The hypothesis that many living systems should exhibit near-critical behavior is well motivated theoretically, and an increasing number of cases have been demonstrated empirically. However, a systematic analysis across biological networks, which would enable identification of the network properties that drive criticality, has not yet been realized. Here, we provide a first comprehensive survey of criticality across a diverse sample of biological networks, leveraging a publicly available database of 67 Boolean models of regulatory circuits. We find all 67 networks to be near critical. By comparing to ensembles of random networks with similar topological and logical properties, we show that criticality in biological networks is not predictable solely from macroscale properties such as mean degree $⟨K⟩$ and mean bias in the logic functions $⟨p⟩$, as previously emphasized in theories of random Boolean networks. Instead, the ensemble of real biological circuits is jointly constrained by the local causal structure and logic of each node. In this way, biological regulatory networks are more distinguished from random networks by their criticality than by other macroscale network properties such as degree distribution, edge density, or fraction of activating conditions.

We employ fast scanning calorimetry to assess the thermodynamic state attained after a given cooling rate and the molecular mobility of glassy poly(4-tert-butylstyrene) confined at the micrometer length scale. We show that, for such a large confinement length scale, thermodynamic states with a fictive temperature ($T_f$) 80 K below the polymer glass transition temperature ($T_g$) are attained, which allows to bypass the geological timescales required for bulk glasses. Access to such states is promoted by a fast mechanism of equilibration. Importantly, the tremendous $T_f$ decrease takes place while the molecular mobility remains bulklike, indicating marked decoupling between vitrification kinetics and molecular mobility.

We study hairpin folding dynamics by means of extensive molecular dynamics simulations, with particular attention paid to the influence of helicity on the folding time. We find that the dynamical exponent $\alpha$ in the anomalous scaling $n(t)\sim t^{1/\alpha }$ of the hairpin length $n$ with time changes from 1.6 ($\simeq 1+\nu$, where $\nu$ is the Flory exponent) to 1.2 ($\simeq 2\nu$) in three dimensions, when duplex helicity is removed. The relation $\alpha =2\nu$ in rotationless hairpin folding is further verified in two dimensions ($\nu =0.75$) and for a ghost chain ($\nu =0.5$). Our findings suggest that the folding dynamics in long helical chains is governed by the duplex dynamics, contrasting the earlier understanding based on the stem-flower picture of unpaired segments. We propose a scaling argument for $\alpha =1+\nu$ in helical chains, assuming that duplex relaxation required for orientational positioning of the next pair of bases is the rate-limiting process.

Transition points mark qualitative changes in the macroscopic properties of large complex systems. Explosive transitions, exhibiting properties of both continuous and discontinuous phase transitions, have recently been uncovered in network growth processes. Real networks not only grow but often also restructure; yet common network restructuring processes, such as small world rewiring, do not exhibit phase transitions. Here, we uncover a class of intrinsically discontinuous transitions emerging in network restructuring processes controlled by adhesion—the preference of a chosen link to remain connected to its end node. Deriving a master equation for the temporal network evolution and working out an analytic solution, we identify genuinely discontinuous transitions in nongrowing networks, separating qualitatively distinct phases with monotonic and with peaked degree distributions. Intriguingly, our analysis of empirical data indicates a separation between the same two forms of degree distributions distinguishing abstract from face-to-face social networks.

We present a model for the order-disorder transition of symmetric $A\text{−}B$ diblock copolymer melts in which the disordered phase is treated as a bicontinuous network, and in which self-consistent field predictions of properties of an analogous ordered network are used to estimate some properties. Such a model is shown to accurately predict the latent heat of this transition. The dependence of the location of the transition upon the invariant degree of polymerization $\overline{N}$ is shown to be consistent with a simple hypothesis that the disordered bicontinuous structure is stabilized relative to an analogous ordered network by a nearly constant entropy per network junction.

We model the formation of multilayer transportation networks as a multiobjective optimization process, where service providers compete for passengers, and the creation of routes is determined by a multiobjective cost function encoding a trade-off between efficiency and competition. The resulting model reproduces well real-world systems as diverse as airplane, train, and bus networks, thus suggesting that such systems are indeed compatible with the proposed local optimization mechanisms. In the specific case of airline transportation systems, we show that the networks of routes operated by each company are placed very close to the theoretical Pareto front in the efficiency-competition plane, and that most of the largest carriers of a continent belong to the corresponding Pareto front. Our results shed light on the fundamental role played by multiobjective optimization principles in shaping the structure of large-scale multilayer transportation systems, and provide novel insights to service providers on the strategies for the smart selection of novel routes.

We present a phenomenological model for granular suspension rheology in which particle interactions enter as constraints to relative particle motion. By considering constraints that are formed and released by stress respectively, we derive a range of experimental flow curves in a single treatment and predict singularities in viscosity and yield stress consistent with literature data. Fundamentally, we offer a generic description of suspension flow that is independent of bespoke microphysics.

We report a transition from asynchronous to oscillatory behavior in balanced inhibitory networks for class I and II neurons with instantaneous synapses. Collective oscillations emerge for sufficiently connected networks. Their origin is understood in terms of a recently developed mean-field model, whose stable solution is a focus. Microscopic irregular firings, due to balance, trigger sustained oscillations by exciting the relaxation dynamics towards the macroscopic focus. The same mechanism induces in balanced excitatory-inhibitory networks quasiperiodic collective oscillations.

Drawing an analogy to the paradigm of quasielastic neutron scattering, we present a general approach for quantitatively investigating the spatiotemporal dependence of structural anisotropy relaxation in deformed polymers by using small-angle neutron scattering. Experiments and nonequilibrium molecular dynamics simulations on polymer melts over a wide range of molecular weights reveal that their conformational relaxation at relatively high momentum transfer $Q$ and short time can be described by a simple scaling law, with the relaxation rate proportional to $Q$. This peculiar scaling behavior, which cannot be derived from the classical Rouse and tube models, is indicative of a surprisingly weak direct influence of entanglement on the microscopic mechanism of single-chain anisotropy relaxation.

The emergence and maintenance of polymers with complex sequences pose a major question in the study of the origin of life. To answer this, we study a model polymerization reaction, where polymers are synthesized by stepwise ligation from two types of monomers, catalyzed by a long polymer as a template. Direct stochastic simulation and dynamical systems analysis reveal that the most dominant polymer sequence in a population successively changes, depending on the flow rate of monomers to the system, with more complex sequences selected at a lower flow rate. We discuss the relevance of this kinetic sequence selection through nonequilibrium flow to the origin of complex polymers.

Bacteria can adjust the structure of colonies and biofilms to enhance their survival rate under external stress. Here, we explore the link between bacterial interaction forces and colony structure. We show that the activity of extracellular pilus motors enhances local ordering and accelerates fusion dynamics of bacterial colonies. The radial distribution function of mature colonies shows local fluidlike order. The degree and dynamics of ordering are dependent on motor activity. At a larger scale, the fusion dynamics of two colonies shows liquidlike behavior whereby motor activity strongly affects surface tension and viscosity.

A recent study of red blood cells (RBCs) in shear flow [Lanotte et al., Proc. Natl. Acad. Sci. U.S.A. 113, 13289 (2016)] has demonstrated that RBCs first tumble, then roll, transit to a rolling and tumbling stomatocyte, and finally attain polylobed shapes with increasing shear rate, when the viscosity contrast between cytosol and blood plasma is large enough. Using two different simulation techniques, we construct a state diagram of RBC shapes and dynamics in shear flow as a function of shear rate and viscosity contrast, which is also supported by microfluidic experiments. Furthermore, we illustrate the importance of RBC shear elasticity for its dynamics in flow and show that two different kinds of membrane buckling trigger the transition between subsequent RBC states.

We formulate the statistical dynamics of topological defects in the active nematic phase, formed in two dimensions by a collection of self-driven particles on a substrate. An important consequence of the nonequilibrium drive is the spontaneous motility of strength $+1/2$ disclinations. Starting from the hydrodynamic equations of active nematics, we derive an interacting particle description of defects that includes active torques. We show that activity, within perturbation theory, lowers the defect-unbinding transition temperature, determining a critical line in the temperature-activity plane that separates the quasi-long-range ordered (nematic) and disordered (isotropic) phases. Below a critical activity, defects remain bound as rotational noise decorrelates the directed dynamics of $+1/2$ defects, stabilizing the quasi-long-range ordered nematic state. This activity threshold vanishes at low temperature, leading to a reentrant transition. At large enough activity, active forces always exceed thermal ones and the perturbative result fails, suggesting that in this regime activity will always disorder the system. Crucially, rotational diffusion being a two-dimensional phenomenon, defect unbinding cannot be described by a simplified one-dimensional model.

It has recently been argued that steady-state vorticity bands cannot arise in shear thickening suspensions because the normal stress imbalance across the interface between the bands will set up particle migrations. In this Letter, we develop a simple continuum model that couples shear thickening to particle migration. We show by linear stability analysis that homogeneous flow is unstable towards vorticity banding, as expected, in the regime of negative constitutive slope. In full nonlinear computations, we show, however, that the resulting vorticity bands are unsteady, with spatiotemporal patterns governed by stress-concentration coupling. We furthermore show that these dynamical bands also arise in direct particle simulations, in good agreement with the continuum model.

In this Letter, we present a new mechanism under the action of which a shear thickening suspension transitions from a continuous to a discontinuous regime. This transition occurs by adding high concentrations of large spheres to a continuous shear thickening suspension. We show that the solid volume fraction of the interstitial shear thickening matrix is locally enhanced due to the presence of large particles and the excluded-volume shells surrounding the large particles, thus leading to a continuous to discontinuous shear thickening transition at the local scale.