Thin nematic elastomers, composite hydrogels, and plant tissues are among many systems that display uniform anisotropic deformation upon external actuation. In these materials, the spatial orientation variation of a local director field induces intricate global shape changes. Despite extensive recent efforts, to date there is no general solution to the inverse design problem: How to design a director field that deforms exactly into a desired surface geometry upon actuation, or whether such a field exists. In this work, we phrase this inverse problem as a hyperbolic system of differential equations. We prove that the inverse problem is locally integrable, provide an algorithm for its integration, and derive bounds on global solutions. We classify the set of director fields that deform into a given surface, thus paving the way to finding optimized fields.

We present a scalable nonparametric Bayesian method to perform network reconstruction from observed functional behavior that at the same time infers the communities present in the network. We show that the joint reconstruction with community detection has a synergistic effect, where the edge correlations used to inform the existence of communities are also inherently used to improve the accuracy of the reconstruction which, in turn, can better inform the uncovering of communities. We illustrate the use of our method with observations arising from epidemic models and the Ising model, both on synthetic and empirical networks, as well as on data containing only functional information.

Conformations of partially or fully adsorbed semiflexible polymer chains are studied varying both contour length $L$, chain stiffness, $\kappa$, and the strength of the adsorption potential over a wide range. Molecular dynamics simulations show that partially adsorbed chains (with “tails,” surface attached “trains,” and “loops”) are not described by the Kratky-Porod wormlike chain model. The crossover of the persistence length from its three-dimensional value (${\ell }_p$) to the enhanced value in two dimensions ($2{\ell }_p$) is analyzed, and excluded volume effects are identified for $L\gg {\ell }_p$. Consequences for the interpretation of experiments are suggested. We verify the prediction that the adsorption threshold scales as ${\ell }_p^{-1/3}$.

Recent experimental results have shown that enzymes can diffuse faster when they are in the presence of their reactants (substrate). This faster diffusion has been termed enhanced diffusion. Fluorescence correlation spectroscopy (FCS), which has been employed as the only method to make these measurements, relies on analyzing the fluctuations in fluorescence intensity to measure the diffusion coefficient of particles. Recently, artifacts in FCS measurements due to its sensitivity to environmental conditions have been evaluated, calling prior enhanced diffusion results into question. It behooves us to adopt complementary and direct methods to measure the mobility of enzymes. Herein, we use a technique of direct single molecule imaging to observe the diffusion of individual enzymes in solution. This technique is less sensitive to intensity fluctuations and deduces the diffusion coefficient directly based on the trajectory of the enzyme. Our measurements recapitulate that enzyme diffusion is enhanced in the presence of its substrate and find that the relative increase in diffusion of a single enzyme is even higher than those previously reported using FCS. We also use this complementary method to test if the total enzyme concentration affects the relative increase in diffusion and if the enzyme oligomerization state changes during its catalytic turnover. We find that the diffusion increase is independent of the total concentration of enzymes and the presence of substrate does not change the oligomerization state of enzymes.

Dense suspensions often become more dilute as they move downstream through a constriction. We find that as a shear-thickening suspension is extruded through a narrow die and undergoes such liquid migration, the extrudate maintains a steady concentration ${\varphi }_{\mathrm{out}}^{\mathrm{LM}}$, independent of time or initial concentration. At low volumetric flow rate $Q$, ${\varphi }_{\mathrm{out}}^{\mathrm{LM}}$ is a universal function of $Q/r_d^3$, a characteristic shear rate in the die of radius $r_d$, and coincides with the critical input concentration for the onset of LM, ${\varphi }_{\mathrm{in}}^{\mathrm{crit}}$. We predict this function by coupling the Wyart-Cates model for shear thickening and the “suspension balance model” for solvent permeation through particles.

There is increasing evidence that mammalian cells not only crawl on substrates but can also swim in fluids. To elucidate the mechanisms of the onset of motility of cells in suspension, a model which couples actin and myosin kinetics to fluid flow is proposed and solved for a spherical shape. The swimming speed is extracted in terms of key parameters. We analytically find super- and subcritical bifurcations from a nonmotile to a motile state and also spontaneous polarity oscillations that arise from a Hopf bifurcation. Relaxing the spherical assumption, the obtained shapes show appealing trends.

We describe simulations of a quasi-one-dimensional, vibrated granular gas which exhibits an apparent phase separation into a liquidlike phase and a gaslike phase. In thermal equilibrium, such a phase separation in one dimension is prohibited by entropic considerations. We propose that the granular gas minimizes a function of the conserved mechanical variables alone: the particle number and volume. Simulations in small cells can be used to extract the equation of state and predict the coexisting pressure and densities, as confirmation of the minimization principle. Fluctuations in the system manifest themselves as persistent density waves but they do not destroy the phase-separated state.

Narrow escape from confinement through a nanochannel is the critical step of complex transport processes including size-exclusion-based separations, oil and gas extraction from the microporous subsurface environment, and ribonucleic acid translocation through nuclear pore complex channels. While narrow escape has been studied using theoretical and computational methods, experimental quantification is rare because of the difficulty in confining a particle into a microscopic space through a nanoscale hole. Here, we studied narrow escape in the context of continuous nanoparticle diffusion within the liquid-filled void space of an ordered porous material. Specifically, we quantified the spatial dependence of nanoparticle motion and the sojourn times of individual particles in the interconnected confined cavities of a liquid-filled inverse opal film. We found that nanoparticle motion was inhibited near cavity walls and cavity escape was slower than predicted by existing theories and random-walk simulations. A combined computational-experimental analysis indicated that translocation through a nanochannel is barrier controlled rather than diffusion controlled.

Nonequilibrium stochastic reaction networks are commonly found in both biological and nonbiological systems, but have remained hard to analyze because small differences in rate functions or topology can change the dynamics drastically. Here, we conjecture exact quantitative inequalities that relate the extent of fluctuations in connected components, for various network topologies. Specifically, we find that regardless of how two components affect each other’s production rates, it is impossible to suppress fluctuations below the uncontrolled equivalents for both components: one must increase its fluctuations for the other to be suppressed. For systems in which components control each other in ringlike structures, it appears that fluctuations can only be suppressed in one component if all other components instead increase fluctuations, compared to the case without control. Even the general $N$-component system—with arbitrary connections and parameters—must have at least one component with increased fluctuations to reduce fluctuations in others. In connected reaction networks it thus appears impossible to reduce the statistical uncertainty in all components, regardless of the control mechanisms or energy dissipation.

Macromolecules contain molecular units as the coding information for their correlated structures in physical dimensions. The relationship between these two features is governed by the interaction energies of the involved molecular units and their encoded sequences. We present a neural network algorithm that treats molecular units themselves as neural networks, which has the flexibility to allow each unit to respond to its own environment and to influence others in the system. Through a deep neural network and a self-consistent procedure, molecular units in the network establish a strong correlation to produce the desirable features in the physical world. The proposed framework is applied to the HP model. Both the forward problem of predicting folded structures from given sequences and the inverse problem of predicting required sequences for a given structure are examined.

We study the emergence of critical dynamics in the steady shear rheology of fluidized soft glassy materials. Within a mesoscale elastoplastic model accounting for a shear band instability, we show how additional noise can induce a transition from a phase separated to homogeneous flow, accompanied by critical-like fluctuations of the macroscopic shear rate. Both macroscopic quantities and fluctuations exhibit power law behaviors in the vicinity of this transition, consistent with previous experimental findings on vibrated granular media. Altogether, our results suggest a generic scenario for the emergence of criticality when shear weakening mechanisms compete with a fluidizing noise.

Frictional granular matter is shown to be fundamentally different in its plastic responses to external strains from generic glasses and amorphous solids without friction. While regular glasses exhibit plastic instabilities due to the vanishing of a real eigenvalue of the Hessian matrix, frictional granular materials can exhibit a previously unnoticed additional mechanism for instabilities, i.e., the appearance of a pair of complex eigenvalues leading to oscillatory exponential growth of perturbations that are tamed by dynamical nonlinearities. This fundamental difference appears crucial for the understanding of plasticity and failure in frictional granular materials. The possible relevance to earthquake physics is discussed.

The nematic liquid crystal (LC) director field can contain defects that are both singular and nonsingular, but nonsingular defects with an integer winding number of the director are typically metastable because of their high energy. We demonstrate topology-mediated generation and stabilization of nonsingular wall loops in a sandwich-type LC cell by combining a patterned substrate with a planar substrate. We implement a design which imposes a topological constraint on a singular disclination loop such that it irreversibly annihilates upon application of a field, and it results in the generation of a stable nonsingular wall loop when the field is removed. Theoretical modeling agrees with experimental observations, providing insight into the wall generation mechanism and its stability. The concept to stabilize high-energy structures through orientation-patterning-defined topological constraints extends our ability to control orientationally ordered matter.

We report a straightforward, model-free approach for measuring pair potentials from particle-coordinate data, based on enforcing consistency between the pair distribution function measured separately by the distance-histogram and test-particle insertion routes. We demonstrate the method’s accuracy and versatility in simulations of simple fluids, before applying it to an experimental system composed of superparamagnetic colloidal particles. The method will enable experimental investigations into many-body interactions and allow for effective coarse graining of interactions from simulations.

Switching on high activity in a relatively dense system of active Janus colloids, we observe fast clustering, followed by cluster aggregation towards full phase separation. The phase separation process is however interrupted when large enough clusters start breaking apart. Following the cluster size distribution as a function of time, we identify three successive dynamical regimes. Tracking both the particle positions and orientations, we characterize the structural ordering and alignment in the growing clusters and thereby unveil the mechanisms at play in these regimes. In particular, we identify how alignment between the neighboring particles is responsible for the interruption of the full phase separation. Our large scale quantification of the phase separation kinetics in active colloids points towards the new physics observed when both alignment and short-range repulsions are present.

We present a controlled cascade of self-assemblings of colloidal droplets at a nematic liquid crystal–air interface into large-scale ordered structures. Changing the tilt of the droplet-induced elastic dipoles via its dependence on the nematic film thickness, we are able to control the dipole-dipole interaction and thus the self-assembling regime. For a progressively large tilt, droplets form anisotropic lattices, which then transform into arrays of repulsive chains, then to bands of half-period-shifted densely bound chains. These structures with chain order at the inner scale aggregate into different large-scale clusters that have a pronounced circular pattern and are stabilized by the many-body elastocapillary attraction.

Scaling arguments used to predict the radius of gyration of passive self-avoiding flexible polymers have been shown to hold for polymers under the influence of active fluctuations. In this Letter, we establish how the standard blob scaling theory representation of a polymer, capable of capturing the essential physics of passive polymers under a variety of settings, breaks down when dealing with active polymers under confinement. Using numerical simulations, we show how the predicted exponents associated to the forces applied by a polymer when restricted within cavities of different geometries hold only whenever the persistence length generated on the polymer by the active forces is much smaller than the size of the characteristic blob in the scaling theory.

We study a spatial network model with exponentially distributed link lengths on an underlying grid of points, undergoing a structural crossover from a random, Erdős-Rényi graph, to a $d$-dimensional lattice at the characteristic interaction range $\zeta$. We find that, whilst far from the percolation threshold the random part of the giant component scales linearly with $\zeta$, close to criticality it extends in space until the universal length scale ${\zeta }^{6/(6-d)}$, for $d<6$, before crossing over to the spatial one. We demonstrate the universal behavior of the spatiotemporal scales characterizing this critical stretching phenomenon of mean-field regimes in percolation and in dynamical processes on $d=2$ networks, and we discuss its general implications to real-world phenomena, such as neural activation, traffic flows or epidemic spreading.