The Voronoi-based cellular model is highly successful in describing the motion of two-dimensional confluent cell tissues. In the homogeneous version of this model, the energy of each cell is determined solely by its geometric shape and size, and the interaction between adjacent cells is a by-product of this additive energy. We generalize this model so as to allow zero or partial contact between cells. We identify several phases, two of which (solid confluent and liquid confluent) were found in previous studies that imposed confluency as well as others that were not. Transitions in this model may be relevant for understanding both normal development as well as cancer metastasis.

We report our measurements of the dynamics of histonelike nucleoid-structuring (H-NS) proteins, which interact with both proteins and DNA simultaneously, in live Escherichia coli bacteria. The dynamics turn out to differ significantly from other molecules reported previously. A power-law distribution was observed for the diffusion coefficients of individual H-NS proteins. In addition, we observed a distribution of displacements which does not follow the Gaussian, Cauchy, or Laplace distributions but the Pearson Type VII distribution. Furthermore, we experimentally measured the time and frequency dependence of the complex modulus of the bacterial cytoplasm, which deviates from the viscoelasticity of homogeneous protein solutions and shows a glass-liquid transition. Last, we observed that the dynamics of H-NS proteins is cell length and cell age dependent. The findings are expected to fundamentally change the current views on bacterial cytoplasm and diffusional dynamics of molecules in bacteria.

The passive attributes of skeletal muscle “material” often have origins in nanoscale architecture and functionality where geometric frustrations directly influence macroscale mechanical properties. Drawing from concepts of the actomyosin network, this study investigates a modular, architected material system that leverages spatial constraints to generate multiple stable material topologies and to yield large adaptability of material mechanical properties. By exploiting the shearing actions induced on an actomyosin-inspired assembly of modular material constituents, intriguing material behaviors are cultivated, including strong metastability and energy-releasing state transitions. Experimental, numerical, and analytical studies reveal that such passive attributes can be tailored by geometric constraints imposed on the modular material system. The geometric parameters can also introduce a bias to the deformations, enabling a programmable response. By invoking the spatial constraints and oblique, shearlike motions inherent to skeletal muscle architecture, this research uncovers potential for architected material systems that exploit locally tunable properties to achieve targeted macroscopic behaviors.

Colloidal clusters consist of small numbers of colloidal particles bound by weak short-range attractions. The equilibrium probability of observing a cluster in a particular geometry is well described by a statistical mechanical model originally developed for molecules. To explain why this model fits experimental data so well, we derive the partition function classically, with no quantum-mechanical considerations. Then, by comparing and contrasting the derivation in particle coordinates with that in center-of-mass coordinates, we physically interpret the terms in the center-of-mass formulation, which is equivalent to the high-temperature partition function for molecules. We discuss, from a purely classical perspective, how and why cluster characteristics such as the symmetry number, moments of inertia, and vibrational frequencies affect the equilibrium probabilities.

A minimal description of the inherent states of amorphous solids is presented. Using field theory, applicable when a system is probed at long length scales, it is shown that athermal amorphous solids have long-range correlations in their stresses, as recently observed in supercooled liquids, colloids, and granular matter. Explicit predictions for the correlators are presented, in both two and three dimensions, in excellent agreement with simulation data on supercooled liquids. It is shown that when applied to solids with strictly repulsive interactions the simplest naïve theory leads to a paradox. This paradox is resolved, and it is shown that a nontrivial non-Gaussian theory is necessary for such materials. Modifications to the correlators are shown, at the saddle-point level. In all cases, “equations of state” relating fluctuations to imposed stresses are derived, as well as field equations that fix the spatial structure of stresses in arbitrary geometries. A holographic quantity in three-dimensional amorphous systems is identified.

We consider several quadrilateral origami tilings, including the Miura-ori crease pattern, allowing for crease-reversal defects above the ground state which maintain local flat foldability. Using exactly solvable models, we show that these origami tilings can have phase transitions as a function of crease state variables, as a function of the arrangement of creases around vertices, and as a function of local layer orderings of neighboring faces. We use the exactly solved cases of the staggered odd eight-vertex model as well as Baxter's exactly solved three-coloring problem on the square lattice to study these origami tilings. By treating the crease-reversal defects as a lattice gas, we find exact analytic expressions for their density, which is directly related to the origami material's elastic modulus. The density and phase transition analysis has implications for the use of these origami tilings as tunable metamaterials; our analysis shows that Miura-ori's density is more tunable than Barreto's Mars density, for example. We also find that there is a broader range of tunability as a function of the density of layering defects compared to as a function of the density of crease order defects before the phase transition point is reached; material and mechanical properties that depend on local layer ordering properties will have a greater amount of tunability. The defect density of Barreto's Mars, on the other hand, can be increased until saturation without passing through a phase transition point. We further consider relaxing the requirement of local flat foldability by mapping to a solvable case of the 16-vertex model, demonstrating a different phase transition point for this case.

Using analytic and numerical approaches, we study the spatiotemporal evolution of a conserved order parameter of a fluid in film geometry, following an instantaneous quench to the critical temperature $T_c$ as well as to supercritical temperatures. The order parameter dynamics is chosen to be governed by model B within mean-field theory and is subject to no-flux boundary conditions as well as to symmetric surface fields at the confining walls. The latter give rise to critical adsorption of the order parameter at both walls and provide the driving force for the non-trivial time evolution of the order parameter. During the dynamics, the order parameter is locally and globally conserved; thus, at thermal equilibrium, the system represents the canonical ensemble. We furthermore consider the dynamics of the nonequilibrium critical Casimir force, which we obtain based on the generalized force exerted by the order parameter field on the confining walls. We identify various asymptotic regimes concerning the time evolution of the order parameter and the critical Casimir force and we provide, within our approach, exact expressions of the corresponding dynamic scaling functions.

We theoretically explore fluidization of epithelial tissues by active T1 neighbor exchanges. We show that the geometry of cell-cell junctions encodes important information about the local features of the energy landscape, which we support by an elastic theory of T1 transformations. Using a 3D vertex model, we show that the degree of active noise driving forced cell rearrangements governs the stress-relaxation timescale of the tissue. We study tissue response to in-plane shear at different timescales. At short time, the tissue behaves as a solid, whereas its long-time fluid behavior can be associated with an effective viscosity which scales with the rate of active T1 transformations. Furthermore, we develop a coarse-grained theory, where we treat the tissue as an active fluid and confirm the results of the vertex model. The impact of cell rearrangements on tissue shape is illustrated by studying axial compression of an epithelial tube.

We analyze the influence of long-range correlated (colored) external noise on extinction phase transitions in growth and spreading processes. Uncorrelated environmental noise (i.e., temporal disorder) was recently shown to give rise to an unusual infinite-noise critical point [Europhys. Lett. 112, 30002 (2015)]. It is characterized by enormous density fluctuations that increase without limit at criticality. As a result, a typical population decays much faster than the ensemble average, which is dominated by rare events. Using the logistic evolution equation as an example, we show here that positively correlated (red) environmental noise further enhances these effects. This means, the correlations accelerate the decay of a typical population but slow down the decay of the ensemble average. Moreover, the mean time to extinction of a population in the active, surviving phase grows slower than a power law with population size. To determine the complete critical behavior of the extinction transition, we establish a relation to fractional random walks, and we perform extensive Monte Carlo simulations.

The recent trend for acquiring big data assumes that possessing quantitatively more and qualitatively finer data necessarily provides an advantage that may be critical in competitive situations. Using a model complex adaptive system where agents compete for a limited resource using information coarse grained to different levels, we show that agents having access to more and better data perform worse than others in certain situations. The relation between information asymmetry and individual payoffs is seen to be complex, depending on the composition of the population of competing agents.

The quantitative characterization of the microstructure of random heterogeneous media in $d$-dimensional Euclidean space ${\mathbb{R}}^d$ via a variety of $n$-point correlation functions is of great importance, since the respective infinite set determines the effective physical properties of the media. In particular, surface-surface $F_{\text{ss}}$ and surface-void $F_{\text{sv}}$ correlation functions (obtainable from radiation scattering experiments) contain crucial interfacial information that enables one to estimate transport properties of the media (e.g., the mean survival time and fluid permeability) and complements the information content of the conventional two-point correlation function. However, the current technical difficulty involved in sampling surface correlation functions has been a stumbling block in their widespread use. We first present a concise derivation of the small-$r$ behaviors of these functions, which are linked to the mean curvature of the system. Then we demonstrate that one can reduce the computational complexity of the problem, without sacrificing accuracy, by extracting the necessary interfacial information from a cut of the $d$-dimensional statistically homogeneous and isotropic system with an infinitely long line. Accordingly, we devise algorithms based on this idea and test them for two-phase media in continuous and discrete spaces. Specifically for the exact benchmark model of overlapping spheres, we find excellent agreement between numerical and exact results. We compute surface correlation functions and corresponding local surface-area variances for a variety of other model microstructures, including hard spheres in equilibrium, decorated “stealthy” patterns, as well as snapshots of evolving pattern formation processes (e.g., spinodal decomposition). It is demonstrated that the precise determination of surface correlation functions provides a powerful means to characterize a wide class of complex multiphase microstructures.

Using laboratory experiments, we investigate the influence of water and sediment discharges on the morphology of an alluvial fan. In our flume, a single-thread laminar river deposits corundum sand into a conical fan. We record the fan progradation with top-view images and measure its shape using the deformation of a Moiré pattern. The fan remains virtually self-affine as it grows, with a nearly constant slope. We find that, when the sediment discharge is small, the longitudinal slope of the fan remains close to that of a river at the threshold for sediment transport. Consequently the slope depends on the water discharge only. A higher sediment discharge causes the fan's slope to depart from the threshold value. Due to the downstream decrease of the sediment load, this slope gets shallower towards the fan's toe. This mechanism generates a concave fan profile. This suggests that we could infer the sediment flux that feeds a fan based on its proximal slope.

A thin, elastic sheet floating on the surface of a liquid bath wrinkles when poked at its center. We study the onset of wrinkling as well as the evolution of the pattern as indentation progresses far beyond the wrinkling threshold. We use tension field theory to describe the macroscopic properties of the deformed film and show that the system passes through a host of different regimes, even while the deflections and strains remain small. We show that the effect of the finite size of the sheet ultimately plays a key role in determining the location of the wrinkle pattern, and obtain scaling relations that characterize the number of wrinkles at threshold and its variation as the indentation progresses.

We report a joint experimental and theoretical investigation of the probability distribution functions (PDFs) of the normal and tangential (frictional) forces in amorphous frictional media. We consider both the joint PDF of normal and tangential forces together, and the marginal PDFs of normal forces separately and tangential forces separately. A maximum entropy formalism is utilized for all these cases after identifying the appropriate constraints. Excellent agreements with both experimental and simulation data are reported. The proposed joint PDF predicts giant slip events at low pressures, again in agreement with observations.

We consider a two-dimensional Lorentz gas with infinite horizon. This paradigmatic model consists of pointlike particles undergoing elastic collisions with fixed scatterers arranged on a periodic lattice. It was rigorously shown that when $t\to \infty$, the distribution of particles is Gaussian. However, the convergence to this limit is ultraslow, hence it is practically unattainable. Here, we obtain an analytical solution for the Lorentz gas' kinetics on physically relevant timescales, and find that the density in its far tails decays as a universal power law of exponent $-3$. We also show that the arrangement of scatterers is imprinted in the shape of the distribution.

Access resistance indicates how well current carriers from a bulk medium can converge to a pore or opening and is an important concept in nanofluidic devices and in cell physiology. In simplified scenarios, when the bulk dimensions are infinite in all directions, it depends only on the resistivity and pore radius. These conditions are not valid in all-atom molecular dynamics simulations of transport, due to the computational cost of large simulation cells, and can even break down in micro- and nanoscale systems due to strong confinement. Here, we examine a scaling theory for the access resistance that predicts a special simulation cell aspect ratio—the golden aspect ratio—where finite-size effects are eliminated. Using both continuum and all-atom simulations, we demonstrate that this golden aspect ratio exists and that it takes on a universal value in linear response and moderate concentrations. Outside of linear response, it gains an apparent dependence on characteristics of the transport scenario (concentration, voltages, etc.) for small simulation cells, but this dependence vanishes at larger length scales. These results will enable the use of all-atom molecular dynamics simulations to study contextual properties of access resistance—its dependence on protein and molecular-scale fluctuations, the presence of charges, and other functional groups—and yield the opportunity to quantitatively compare computed and measured resistances.

We consider the numerical integration of Langevin equations for particles in a channel, in the presence of boundary conditions fixing the concentration values at the ends. This kind of boundary condition appears, for instance, when considering the diffusion of ions in molecular channels, between the different concentrations at both sides of the cellular membrane. For this application the overdamped limit of Brownian motion (leading to a first order Langevin equation) is most convenient, but in previous works some difficulties associated with this limit were found for the implementation of the boundary conditions. We derive here an algorithm that, unlike previous attempts, does not require the simulation of particle reservoirs or the consideration of velocity variables or adjustable parameters. Simulations of Brownian particles in simple cases show that results agree perfectly with theory, both for the local concentration values and for the resulting particle flux in nonequilibrium situations. The algorithm is appropriate for the modeling of more complex ionic channels and, in general, for the treatment of analogous boundary conditions in other physical models using first order Langevin equations.

Networks of randomly connected neurons are among the most popular models in theoretical neuroscience. The connectivity between neurons in the cortex is however not fully random, the simplest and most prominent deviation from randomness found in experimental data being the overrepresentation of bidirectional connections among pyramidal cells. Using numerical and analytical methods, we investigate the effects of partially symmetric connectivity on the dynamics in networks of rate units. We consider the two dynamical regimes exhibited by random neural networks: the weak-coupling regime, where the firing activity decays to a single fixed point unless the network is stimulated, and the strong-coupling or chaotic regime, characterized by internally generated fluctuating firing rates. In the weak-coupling regime, we compute analytically, for an arbitrary degree of symmetry, the autocorrelation of network activity in the presence of external noise. In the chaotic regime, we perform simulations to determine the timescale of the intrinsic fluctuations. In both cases, symmetry increases the characteristic asymptotic decay time of the autocorrelation function and therefore slows down the dynamics in the network.

In recent years nondemographic variability has been shown to greatly affect dynamics of stochastic populations. For example, nondemographic noise in the form of a bursty reproduction process with an a priori unknown burst size, or environmental variability in the form of time-varying reaction rates, have been separately found to dramatically impact the extinction risk of isolated populations. In this work we investigate the extinction risk of an isolated population under the combined influence of these two types of nondemographic variation. Using the so-called momentum-space Wentzel–Kramers–Brillouin (WKB) approach and accounting for the explicit time dependence in the reaction rates, we arrive at a set of time-dependent Hamilton equations. To this end, we evaluate the population's extinction risk by finding the instanton of the time-perturbed Hamiltonian numerically, whereas analytical expressions are presented in particular limits using various perturbation techniques. We focus on two classes of time-varying environments: periodically varying rates corresponding to seasonal effects and a sudden decrease in the birth rate corresponding to a catastrophe. All our theoretical results are tested against numerical Monte Carlo simulations with time-dependent rates and also against a numerical solution of the corresponding time-dependent Hamilton equations.

We derive a bound on generalized currents for Langevin systems in terms of the total entropy production in the system and its environment. For overdamped dynamics, any generalized current is bounded by the total rate of entropy production. We show that this entropic bound on the magnitude of generalized currents imposes power-efficiency tradeoff relations for ratchets in contact with a heat bath: Maximum efficiency—Carnot efficiency for a Smoluchowski-Feynman ratchet and unity for a flashing or rocking ratchet—can only be reached at vanishing power output. For underdamped dynamics, while there may be reversible currents that are not bounded by the entropy production rate, we show that the output power and heat absorption rate are irreversible currents and thus obey the same bound. As a consequence, a power-efficiency tradeoff relation holds not only for underdamped ratchets but also for periodically driven heat engines. For weak driving, the bound results in additional constraints on the Onsager matrix beyond those imposed by the second law. Finally, we discuss the connection between heat and entropy in a nonthermal situation where the friction and noise intensity are state dependent.