It is often stated that human languages, as other biological systems, are shaped by cost-cutting pressures but, to what extent? Attempts to quantify the degree of optimality of languages by means of an optimality score have been scarce and focused mostly on English. Here we recast the problem of the optimality of the word order of a sentence as an optimization problem on a spatial network where the vertices are words, arcs indicate syntactic dependencies, and the space is defined by the linear order of the words in the sentence. We introduce a score to quantify the cognitive pressure to reduce the distance between linked words in a sentence. The analysis of sentences from 93 languages representing 19 linguistic families reveals that half of languages are optimized to a $70\%$ or more. The score indicates that distances are not significantly reduced in a few languages and confirms two theoretical predictions: that longer sentences are more optimized and that distances are more likely to be longer than expected by chance in short sentences. We present a hierarchical ranking of languages by their degree of optimization. The score has implications for various fields of language research (dependency linguistics, typology, historical linguistics, clinical linguistics, and cognitive science). Finally, the principles behind the design of the score have implications for network science.

Liquids near the glass transition exhibit dynamical heterogeneity, i.e., correlated regions in the liquid relax at either a much faster rate or a much slower rate than the average. This collective phenomenon has been characterized by measurements of a dynamic susceptibility ${\chi }_4\left(t\right)$, which is sometimes interpreted in terms of the size of those relaxing regions and the intensity of the fluctuations. We show that the results of those measurements can be affected not only by the collective fluctuations in the relaxation rate, but also by density fluctuations in the initial state and by single-particle fluctuations. We also show that at very long times the average overlap $C\left(t\right)$ probing the similarity between an initial and a final state separated by a time interval $t$ decays as a power law $C\left(t\right)\sim t^{-d/2}$. This is much slower than the stretched exponential behavior $C\left(t\right)\sim e^{-{(t/\tau )}^{\beta }}$ previously observed at times within one or two orders of magnitude of the $\alpha$-relaxation time ${\tau }_{\alpha }$. We find that for times longer than $10–100{\tau }_{\alpha }$, the dynamic susceptibility ${\chi }_4\left(t\right)$ is dominated by single-particle fluctuations, and that ${\chi }_4\left(t\right)\approx C\left(t\right)\sim t^{-d/2}$. Finally, we introduce a method to extract the collective relaxation contribution to the dynamic susceptibility ${\chi }_4\left(t\right)$ by subtracting the effects of single-particle fluctuations and initial state density fluctuations. We apply this method to numerical simulations of two glass-forming models: a binary hard sphere system and a Kob-Andersen Lennard-Jones system. This allows us to extend the analysis of numerical data to timescales much longer than previously possible, and opens the door for further future progress in the study of dynamic heterogeneities, including the determination of the exchange time.

Understanding the relaxation dynamics of colloidal suspensions is crucial to identifying the elements that influence the mobility of their constituents, assessing their macroscopic response across the relevant time and length scales, and thus disclosing the fundamentals underpinning their exploitation in formulation engineering. In this work, we specifically assess the impact of long-ranged ordering on the relaxation dynamics of suspensions of soft repulsive rodlike particles, which are able to self-organize into nematic and smectic liquid-crystalline phases. Rods are modeled as soft repulsive spherocylinders with a length-to-diameter ratio $L^{★}=5$, interacting via the truncated and shifted Kihara potential. By performing dynamic Monte Carlo simulations, we analyze the effect of translational and orientational order on the diffusion of the rods along the relevant directions imposed by the morphology of the background phases. To provide a clear picture of the resulting dynamics, we assess its dependence on temperature, which can dramatically determine the response time of the system relaxation and the self-diffusion coefficients of the rods. The computation of the van Hove correlation functions allows us to identify the existence of rods that diffuse significantly faster than the average and whose concentration can be accurately adjusted by a suitable choice of temperature.

Microstructure characterization and reconstruction (MCR) is one of the most important components of discovering processing-structure-property relations of porous media behavior and inverse porous media design in computational materials science. Since the algorithms for describing and controlling the geometric configuration of microstructures need to solve a large number of variables and involve multiobjective conditions, the existing MCR methods have difficulty in gaining a perfect trade-off among the quantitative generation and characterization capability and the reconstruction quality. In this work, an improved 3D Porous Media Microstructure (3DPmmGAN) generative adversarial network based on deep-learning algorithm is demonstrated for high-quality microstructures generation with high controllability and high prediction accuracy. The proposed 3DPmmGAN allows the model to utilize unlabeled data for complex high-randomness microstructures end-to-end training within an acceptable time consumption. Further analysis shows that the trained network has good adaptivity for microstructures with different random geometric configurations, and can quantitatively control the generated structure according to semantic conditions, and can also quantitatively predict complex microstructure features. The key results suggest the proposed 3DPmmGAN is a powerful tool to accelerate the preparation and the initial characterization of 3D porous media, and potentially maximize the design efficiency for porous media.

Event-chain Monte Carlo (ECMC) accelerates the sampling of hard-sphere systems, and has been generalized to the potentials used in classical molecular simulations. Rather than imposing detailed balance on the transition probabilities, the method enforces a weaker global-balance condition in order to guarantee convergence to equilibrium. In this paper, we generalize the factor-field variant of ECMC to higher space dimensions. In the two-dimensional fluid phase, factor-field ECMC saturates the lower bound $z=0$ for the dynamical scaling exponent for local dynamics, whereas molecular dynamics is characterized by $z=1$ and local Metropolis Monte Carlo by $z=2$. In the presence of hexatic order, factor fields are not found to speed up the convergence. We note that generalizations of factor fields could couple to orientational order.

Polygonal billiards constitute some of the simplest yet counterintuitive dynamical systems in physics. Even basic features of the dynamics, such as ergodicity of the microcanonical distribution or the decay of correlations have not been settled in general. In this Letter, we will highlight the importance of symmetries of the billiard table for the resulting dynamics. Although typical triangular billiards appear to show correlation decay, symmetric billiards may not even be ergodic with respect to the uniform distribution in phase space.

We investigate the nonergodicity of the generalized Lévy walk introduced by Shlesinger et al. [Phys. Rev. Lett. 58, 1100 (1987)] with respect to the squared displacements. We present detailed analytical derivations of our previous findings outlined in a recent letter [Phys. Rev. Lett. 120, 104501 (2018)], give detailed interpretations, and in particular emphasize three surprising results. First, we find that the mean-squared displacements can diverge for a certain range of parameter values. Second, we show that an ensemble of trajectories can spread subdiffusively, whereas individual time-averaged squared displacements show superdiffusion. Third, we recognize that the fluctuations of the time-averaged squared displacements can become so large that the ergodicity breaking parameter diverges, what we call infinitely strong ergodicity breaking. This phenomenon can also occur for paramter values where the lag-time dependence of the mean-squared displacements is linear indicating normal diffusion. In order to numerically determine the full distribution of time-averaged squared displacements, we use importance sampling. For an embedding of our findings into existing results in the literature, we define a more general model which we call variable speed generalized Lévy walk and which includes well-known models from the literature as special cases such as the space-time coupled Lévy flight or the anomalous Drude model. We discuss and interpret our findings regarding the generalized Lévy walk in detail and compare them with the nonergodicity of the other space-time coupled models following from the more general model.

In this work, using the generalized Boltzmann equation of Zadehgol [Phys. Rev. E 94, 023316 (2016)] a lattice Boltzmann time-domain (LBTD) method is proposed. The time-domain methods, such as the finite-difference time-domain method (FDTD), have been proposed by researchers, as tools in the study and design of semiconductor and optoelectronic devices. The LBTD inherits the main advantages of the lattice Boltzmann methods over the conventional methods, i.e., simplicity of the implementation, easy handling of complex geometries, and explicit algorithms which make the method highly suitable for efficient parallel processing. The theoretical findings have been verified by performing LBTD analysis on some benchmark structures.

Oscillations in the preexponential of the nucleation rate are due to the discrete nature of small nuclei. An accurate elementary expression to describe such oscillations is derived in the limit of a high nucleation barrier. The result is applied to the standard Becker-Döring equation in two and three dimensions, and to the lowest-energy nucleation path in a cold lattice gas with Glauber and Metropolis dynamics (equivalent to an Ising model on a square lattice) where oscillation effects can be more pronounced.

We study the enumeration of closed walks of given length and algebraic area on the honeycomb lattice. Using an irreducible operator realization of honeycomb lattice moves, we map the problem to a Hofstadter-like Hamiltonian and show that the generating function of closed walks maps to the grand partition function of a system of particles with exclusion statistics of order $g=2$ and an appropriate spectrum, along the lines of a connection previously established by two of the authors. Reinterpreting the results in terms of the standard Hofstadter spectrum calls for a mixture of $g=1$ (fermion) and $g=2$ exclusion particles whose properties merit further studies. In this context we also obtain some unexpected Fibonacci sequences within the weights of the combinatorial factors appearing in the counting of walks.

Over the past few decades, formation of Turing patterns in reaction-diffusion systems has been shown to be the underlying process in several examples of biological morphogenesis, confirming Alan Turing's hypothesis, put forward in 1952. However, theoretical studies suggest that Turing patterns formation via classical “short-range activation and long-range inhibition” concept in general can happen within only narrow parameter ranges. This feature seemingly contradicts the accuracy and reproducibility of biological morphogenesis given the stochasticity of biochemical processes and the influence of environmental perturbations. Moreover, it represents a major hurdle to synthetic engineering of Turing patterns. In this work it is shown that this problem can be overcome in some systems under certain sets of interactions between their elements, one of which is immobile and therefore corresponding to a cell-autonomous factor. In such systems Turing patterns formation can be guaranteed by a simple universal control under any values of kinetic parameters and diffusion coefficients of mobile elements. This concept is illustrated by analysis and simulations of a specific three-component system, characterized in absence of diffusion by a presence of codimension two pitchfork-Hopf bifurcation.

We analyze the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modeling the stability of fixed points in large systems defined on complex networks, such as ecosystems consisting of a large number of species that interact through a food web. We develop an exact theory for the spectral distribution and the leading eigenvalue of the corresponding sparse Jacobian matrices. This theory reveals that the nature of local interactions has a strong influence on a system's stability. We show that, in general, linear dynamical systems defined on random graphs with a prescribed degree distribution of unbounded support are unstable if they are large enough, implying a tradeoff between stability and diversity. Remarkably, in contrast to the generic case, antagonistic systems that contain only interactions of the predator-prey type can be stable in the infinite size limit. This feature for antagonistic systems is accompanied by a peculiar oscillatory behavior of the dynamical response of the system after a perturbation, when the mean degree of the graph is small enough. Moreover, for antagonistic systems we also find that there exist a dynamical phase transition and critical mean degree above which the response becomes nonoscillatory.

We consider the mean-field analog of the $p$-star model for homogeneous random networks, and we compare its behavior with that of the $p$-star model and its classical mean-field approximation in the thermodynamic regime. We show that the partition function of the mean-field model satisfies a sequence of partial differential equations known as the heat hierarchy, and the models connectance is obtained as a solution of a hierarchy of nonlinear viscous PDEs. In the thermodynamic limit, the leading-order solution develops singularities in the space of parameters that evolve as classical shocks regularized by a viscous term. Shocks are associated with phase transitions and stable states are automatically selected consistently with the Maxwell construction. The case $p=3$ is studied in detail. Monte Carlo simulations show an excellent agreement between the $p$-star model and its mean-field analog at the macroscopic level, although significant discrepancies arise when local features are compared.

The impact of ribosome exit tunnel electrostatics on the protein elongation rate or on forces acting upon the nascent polypeptide chain are currently not fully elucidated. In the past, researchers have measured the electrostatic potential inside the ribosome polypeptide exit tunnel at a limited number of spatial points, at least in rabbit reticulocytes. Here we present a basic electrostatic model of the exit tunnel of the ribosome, providing a quantitative physical description of the tunnel interaction with the nascent proteins at all centro-axial points inside the tunnel. We show that a strong electrostatic screening is due to water molecules (not mobile ions) attracted to the ribosomal nucleic acid phosphate moieties buried in the immediate vicinity of the tunnel wall. We also show how the tunnel wall components and local ribosomal protein protrusions impact on the electrostatic potential profile and impede charged amino acid residues from progressing through the tunnel, affecting the elongation rate in a range of $-40\%$ to $+85\%$ when compared to the average elongation rate. The time spent by the ribosome to decode the genetic encrypted message is constrained accordingly. We quantitatively derive, at single-residue resolution, the axial forces acting on the nascent peptide from its particular sequence embedded in the tunnel. The model sheds light on how the experimental data point measurements of the potential are linked to the local structural chemistry of the inner wall, shape, and size of the tunnel. The model consistently connects experimental observations coming from different fields in molecular biology, x-ray crystallography, physical chemistry, biomechanics, and synthetic and multiomics biology. Our model should be a valuable tool to gain insight into protein synthesis dynamics, translational control, and the role of the ribosome's mechanochemistry in the cotranslational protein folding.

Here we study how curvature affects the structure of two-dimensional crystals growing on spheres. The mechanism of crystal growth is described by means of a Landau model in curved space that accounts for the excess of strain on crystal bonds caused by the substrate's curvature (packing frustration). In curved space elastic energy penalization strongly dictates the geometry of growing crystals. While compact faceted crystals are observed when elastic energy contribution can be neglected, cracked crystals with ribbonlike forms appear as the main mechanisms to reduce elastic frustration for highly curved systems.

The capability to simulate a two-way coupled interaction between a rarefied gas and an arbitrary-shaped colloidal particle is important for many practical applications, such as aerospace engineering, lung drug delivery, and semiconductor manufacturing. By means of numerical simulations based on the direct-simulation Monte Carlo (DSMC) method, we investigate the influence of the orientation of the particle and rarefaction on the drag and lift coefficients, in the case of prolate and oblate ellipsoidal particles immersed in a uniform ambient flow. This is done by modeling the solid particles using a cut-cell algorithm embedded within our DSMC solver. In this approach, the surface of the particle is described by its analytical expression and the microscopic gas-solid interactions are computed exactly using a ray-tracing technique. The measured drag and lift coefficients are used to extend the correlations, based on the sine-squared drag law, available in the continuum regime to the rarefied regime, focusing on the transitional and free-molecular regimes. The functional forms of the correlations for the ellipsoidal particles are chosen as a generalization from the spherical case. We show that the fits over the data from numerical simulations can be extended to regimes outside the simulated range of Kn. Our approach allows to achieve a higher precision when compared with existing predictive models from the literature. Finally, we underline the importance of this work in providing correlations for nonspherical particles that can be used for point-particle Euler-Lagrangian simulations to address the problem of contamination from finite-size particles in high-tech mechanical systems.

We apply the concept of Lagrangian descriptors to the dynamics on the Bunimovich stadium billiard, a two-dimensional ergodic system with singular families of trajectories, namely, the bouncing ball and the whispering gallery orbits. They play a central role in structuring the phase space, which is unveiled here by means of the Lagrangian descriptors applied to the associated map on the boundary. More interestingly, we also consider the open stadium, which in the optical case (Fresnel's laws) can be directly related to recent microlaser experiments. We find that the structure of the emission profile of these systems can be easily described thanks to the open version of the Lagrangian descriptors.

Reaction-diffusion systems implemented as dynamical processes on networks have recently renewed the interest in their self-organized collective patterns known as Turing patterns. We investigate the influence of network topology on the emerging patterns and their diversity, defined as the variety of stationary states observed with random initial conditions and the same dynamics. We show that a seemingly minor change, the removal or rewiring of a single link, can prompt dramatic changes in pattern diversity. The determinants of such critical occurrences are explored through an extensive and systematic set of numerical experiments. We identify situations where the topological sensitivity of the attractor landscape can be predicted without a full simulation of the dynamical equations, from the spectrum of the graph Laplacian and the linearized dynamics. Unexpectedly, the main determinant appears to be the degeneracy of the eigenvalues or the growth rate and not the number of unstable modes.

Despite substantial evidence that mechanical variables play a crucial role in transmembrane voltage regulation, most research efforts focus mostly on the nerve cell's biochemical or electrophysiological activities. We propose an electromechanical model of a nerve in order to advance our understanding of how mechanical forces and thermodynamics also regulate neural electrical activities. We explore the spatiotemporal dynamics of the transmembrane potential using the proposed nonlinear model with a sinusoid as the initial transmembrane potential and periodic boundary conditions. The localized wave from our numerical simulation and transmembrane potentials in nerves are solitary and show the three stages of action potential (depolarization, repolarization, and hyperpolarization), as well as threshold and saturation effects. We show that the mechanical properties of membranes affect the localization of the transmembrane potential. According to simulation data, mechanical pulses of sufficient magnitude can modulate a transmembrane voltage. The current model could be used to describe the dynamics of a transmembrane potential modulated by sound. Mechanical perturbations that modulate an electrical signal have a lot of clinical potential for treating pain and other neurological diseases.