The size effect obtained when studying the effective properties of plates is investigated by producing a third-order correlation approximation and Hashin-Shtrikman bounds for the effective in-plane conductivity of heterogeneous plates. The boundary condition of the plates is taken into account by obtaining the exact Green operator for the boundary problem. Results are obtained for a two-dimensional (2D) random distribution of disks and a 3D distribution of spheres. All results recover those obtained for an infinite medium when the heterogeneity size becomes small compared to plate thickness. They show that the size effect is more significant in the case of a 2D distribution of heterogeneities than for a 3D distribution.

Suture joints are remarkable mechanical structures found throughout nature composed of compliant interlocking seams connecting stiffer components. This study investigates the underlying mechanisms and the role of geometry governing the unique mechanical behavior of suture joints. Analytical and numerical composite models are formulated for two suture geometries characterized by a single repeating wavelength (e.g., triangular and rectangular). Stiffness, strength, and local stress distributions are predicted to assess variations in deformation and failure mechanisms. A unique homogeneous stress field is observed throughout both the skeletal and interfacial components of the triangular geometry, thus providing advantages in load transmission, weight, stiffness, strength, energy absorption, and fatigue over the rectangular geometry. The results obtained have relevance to biomimetic design and optimization, suture growth and fusion, and evolutionary phenotype diversity.

The higher-order statistics of magnetic field magnitude fluctuations in the fast quiet solar wind are quantified systematically, scale by scale. We find a single global non-Gaussian scale-free behavior from minutes to over 5 h. This spans the signature of an inertial range of magnetohydrodynamic turbulence and a $\sim 1/f$ range in magnetic field components. This global scaling in field magnitude fluctuations is an intrinsic component of the underlying texture of the solar wind and puts a strong constraint on any theory of solar corona and the heliosphere. Intriguingly, the magnetic field and velocity components show scale-dependent dynamic alignment outside of the inertial range.

Pattern formation in ultracold quantum systems has recently received a great deal of attention. In this work, we investigate a two-dimensional model system simulating the dynamics of trapped ions. We find a spiral wave that is rigidly rotating, but with a peculiar core region in which adjacent ions oscillate in antiphase. The formation of this spiral wave is ascribed to the excitability previously reported by Lee and Cross. The breakup of the spiral wave is probed and, especially, an extraordinary scenario of the disappearance of the spiral wave, caused by spontaneous expansion of the antiphase core, is unveiled.

The thermoelectric transport coefficients of silver and gold plasma have been calculated within the relaxation-time approximation. We considered temperatures of 10–100 kK and densities of $\rho \lesssim 1$ g/cm${}^3$. The plasma composition was calculated using a corresponding system of coupled mass action laws, including the atom ionization up to $+$4. For momentum cross sections of electron-atom scattering we used the most accurate expressions available. The results of our modeling have been compared with other researchers' data whenever possible.

We propose a type of asymmetric simple exclusion process by introducing an adsorption lane. In the system, each particle can be adsorbed by the adsorption lane only once per travel. The adsorption and desorption probabilities control the density of adsorption sites and the number of adsorbed particles. The ratio of the adsorbed particles shows reversal dynamics for congestion of the system, which is called the “positive congestion effect.” We analyze this phenomenon by simulations and an approximation and successfully derive its critical condition. The spatial distribution of particles controlled by the adsorption and desorption probabilities is also investigated through balance equations of particles.

The octahedron model introduced recently has been implemented onto graphics cards, which permits extremely large-scale simulations via binary lattice gases and bit-coded algorithms. We confirm scaling behavior belonging to the two-dimensional Kardar-Parisi-Zhang universality class and find a surface growth exponent: $\beta =0.2415\left(15\right)$ on $2^{17}\times 2^{17}$ systems, ruling out $\beta =1/4$ suggested by field theory. The maximum speedup with respect to a single CPU is 240. The steady state has been analyzed by finite-size scaling and a growth exponent $\alpha =0.393\left(4\right)$ is found. Correction-to-scaling-exponent are computed and the power-spectrum density of the steady state is determined. We calculate the universal scaling functions and cumulants and show that the limit distribution can be obtained by the sizes considered. We provide numerical fitting for the small and large tail behavior of the steady-state scaling function of the interface width.

Long-lived quasistationary states, associated with stationary stable solutions of the Vlasov equation, are found in systems with long-range interactions. Studies of the relaxation time in a model of $N$ globally coupled particles moving on a ring, the Hamiltonian mean-field model (HMF), have shown that it diverges as $N^{\gamma }$ for large $N$, with $\gamma \simeq 1.7$ for some initial conditions with homogeneously distributed particles. We propose a method for identifying exact inhomogeneous steady states in the thermodynamic limit, based on analyzing models of uncoupled particles moving in an external field. For the HMF model, we show numerically that the relaxation time of these states diverges with $N$ with the exponent $\gamma \simeq 1$. The method, applicable to other models with globally coupled particles, also allows an exact evaluation of the stability limit of homogeneous steady states. In some cases, it provides a good approximation for the correspondence between the initial condition and the final steady state.

A three-dimensional symmetric binary fluid is studied, as a function of temperature, in the two-phase (liquid-liquid) coexistence region via Monte Carlo simulations. Particular focus has been in the understanding of curvature-dependent interfacial tension, which is observed to vary as $\sigma \left(R\right)=\sigma \left(\infty \right)/[1+2{\left(\frac{\ell }{R}\right)}^2]$, implying that a Tolman length is zero in the limit $R\to \infty$. The length $\ell$ is found to have a critical divergence the same as the correlation length, but its amplitude is significantly larger ($\ell \simeq 4\xi$). Our findings hence imply that the barrier against homogeneous nucleation is significantly reduced (in comparison with the classical nucleation theory) in the critical region. We also report results for the critical behavior of the flat interfacial tension $\sigma \left(\infty \right)$ and the concentration susceptibility, as well as the amplitude ratios involving these thermodynamic quantities. Noting that the interatomic potential in our model is described by the Lennard-Jones form that decays faster that $1/r^3$, all of our results for critical phenomena are expectedly consistent with the Ising universality class of three spatial dimensions.

We study the smectic to nematic (Sm$A$-$N$) phase transition taking place at the center of a free-standing film that exhibits enhanced surface order due to the anchoring promoted by a surrounding gas. The usual McMillan mean-field approach predicts that the Sm$A$-$N$ transition in bulk samples can be continuous or discontinuous (first or second order) depending on the molecular geometry, with a tricritical point separating these two regimes. Here we show that the additional orientational order imposed by the surface anchoring stabilizes the surface-induced smectic and nematic phases, leading to the breakdown of the tricritical point and to the emergence of a critical end point. We report the full phase diagram, which depicts four distinct structures as the film thickness is reduced.

Empirical studies of the genome-wide length distribution of duplicated sequences have revealed an algebraic tail common to nearly all clades. The decay of the tail is often well approximated by a single exponent that takes values within a limited range. We propose and study here scale-free duplication dynamics, a class of model for genome sequence evolution that generates the observed shapes of this distribution. A transition between self-similar and non-self-similar regimes is exhibited. Our model accounts plausibly for the observed form of the algebraic tail, which is not produced by standard models for generating long-range sequence correlations.

Velocity-jump processes are discrete random-walk models that have many applications including the study of biological and ecological collective motion. In particular, velocity-jump models are often used to represent a type of persistent motion, known as a run and tumble, that is exhibited by some isolated bacteria cells. All previous velocity-jump processes are noninteracting, which means that crowding effects and agent-to-agent interactions are neglected. By neglecting these agent-to-agent interactions, traditional velocity-jump models are only applicable to very dilute systems. Our work is motivated by the fact that many applications in cell biology, such as wound healing, cancer invasion, and development, often involve tissues that are densely packed with cells where cell-to-cell contact and crowding effects can be important. To describe these kinds of high-cell-density problems using a velocity-jump process we introduce three different classes of crowding interactions into a one-dimensional model. Simulation data and averaging arguments lead to a suite of continuum descriptions of the interacting velocity-jump processes. We show that the resulting systems of hyperbolic partial differential equations predict the mean behavior of the stochastic simulations very well.

We introduce a model of biological evolution in which species evolve in response to biotic interactions and fluctuating environmental stress. The species may either become extinct or mutate to acquire a new fitness value when the effective stress level is greater than their individual fitness. The model exhibits a phase transition to a completely extinct phase as the environmental stress or the mutation rate is varied. We discuss the generic conditions for which this transition is continuous. The model is exactly solvable and the critical behavior is characterized by an unusual dynamic exponent $z=1/3.$ Apart from predicting large-scale evolution, the model can be applied to understand the trends in the available fossil data.

We propose a model to describe the physical mechanisms by which chemical substances separate in the vicinity of a membrane. We assume that the adsorption of the different components of a complex liquid on a membrane is governed by interactions that couple them to the spontaneous curvature of the membrane. This problem is relevant to many fields in science, as cell constriction and division, micelles with cosurfactants, holometamorphosis, and morphogenesis in general.

An assembly of packed and oriented rodlike particles exhibit anisotropic physical properties. We investigate in the present work the anisotropic conductivity of films made of intrinsically conducting rods. These films are obtained from more or less ordered carbon nanotube liquid crystals. Their orientational order parameter is measured by polarized Raman spectroscopy. A relationship between the anisotropy of surface conductivity and orientational order parameter is determined. The experimental results are accounted for by a model that takes into account the number of intertube contacts and density of conductive pathways in different directions, as introduced by J. Fischer et al. for magnetically aligned nanotubes. We find that a good agreement, without any fitting parameter, of the proposed model and experiments is obtained when we consider a two-dimensional (2D) Gaussian distribution of the nanotube orientation. The conductivities parallel and perpendicular to the nematic director differ by almost an order of magnitude. This anisotropy is much greater than that of conventional dielectric liquid crystals, where the behavior is governed by the mobility anisotropy of ionic current carriers. The present results do not depend on the intrinsic properties of the nanotubes and are expected to be relevant for other assemblies of conducting rodlike particles, such as metallic or semi-conducting nanowires and ribbons.

We study the dynamical properties of the canonical ordered phase of the Hamiltonian mean-field (HMF) model, in which $N$ particles, globally coupled via pairwise attractive interactions, form a rotating cluster. Using a combination of numerical and analytical arguments, we first show that the largest Lyapunov exponent remains strictly positive in the infinite-size limit, converging to its asymptotic value with $1/\ln N$ corrections. We then elucidate the scaling laws ruling the behavior of this asymptotic value in the critical region separating the ordered, clustered phase and the disordered phase present at high-energy densities. We also show that the full spectrum of Lyapunov exponents consists of a bulk component converging to the (zero) value taken by a test oscillator forced by the mean field, plus subextensive bands of $O\left(\ln N\right)$ exponents taking finite values. We finally investigate the robustness of these results by studying a “2D” extension of the HMF model where each particle is endowed with 4 degrees of freedom, thus allowing the emergence of chaos at the level of a single particle. Altogether, these results illustrate the subtle effects of global (or long-range) coupling and the importance of the order in which the infinite-time and infinite-size limits are taken: For an infinite-size HMF system represented by the Vlasov equation, no chaos is present, while chaos exists and subsists for any finite system size.

We find a statistical mechanism that can adjust orientations of intracellular filaments to cell geometry in the absence of organizing centers. The effect is based on random and isotropic filament (de-)polymerization dynamics and is independent of filament interactions and explicit regulation. It can be understood by an analogy to electrostatics and appears to be induced by the confining boundaries; for periodic boundary conditions, no orientational bias emerges. Including active transport of particles, the model reproduces experimental observations of vesicle accumulations in transected axons.

We have proved an exact solution of a multilane totally asymmetric simple exclusion process (TASEP) with heterogeneous lane-changing rates on a torus. In the expression, the TASEP in each lane and lane-changing transition can be separable. Moreover, the lane-changing transitions satisfy the detailed balance condition, and this is the key to constructing the solution. Using the saddle-point method, the current of particles has been derived in a simple form in a thermodynamic limit. It is interesting that the dynamics depends only on a set of lane-changing parameters, not on the configuration of lanes.

The statistical thermodynamics of straight rigid rods of length $k$ ($k$-mers) with nonadditive lateral interactions was developed on a generalization in the spirit of the lattice-gas model and the classical Bragg-Williams approximation (BWA) and the quasichemical approximation (QCA). The new theoretical framework is obtained by combining (i) the exact analytical expression for the partition function of noninteracting linear $k$-mers adsorbed in one dimension and its extension to higher dimensions, and (ii) a generalization of BWA and QCA in which the adsorbate can occupy more than one adsorption site. The traditional assumption of a strictly pairwise additive nearest-neighbors interaction is replaced by a more general one, namely that the bond linking a certain atom with any of its neighbors depends considerably on how many of them are actually present (or absent) on the sites in the first coordination shell of the atom. The coverage and temperature dependence of the Helmholtz free energy, chemical potential, configurational entropy, and differential heat of adsorption are given. The formalism (i) reproduces the classical results for monomers, (ii) leads to the exact statistical thermodynamics of nonadditive interacting $k$-mers adsorbed in one dimension, and (iii) provides a close approximation for two-dimensional systems, taking into account multisite occupancy and nonadditive lateral interactions. Comparisons with Monte Carlo simulations are performed in order to test the validity of the theoretical model. Significant quantitative differences are shown and discussed. In all cases, the QCA appears to be the more accurate approach.