Papers

Granular slip forecasting can conflate material state, loading progress, and the geometry of event-centered sampling. We separated these contributions in slowly sheared two-dimensional frictional disks using a compact neural score of stress, pressure, coordination, non-affine motion, and force-network observables. The model was developed on 36 trajectories and frozen efore testing on 18 new trajectories under two nested stress-drop definitions. Inspection of held-out results revealed post-event sampling asymmetry; recovery-aware analyses are therefore descriptive. With trajectories weighted equally, the compact score ranked near-slip windows above both prevalence and within-trajectory circular-phase controls under both definitions (representative average precision 0.310 versus prevalence 0.173; phase-null upper bound 0.257). Loading-history coordinates ranked more strongly, reaching 0.534 for causal elapsed strain. The recovery-aware rule retained 78.4% of activity-gated events and preferentially selected longer preceding intervals; ranking by time since the previous catalogued event remained compatible with a count-conditioned geometry null. Compact observables thus contain temporally aligned slip information, but stronger loading-history baselines and window-geometry sensitivity bound that evidence. These startup data do not isolate a state-specific short-horizon precursor beyond loading history or support a renewal interpretation of elapsed-strain ranking.

The Jarzynski relation enables the estimation of equilibrium free energy differences from non-equilibrium, finite-time switching simulations. These estimates usually converge poorly because rare trajectories dominate the exponential work average. Here, we numerically determined and explored the sequence of intermediate Hamiltonians connecting initial and final states that minimize the mean squared error (MSE) of the Jarzynski estimator and thereby enhance convergence. For discrete-time Markov models, an exact tilted-master-equation representation of the MSE in the large-sample limit, combined with automatic differentiation, enables efficient gradient-based minimization over all intermediate energies. We applied our approach to three model systems of increasing complexity: a two-state model, a double-well potential, and a shifted potential well. In all three systems, the optimal intermediate Hamiltonians jump at the initial and final times. Extensive Monte Carlo simulations show that optimal intermediates can reduce the MSE by more than an order of magnitude compared with linear and logarithmic interpolation, most strongly for large changes in the energy landscape. Remarkably, they need not dissipate less work than intermediates yielding larger errors. Our results suggest heuristics for more efficient non-equilibrium free energy calculations of realistic molecular systems: optimal intermediate Hamiltonians jump at the initial and final times; for barrier-crossing problems, the barrier should be lowered rapidly and raised again later; and minimizing dissipation does not guarantee faster convergence.

A compressible, non-isothermal dilute polymer solution is formulated as a Class-II binary mixture with separate solvent and polymer mass and momentum balances and with total energy and entropy balances for the complete mixture. The entropy exploitation is sharpened by a balance-anchoring axiom introduced here: in a fixed balance representative, each selected binary dissipative product contains a constitutive factor from an unclosed balance flux or source. Polymer configuration is resolved first by a connector distribution and then by its conformation tensor. Population kinematics fix polymer transport and, by moments, yield a two-velocity upper-convected rate; objectivity verifies covariance rather than selecting it. Within the total entropy balance, configurational transport and deformation powers cancel their chemical-potential and elastic partial-stress counterparts when deformation and stress-decomposition weights match. A Gordon–Schowalter test independently requires the affine upper-convected choice for the stated dumbbell free energy and Kramers stress unless an additional reversible channel is supplied. Coordinated stress–interaction changes shift the local entropy flux/production pair by a divergence, exposing representation dependence of local mechanism-wise production. An entropy-invariant Class-II-to-Class-I reduction selects a descendant entropy flux preserving the parent production and yields thermo-chemical, configurational-stress and partial-viscous-stress diffusion terms. The omitted quadratic relative-inertia flux is paired with relative kinetic-energy storage and transport and is a reversible truncation, not missing entropy production. The resulting compressible non-isothermal Hookean stress and temperature equations reduce to Oldroyd-B/UCM only after one-velocity, incompressible and isothermal limits.

Quantifying the degree of order/disorder in many-particle systems remains an outstanding problem in physics, materials science, and mathematics. To this end, we consider the translational order metric $\tau_T$, defined as the squared $L^2$ norm of the total correlation function $h(\mathbf{r})$, and introduce its bond-orientational analogue $\tau_O$, defined from the weighted total correlation function $h_{\mathbf{f}}(\mathbf{r})$ using local orientational weights (S. Torquato et al., Phys. Rev. X 16, 011042 (2026)). The pair $(\tau_T,\tau_O)$ places both forms of order on a common two-point statistical footing. We compute both metrics for two nonhyperuniform sphere-packing models in 2D and 3D as functions of packing fraction $\phi$: 1) equilibrium hard particles and 2) nonequilibrium random sequential addition (RSA) packings. For the nonhyperuniform systems, bond-orientational order remains subdominant along the equilibrium-fluid and RSA configurations; however, its magnitude relative to the translational metric increases near the upper end of the equilibrium-fluid branches, much more strongly in 2D than in 3D, and the two metrics become comparable along the sampled crystal branches. At common packing fractions, equilibrium fluids and RSA packings trace distinct $(\tau_T,\tau_O)$ trajectories, revealing preparation-dependent differences in structural order. As a representative hyperuniform family, we study 2D disordered stealthy hyperuniform (SHU) ground states for $0<\chi<1/2$, where $\chi$ is the stealthiness parameter. Within the disordered SHU phase, bond-orientational order remains subdominant, but its magnitude relative to the translational metric increases toward the disorder-to-order threshold. In all three models, $\tau_T$ and $\tau_O$ are positively correlated beyond the Poisson-reference regime: $\tau_O$ increases monotonically with $\tau_T$ across the sampled state points.

We compare three particle-scale measures of rearrangement in highly polydisperse materials under driven flow: (a) nonaffine motion defined relative to the time-averaged mean flow, (b) changes in nearest-neighbor connectivity, and (c) $D^2_{\min}$, which measures nonaffine motion relative to an affine deformation fitted locally in space and time [Falk and Langer, Phys. Rev. E 57, 7192 (1998)]. We apply these measures to previously published two-dimensional simulations [Jiang, Sussman, and Weeks, Phys. Rev. E 108, 054605 (2023)] and granular-flow experiments [Illing and Weeks, Phys. Rev. E 111, 045422 (2025)] with polydispersities up to $\delta\approx0.50$. Changes in connectivity and $D^2_{\min}$ both require a definition of neighboring particles, making the choice of neighborhood nontrivial in highly polydisperse systems. For detecting changes in connectivity, we recommend radical Delaunay triangulation, which provides a size-aware topological definition of neighbors. For calculating $D^2_{\min}$, we recommend a size-aware pairwise cutoff distance method. We further show that changing the neighborhood definition can reverse the apparent dependence of $D^2_{\min}$ on particle size in experimental data. Thus, trends in $D^2_{\min}$ cannot be interpreted independently of the neighborhood used to calculate it. Overall, the three measures presented provide complementary information about rearrangements in highly polydisperse systems.

The organization of multiple knots along a polymer contour can depend sensitively on the topology of the constituent knots. Using coarse-grained Brownian-dynamics simulations, we investigate topology-dependent mixing of two knots in a flexible polymer at controlled normalized wall separation. We compare homogeneous ($3_1\otimes 3_1$) and heterogeneous ($3_1\otimes 5_1$) knot pairs using a contour-based coordinate that distinguishes mixed and demixed configurations. Starting from partially overlapping configurations, the $3_1\otimes 5_1$ pair is observed in mixed configurations more frequently over the simulation time window than the $3_1\otimes 3_1$ pair at intermediate wall separation. We further find that, over the intermediate range of normalized wall separation, mixing of the $3_1\otimes5_1$ pair produces a composite knotted region that occupies substantially less polymer contour than the two constituent knots collectively occupy in demixed configurations. The corresponding reduction in contour occupancy is much smaller for the $3_1\otimes3_1$ pair. This indicates that the heterogeneous constituent topologies can be accommodated within a smaller portion of the polymer contour in the composite configuration. These results establish that constituent topology can strongly influence multiple-knot organization in flexible polymers.

We studied the 2-Temperature induced phase separation (2-TIPS) in a system of soft repulsive sphe rocylinders (SRS), confined on the surface of a sphere. We used two different anchoring conditions for the SRS on the spherical surface- free and tangential. For the free anchoring, increasing either the packing fraction or the rod aspect ratio suppresses phase separation between the active and passive subsystems, and the system corresponds to a dense-dilute phase co-existence. These phenomena can be explained via the trapping effect and are emergent due to the confinement. For the tangential anchoring, the system phase separates from its initial isotropic state into a locally ordered dense region and a disordered dilute region. Our work provides useful insights into phase separation in binary mixtures under spherical confinement.

Self-assembly of hard particles with diverse shapes gives rise to a rich variety of structures through excluded-volume constraints alone. Here we show that even a minimal system of three hard squares confined in a two-dimensional periodic box exhibits nontrivial configurational behavior relevant to structure selection. As the packing fraction increases, radial distribution functions obtained from Markov-chain Monte Carlo and uniform non-overlapping insertion sampling agree at low densities, deviate markedly over an intermediate range, and converge again at higher densities. Pressure measurements provide strong numerical evidence that the discrepancy originates from the separation of the allowed configurational space into two disconnected regions above a characteristic density. We identify the separation density as $\phi_{\rm sep}=3/5$, construct explicit overlap-free transition pathways connecting the two regions immediately below it, and quantify their relative configurational-space volumes. At higher packing fractions, an approximately L-shaped arrangement of the particle centers becomes strongly favored over a staggered one, revealing a structural motif characteristic of tetratic and square-lattice ordering in larger hard-square systems. These results show that excluded-volume geometry can govern both configurational connectivity and local structure selection even in a three-particle system, revealing how signatures of many-particle self-assembly can already emerge in the few-particle limit.

Hydrophobic eutectic solvents (HES) based on natural compounds represent promising green alternatives to conventional solvents. In this work, we investigate the physicochemical, structural, and dynamical properties of an ES formed by L-menthol and octanoic acid using a combined experimental and molecular dynamics simulation approach. Five compositions with molar ratios from 1:3 to 3:1 were studied with molecular dynamics simulation in the temperature range 15 degrees C to 35 degrees C. Experimental measurements of density and viscosity in the temperature range from 5 degrees C to 35 degrees C were complemented with results obtained from MD simulations employing the OPLS force field. Structural analyses based on radial distribution functions and Kirkwood-Buff integrals reveal that the dominant interactions in the mixture are hydrogen bonds between L-menthol and octanoic acid molecules. Dynamic properties, including self-diffusion coefficients and hydrogen-bond lifetimes, indicate that intermolecular hydrogen bonds between the two components are stronger and longer-lived than bonds between identical species. These findings provide molecular-level insight into the structure and transport properties of menthol-based ESs relevant for green solvent applications.

Active particles on curved surfaces can become trapped along closed geodesics even without physical barriers. We show that escape from these geometric traps exposes a fundamental distinction between continuous and discrete reorientation. At high Péclet numbers, active Brownian particles escape efficiently through rotational diffusion, whereas run-and-tumble particles remain trapped much longer; at low Péclet numbers, both reduce to passive diffusion. Gaussian curvature controls escape by focusing or defocusing neighboring geodesics, producing distinct asymptotic scalings of the mean exit time.

Although minimalist models for patchy attractive particles have revealed powerful design rules for how particle valence directs colloidal assembly, less work has focused on comparably simple models of reversible, network-forming star polymers. Here, we use relative-entropy coarse-graining and simulation results from finer-resolution bead–spring star polymers to generate 5-bead models of dynamic, end-associating four-armed poly(ethylene glycol) macromers. Our results comparing structural correlations, network connectivity, and phase behavior of the coarse- and fine-grained models provide insight into how the accuracy and transferability of the coarse-grained models depend on the state point chosen for coarse-graining. The results also reveal intrinsic trade-offs between reducing degrees of freedom and expanding the range of effective interactions in coarse-graining that impact the total number of pairwise interactions in the resulting model, with implications for its computational efficiency.

Ionic liquids (ILs) exhibit supercooled liquids behavior even above room temperature and the Stokes-Einstein (SE) relation is often considered to be invalid in ILs as that in supercooled liquids. However, the conclusion is usually drawn based on some variants of SE relation. In this work, we have systematically investigated the validity of the Stokes-Einstein relation in ILs by performing molecular dynamics simulations of coarse-grained IL within the temperature range of 400-800 K. Both the original SE formulation, and two commonly employed variants, were examined to assess their applicability and consistency. These three formulas yield distinctly different results, indicating that the two variants are not reliable substitutes for the original SE relation. The inconsistency suggests the fact that the r in Stokes law varies with conditions. The breakdown arises from the ion correlations introduced by the strong electrostatic interactions. This proposition is further confirmed by simulations.

We present an extensive molecular dynamics (MD) study of the dynamical properties of a binary hard-sphere fluid over a wide range of packing fractions, $\phi \approx 0.357-0.582$. The self-diffusivity, $D$, and shear viscosity, $\eta$, are computed using an efficient implementation of the Einstein–Helfand method. The finite-size effects in $D$ scale as $1/N^\alpha$, with $\alpha$ increasing from approximately $1/3$ to $3/4$ with increasing $\phi$, whereas those in $\eta$ are negligible except for $\phi \gtrsim 0.554$, where they scale as $1/N$. The data are then extrapolated to the thermodynamic limit to obtain $D_{\infty}$ and $\eta_{\infty}$. Both coefficients show a super-Arrhenius dependence on $\phi$ for dense states, accompanied by a breakdown of the Stokes–Einstein relation. Although both $D_{\infty}(\phi)$ and $\eta_{\infty}(\phi)$ data are well described by an exponential form, we demonstrate that these fits do not provide reliable estimates of the critical packing fraction, $\phi_0$, owing to the substantial extrapolation required beyond the accessible equilibrium range. We find the commonly assumed proportionality between $\eta$ and the structural relaxation time, $\tau_\alpha$ , to not hold for this system. For $\phi\gtrsim 0.570$, the van Hove self-correlation function $G_s(r, \tau)$ exhibits a spatial exponential decay at intermediate times, $\tau$, signaling dynamic heterogeneity. The characteristic decay length scales as $\lambda \sim \tau^\nu$, with $\nu \approx 1/3$, in contrast to the conventional square-root scaling. We also investigate temporal heterogeneity through the four-point dynamic susceptibility, $\chi_4(\tau)$, and its peak time, $\tau_4$. These findings provide rigorous benchmark MD data for computational studies of glassy dynamics and establish a reference for testing theoretical models in dense disordered systems.

Dense granular flows are a common occurrence throughout nature and industry, but still exhibit phenomena that are not fully understood. One of these phenomena is the segregation of particles that constitute a dense granular flow, where particles separate due to differences in properties such as size and density. This work approaches segregation from a new perspective by developing a force model for a single particle based on the observation that there are two opposing drag forces acting on the particle. Validation of the model in mono-disperse flows reveals a family of velocity profiles, including a Bagnold profile. Further validation is done by comparing with known particle scaling laws in literature. The force model shows that the mechanism of segregation is always present in dense granular flows and that mono-disperse flows are a unique case where it is not distinctly visible. The insights in this paper prove a fundamental new way of thinking about dense granular flows and its individual particles, opening the field for new research directions.

Discrete models are frequently used in multiparticle dynamics simulations to capture hydrodynamic interactions between colloidal particles and the solvent as well as to represent anisotropic pairwise interactions between colloidal particles; however, there is currently limited guidance on how to reliably parameterize these models. Here, we first compare strategies for selecting the density and mass of discrete surface sites used to couple colloidal particles to the solvent, finding that using a minimum of 2 sites per unit area with a scheme that matches the total mass and moment of inertia for a neutrally buoyant solid particle produces reliable and accurate results for the transport properties of colloidal particles at both infinite dilution and in suspension. We then compare strategies for representing the excluded volume of nearly-hard shape-anisotropic colloidal particles using a collection of discrete interaction sites with isotropic repulsion, finding that having a discrepancy between the nominal volume and the excluded volume of the particle can significantly affect suspension transport properties. This discrepancy can be mitigated by placing the interaction sites inside and tangent to the surface of the colloidal particle. We expect these findings to help construct discrete models for colloidal particles with less sensitivity to parameterization.

The paper presents a broad thermomechanic framework for the isothermal rate-independent constitutive behavior of dense granular materials. The essential quantities in this framework are directly measurable in discrete element (DEM) simulations: free energy, dissipation, stress, and strain. The paper proposes that energy and dissipation are governed by two sets of internal variables: fabric variables that control the reversible stiffness and structure variables associated with internal sliding. The relevant fabric variables are identified and measured with simulations. Two hypotheses are considered for the structure variables: the macro-scale irreversible strain and an aggregate measure of the micro-scale frictional forces among sliding contacts. Both hypotheses are tested with simulations, which allow direct calculation of the internal variables. The paper then demonstrates the manner in which the measured variables are applied in incremental constitutive models. Among other findings are the following. (1) Dissipation from contact sliding is pervasive and occurs in all directions of incremental loading. (2) Contact motions are not reversed by a reversal of the strain direction, and contacts continue to slide when loading is reversed. (3) The free energy can not be assumed smoothly differentiable; instead, Gâteaux derivatives must be used with irreversible effects. (4) Basic assumptions of elastoplasticity are contravened: no region of purely reversible strain exists, no uniform yield direction exists, no uniform flow direction exists, and irreversible strain is not proportional to the projected total strain. A three-mechanism elastoplasticity model, however, closely fit the DEM results, and methods are demonstrated for quantifying the model. The results emphasize that advanced constitutive models are needed for capturing the general incremental behavior of granular materials.

Nonreciprocity is increasingly recognized as a unifying concept linking diverse nonequilibrium phenomena found across physics, chemistry, and biology. It gives rise to distinctive behavior including run-and-chase dynamics and spatio-temporal patterns, often associated with a breaking of time-reversal symmetry. However, nonreciprocity and its nonequilibrium signatures are fundamentally scale-dependent, and may emerge or disappear under coarse-graining. A central challenge is therefore to understand when and how nonreciprocity manifests itself on different scales, for example via irreversible fluctuations or macroscopic currents. In this Perspective, we discuss the physical origin and fate of effective nonreciprocal interactions and the characteristic irreversible dynamics they give rise to across scales.

Molecular diffusion in fluctuating amorphous and macromolecular media governs key transport processes across soft-matter physics, energy storage, and biological membranes. Extracting localized trapping states from single-particle tracking trajectories remains a fundamental challenge; because thermal structural breathing continuously reconfigures pore boundaries, conventional geometric algorithms suffer from severe systematic biases, erroneously merging distinct localized states during cyclic molecular returns. Here, we address this deadlock by shifting the paradigm from local geometric recurrence to a structure-informed Bayesian regularization. Leveraging discrete Morse theory, we extract the time-invariant topological skeleton of the fluctuating host matrix to construct robust, gas-specific physical priors that account for individual molecular dimensions. Trajectory steps are sequentially partitioned via a two-stage probabilistic refinement that dynamically adapts to the transport landscape. Benchmarked against a rigorous environment where synthetic particles explore the actual interconnected matrix graph, our approach eliminates systemic biases, restricting macroscopic trapping parameter deviations to just a few percent under optimal linear $O(N)$ computational scaling. Applied to hydrogen and methane transport within a type-I kerogen matrix, serving as a prototype for highly tortuous, flexible macromolecular networks, the method successfully decodes the hidden microscopic mechanisms of confined diffusion. To ensure immediate broad impact, the documented open-source code and data are made publicly available, offering an accessible strategy readily adaptable to a broad spectrum of tracking phenomena, from ion transport in battery polymers to protein trafficking within cellular environments.

We numerically investigate how particle surface roughness affects the static and dynamic properties of a hard-particle fluid across a wide range of densities, rho. These simulations of a simple model of granular systems reveal that, although the amplitude and coverage of surface corrugation significantly influence the rho-dependence of system properties, the qualitative behavior of this dependence remains unchanged. These findings can be described quantitatively by introducing an effective particle size, which enables a direct mapping of the rough particle systems to equivalent hard-disk systems. Analytical calculations provide an explicit form of this mapping, and allow us to predict the static and dynamic properties of rough particles using standard liquid-state theories for hard disks.

We investigate flow-induced scission of wormlike micelles under different flow kinematics using dissipative particle dynamics simulations of surfactant solutions in shear, uniaxial extensional, planar extensional, and biaxial extensional flows. The average lifetime of wormlike micelles is used to quantify the degree of scission. While flow-induced scission occurs in all flow types when the deformation rate is sufficiently high, the dependence of the average lifetime on the deformation rate differs among flow types. To provide a unified description, we introduce an effective extension rate determined by the velocity gradient tensor and micellar orientation. When expressed in terms of this effective extension rate, the average lifetimes obtained under all flow types considered collapse onto a single curve. These results demonstrate that a unified description of flow-induced scission requires not only the strength and kinematics of the imposed flow, but also the micellar orientation relative to the extensional direction.

A magnetic particle driven by a rotating magnetic field undergoes a transition from synchronous to asynchronous rotation at a critical driving frequency. The asynchronous dynamics is well understood in Newtonian fluids but remains unclear in viscoelastic media. Here, we develop a theoretical description of the asynchronous rotation of a magnetic particle in a Jeffreys-type viscoelastic fluid. The particle's time-averaged angular velocity exhibits a nontrivial frequency dependence that changes from non-monotonic to monotonic as the polymer relaxation time increases. This behavior is explained by the interplay among magnetic driving, viscoelastic relaxation, and frequency-dependent viscous dissipation. We further derive an asymptotic expression that captures the non-monotonic dependence. These results clarify how solvent and polymer contributions jointly control asynchronous rotation and provide a physical basis for guiding relevant applications in complex fluids.

The paper presents a consistent thermomechanical framework for strongly nonlocal continua, a type of generalized media in which a material's response at a point depends on deformation and temperature gradients within its neighborhood. Such dependence is responsible for localization phenomena having an intrinsic size, and nonlocal modeling also serves as a practical regularization tool to prevent mesh dependence. Nonlocality is of the integral type, using a kernel function that gives the relative influence of neighboring points on a central point. The paper develops three sources of nonlocality: (1) nonlocal momentum balance equations; (2) nonlocal conservation laws (including the first and second laws of thermodynamics); and (3) a material's nonlocal constitutive structure. Balance equations are derived using the principle of virtual power, permitting non-smooth force and displacement fields and non-smooth boundary surfaces with indistinct normal directions. The balance equations differ from those of classical local continua. Conservation laws also differ from those of local continua, with the mechanical power and heating at a point being averaged over its neighborhood. These laws are developed for processes that are sufficiently slow to minimize additional meso-scale kinetic energy due to internal turbulence. Stress, entropy, and dissipative forces are obtained as averaged derivatives of the free energy function with respect to strain, temperature, and internal variables. An example is presented of a stretched elastoplastic bar with a small defect, and nonlocality is shown to impart a characteristic size to the deformation pattern.

Crystallisation of liquids often occurs at solid surfaces, via heterogeneous nucleation or prefreezing. Understanding this process is crucial for controlling crystal morphology in thin films and developing efficient nucleating agents - especially for polymers, typically processed in a molten state. However, the efficiency of nucleation and prefreezing with respect to crystallisation kinetics and semicrystalline polymer morphology has not been well studied and remains unclear. Here, we address this challenge by conducting a systematic study of substrate-induced crystallisation in dewetted droplets of the model polymer poly($\varepsilon$-caprolactone) (PCL) on various crystalline and amorphous substrates. Using polarized light optical microscopy, droplet crystallisation temperature was monitored and varied across the substrates, revealing three scenarios: close-to-homogeneous nucleation on glass and silicon; heterogeneous nucleation on ordered and disordered carbon-rich substrates; and prefreezing on graphene. The temperature-dependent nucleation rate was analysed and found to obey classical nucleation theory for all systems except PCL on graphene, where it diverges as all the droplets crystallise simultaneously. The highest in- and out-of-plane PCL crystal orientation is found on graphene, where the epitaxially grown lamellae extend vertically over several hundred nanometres. These results demonstrate that prefreezing has a superior influence on crystallisation kinetics and crystal morphology, making prefreezing substrates perfect nucleating agents.

Many systems in soft and living matter bind through a limited number of bonds per particle: proteins associate via discrete surface patches, nucleic acids form one-to-one contacts, and the phase behaviour of multivalent biomolecules is governed by the number of binding sites they carry. In simulations, valency limits are typically enforced with patchy particles, whose anisotropic potentials require integration of rotational degrees of freedom and combine hard cores with narrow patches, which forces small timesteps and commits the model to a fixed binding-site geometry that is often unknown, flexible or mobile. We introduce the valency-bounding correction (VBC), a many-body modification of generic short-range pairwise potentials that smoothly suppresses attraction once the neighbour count of either interacting particle exceeds a prescribed valency. The correction carries no angular degrees of freedom, applies on top of soft repulsive cores and evaluates in two passes over the neighbour list at the cost of a standard pairwise potential. The VBC drives the coordination number to the prescribed valency with low error, while its cluster statistics depart from Wertheim and Flory-Stockmayer predictions through unrestricted ring formation. A tuned variant exchanges bonded partners through ordinary molecular dynamics, reducing bond lifetimes at high saturation by an order of magnitude. On GPUs the cost of the correction is nearly independent of valency, reaching an almost tenfold advantage over a patchy-particle reference. We illustrate large-scale applications by reproducing the reentrant aggregation of repeat-expanded RNA, and show that the VBC also remedies the Fisher-Ruelle thermodynamic instability of soft-core potentials with attraction. The VBC is available as an open-source GPU plugin for HOOMD-blue.

Cahn-Hilliard phase separation turns small composition fluctuations into coarsening domains. In Fourier space, the pattern forms a ring whose angular intensity favors an axis. We ask whether the axis favored early in an evolution remains related to the axis favored later in the same evolution. We analyze two-dimensional simulations with isotropic initial fluctuations and no imposed direction. We introduce $Q_2$, a normalized angular average over the Fourier spectrum, as a measure of the strength and direction of spectral anisotropy. Linear growth amplifies different wave numbers at different rates, selecting an early axis from the angular imbalances in the initial spectrum. This axis remains correlated with the late axis during coarsening. At a fixed time, shallow quenches show stronger early-late alignment. This advantage disappears when the quenches are compared at similar stages of domain growth. Adding the early $Q_2$ to a prediction based on quench depth, mean composition, and box size reduces the mean absolute error for late $Q_2$ by $3.53\%$. This reduction disappears when only the magnitude of the early $Q_2$ is retained, or when its direction is replaced by the direction from another evolution. The early Fourier intensity therefore carries information about the later state of the same evolving field.

Using Vicsek-like self-propulsion rule, we study kinetics of liquid-liquid phase separation in mixtures of passive and active particles. For evolutions following temperature quenches of homogeneous configurations to the immiscible region of the phase diagram, we identify a remarkably strong dependence of the domain growth exponent on the choice of final state point. The singular dependence is indicative of the possibility of even an exponentially fast growth for suitable choices of system parameters. This striking observation, supported by finite-size scaling and other advanced analyses, is despite the fact that the overall mixture density is quite high that risks congestion with the prospect of slowing down particle transport. From flocking in pure biological systems to robotic swarming, these results are of much practical relevance. Theoretical pictures suitable for interpreting such high growth rates are discussed. In this regard, we discuss coarsening in the velocity field as well that describes how the density field coarsening follows the latter.

Active systems navigate complex environments through non-equilibrium fluctuations, rendering standard equilibrium transition-rate theories inadequate. Moreover, transition rates provide only partial information on how stochastic dynamics explore metastable states, whereas knowledge of the optimal paths offers deeper physical insight. Using an active Ornstein-Uhlenbeck particle, i.e., a particle driven by exponentially correlated noise, as a paradigmatic model, we establish an exact mapping of the non-Markovian optimal path onto a higher-dimensional Hamiltonian dynamical system so that, for arbitrary force fields, optimal paths can be computed systematically by solving the corresponding Hamilton equations. Tuning the conserved energy allows us to explore diverse dynamical regimes, ranging from classical instanton trajectories strictly confined to the zero-energy surface to finite-time optimal paths at non-zero energies, which can spiral around shoulders of the energy landscape, a distinct signature of the non-Markovian active dynamics.

Condensates can accelerate reactions by concentrating reactants, yet product accumulation can eliminate this advantage. We show that product-induced suppression of condensation generates rotating, deforming, and propagating condensate domains through spontaneous symmetry breaking. Their reorganization shifts reaction sites away from accumulated products while retaining reactant enrichment, yielding rates above those of static condensates and homogeneous states. Reaction flows can thus self-organize condensates into dynamic reactors, with implications for biological and synthetic systems.

Frictional relaxation after a sudden velocity change underlies the phenomenological laws that describe the stability of steady sliding and of seismic faults. To connect this relaxation with measurable statistics of microscopic contacts, we introduce a minimal model incorporating logarithmic aging of contact forces and a power-law contact-size distribution reflecting fractal interface roughness, and derive the relaxation function analytically. Depending on the power-law exponent $\alpha$, the intermediate-time response exhibits a plateau, logarithmic decay, or power-law decay, in contrast to the exponential decay assumed in the phenomenological laws. The theory provides experimentally testable links between microscopic contact statistics and macroscopic frictional relaxation.

The mean squared displacement (MSD) is a cornerstone in the analysis of diffusion processes in complex media. When the system is heterogeneous and, in particular, when single-particle trajectories are short, it is essential to extract maximal information from each measured trajectory. This is typically done by time-averaging squared increments and examining the scaling of the time-averaged MSD in log-log space. However, classical regression methods perform poorly in this setting because time-averaging introduces correlations aggravated by those inherent to anomalous diffusion. We tackle these limitations by applying a generalized least squares framework, which substantially reduces variance and bias in diffusion parameter estimates, especially for short (around 100 points) and ultra-short (around 10 points) trajectories. The method is fully automated and requires no supervision. Furthermore, it enables prediction of estimation error probability density, which is asymptotically Gaussian, for both classical and enhanced approaches. Leveraging this prediction, we introduce a specialized deconvolution algorithm that reconstructs the underlying particle ensemble structure from experimental data.