Ribosome profiling experiments have found greater than 100-fold variation in ribosome density along mRNA transcripts, indicating that individual codon elongation rates can vary to a similar degree. This wide range of elongation times, coupled with differences in codon usage between transcripts, suggests that the average codon translation-rate per gene can vary widely. Yet, ribosome run-off experiments have found that the average codon translation rate for different groups of transcripts in mouse stem cells is constant at 5.6 AA/s. How these seemingly contradictory results can be reconciled is the focus of this study. Here, we combine knowledge of the molecular factors shown to influence translation speed with genomic information from Escherichia coli, Saccharomyces cerevisiae and Homo sapiens to simulate the synthesis of cytosolic proteins in these organisms. The model recapitulates a near constant average translation rate, which we demonstrate arises because the molecular determinants of translation speed are distributed nearly randomly amongst most of the transcripts. Consequently, codon translation rates are also randomly distributed and fast-translating segments of a transcript are likely to be offset by equally probable slow-translating segments, resulting in similar average elongation rates for most transcripts. We also show that the codon usage bias does not significantly affect the near random distribution of codon translation rates because only about $10\%$ of the total transcripts in an organism have high codon usage bias while the rest have little to no bias. Analysis of Ribo-Seq data and an in vivo fluorescent assay supports these conclusions.

Team coordination is a basic human behavioral trait observed in many real-life communities. To promote teamwork, it is important to cultivate social skills that elicit team coordination. In the present work, we consider which social skills are indispensable for individuals performing a ball possession game in soccer. We develop a simple social force model that describes the synchronized motion of offensive players. Comparing the simulation results with experimental observations, we uncovered that the cooperative social force, a measure of perception skill, has the most important role in reproducing the harmonized collective motion of experienced players in the task. We further developed an experimental tool that facilitates real players' perceptions of interpersonal distance, revealing that the tool improves novice players' motions as if the cooperative social force were imposed.

The exchange of diffusive metabolites is known to control the spatial patterns formed by microbial populations, as revealed by recent studies in the laboratory. However, the matrices used, such as agarose pads, lack the structured geometry of many natural microbial habitats, including in the soil or on the surfaces of plants or animals. Here we address the important question of how such geometry may control diffusive exchanges and microbial interaction. We model mathematically mutualistic interactions within a minimal unit of structure: two growing reservoirs linked by a diffusive channel through which metabolites are exchanged. The model is applied to study a synthetic mutualism, experimentally parametrized on a model algal-bacterial co-culture. Analytical and numerical solutions of the model predict conditions for the successful establishment of remote mutualisms, and how this depends, often counterintuitively, on diffusion geometry. We connect our findings to understanding complex behavior in synthetic and naturally occurring microbial communities.

In this study we formulate a theoretical approach, based on a Boltzmann-like kinetic equation, to describe pattern formation in two-dimensional mixtures of microtubular filaments and molecular motors. Following the previous work by Aranson and Tsimring [Phys. Rev. E 74, 031915 (2006)] we model the motor-induced reorientation of microtubules as collision rules, and devise a semianalytical method to calculate the corresponding interaction integrals. This procedure yields an infinite hierarchy of kinetic equations that we terminate by employing a well-established closure strategy, developed in the pattern-formation community and based on a power-counting argument. We thus arrive at a closed set of coupled equations for slowly varying local density and orientation of the microtubules, and study its behavior by performing a linear stability analysis and direct numerical simulations. By comparing our method with the work of Aranson and Tsimring, we assess the validity of the assumptions required to derive their and our theories. We demonstrate that our approximation-free evaluation of the interaction integrals and our choice of a systematic closure strategy result in a rather different dynamical behavior than was previously reported. Based on our theory, we discuss the ensuing phase diagram and the patterns observed.

The deterministic Hill function depends only on the average values of molecule numbers. To account for the fluctuations in the molecule numbers, the argument of the Hill function needs to contain the means, the standard deviations, and the correlations. Here we present a method that allows for stochastic Hill functions to be constructed from the dynamical evolution of stochastic biocircuits with specific topologies. These stochastic Hill functions are presented in a closed analytical form so that they can be easily incorporated in models for large genetic regulatory networks. Using a repressive biocircuit as an example, we show by Monte Carlo simulations that the traditional deterministic Hill function inaccurately predicts time of repression by an order of two magnitudes. However, the stochastic Hill function was able to capture the fluctuations and thus accurately predicted the time of repression.

Networks of semiflexible filaments are building blocks of different biological and structural materials such as cytoskeleton and extracellular matrix. The mechanical response of these systems when subjected to an applied strain at zero temperature is often investigated numerically using networks composed of filaments, which are either rigidly welded or pinned together at their crosslinks. In the latter, filaments during deformation are free to rotate about their crosslinks while the relative angles between filaments remain constant in the former. The behavior of crosslinks in actual semiflexible networks is different than these idealized models and there exists only partial constraint on torques at crosslinks. The present work develops a numerical model in which two intersecting filaments are connected to each other by torsional springs with arbitrary stiffness. We show that fiber networks composed of rigid and freely rotating crosslinks are the limiting case of the present model. Furthermore, we characterize the effects of stiffness of crosslinks on effective Young's modulus of semiflexible networks as a function of filament flexibility and crosslink density. The effective Young's modulus is determined as a function of the mechanical properties of crosslinks and is found to vanish for networks composed of very weak torsional springs. Independent of the stiffness of crosslinks, it is found that the effective Young's modulus is a function of fiber flexibility and crosslink density. In low density networks, filaments primarily bend and the effective Young's modulus is much lower than the affine estimate. With increasing filament bending stiffness and/or crosslink density, the mechanical behavior of the networks becomes more affine and the stretching of filaments depicts itself as the dominant mode of deformation. The torsional stiffness of the crosslinks significantly affects the effective Young's modulus of the semiflexible random fiber networks.

The electrical responses of a nematic liquid crystal sample confined between two cylindrical surfaces are investigated in the framework of elastic continuum theory. The responses are the result of the molecular reorientation induced by both the applied electric field and the cylindrical geometry of the sample. The nematic medium is considered as a parallel $\mathit{RC}$ circuit since the capacitance and the resistance are under the same difference of potential. The electrical properties, including the total electric current, are determined from the molecular reorientation of the director. The elastic anisotropy has been shown to influence substantially the profile of the electrical current, capacitance, and resistance characterizing the equivalent circuit for the medium.

We present a framework for the study of disclinations in two-dimensional active nematic liquid crystals and topological defects in general. The order tensor formalism is used to calculate exact multiparticle solutions of the linearized static equations inside a planar uniformly aligned state so that the total charge has to vanish. Topological charge conservation then requires that there is always an equal number of $q=1/2$ and $q=-1/2$ charges. Starting from a set of hydrodynamic equations, we derive a low-dimensional dynamical system for the parameters of the static solutions, which describes the motion of a half-disclination pair or of several pairs. Within this formalism, we model defect production and annihilation, as observed in experiments. Our dynamics also provide an estimate for the critical density at which production and annihilation rates are balanced.

We report on the results of a molecular dynamics simulation study of porous glassy media, formed in the process of isochoric rapid quenching from a high-temperature liquid state. The transition to a porous solid occurs due to the concurrent processes of phase separation and material solidification. The study is focused on topographies of the model porous structures and their dependence on temperature and average density. To quantify the pore-size distributions, we put forth a scaling relation that provides a satisfactory data collapse in systems with high porosity. We also find that the local density of the solid domains in the porous structures is broadly distributed, and, with increasing average density, a distinct peak in the local density distribution is displaced toward higher values.

A “flutter machine” is introduced for the investigation of a singular interface between the classical and reversible Hopf bifurcations that is theoretically predicted to be generic in nonconservative reversible systems with vanishing dissipation. In particular, such a singular interface exists for the Pflüger viscoelastic column moving in a resistive medium, which is proven by means of the perturbation theory of multiple eigenvalues with the Jordan block. The laboratory setup, consisting of a cantilevered viscoelastic rod loaded by a positional force with nonzero curl produced by dry friction, demonstrates high sensitivity of the classical Hopf bifurcation onset to the ratio between the weak air drag and Kelvin-Voigt damping in the Pflüger column. Thus, the Whitney umbrella singularity is experimentally confirmed, responsible for discontinuities accompanying dissipation-induced instabilities in a broad range of physical contexts.

We study the linear stability and nonlinear behavior of the electroconvection between two concentric half-cylinders with no-slip conditions on all boundaries. The no-slip condition makes impossible to apply the standard modal approach. Hence, we apply a finite element technique similar to the one we have used in a previous paper about the electroconvection in a rectangular enclosed domain. When compared to the classical problem of electroconvection between two full concentric cylinders, the linear criterion is higher, due to the viscous shear introduced by the lateral walls. As a consequence, the structure of the eigenmodes is very different. There is a repulsion between modes with the same symmetry, forcing pairs of modes to cross each other repeatedly. For inner injection and small value of the ratio between the inner and outer radii the no-slip condition changes the nature of the bifurcation from subcritical to supercritical, while it is always subcritical for outer injection. To understand this behavior, we perform a modal analysis using the eigenfunctions obtained from the linear stability analysis as modal basis. We show that the supercritical branch is originated by the nonorthogonality of the modes when no-slip boundary conditions are imposed. These mechanism explains the previously unexplained appearance of the supercritical branch in the enclosed rectangular configuration.

Three-dimensional, compressible, magnetohydrodynamic turbulence of an isothermal, self-gravitating fluid is analyzed using two-point statistics in the asymptotic limit of large Reynolds numbers (both kinetic and magnetic). Following an alternative formulation proposed by Banerjee and Galtier [Phys. Rev. E 93, 033120 (2016); J. Phys. A: Math. Theor. 50, 015501 (2017)], an exact relation has been derived for the total energy transfer. This approach results in a simpler relation expressed entirely in terms of mixed second-order structure functions. The kinetic, thermodynamic, magnetic, and gravitational contributions to the energy transfer rate can be easily separated in the present form. By construction, the new formalism includes such additional effects as global rotation, the Hall term in the induction equation, etc. The analysis shows that solid-body rotation cannot alter the energy flux rate of compressible turbulence. However, the contribution of a uniform background magnetic field to the flux is shown to be nontrivial unlike in the incompressible case. Finally, the compressible, turbulent energy flux rate does not vanish completely due to simple alignments, which leads to a zero turbulent energy flux rate in the incompressible case.

We propose a fluid-structure interaction (FSI) scheme using the entropic multi-relaxation time lattice Boltzmann (KBC) model for the fluid domain in combination with a nonlinear finite element solver for the structural part. We show the validity of the proposed scheme for various challenging setups by comparison to literature data. Beyond validation, we extend the KBC model to multiphase flows and couple it with a finite element method (FEM) solver. Robustness and viability of the entropic multi-relaxation time model for complex FSI applications is shown by simulations of droplet impact on elastic superhydrophobic surfaces.

An efficient third-order discrete unified gas kinetic scheme (DUGKS) is presented in this paper for simulating continuum and rarefied flows. By employing a two-stage time-stepping scheme and the high-order DUGKS flux reconstruction strategy, third order of accuracy in both time and space can be achieved in the present method. It is also analytically proven that the second-order DUGKS is a special case of the present method. Compared with the high-order lattice Boltzmann equation-based methods, the present method is capable to deal with the rarefied flows by adopting the Newton-Cotes quadrature to approximate the integrals of moments. Instead of being constrained by the second order (or lower order) of accuracy in the time-splitting scheme as in the conventional high-order Runge-Kutta-based kinetic methods, the present method solves the original Boltzmann equation, which overcomes the limitation in time accuracy. Typical benchmark tests are carried out for comprehensive evaluation of the present method. It is observed in the tests that the present method is advantageous over the original DUGKS in accuracy and capturing delicate flow structures. Moreover, the efficiency of the present third-order method is also shown in simulating rarefied flows.

Accurate characterization of heterogeneous materials is of great importance for different fields of science and engineering. Such a goal can be achieved through imaging. Acquiring three- or two-dimensional images under different conditions is not, however, always plausible. On the other hand, accurate characterization of complex and multiphase materials requires various digital images (I) under different conditions. An ensemble method is presented that can take one single (or a set of) I(s) and stochastically produce several similar models of the given disordered material. The method is based on a successive calculating of a conditional probability by which the initial stochastic models are produced. Then, a graph formulation is utilized for removing unrealistic structures. A distance transform function for the Is with highly connected microstructure and long-range features is considered which results in a new I that is more informative. Reproduction of the I is also considered through a histogram matching approach in an iterative framework. Such an iterative algorithm avoids reproduction of unrealistic structures. Furthermore, a multiscale approach, based on pyramid representation of the large Is, is presented that can produce materials with millions of pixels in a matter of seconds. Finally, the nonstationary systems—those for which the distribution of data varies spatially—are studied using two different methods. The method is tested on several complex and large examples of microstructures. The produced results are all in excellent agreement with the utilized Is and the similarities are quantified using various correlation functions.

We present a generalized network model for simulating capillary-dominated two-phase flow through porous media at the pore scale. Three-dimensional images of the pore space are discretized using a generalized network—described in a companion paper [A. Q. Raeini, B. Bijeljic, and M. J. Blunt, Phys. Rev. E 96, 013312 (2017)]—which comprises pores that are divided into smaller elements called half-throats and subsequently into corners. Half-throats define the connectivity of the network at the coarsest level, connecting each pore to half-throats of its neighboring pores from their narrower ends, while corners define the connectivity of pore crevices. The corners are discretized at different levels for accurate calculation of entry pressures, fluid volumes, and flow conductivities that are obtained using direct simulation of flow on the underlying image. This paper discusses the two-phase flow model that is used to compute the averaged flow properties of the generalized network, including relative permeability and capillary pressure. We validate the model using direct finite-volume two-phase flow simulations on synthetic geometries, and then present a comparison of the model predictions with a conventional pore-network model and experimental measurements of relative permeability in the literature.

Aiming to study the bubble cavitation problem in quiescent and sheared liquids, a third-order isothermal lattice Boltzmann model that describes a two-dimensional (2D) fluid obeying the van der Waals equation of state, is introduced. The evolution equations for the distribution functions in this off-lattice model with 16 velocities are solved using the corner-transport-upwind (CTU) numerical scheme on large square lattices (up to $6144\times 6144$ nodes). The numerical viscosity and the regularization of the model are discussed for first- and second-order CTU schemes finding that the latter choice allows to obtain a very accurate phase diagram of a nonideal fluid. In a quiescent liquid, the present model allows us to recover the solution of the 2D Rayleigh-Plesset equation for a growing vapor bubble. In a sheared liquid, we investigated the evolution of the total bubble area, the bubble deformation, and the bubble tilt angle, for various values of the shear rate. A linear relation between the dimensionless deformation coefficient $D$ and the capillary number Ca is found at small Ca but with a different factor than in equilibrium liquids. A nonlinear regime is observed for $\text{Ca}\gtrsim 0.2$.

We discuss the steady-state dynamics of interfaces with periodic boundary conditions arising from body-centered solid-on-solid growth models in $1+1$ dimensions involving random aggregation of extended particles (dimers, trimers, $...,k$-mers). Roughening exponents as well as width and maximal height distributions can be evaluated directly in stationary regimes by mapping the dynamics onto an asymmetric simple exclusion process with $k$-type of vacancies. Although for $k\ge 2$ the dynamics is partitioned into an exponentially large number of sectors of motion, the results obtained in some generic cases strongly suggest a universal scaling behavior closely following that of monomer interfaces.

This paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete and the binary aggregation alone governs the time evolution of the systems. By considering the growth histories of all possible clusters, an exact expression is derived for the probability of a coagulating system with an arbitrary kernel being found in a given cluster configuration when monodisperse initial conditions are applied. Then this probability is used to calculate the time-dependent distribution for the number of clusters of a given size, the average number of such clusters, and that average's standard deviation. The correctness of our general expressions is proved based on the (analytical and numerical) results obtained for systems with the constant kernel. In addition, the results obtained are compared with the results arising from the solutions to the mean-field Smoluchowski coagulation equation, indicating its weak points. The paper closes with a brief discussion on the extensibility to other systems of the approach presented herein, emphasizing the issue of arbitrary initial conditions.

We introduce a semiclassical theory for strong localization that may arise in the context of many-body thermalization. As a minimal model for thermalization we consider a few-site Bose-Hubbard model consisting of two weakly interacting subsystems that can exchange particles. The occupation of a subsystem ($x$) satisfies in the classical treatment a Fokker-Planck equation with a diffusion coefficient $D\left(x\right)$. We demonstrate that it is possible to deduce from the classical description a quantum breaktime $t^{*}$ and, hence, the manifestations of a strong localization effect. For this purpose it is essential to take the geometry of the energy shell into account and to make a distinction between different notions of phase-space exploration.