden nodes a factor-analysis bound caps what outside electrodes can expose. It is attained when every pocket node meets every neighbor and no edge joins two of those neighbors, so past a threshold further electrodes outside such a pocket expose nothing. An electrode inside such a pocket, when its hidden nodes form a clique, is worth h-1 directions where one outside is worth none. Read as vector displacements rather than potentials, the same nodes left no deficit beyond counting in all 90 spring networks tested, each a pocket fully joined to five or more accessible nodes, and nothing blind in 88. What limits the reading is the quantity measured as much as the number of contacts. Maximum-weight spanning forests give a proved upper bound on the blind dimension. The matching equality is proved for one hidden node and conjectured beyond. It holds in all 5,343 components whose maximum could be attained and certified, and the forest count matched the certified blind dimension in 1,448 of 1,500 held-out networks, where the maximum must be searched. A self-learning circuit shows the split on hardware.

A time fractional extension of the Hunter Saxton equation is examined, in which the temporal derivative of u_x is replaced by a Caputo derivative of order 0 < alpha <= 1. This modification introduces memory effects into a model traditionally associated with director field dynamics in nematic liquid crystals. By employing a fractional separation of variables strategy together with the exponential spatial profile phi(x) = exp(b+x), which cancels the nonlinear structure exactly, the governing nonlinear partial differential equation is reduced to a fractional relaxation ODE, whose closed form solution is the one-parameter Mittag Leffler function. The exact analytic solution is derived algebraically from the separation process. This appears to be the first exact closed form solution of the Caputo time fractional Hunter Saxton equation. The result is validated symbolically using the MathHandbook computer-algebra system. Quantitative analysis in both the fractional (0 < alpha < 1) and classical (alpha -> 1) limits demonstrates how fractional-order memory slows temporal relaxation relative to the exponential baseline. The solution provides a reliable benchmark for numerical schemes and clarifies how fractional dynamics influence nonlinear wave propagation in orientationally ordered fluids.

Our understanding of inertial particle dynamics in turbulence is mostly based on flows held in a statistically stationary state, a particular regime that differs from many natural flows where energy input can often be intermittent or cyclic, or may abruptly cease. Here we investigate inertial particle and bubble dynamics in freely decaying turbulence through complementary experiments and direct numerical simulations. While particle accelerations decay monotonically in time, we find evidence that the clustering can exhibit a non-monotonic evolution, intensifying sharply before subsequently weakening. We demonstrate that both the acceleration and clustering behaviors can be mapped onto their counterparts in stationary turbulence using a dynamic rescaling of the evolving length and time scales of the turbulence. Validity conditions for the dynamic rescaling, satisfied by both the experimental and numerical datasets, are derived. The proposed mappings remain applicable across a broad range of density ratios, from light to heavy particles, and particle sizes spanning two orders of magnitude in Stokes number.

The conventional interpretation of elastomeric fracture treats the tearing energy G as an output determined by tear speed, taken to equal crack velocity vc, concluding that higher vc produced greater viscoelastic dissipation to increase G. Based on spatially and temporally resolved polarized optical microscopic (str-POM) measurements of tip stress tip stress, we use prenotched pure shear experiments to clarify the causality: Local crack-tip stress determines the network lifetime, making vc the passive kinetic output. In the elastic limit that can be readily achieved for a well crosslinked elastomer in a wide range of temperatures, Rivlin-Thomas scaling holds, and vc depends only on the applied strain, independent of stretch rate, indicating one-to-one correspondence between vc and tip stress. In a highly stretchable elastomer made with reduced crosslink density, vc no longer correlates well with the far-field load as rate-dependent viscoelastic processes emerge to affect network lifetime. Because of the rheological effects on how chain tension builds in the elastomeric network, vc is higher at a common nominal strain when it is imposed with higher stretch rate. confirm that different stretch rates produce different levels of tip stress. The same tip stress still produces the same vc. With str-POM measurements we are also able to elucidate the nature of temperature dependence: at a given tip stress,, crack growth is slower at lower temperatures; conversely it requires higher tip stress to produce the same vc at lower temperatures.

Evaporating sessile water droplets universally deposit surface charges while simultaneously becoming self-charged—a phenomenon that remains under-appreciated despite its potentially important consequences. Here, we investigate one such consequence: droplet self-propulsion driven by self-charging. This self-propulsion arises spontaneously in the absence of external stimuli and produces self-avoiding trajectories that can displace droplets by many times their own diameter. Our results have important practical implications for processes requiring spatial precision, such as inkjet printing. The coupling between self-charging and self-propulsion produces mosaic surface charge patterns characterized by alternating polarities, which we explain with a physical model based on properties of the electric double layer.

Rotating magnetic microparticles are building blocks for field-driven assembly and microrobotic control. As the elementary interaction rule for larger assemblies, pair motion in these systems is governed not only by magnetic forcing, but also by hydrodynamic coupling and other long-range interactions. Here we develop a reduced framework for two synchronized rotating magnetic particles by resolving the interactions into radial components that change the interparticle distance and transverse components that rotate the line of centers. The competition between magnetic dipolar interaction, additional radial repulsion, and rotation-induced transverse coupling selects three pair-motion modes: rigid-body rotation, contact-separation rotation, and irreversible separation. We derive transition criteria for the rigid-body state, reversed orbital motion, and the separation boundary, and obtain an asymptotic solution for the separation dynamics. Lattice Boltzmann simulations of particles rotating near a wall provide a hydrodynamic realization of the model, in which inertial secondary flow generates radial repulsion and rotational flow produces transverse coupling. The resulting phase diagram in the physical $(\mathrm{Re},C_m)$ plane is consistent with the reduced-model predictions. These results provide design rules for programming elementary pair interactions in rotating magnetic-particle systems and may help guide the control of microrobotic assemblies.

Functional materials realize functionalities through pre-designed structures, whereas physical neural networks are trained by prescribing input-output behavior. Unifying these views would allow materials to acquire functions directly from dynamical tasks. Here we introduce an in situ local learning framework for dynamic network materials. A forward drive and a time-reversed adjoint error drive are applied to the same mechanical network, enabling the material to compute gradients of a time-domain loss through its own dynamics. The resulting update rules are local, compatible with the principle of physical learning. Each bond or node requires only co-located forward and adjoint fields. The method trains spring constants, nodal masses, bond damping coefficients and nodal damping coefficients, and programs dynamical functions including broadband wave cloaking, evanescent-wave imaging, passive transient output enhancement and vowel classification. These examples involve distinct physical mechanisms, such as wave scattering, near-field information transfer, dissipative non-normal dynamics and machine learning, but are obtained by simply changing the loss function, rather than leveraging expert knowledge. Therefore, dynamic network materials can act both as programmable matter and as physical neural networks, providing a route to material systems that learn temporal responses in situ.

Elastic buckling has explained shape formation in growing tissues, yet the role of tissue fluidity remains elusive. We derive a minimal fluidized growth-elasticity model as a nonlinear analogue of Maxwell rheology. Analysis of a growing strip reveals a different picture of growth-induced morphogenesis: rather than emerging at a critical stress, symmetry breaking develops continuously during growth. Fluidity regulates stress evolution, the rate of shape-symmetry breaking, and flow patterns, establishing it as an active regulator of morphogenesis beyond its intuitive role in stress relaxation.

Multiscale simulation requires coupling physics models that operate at different characteristic length and time scales, because no single method spans the range needed for most problems of interest. Moving to a coarser-grained representation unlocks longer length and time scales, but it discards the microscopic interactions that build morphology. A fine-grained model can be initialized from an arbitrary packing and left to self-assemble into a physically meaningful structure; a lower-resolution model cannot, and must inherit its starting configuration from a higher-fidelity simulation. The length scales accessible to the coarse-grained model are therefore set not by the coarse-grained method itself, but by the largest fine-grained configuration that can be affordably equilibrated. A representative example is the scale-up from particle-based molecular dynamics (MD) to a lattice-based representation such as kinetic Monte Carlo (kMC). In this work, we present a cellular automata (CA) approach for generating arbitrarily large lattice starting configurations. CA is a natural fit for this task: short-ranged local rules drive the evolution of a lattice, and their repeated application gives rise to emergent long-range order, thematically mirroring how short-ranged interactions in MD produce self-assembled morphology. We use a configuration from a higher-fidelity simulation as a training set and learn the CA rules from it via logistic regression. As a proof of principle, we develop these rules for a hydrated anion exchange membrane (AEM), generate new starting configurations, and benchmark their performance in mesoscale kMC simulations against an MD-derived "ground truth." We then demonstrate the ability to generate substantially larger lattices and show that their behavior in kMC is consistent with that of the smaller CA benchmark configurations.

Framewise variance normalization removes fluctuation amplitude from an observation, but not from the dynamics that generate later patterns. The current normalized spectrum therefore need not determine its own future. We study this effect in three two-dimensional phase-separation models that change transport, add active driving, or suppress large-scale separation. For paired initial fields, their normalized spectra evolve identically in the linear regime. The restoring model provides an exact example: damping does not directly change how the normalized spectrum evolves when both equations are applied to the same field. It nevertheless changes the hidden amplitude, which alters the later nonlinear shape. An exact comparison separates the immediate effect of changing the equation from the effect of reaching a different state through earlier evolution. It also reveals strong cancellation between these effects in the mobility and active models. As a practical test, spectral histories improve classification by about 4-6 percentage points at several later observation windows, although the gain depends on quench depth and spectral construction. Temporal spectra can therefore reveal dynamical consequences of information absent from every individual normalized frame.

Massive jellyfish swarms observed at sea can extend over tens of kilometres and contain millions of individuals, yet the mechanisms governing their formation and large-scale dynamics remain poorly understood. Agent-based models provide a framework for describing this dynamics based on jellyfish responses to ocean currents and environmental cues, but become computationally prohibitive when extended to large populations and spatial scales relevant to ocean circulation. Here we derive a continuous kinetic theory from an active-particle model of jellyfish motion. The resulting Fokker-Planck framework incorporates transport by prescribed currents, stochastic reorientation, direct interactions and stimulated steering, allowing chemical signalling to be represented through a coupled field. We further derive a hydrodynamic closure for large swarms by exploiting the separation between fast orientational and slow spatial dynamics, yielding a reduced density equation suitable for implementation in ocean-current models. This framework provides a route from individual behavioural mechanisms to continuum descriptions of jellyfish populations and establishes a basis for constraining model parameters using observations and in-situ measurements. This approach offers a theoretical foundation for future numerical prediction of large jellyfish swarm formation and evolution in realistic ocean flows.

We develop a method to extract the shear viscosity of a lipid membrane from equilibrium molecular dynamics simulations. The method characterizes the rheology of general interfacial systems embedded in three-dimensional media; we term it molecular interfacial rheology. In our simulations the planar bilayer and surrounding water are confined between solid, parallel walls. Following Onsager's regression hypothesis, membrane and water fluctuations are assumed to relax according to the coupled continuum-mechanical equations governing the confined system—which predict that the membrane transverse velocity autocorrelation function (TVACF) decays exponentially, at a rate set by the membrane and water viscosities. The measured TVACF, however, exhibits damped oscillations followed by a slowly decaying tail. We reconcile these behaviors using the Mori–Zwanzig formalism, and extract the wavevector-dependent membrane viscosity from the time-integral of the TVACF. Results from theory and simulations agree over a decade of wavevectors, and extrapolating to long wavelengths yields shear viscosities ranging from 0.064 to 0.18 pN*us/nm across two representative single-component, fluid-phase bilayers. Our results are corroborated by nonequilibrium simulations where a spatially varying in-plane body force is applied to lipid molecules, thus validating the framework of molecular interfacial rheology.

Establishing a robust and physically interpretable link between static structure and heterogeneous relaxation dynamics remains a fundamental challenge in glass physics. Here, we introduce a weighted pair-entropy descriptor based on the conventional two-body excess entropy. For this, we multiply the integrand used to calculate the excess entropy by a weight function that is directly related to the length scale of the pair correlation function. This multiplication does not affect the contribution of the short range order to the local excess entropy, but allows to take into account the structure present on intermediate distances, i.e., the medium-range order. For a canonical two-dimensional Lennard-Jones glass former, the resulting descriptor exhibits a strong correlation with particle-level dynamical propensity at long times (multiples of the alpha-relaxation time), with a maximum structure–dynamics correlation reaching about 0.9, substantially outperforming the predictive power of the conventional local pair excess entropy. These results demonstrate that incorporating a physically motivated structural length scale into entropy-based descriptors markedly enhances their predictive power while preserving physical interpretability. Our findings provide a simple and general framework for investigating structure–dynamics correlations in glass-forming systems.

We generalize the Mori-Zwanzig projection operator formalism by introducing an oblique projector using biorthogonal variables to coarse-grain the dynamics of systems far from equilibrium, such as active or living matter. Improving on previously used orthogonal projectors, the oblique projector correctly decomposes the emergent interactions of the coarse-grained particles into systematic and stochastic contributions. We show that the formalism directly connects to established results in non-equilibrium linear response theory and adiabatic perturbation theory. Based on this formalism, we develop a coarse-graining algorithm which we apply to extract the emergent non-equilibrium chiral dynamics of a passive tracer in a chiral active bath. Our theory correctly predicts the odd transport properties and a confinement-induced shift of the chiral frequency of the tracer.

We investigate the slowing down of dynamics in a glass-forming mixture interacting via an inverse-power-law (IPL) potential using a combination of theory and large-scale molecular dynamics simulations. We measure the static pair-correlation function, configurational entropy, inherent-structure energy, and structural relaxation time. We employ a theoretical framework to calculate the structural relaxation time $\tau_{\alpha}$, which is found to be in very good agreement with the simulation results. The theory identifies a local structural order which defines the cooperativity of the relaxation and brings forth a fluctuation induced parameter $\psi ( T )$ and a crossover temperature $T_a$ that characterize the density and temperature dependence of the glassy dynamics. Furthermore, we determine a crossover temperature using independent dynamical and thermodynamic criteria and compare with the theoretically predicted crossover temperature $T_a$. Relaxation dynamics is shown to obey density-temperature scaling, similar to thermodynamic properties, in terms of a variable $\Gamma$ formed by an appropriate combination of density and temperature, characteristic of IPL interactions. Finally, we show that, when the excess thermodynamic and dynamic quantities obtained at different densities are plotted as functions of the reduced temperature $T/T_a$ (or $T_a/T$), the data collapse onto master curves with excellent agreement between theory and simulation. These scaling relations provide a unified description of the thermodynamics and dynamics in IPL systems, enabling the prediction of relaxation behavior over a wide range of densities from data at a single state point.

Understanding the structural evolution of supercooled water-glycerol solutions is important for cryopreservation, yet distinguishing liquid-state transformations from ice crystallization remains challenging. Here, we investigate a deeply supercooled water-glycerol solution by X-ray photon correlation spectroscopy (XPCS) in ultra-small-angle X-ray scattering (USAXS) geometry, combined with wide-angle X-ray scattering (WAXS). This combination simultaneously captures the structural and dynamical evolution of the supercooled liquid upon quenching to cryogenic temperatures (172 K). We observe discontinuous changes in the liquid structure on molecular length scales and formation of microscale domains. The dynamics slow down during this stage and exhibit hyper-diffusive, ballistic-like relaxation. This transformation precedes ice crystallization, which we identify from the emergence of ice Bragg peaks in WAXS, allowing the two processes to be temporally separated. Phase-field (Cahn-Hilliard) simulations qualitatively reproduce the experimental observations and show that a spinodal-decomposition scenario is consistent with the measured scattering evolution. These findings are consistent with a liquid-liquid phase separation scenario preceding ice crystallization and provide a route to disentangle the two processes in supercooled aqueous systems.

Many semiflexible filaments exhibit structural asymmetries that lead to a curved ground state (curvature in the absence of thermal fluctuations, external forces, or torques). This property is known as spontaneous curvature. Many semiflexible polymers can reversibly develop spontaneous curvature through internal conformational transitions or through transient interactions with their molecular environment. In this article, we show that such reversible spontaneous curvature, even in the absence of transitions in the value of the bending stiffness, provides a minimal mechanism for ensemble-dependent elasticity. We formulate an analytically tractable two-state modified wormlike-chain model in two dimensions, in which an uncurved state (without spontaneous curvature) competes with a curved state (possessing spontaneous curvature). The transition is controlled by an activation energy. Within the weak-bending approximation, we obtain the Gibbs and Helmholtz partition functions for a stretched filament with reversible constant (uniform along the backbone) or sinusoidal spontaneous curvature and for a grafted bistable filament driven either by an end torque or a bending force. Stretching or bending induces a crossover from spontaneous-curvature-dominated to entropic elasticity. We show how the elastic response differs in the two ensembles (Gibbs vs Helmholtz). In addition, we consider the case where the curved state is also characterized by a higher value of the bending stiffness. In that case, a reentrant transition is possible as we stretch the bistable filament.

Elastic turbulence (ET) in straight geometries has been extensively studied in idealised configurations such as periodic shear and planar channel flow, yet experiments are typically restricted to confined systems like ducts and pipes. While chaotic elastic fluctuations are observed in ducts, their onset in pipes is debated due to geometric constraints. Here we report sustained chaotic dynamics in both geometries and show they correspond to the same ET state identified in idealised setups. Our results establish ET as a geometry-independent attractor and point to a distinct transition mechanism in pipes.

Crack-tip fields govern deformation localization and failure initiation. Classical continuum fracture mechanics describes these fields through theories such as the Hutchinson-Rice-Rosengren (HRR) field for nonlinear power-law solids. However, continuum descriptions break down near cracks in soft and architected materials, where load is transmitted through discrete chains, fibers, or struts. Here, we develop a discrete crack-tip theory for lattice networks with nonlinear chains. The theory has two central components. First, at large deformation, the strain of a representative chain in layer $i$ depends approximately linearly on the applied macroscopic strain, $\varepsilon_i\approx k_i(\lambda-1)$, defining a layer-dependent strain-amplification factor $k_i$. Second, along topology-selected chain directions, termed discrete HRR lines, the layer-to-layer ratios of $k_i$ follow a two-regime scaling law. Together, for a power-law chain force-strain relation with exponent $p$, the inner discrete regime predicts $\varepsilon_i\sim i^{-1/p}$ and $f_i\sim i^{-1}$, which differs from the classical continuum HRR prediction. The theory also explains why the intrinsic fracture energy approaches a size-independent limit as the network size increases. Photoelastic hydrogel experiments further validate our theory. These results reveal a two-regime crack-tip scaling law in nonlinear lattice networks and provide a framework for predicting chain deformation and intrinsic fracture energy.

Dynamic self-consistent field theory (DSCFT) provides an efficient continuum framework for studying structure formation in inhomogeneous polymer systems, but its predictive accuracy depends on the choice of the nonlocal mobilities. Here, we construct mobility functions for moderately and strongly entangled homopolymer and diblock copolymer systems from the relaxation dynamics of single-chain structure factors, based on molecular dynamics (MD) simulations of the Kremer-Grest model and analytical reptation theory. Single- chain mobilities are combined such that the resulting DSCFT accounts for the dependence of fluxes on local chain densities. The theory is then applied to the spinodal decomposition of symmetric homopolymer blends and diblock copolymer melts following a quench into the (micro)phase-separation regime. Predictions of DSCFT are systematically compared with MD simulations. Mobility functions derived from single-chain dynamics are found to reproduce the kinetics of structure formation more accurately than conventional Debye-type mobilities. We additionally investigate the influence of adding stochastic currents (noise) that are correlated according to the fluctuation-dissipation relation. At low noise levels, they enable the generation of equilibrium initial states and facilitate defect annealing. At high noise levels, however, nonolinear effects lead to discrepancies between DSCFT and MD simulations.

Digital materials fabricated by multi-material 3D printing are designed as controlled mixtures of stiff and compliant constituents, yielding effective responses that span more than an order of magnitude in apparent stiffness and exhibit strongly nonlinear, composition-dependent, and rate-dependent dissipative behavior. Classical finite-strain viscoelastic models represent such behavior with closed-form strain energy functions for equilibrium and non-equilibrium stresses as well as evolution of internal variables, which may limit flexibility when a single constitutive model is expected to generalize across materials and loading rates. Here, we present a data-driven multi-material constitutive modeling framework that generalizes a formulation by Bergström and Boyce. The proposed framework retains the structure of the classical model, namely multiplicative kinematics, invariant-based strain-energy functions, and a scalar dissipative evolution law directed along the normalized nonequilibrium deviatoric stress. For the equilibrium branch, the data-driven discovery framework either directly predicts closed-form model parameters as functions of composition or automatically constructs a polyconvex strain-energy function using neural ordinary differential equations (NODEs). The nonequilibrium branch kinetics are learned similarly, either by directly identifying closed-form parameters across compositions or by using appropriately constrained artificial neural networks. Using multi-rate uniaxial compression data across multiple material compositions, we show that the proposed formulation captures rate-dependent stiffness and hysteresis across compositions while preserving thermodynamic consistency.

What controls heat transport when liquid water interacts with ice? Answering this question is essential for understanding water bodies undergoing phase change. Yet experimental progress remains limited by the lack of a minimally invasive methodology for simultaneously resolving temperature fields in coupled liquid water and non-isothermal ice systems. Here, we introduce a physics-based data-assimilation method for reconstructing temperature fields in buoyancy-driven flows interacting with non-isothermal ice. Particle tracking velocimetry provides the liquid velocity field, while thermal and kinematic boundary conditions constrain the inverse problem. The method couples advection–diffusion in liquid water with conduction in ice to reconstruct simultaneous mean temperature fields and quantify heat transport across the water–ice interface, while remaining minimally invasive and compatible with free-surface systems. We demonstrate the method in laboratory experiments in which the temperature range across the liquid water in contact with ice drives cabbeling-induced convection. This framework enables investigation of coupled thermo-fluid dynamics in cryospheric aquatic systems, including heat exchange at the ice-water interface and liquid-phase energetics, with broader applications to phase-change processes in food and energy industries.

Transferable coarse-grained (CG) force fields compress chemical space: by aggregating atoms into a reduced set of interaction beads, models such as MARTINI reduce the number of distinguishable compounds by roughly three orders of magnitude, making high-throughput screening of thermodynamic properties tractable across soft matter, with drug–membrane permeability as a well-developed example. The compression is lossy and, so far, one-way: a screen returns a combination of beads, with no established route back to the compounds it stands for. Recovering those compounds–compositional backmapping–is a one-to-many inverse map, distinct from the better-studied conformational problem of rebuilding atomic coordinates from a known mapping. Here we formulate compositional backmapping as conditional graph generation by introducing juniper, a discrete denoising diffusion model over molecular graphs conditioned on the octanol–water partition free energy $\Delta G_{\mathrm{W} \mapsto \mathrm{O}}$, the principal driver of MARTINI bead type assignment and hence a proxy for bead identity. Trained on molecules of up to 9 heavy atoms mapped onto one or two beads, juniper generates molecules that are 93% valid and 92% unique for two-bead targets, and whose $\Delta G_{\mathrm{W} \mapsto \mathrm{O}}$ distributions track the target $\Delta G^{\mathrm{CG}}_{\mathrm{W} \mapsto \mathrm{O}}$ linearly ($r^{2} \geq 0.96$), departing only in the hydrophobic and hydrophilic tails. Although the model receives no chemical information beyond a single scalar, the functional groups shift systematically with the imposed free energy, from branched hydrocarbons at the apolar end to amides, imides, and isocyanates at the polar end. A bead combination flagged by a CG screen can therefore be turned into candidate molecules for atomistic study or synthesis.

Multi-material PolyJet printing produces voxel-scale digital mixtures of an elastomeric photopolymer (Agilus) and a glassy photopolymer (Vero), giving a material family whose room-temperature response ranges from elastomeric to glassy; a unified description spanning the family has remained challenging. Large-deformation uniaxial compression over nearly three orders of magnitude in strain rate reveals a nonlinear, rate-dependent load-unload response that evolves continuously with composition, from recoverable elastomeric hysteresis to glassy yield with post-yield softening, hardening, and substantial residual strain. Dynamic mechanical analysis (DMA) shows that each mixture has a single glass transition temperature ($T_g$) that shifts to higher temperature with both Vero fraction and frequency, so composition acts much as temperature or loading rate does. This time-composition equivalence motivates one constitutive structure for the whole family rather than a separate property set per mixture: an equilibrium hyperelastic network with three non-equilibrium, rate-dependent branches carrying reptational, intermolecular, and glassy resistance. Its properties are anchored at the two endpoints and interpolated by smooth composition scaling laws. The model captures the compression response of all seven calibrated compositions and predicts a withheld mixture from the scaling laws alone. Resolving the predicted stress into its branches shows the load passing from the elastomeric to the glassy mechanism, and the work from elastic storage to dissipation, as Vero content and rate rise. The glass transition that DMA maps at small strain therefore governs the large-strain deformation mechanisms. The framework gives a compact, physically based description of digitally mixed polymers and a predictive basis for designing functionally graded, architected multi-material structures.

Eukaryotic cells rely on membrane-mediated processes to compartmentalize biomolecules, counteracting diffusion-driven homogenization. These processes involve the selective sorting and packing of molecules into lipid vesicles, which are then dispatched to appropriate intracellular destinations. Previous works introduced an abstract statistical physics framework for studying this molecular distillation process, where the membrane was treated as static and the focus was on molecular aggregation and extraction. Here, we extend this framework to explicitly incorporate dynamic membrane behavior, including bending, curvature generation, and changes in membrane size due to vesicle fusion and fission events. Sorting domains drive membrane curvature, leading to vesicle formation, detachment, and a molecular distillation process that alters membrane size. Using mesoscopic modeling and numerical tools, we investigate the resulting interplay between membrane mechanics and molecular sorting. We determine a well-defined parameter region where vesicle fission and efficient molecular sorting occur, controlled by membrane rigidity, spontaneous curvature, and pressure difference across the membrane. We further identify a trade-off between speed and quality of molecular distillation: parameters that accelerate vesicle formation tend to reduce the quality of distillation, and vice versa. We propose maximization of the rate of negative entropy production as a natural criterion to optimally balance these competing effects. In this context, optimal parameters emerge naturally from the coupled dynamics of molecular aggregation and membrane mechanics, suggesting a possible strategy for cellular sorting systems to strike an efficient balance between rapid vesicle formation and high sorting quality.

A passive, reciprocal, linear network driven by forces or currents and read at points it drives cannot be trained below an error floor computed from the target beforehand. The usual parameter count for such networks does not charge for Maxwell-Betti reciprocity. We prove that when such an elastic, resistor or flow network has a symmetric response operator and p driven degrees of freedom are also read, its reachable response blocks lie in a subspace of codimension p(p-1)/2, whatever its size and topology, and the floor is the distance to it. On targets with a reachable symmetric part, a second-order optimiser ends within 0.1% of the floor in 142 of 144 simulated runs, and a contrastive rule with a bond-local update direction, within its step budget, in 22 of 24. Reciprocity charges a list of single drive-read tasks only for the pairs it instruments in both directions, and a rank test on the passive network says in advance whether, and on which bonds, odd couplings locally restore the lost directions, at a cost in non-reciprocity that the target bounds from below. Under an imposed-displacement drive, the one most physical-learning hardware uses, reciprocity survives as a weaker law, an exact balance between forward and reverse transmissions once each is weighted by the driving-point compliance at its input, and an inequality on their product, under which no symmetric positive-definite chain meets both targets of a published robotic metamaterial. All nineteen published layouts we tabulated pay nothing; a force-driven layout that asks one pair to respond differently in its two directions will.

We derive nonasymptotic upper bounds on the probability that a generalized current of a geometrically ergodic diffusion observed for any amount of time, or its sample mean over any arbitrary sample size, deviates from the stationary mean by more than any given amount. The concentration-of-measure behavior of generalized currents is universally governed by the relaxation time of the underlying dynamics, the locally observed dissipation rate, and the intrinsic local fluctuations of the observable. We uncover stark qualitative and quantitative differences in fluctuations in and out of thermodynamic equilibrium. We further obtain refined inverse thermodynamic uncertainty relations, bounding the variance of generalized currents from above. We construct nonasymptotic confidence intervals for controlling uncertainty in thermodynamic inference from small data, i.e., from short trajectories and small samples, and provide the first quantitative answer to when a trajectory is sufficiently long and a sample is sufficiently large. As an illustration, we apply our results to currents observed on a two-dimensional Ornstein-Uhlenbeck process in and out of equilibrium and show how they can be used to rigorously detect broken detailed balance.