In the infinite dilution limit, we show that the solvent-mediated potential of mean force (PMF) between solutes, extracted from the hypernetted-chain (HNC) closure of the Ornstein-Zernike equations, can expressed as a convolution between solute-specific generalised excluded volume functions. In the limit of a structureless solvent of point particles and hard core solutes, this recovers the exact Asakura-Oosawa depletion potential as the overlap between excluded volume spheres. The methodology can be deployed for ultrasoft particle systems such as those encountered in dissipative particle dynamics (DPD), where the solvent-mediated PMF can be recovered with considerable accuracy. These results confirm that in coarse-grained molecular DPD simulations the parametrisation of the non-bonded repulsions is sensitive to the assumed intramolecular bond lengths if they are smaller than the range of the DPD potential, due to the overlap of the soft excluded volume functions.

Origami-inspired metamaterials exploit the interplay between geometry and elasticity to achieve programmable mechanical responses. Yet the origin and tunability of snap-through instabilities in non-rigidly foldable patterns remain poorly understood. Here we show that the Mars tessellation, a degree-4 vertex origami pattern composed of alternating square and rhombic faces, is not rigidly foldable because the folding-speed ratios required for vertex compatibility cannot be propagated consistently across neighboring units. This geometric incompatibility forces the facets to bend during folding, giving rise to a reproducible snap-through discontinuity in the force-displacement curve with a mean force drop of about 92.6 +/- 5.5 %, marking a transition between metastable states. Laser scoring of additional diagonal creases, guided by strain-field simulations, enables continuous tuning of the snap magnitude. These results reveal a general mechanism by which geometric frustration can be harnessed to program multistability in thin-sheet metamaterials.

We study the roughening of an interface with nonlinear elasticity driven by temporally correlated noise, which breaks statistical tilt symmetry. Using scaling arguments and a self-consistent Hartree approximation, we derive the crossover diagram and the steady-state structure factor. We identify three scaling regimes associated with the Larkin, anharmonic Larkin, and Edwards--Wilkinson universality classes, and obtain the crossover lengths separating them. Numerical simulations of large systems confirm the analytical predictions over the full parameter range. Our results provide a unified description of finite-size and crossover effects in a minimal nonlinear-elastic Ornstein--Uhlenbeck active interface.

Particulate contaminants decrease the power output of solar panels, the transparency of windows, and are detrimental to microelectronics, where even a single particle can induce a short circuit. Despite significant research on particle adhesion and self-cleaning, it remains unclear when and how a drop can remove a particle from a surface, thus efficiently cleaning the surface. Here, by combining lattice Boltzmann simulations and confocal microscopy experiments, we show that at least six different scenarios arise from the complex interplay between capillary and friction forces when a drop collides with a particle. Notably, the capillary force plays a dual role in particle removal: while its tangential component always drives removal, its normal component can also hinder it. By introducing a dimensionless capillary capture parameter, we can predict particle removal across a wide range of particle and surface properties. These results provide quantitative design principles for easy-to-clean surfaces that minimize water and chemical usage.

The physics of active matter, wherein constituent particles consume energy to generate autonomous motion, has revolutionized non-equilibrium statistical mechanics. While a large body of work has successfully elucidated the behavior of dilute active systems, the dense regime -- characterized by ``active glasses and active solids'' -- presents profound challenges that defy conventional theoretical frameworks. Recent observations reveal two striking features in these dense systems: an apparent enhancement of Mermin-Wagner-Hohenberg (MWH) fluctuations leading to anomalous long-wavelength density fluctuations, and a remarkable correspondence between activity-induced annealing and annealing via oscillatory shear. In this perspective article, we propose a novel approach toward a deeper understanding of dense active matter: by developing active Hamiltonian models as equilibrium reference frameworks, we map out pathways toward non-equilibrium active systems. This strategy allows us to elucidate both the correspondence between driven and active systems and the enhanced MWH fluctuations, which likely arise from a strong coupling between spatially random active forces and long-wavelength density (phonon) modes. We outline a comprehensive roadmap employing complementary approaches, including the active Hamiltonian formalism, comparative studies of oscillatory shear in active and passive solids, and investigations of chiral active matter. Establishing this activity-oscillatory shear correspondence across diverse systems is essential to demonstrate its universality, reveal the underlying large-scale emergent physics, and place our hypothesis on a firmer theoretical ground.

The dynamics of nanoparticles within nanoscale liquid environments exhibit a range of complex phenomena driven by the interplay of processes at varying length scales. While these dynamics have profound technical implications, such as in nanoscale catalytic kinetics, ion-transport pathways in energy storage, and macromolecular crowding in biological systems, real-space imaging of dense, confined nanoparticle assemblies remains a significant challenge. Here, we present a liquid-phase transmission electron microscopy approach in which dense clouds of gold nanoparticles are formed within microfluidic channels, rendering the particle ensemble visible in bright-field electron imaging. This strategy enables direct imaging of different density-dependent particle ordering phenomena, including a local structuring of the colloidal liquid in nanoscale spaces, disordered dynamic clouds at high nanoparticle densities and the reversible formation of superlattice structures. Our results provide a unique window into the complex processes of colloidal self-organization at the nanoscale.

Cells dynamically generate, transmit, and dissipate stress. Central to these processes is the actomyosin cortex, an active contractile material that drives cellular mechanical behavior. While prior studies have focused on freely contracting actomyosin systems, the role of mechanical constraints such as adhesion to boundaries remains less explored. To address this, we employ reconstituted actomyosin gels to investigate cellular contractility. We study contraction dynamics under pinned boundary conditions, where the gel is adhered transversely to two opposing surfaces, mimicking supracellular actomyosin networks in tissues and embryos. We find that pinned contraction leads to stress buildup, delaying contraction, producing intermittent dynamics, and generating spatially nonuniform strain fields. Stress is relieved through several pathways, including active-stress-driven symmetric constriction and defect-driven processes such as boundary detachment and internal rupture. We develop a hydrodynamic model incorporating elastic, viscous, and active stress contributions that distinguishes between stress-accumulation and stress-release phases and links variations in active stress to the observed intermittent dynamics. The model predicts distinct energy relaxation rates before and after detachment events, providing insight into stress dissipation. We compare experiments with numerical simulations, which reproduce the observed behavior and reveal how internal energy is generated and dissipated during stress buildup and relaxation. Together, our results demonstrate how boundary conditions and spatial heterogeneity govern the mechanical behavior of contractile active gels. These findings provide insight into stress regulation in cellular and tissue-scale systems and may inform the design of adaptive soft materials and bioinspired robotic systems.

Earthquakes propagating faster than the shear wave-speed are commonly thought to undergo a super-shear transition upon which they discontinuously jump from the sub-Rayleigh regime to the super-shear one. The super-Rayleigh regime, i.e., the range of propagation speeds between the Rayleigh and shear wave-speeds, is regarded as "forbidden" by the two-dimensional classical rupture theory. Here, we revisit the assumptions underlying the classical theory and develop a rupture theory that takes into account the dependence of the fault strength (frictional resistance) on the slip rate. The theory quantitatively agrees with numerical simulations nearly up to the Rayleigh wave-speed. Yet, very close to the latter, two-dimensional rupture solutions change their character due to frictional rate nonlinearity and rupture continuously propagates through the "forbidden" super-Rayleigh range into the super-shear regime, without a sharp super-shear transition. These results demonstrate that frictional rate dependence, generically observed in experiments, can have profound implications for fast earthquake propagation.

The temperature increase in the contact regions between solids in sliding contact can easily reach several hundred Kelvin and thereby dramatically affect friction and wear. Here I extend an earlier multiscale theory for the flash temperature (Ref. \cite{MP}) to the case of accelerated motion, and present numerical results illustrating the theory.

Meta-structures that display axial-twist coupling can be achieved through the emerging kinematics in Kresling origami patterns. A central challenge in these structures is understanding their nonlinear mechanical behaviour, specifically their equilibrium branches and bifurcation diagrams. This involves identifying relationships between desired responses and the geometric variables that define the design space, including the Kresling polygon count, initial twist angle, height, radius, and crease lengths. As the number of constituent units increases in an n-layer chain, we track complex equilibrium branches extending into the post-critical regime under successive instabilities, including branch-point bifurcations and limit-point instabilities. This work begins by establishing the relationship between the geometric design variables and the response curves of the assembled chain by modelling the crease lines as axial-load-carrying elements. Subsequently, equilibrium branches and instabilities are systematically investigated via continuation and bifurcation analysis, beginning with the single-layer system and progressively extending to two- and three-layer configurations. Finally, a generalisation strategy is proposed to extend these findings to an n-layer Kresling chain. This strategy enables the predictive construction of equilibrium paths and the inverse design of multi-layer meta-structures, using prescribed critical points to control post-critical behaviour. It provides a foundation for the inverse design and optimisation of architected mechanical metamaterials with programmable responses.

Nonreciprocal interactions in active solids violate action-reaction symmetry and produce a net response to strain. Assuming invariance under Euclidean symmetries, we derive a shape-space formulation for the elastohydrodynamics of nonreciprocal slender bodies that separates intrinsic deformation from rigid motion. The resulting nonlinear reaction-advection-diffusion system represents a geometric flow whose activity-driven instabilities generate steady, oscillatory, and chaotic patterns. These manifest as rigid, swimming, and chaotic motion, linking nonreciprocal elastohydrodynamics to geometric pattern formation and unifying recent observations in slender active structures.

Soft glassy materials display rich and complex flow behaviors across both macroscopic and molecular scales, and a fundamental understanding of these phenomena remains an outstanding challenge. Here, we propose a theoretical model for the flow of supercooled liquids -- a typical class of glassy fluids -- based on a two-state paradigm that conceptualizes the flow as a dynamic coexistence of transient solid-like and liquid-like regions. The model rests on two essential physical ingredients: a correlation length that captures medium-range structural order, and a localized elasticity-mediated interaction that restricts stress propagation within solid-like regions. Remarkably, with all parameters determined solely from equilibrium state, the model quantitatively reproduces rheological responses -- including both steady-state and start-up shear -- for a broad range of shear rates. Furthermore, it simultaneously captures the evolution of molecular dynamic heterogeneity. This dual success -- spanning macroscopic rheology and microscopic spatiotemporal fluctuations -- underscores the pivotal role of structural and dynamic heterogeneities in governing the rheological response. Moreover, it provides a direct understanding of how the flow behaviors of a supercooled liquid are embedded in its equilibrium properties.

While energy scale competition dictates equilibrium phase behavior, kinetic barriers often drive soft-matter mixtures into dynamically arrested states, rendering conventional phase diagrams incomplete. We extend the classification of binary systems into regions of thermodynamic instability to explore the interplay between phase separation and dynamical arrest. Strong cross-attractions kinetically suppress demixing, whereas competitive energy scales yield either condensation- or demixing-driven amorphous states. We show that this morphological crossover is parameterized by a structural order parameter, $\chi$, providing a unified non-equilibrium framework that reconciles theoretical predictions with experimentally observed arrested mixtures.

Fluid phase equilibrium depends on the external constraints imposed on a system. In a closed system with fixed volume, depending on the average density, a vapor bubble may be stable, metastable, or unstable, with respect to the homogeneous liquid phase. In the case where the bubble is metastable, we study its lifetime, i.e. the average waiting time needed to observe bubble collapse, and the corresponding lifetime of the homogeneous liquid. For the smallest systems, we predict the possibility to observe phase flipping, when the fluid oscillates between states with and without bubble. We provide an example of phase flipping in a simulation of a Lennard-Jones fluid.

Active adaptive matter has attracted considerable interest due to its rich, largely unexplained dynamics and its relevance to a wide range of synthetic and biological materials. An important subclass of such systems consists of active particles that can remodel the network in which they move. Here, we introduce a minimal yet versatile model of active particles moving on an adjustable network. In this model, particles undergo discrete run-and-tumble motion along the links of a triangular lattice and leave behind a trail of temporarily blocked links. These closed links cannot be traversed by other particles and reopen only after a characteristic healing time. The resulting trail-mediated blocking mechanism is fundamentally distinct from more familiar interactions such as excluded-volume effects. In the high-persistence limit, we find a qualitative contrast between the two mechanisms: while steric blocking leads to reduced diffusivity with increasing persistence, trail-induced blocking causes diffusivity to increase monotonically. We characterize this fundamental difference and the associated, unexpected transport properties, and discuss potential applications of our findings.