The Poisson-Nernst-Planck (PNP) model has been widely used for analyzing impedance or dielectric spectra observed for dilute electrolytic cells. In the analysis, the behavior of mobile ions in the cell under an external electric field has been explained by a conductive nature regardless of ionic concentrations. However, if the cell has parallel-plate blocking electrodes, the mobile ions may also play a role as a dielectric medium in the cell by the effect of space-charge polarization when the ionic concentration is sufficiently low. Thus the mobile ions confined between the blocking electrodes can have conductive and dielectric natures simultaneously, and their intensities are affected by the ionic concentration and the adsorption of solvent molecules on the electrodes. The balance of the conductive and dielectric natures is quantitatively determined by introducing an effective dielectric constant to the PNP model in the data analysis. The generalized PNP model with the effective dielectric constant successfully explains the anomalous frequency-dependent dielectric behaviors brought about by the mobile ions in dilute electrolytic cells, for which the conventional PNP model fails in interpretation.

We explore the implications of the conservation law(s) and the corresponding so-called continuity equation(s), resulting from the coupling between the positional and the orientational order in main-chain polymer nematics, by showing that the vectorial and tensorial forms of these equations are in general not equivalent and cannot be reduced to one another, but neither are they disjoint alternatives. We analyze the relation between them and elucidate the fundamental role that the chain backfolding plays in the determination of their relative strength and importance. Finally, we show that the correct penalty potential in the effective free energy, implementing these conservation laws, should actually connect both the tensorial and the vectorial constraints. We show that the consequences of the polymer chains' connectivity for their consistent mesoscopic description are thus not only highly nontrivial but that its proper implementation is absolutely crucial for a consistent coarse-grained description of the main-chain polymer nematics.

The Richtmyer-Meshkov instability (RMI) mixing flow induced by a planar shock wave of Mach 1.6 is investigated using direct numerical simulation method. Interfacial perturbations of different scales between air and sulfur hexafluoride are introduced to study the effect of the initial conditions. Focus is placed on the analysis of the scale-to-scale transfer of kinetic energy in both Fourier and physical spaces. The kinetic energy injected from the perturbation scales is transferred to both larger and smaller scales in an average sense within the inner mixing zone (IMZ) at early times and is mainly passed down into smaller scales at the late stage. The physical-space energy flux due to the subgrid-scale (SGS) stress is studied using a filtering approach in order to shed light on the physical origin of the scale-to-scale kinetic energy transfer. It is found that the pointwise SGS energy flux is highly correlated with the local spike and bubble structures in the IMZ. Moreover, it turns out that the mean SGS energy flux is mainly ascribed to the component in the direction of shock wave propagation. An analysis using the method of conditional averaging manifests that the generation of local SGS energy flux is associated with the property of the surrounding flow induced by quadrupolar or dipolar vortex structures.

An analytical model of highly nonlinear oscillations occurring during a coalescence of two magnetic flux ropes, based upon two-fluid hydrodynamics, is developed. The model accounts for the effect of electric charge separation, and describes perpendicular oscillations of the current sheet formed by the coalescence. The oscillation period is determined by the current sheet thickness, the plasma parameter $\beta$, and the oscillation amplitude. The oscillation periods are typically greater or about the ion plasma oscillation period. In the nonlinear regime, the oscillations of the ion and electron concentrations have a shape of a narrow symmetric spikes.

This paper discusses some convergence properties in the entropic sampling Monte Carlo methods with multiple random walkers, particularly in the Wang-Landau (WL) and $1/t$ algorithms. The classical algorithms are modified by the use of $m$-independent random walkers in the energy landscape to calculate the density of states (DOS). The Ising model is used to show the convergence properties in the calculation of the DOS, as well as the critical temperature, while the calculation of the number $\pi$ by multiple dimensional integration is used in the continuum approximation. In each case, the error is obtained separately for each walker at a fixed time, $t$; then, the average over $m$ walkers is performed. It is observed that the error goes as $1/\sqrt{m}$. However, if the number of walkers increases above a certain critical value $m>m_x$, the error reaches a constant value (i.e., it saturates). This occurs for both algorithms; however, it is shown that for a given system, the $1/t$ algorithm is more efficient and accurate than the similar version of the WL algorithm. It follows that it makes no sense to increase the number of walkers above a critical value $m_x$, since it does not reduce the error in the calculation. Therefore, the number of walkers does not guarantee convergence.

We report a molecular dynamics simulation study of free-standing films of a blend of linear and cyclic polymer chains. We find that the composition of linear chains at the interface is enhanced relative to their bulk value for short chains but is depleted for long chains. Our findings are in agreement with recent experimental evidence reported for blends of short linear and cyclic polystyrene chains and highlight the genuine surface behavior in the short chain-length regime where theoretical predictions are more difficult. We highlight surface enrichment at low-energy surfaces as the result of competition between different entropic and enthalpic contributions to the interfacial free energy of the system.

We investigate the nonconserved critical dynamics of a nonlocal model Hamiltonian incorporating screened long-range interactions in the quartic term. Employing dynamic renormalization group analysis at one-loop order, we calculate the dynamic critical exponent $z=2+\epsilon f_1(\sigma ,\kappa ,n)+O\left({\epsilon }^2\right)$ and the linewidth exponent $w=-\sigma +\epsilon f_2(\sigma ,\kappa ,n)+O\left({\epsilon }^2\right)$ in the leading order of $\epsilon$, where $\epsilon =4-d+2\sigma$, with $d$ the space dimension, $n$ the number of components in the order parameter, and $\sigma$ and $\kappa$ the parameters coming from the nonlocal interaction term. The resulting values of linewidth exponent $w$ for a wide range of $\sigma$ is found to be in good agreement with the existing experimental estimates from spin relaxation measurements in perovskite manganite samples.

We study an integrable spin chain with three spin interactions and the staggered field $\left(\lambda \right)$ while the latter is quenched either slowly [in a linear fashion in time $\left(t\right)$ as $t/\tau$, where $t$ goes from a large negative value to a large positive value and $\tau$ is the inverse rate of quenching] or suddenly. In the process, the system crosses quantum critical points and gapless phases. We address the question whether there exist nonanalyticities [known as dynamical phase transitions (DPTs)] in the subsequent real-time evolution of the state (reached following the quench) governed by the final time-independent Hamiltonian. In the case of sufficiently slow quenching (when $\tau$ exceeds a critical value ${\tau }_1)$, we show that DPTs, of the form similar to those occurring for quenching across an isolated critical point, can occur even when the system is slowly driven across more than one critical point and gapless phases. More interestingly, in the anisotropic situation we show that DPTs can completely disappear for some values of the anisotropy term $\left(\gamma \right)$ and $\tau$, thereby establishing the existence of boundaries in the $\left(\gamma \text{−}\tau \right)$ plane between the DPT and no-DPT regions in both isotropic and anisotropic cases. Our study therefore leads to a unique situation when DPTs may not occur even when an integrable model is slowly ramped across a QCP. On the other hand, considering sudden quenches from an initial value ${\lambda }_i$ to a final value ${\lambda }_f$, we show that the condition for the presence of DPTs is governed by relations involving ${\lambda }_i,{\lambda }_f$, and $\gamma$, and the spin chain must be swept across $\lambda =0$ for DPTs to occur.

Symbolic sequences arising from the coarse graining of deterministic dynamical systems continuous in phase space are considered. The extent to which signatures of the time irreversibility and of the nonequilibrium constraints at the level of the original system, such as fluxes or dissipation, can be identified at the coarse-grained level is analyzed. The roles of the partition, of the time window, and of time averaging in distinguishing in a clear-cut way the equilibrium versus nonequilibrium character of the sequence are brought out.

The nonequilibrium and nonlinear defect modes (NNDMs), localized by a defect in a nonequilibrium microcavity-polariton condensate (MPC), are studied. There are three analytic solutions of NNDMs in a point defect: the bright NNDM, a bound state with two dark solitons for an attractive potential, and a gray soliton bound by a defect for a repulsive potential. We find that the stable NNDMs in a nonequilibrium MPC are the bright NNDM and gray soliton bound by a defect. The bright NNDM, which has the hyperbolic cotangent form, is a bright localized state existing in a uniform MPC. The bright NNDM is a unique state occurring in a nonequilibrium MPC that has pump-dissipation and repulsive-nonlinearity characters. No such state can exist in an equilibrium system with repulsive nonlinearity.

Time-averaged two-point currents are derived and shown to be spatially invariant within domains of local translation or inversion symmetry for arbitrary time-periodic quantum systems in one dimension. These currents are shown to provide a valuable tool for detecting deformations of a spatial symmetry in static and driven lattices. In the static case the invariance of the two-point currents is related to the presence of time-reversal invariance and/or probability current conservation. The obtained insights into the wave functions are further exploited for a symmetry-based convergence check which is applicable for globally broken but locally retained potential symmetries.

We analyze the stretching elasticity of a wormlike chain with a tension discontinuity resulting from a Hookean spring connecting its backbone to a fixed point. The elasticity of isolated semiflexible filaments has been the subject in a significant body of literature, primarily because of its relevance to the mechanics of biological matter. In real systems, however, these filaments are usually part of supramolecular structures involving cross-linkers or molecular motors, which cause tension discontinuities. Our model is intended as a minimal structural element incorporating such a discontinuity. We obtain analytical results in the weakly bending limit of the filament, concerning its force-extension relation and the response of the two parts in which the filament is divided by the spring. For a small tension discontinuity, the linear response of the filament extension to this discontinuity strongly depends on the external tension. For large external tension $f$, the spring force contributes a subdominant correction $\sim 1/f^{3/2}$ to the well-known $\sim 1/\sqrt{f}$-dependence of the end-to-end extension.

Concentration polarization can be induced by the unique ion-perm selectivity of small nanopores, leading to a salt concentration gradient across nanopores. This concentration gradient can create diffusio-osmosis and induce an electric field, affecting ionic currents on DNA that translocates through a nanopore. Here this influence is theoretically investigated by solving the continuum Poisson-Nernst-Planck model for different salt concentrations, DNA surface charge densities, and pore properties. By implementing the perturbation method, we can explicitly compute the contribution of concentration polarization to the ionic current. The induced electric field by concentration polarization is opposite to the imposed electric field and decreases the migration current, and the induced diffusio-osmosis can decrease the convection current as well. Our studies suggest that the importance of the concentration polarization can be determined by the parameter $\lambda /G$ where $\lambda$ is the double-layer thickness and $G$ is the gap size. When $\lambda /G$ is larger than a critical value, the influence of concentration polarization becomes more prominent. This conclusion is supported by the studies on the dependence of the ionic current on salt concentration and pore properties, showing that the difference between two models with and without accounting for concentration polarization is larger for low salts and small pores, which correspond to larger $\lambda /G$.

Based on the stochastic dynamics of interacting agents which reproduce, mutate, and die, the tangled nature model (TNM) describes key emergent features of biological and cultural ecosystems' evolution. While trait inheritance is not included in many applications, i.e., the interactions of an agent and those of its mutated offspring are taken to be uncorrelated, in the family of TNMs introduced in this work correlations of varying strength are parametrized by a positive integer $K$. We first show that the interactions generated by our rule are nearly independent of $K$. Consequently, the structural and dynamical effects of trait inheritance can be studied independently of effects related to the form of the interactions. We then show that changing $K$ strengthens the core structure of the ecology, leads to population abundance distributions better approximated by log-normal probability densities, and increases the probability that a species extant at time $t_w$ also survives at $t>t_w$. Finally, survival probabilities of species are shown to decay as powers of the ratio $t/t_w$, a so-called pure aging behavior usually seen in glassy systems of physical origin. We find a quantitative dynamical effect of trait inheritance, namely, that increasing the value of $K$ numerically decreases the decay exponent of the species survival probability.

We present a theoretical analysis of the dynamic stress-strain state of regions in a solid body that are involved in a collective elastic vortexlike motion. It is shown that the initiation of elastic vortexlike motion in the material is accompanied by the appearance of dilatancy and equivalent strain, the magnitudes of which are proportional to the square of the ratio of linear velocity on the periphery of the elastic vortex to the velocity of longitudinal elastic waves ($P$ wave). Under conditions of dynamic loading the described dynamic effects are able to initiate inelastic deformation or destruction of the material at loading speeds of a few percent of the $P$-wave speed. The obtained analytical estimates suggest that dynamic nonlinear strains can make a significant contribution in a number of widely studied nonlinear dynamic phenomena in solids. Among them are the effect of acoustic (dynamic) dilatancy in solids and granular media, which leads to the generation of longitudinal elastic waves by transverse waves [V. Tournat et al., Phys. Rev. Lett. 92, 085502 (2004)] and the formation of an array of intense “hot spots” (reminiscent of shear-induced hydrodynamic instabilities in fluids) in adiabatic shear bands [P. R. Guduru et al., Phys. Rev. E 64, 036128 (2001)].

When a planar shock hits a corrugated contact surface between two fluids, hydrodynamic perturbations are generated in both fluids that result in asymptotic normal and tangential velocity perturbations in the linear stage, the so called Richtmyer-Meshkov instability. In this work, explicit and exact analytical expansions of the asymptotic normal velocity ($\delta v_i^{\infty }$) are presented for the general case in which a shock is reflected back. The expansions are derived from the conservation equations and take into account the whole perturbation history between the transmitted and reflected fronts. The important physical limits of weak and strong shocks and the high/low preshock density ratio at the contact surface are shown. An approximate expression for the normal velocity, valid even for high compression regimes, is given. A comparison with recent experimental data is done. The contact surface ripple growth is studied during the linear phase showing good agreement between theory and experiments done in a wide range of incident shock Mach numbers and preshock density ratios, for the cases in which the initial ripple amplitude is small enough. In particular, it is shown that in the linear asymptotic phase, the contact surface ripple (${\psi }_i$) grows as ${\psi }_{\infty }+\delta v_i^{\infty }t$, where ${\psi }_{\infty }$ is an asymptotic ordinate different from the postshock ripple amplitude at $t=0+$. This work is a continuation of the calculations of F. Cobos Campos and J. G. Wouchuk, [Phys. Rev. E 90, 053007 (2014)] for a single shock moving into one fluid.

We study extreme-value statistics for spatially extended models exhibiting mixed-order phase transitions (MOT). These are phase transitions that exhibit features common to both first-order (discontinuity of the order parameter) and second-order (diverging correlation length) transitions. We consider here the truncated inverse distance squared Ising model, which is a prototypical model exhibiting MOT, and study analytically the extreme-value statistics of the domain lengths The lengths of the domains are identically distributed random variables except for the global constraint that their sum equals the total system size $L$. In addition, the number of such domains is also a fluctuating variable, and not fixed. In the paramagnetic phase, we show that the distribution of the largest domain length $l_{max}$ converges, in the large $L$ limit, to a Gumbel distribution. However, at the critical point (for a certain range of parameters) and in the ferromagnetic phase, we show that the fluctuations of $l_{max}$ are governed by novel distributions, which we compute exactly. Our main analytical results are verified by numerical simulations.

We investigate the origin of the scaling corrections in ballistic deposition models in high dimensions using the method proposed by Alves et al. [Phys. Rev. E 90, 052405 (2014)] in $d=2+1$ dimensions, where the intrinsic width associated with the fluctuations of the height increments during the deposition processes is explicitly taken into account. In the present work, we show that this concept holds for $d=3+1$ and $4+1$ dimensions. We have found that growth and roughness exponents and dimensionless cumulant ratios are in agreement with other models, presenting small finite-time corrections to the scaling, that in principle belong to the Kardar-Parisi-Zhang (KPZ) universality class in both $d=3+1$ and $4+1$. Our results constitute further evidence that the upper critical dimension of the KPZ class, if it exists, is larger than 4.

Acoustophoresis uses acoustic radiation force to remotely manipulate particles suspended in a host fluid for many scientific, technological, and medical applications, such as acoustic levitation, acoustic coagulation, contrast ultrasound imaging, ultrasound-assisted drug delivery, etc. To estimate the magnitude of acoustic radiation forces, equations derived for an inviscid host fluid are commonly used. However, there are theoretical predictions that, in the case of a traveling wave, viscous effects can dramatically change the magnitude of acoustic radiation forces, which make the equations obtained for an inviscid host fluid invalid for proper estimation of acoustic radiation forces. To date, experimental verification of these predictions has not been published. Experimental measurements of viscous effects on acoustic radiation forces in a traveling wave were conducted using a confocal optical and acoustic system and values were compared with available theories. Our results show that, even in a low-viscosity fluid such as water, the magnitude of acoustic radiation forces is increased manyfold by viscous effects in comparison with what follows from the equations derived for an inviscid fluid.

River bedforms arise as a result of morphological instabilities of the stream-sediment interface. Dunes and antidunes constitute the most typical patterns, and their occurrence and dynamics are relevant for a number of engineering and environmental applications. Although flow variability is a typical feature of all rivers, the bedform-triggering morphological instabilities have generally been studied under the assumption of a constant flow rate. In order to partially address this shortcoming, we here discuss the influence of (periodic) flow unsteadiness on bedform inception. To this end, our recent one-dimensional validated model coupling Dressler's equations with a refined mechanistic sediment transport formulation is adopted, and both the asymptotic and transient dynamics are investigated by modal and nonmodal analyses.