It is shown that Lotka-Volterra interaction terms are not appropriate to describe vertical cultural transmission. Appropriate interaction terms are derived and used to compute the effect of vertical cultural transmission on demic front propagation. They are also applied to a specific example, the Neolithic transition in Europe. In this example, it is found that the effect of vertical cultural transmission can be important (about 30%). On the other hand, simple models based on differential equations can lead to large errors (above 50%). Further physical, biophysical, and cross-disciplinary applications are outlined.

Magnetic flux conservation in turbulent plasmas at high magnetic Reynolds numbers is argued neither to hold in the conventional sense nor to be entirely broken, but instead to be valid in a statistical sense associated to the “spontaneous stochasticity” of Lagrangian particle trajectories. The latter phenomenon is due to the explosive separation of particles undergoing turbulent Richardson diffusion, which leads to a breakdown of Laplacian determinism for classical dynamics. Empirical evidence is presented for spontaneous stochasticity, including numerical results. A Lagrangian path-integral approach is then exploited to establish stochastic flux freezing for resistive hydromagnetic equations and to argue, based on the properties of Richardson diffusion, that flux conservation must remain stochastic at infinite magnetic Reynolds number. An important application of these results is the kinematic, fluctuation dynamo in nonhelical, incompressible turbulence at magnetic Prandtl number (Pr${}_m$) equal to unity. Numerical results on the Lagrangian dynamo mechanisms by a stochastic particle method demonstrate a strong similarity between the Pr${}_m=1$ and 0 dynamos. Stochasticity of field-line motion is an essential ingredient of both. Finally, some consequences for nonlinear magnetohydrodynamic turbulence, dynamo, and reconnection are briefly considered.

Free-energy barrier for entry of a charged polymer into a nanoscale channel by a driving electric field is studied theoretically and using molecular dynamics simulations. Dependence of the barrier height on the polymer length, the driving field strength, and the channel entrance geometry is investigated. Squeezing effect of the electric field on the polymer before its entry to the channel is taken into account. It is shown that lateral confinement of the polymer prior to its entry changes the polymer length dependence of the barrier height noticeably. Our theory and simulation results are in good agreement and reasonably describe related experimental data.

We propose a simple, self-consistent kinetic model for the evolution of a mixture of droplets and vapor expanding adiabatically in vacuum after rapid, almost isochoric heating. We study the evolution of the two-phase fluid at intermediate times between the molecular and the hydrodynamic scales, focusing on out-of-equilibrium and surface effects. We use the van der Waals equation of state as a test bed to implement our model and study the phenomenology of the upcoming second neutralized drift compression experiment (NDCX-II) at Lawrence Berkeley National Laboratory (LBNL) that uses ion beams for target heating. We find an approximate expression for the temperature difference between the droplets and the expanding gas and we check it with numerical calculations. The formula provides a useful criterion to distinguish the thermalized and nonthermalized regimes of expansion. In the thermalized case, the liquid fraction grows in a proportion that we estimate analytically, whereas, in case of too rapid expansion, a strict limit for the evaporation of droplets is derived. The range of experimental situations is discussed.

We investigate lamellar three-phase patterns that form during the directional solidification of ternary eutectic alloys in thin samples. A distinctive feature of this system is that many different geometric arrangements of the three phases are possible, contrary to the widely studied two-phase patterns in binary eutectics. Here, we first analyze the case of stable lamellar coupled growth of a symmetric model ternary eutectic alloy, using a Jackson-Hunt–type calculation in thin film geometry, for arbitrary configurations, and derive expressions for the front undercooling as a function of velocity and spacing. Next, we carry out phase-field simulations to test our analytic predictions and to study the instabilities of the simplest periodic lamellar arrays. For large spacings, we observe different oscillatory modes that are similar to those found previously for binary eutectics and that can be classified using the symmetry elements of the steady-state pattern. For small spacings, we observe a new instability that leads to a change in the sequence of the phases. Its onset can be well predicted by our analytic calculations. Finally, some preliminary phase-field simulations of three-dimensional growth structures are also presented.

The mesophases of two infinitely hard models with chiral and anisotropic characteristics in two dimensions are studied. Evidence for nematic and smectic behavior is provided via Monte Carlo simulations using restrictive values of the molecular parameters. Both models are geometrically chiral; one has polar structure. The concept of smectic phase considered in this work requires translational disorder in one direction and signs of translational order in the perpendicular one. The models presented in this paper show these characteristics. The isotropic-nematic phase transition satisfies the features of the Kosterlitz Thouless type. The smectic phase shows signs of quasi-long-range order.

In the exclusion-process literature, mean-field models are often derived by assuming that the occupancy status of lattice sites is independent. Although this assumption is questionable, it is the foundation of many mean-field models. In this work we develop methods to relax the independence assumption for a range of discrete exclusion-process-based mechanisms motivated by applications from cell biology. Previous investigations that focused on relaxing the independence assumption have been limited to studying initially uniform populations and ignored any spatial variations. By ignoring spatial variations these previous studies were greatly simplified due to translational invariance of the lattice. These previous corrected mean-field models could not be applied to many important problems in cell biology such as invasion waves of cells that are characterized by moving fronts. Here we propose generalized methods that relax the independence assumption for spatially inhomogeneous problems, leading to corrected mean-field descriptions of a range of exclusion-process-based models that incorporate (i) unbiased motility, (ii) biased motility, and (iii) unbiased motility with agent birth and death processes. The corrected mean-field models derived here are applicable to spatially variable processes including invasion wave-type problems. We show that there can be large deviations between simulation data and traditional mean-field models based on invoking the independence assumption. Furthermore, we show that the corrected mean-field models give an improved match to the simulation data in all cases considered.

An analytical solution is presented of the governing equations for the coupled radial and longitudinal displacements and stresses within the finite thickness of the arterial wall in pulsatile flow. The results are used to examine the extent of coupling between the radial and longitudinal dynamics within the vessel wall, particularly when the wall is fully tethered. In the case of a free wall, it is found that the dynamics in the two directions are fairly decoupled from each other when the wavelength is at least of the order of $100$ times the vessel radius. At $10$ times the vessel radius, however, there is strong coupling between the two. These findings are consistent with expectations in the case of a free wall where the long-wave approximation has been applied in the past. In the case of a tethered wall, however, the results indicate that in general the long-wave approximation is strictly valid only when the combination of wall material and tethering allow the wave to be long.

This paper aims to investigate Gaussian colored-noise-induced stochastic bifurcations and the dynamical influence of correlation time and noise intensity in a bistable Duffing–Van der Pol oscillator. By using the stochastic averaging method, theoretically, one can obtain the stationary probability density function of amplitude for the Duffing–Van der Pol oscillator and can reveal interesting dynamics under the influence of Gaussian colored noise. Stochastic bifurcations are discussed through a qualitative change of the stationary probability distribution, which indicates that system parameters, noise intensity, and noise correlation time, respectively, can be treated as bifurcation parameters. They also imply that the effects of multiplicative noise are rather different from that of additive noise. The results of direct numerical simulation verify the effectiveness of the theoretical analysis. Moreover, the largest Lyapunov exponent calculations indicate that $P$ and $D$ bifurcations have no direct connection.

The response of a cold electron gas is generalized to include the spin of the electron described by the relativistically correct quasiclassical Bargmann-Michel-Telegdi (BMT) equation. The magnetization of the electron gas is assumed to be along the background magnetic field $\mathbf{B}$ and the spin-dependent contribution to the response tensor is proportional to the magnitude of the magnetization. The dispersion equation is shown to be quadratic in the refractive index squared, and dispersion curves for the two wave modes are plotted for cases where the magnetic field associated with magnetization is comparable with $\mathbf{B}$. Two intrinsically spin-dependent wave modes are identified: one bounded by two resonances and the other by two cutoffs. The counterpart of the $z$ mode can escape without encountering a resonance or a cutoff.

We conduct a comparative study to evaluate several lattice Boltzmann (LB) models for solving the near incompressible Navier-Stokes equations, including the lattice Boltzmann equation with the multiple-relaxation-time (MRT), the two-relaxation-time (TRT), the single-relaxation-time (SRT) collision models, and the entropic lattice Boltzmann equation (ELBE). The lid-driven square cavity flow in two dimensions is used as a benchmark test. Our results demonstrate that the ELBE does not improve the numerical stability of the SRT or the lattice Bhatnagar-Gross-Krook (LBGK) model. Our results also show that the MRT and TRT LB models are superior to the ELBE and LBGK models in terms of accuracy, stability, and computational efficiency and that the ELBE scheme is the most inferior among the LB models tested in this study, thus is unfit for carrying out numerical simulations in practice. Our study suggests that, to optimize the accuracy, stability, and efficiency in the MRT model, it requires at least three independently adjustable relaxation rates: one for the shear viscosity $\nu$ (or the Reynolds number $\text{Re}$), one for the bulk viscosity $\zeta$, and one to satisfy the criterion imposed by the Dirichlet boundary conditions which are realized by the bounce-back-type boundary conditions.

From inelastic neutron-scattering experiments and all atom molecular dynamics simulations we present evidence for a low-energy dynamical mode in the fluid phase of a 1,2-dimyristoyl-sn-glycero-3-phoshatidylcholine (DMPC) bilayer immersed in a 5% water/ethanol solution. In addition to the well-known phonon that shows a liquidlike dispersion with energies up to 4.5 meV, we observe an additional mode at smaller energies of 0.8 meV, which shows little or no dispersion. Both modes show transverse properties and might be related to molecular motion perpendicular to the bilayer.

Recently, the stationary state of a parallel-update totally asymmetric simple exclusion process with varying system length, which can be regarded as a queueing process with excluded-volume effect (exclusive queueing process), was obtained [C Arita and D Yanagisawa, J. Stat. Phys. 141, 829 (2010)]. In this paper, we analyze the dynamical properties of the number of particles $\langle N_t\rangle$ and the position of the last particle (the system length) $\langle L_t\rangle$, using an analytical method (generating function technique) as well as a phenomenological description based on domain-wall dynamics and Monte Carlo simulations. The system exhibits two phases corresponding to linear convergence or divergence of $\langle N_t\rangle$ and $\langle L_t\rangle$. These phases can both further be subdivided into high-density and maximal-current subphases. The predictions of the domain-wall theory are found to be in very good agreement quantitively with results from Monte Carlo simulations in the convergent phase. On the other hand, in the divergent phase, only the prediction for $\langle N_t\rangle$ agrees with simulations.

Here, a scenario is proposed, according to which a generic self-organized critical (SOC) system can be looked upon as a Witten-type topological field theory (W-TFT) with spontaneously broken Becchi-Rouet-Stora-Tyutin (BRST) symmetry. One of the conditions for the SOC is the slow driving noise, which unambiguously suggests Stratonovich interpretation of the corresponding stochastic differential equation (SDE). This, in turn, necessitates the use of Parisi-Sourlas-Wu stochastic quantization procedure, which straightforwardly leads to a model with BRST-exact action, i.e., to a W-TFT. In the parameter space of the SDE, there must exist full-dimensional regions where the BRST symmetry is spontaneously broken by instantons, which in the context of SOC are essentially avalanches. In these regions, the avalanche-type SOC dynamics is liberated from overwise a rightful dynamics-less W-TFT, and a Goldstone mode of Fadeev-Popov ghosts exists. Goldstinos represent moduli of instantons (avalanches) and being gapless are responsible for the critical avalanche distribution in the low-energy, long-wavelength limit. The above arguments are robust against moderate variations of the SDE’s parameters and the criticality is “self-tuned.” The proposition of this paper suggests that the machinery of W-TFTs may find its applications in many different areas of modern science studying various physical realizations of SOC. It also suggests that there may in principle exist a connection between some SOC‘s and the concept of topological quantum computing.

The simulation of granular media is usually done either with event-driven codes that treat collisions as instantaneous but have difficulty with very dense packings, or with molecular dynamics (MD) methods that approximate rigid grains using a stiff viscoelastic spring. There is a little-known method that combines several collision events into a single timestep to retain the instantaneous collisions of event-driven dynamics, but also be able to handle dense packings. However, it is poorly characterized as to its regime of validity and failure modes. We present a modification of this method to reduce the introduction of overlap error, and test it using the problem of two-dimensional (2D) granular Couette flow, a densely packed system that has been well characterized by previous work. We find that this method can successfully replicate the results of previous work up to the point of jamming, and that it can do so a factor of 10 faster than comparable MD methods.

Polymer chain aggregates grown by ($1+1$)-dimensional Monte Carlo simulations of vapor deposition polymerization (VDP) were studied. The dynamic scaling behavior of polymer chain length distribution $n_s(t)$ was studied as a function of chain length ($s$), deposition time ($t$), and the ratio $G=D/F$ of deposition rate ($F$) and free monomer diffusion ($D$). The dynamic scaling approach was employed to highlight the dependence of $n_s(t)$ on $t$, $s$, and $G$. With an increase in $t$, we found a power law increase in $n_s(t)$ and total number of polymer chains $N_{\mathrm{total}}(t)$, given by $N_{\mathrm{total}}(t)~t^{\omega }$ and $n_s(t)~t^{\omega }$ with exponent $\omega =1.01(2)$ that was invariant for a range of $G=10$ to ${10}^4$. For small $s$ and $t={10}^3$, $5\times {10}^3$, and ${10}^4$, $n_s(t)$ decreased according to $n_s(t)~s^{-\tau }$ with $\tau =0.58(2)$. As $G$ was increased from $10$ to ${10}^4$, we observed a systematic influence of $G$ on the rescaled $n_s(t)$ data that prevented the manifestation of unique scaling function for polymer chain aggregates. The dependence of scaling functions of $n_s(t)$ on $G$ elucidates the sensitivity of polymer chain aggregates to $G$ and is thought to be a characteristic of VDP.

The differential elastic modulus of an active actomyosin network is computed as a function of applied stress, taking into account both thermal and motor contributions to filament compliance in the low-frequency domain. It is shown that, due to a dual nature of motor activity, increasing motor concentration may either stiffen the network due to stronger prestress or soften it due to motor agitation, in accordance with experimental data. Prestress anisotropy, which may be induced by redistribution of motors triggered by external force, causes anisotropy of the elastic moduli. This helps to explain the contradictory phenomena of cell fluidization and resolidification in response to transient stretch observed in recent experiments.

Particles embedded in a fluctuating interface experience forces and torques mediated by the deformations and by the thermal fluctuations of the medium. Considering a system of two cylinders bound to a fluid membrane, we show that the entropic contribution enhances the curvature-mediated repulsion between the two cylinders. This is contrary to the usual attractive Casimir force in the absence of curvature-mediated interactions. For a large distance between the cylinders, we retrieve the renormalization of the surface tension of a flat membrane due to thermal fluctuations.