Collective behavior of self-propelled particles is observed on a microscale for swimmers such as sperm and bacteria as well as for protein filaments in motility assays. The properties of such systems depend both on their dimensionality and the interactions between their particles. We introduce a model for self-propelled rods in two dimensions that interact via a separation-shifted Lennard-Jones potential. Due to the finite potential barrier, the rods are able to cross. This model allows us to efficiently simulate systems of self-propelled rods that effectively move in two dimensions but can occasionally escape to the third dimension in order to pass each other. Our quasi-two-dimensional self-propelled particles describe a class of active systems that encompasses microswimmers close to a wall and filaments propelled on a substrate. Using Monte Carlo simulations, we first determine the isotropic-nematic transition for passive rods. Using Brownian dynamics simulations, we characterize cluster formation of self-propelled rods as a function of propulsion strength, noise, and energy barrier. Contrary to rods with an infinite potential barrier, an increase of the propulsion strength does not only favor alignment but also effectively decreases the potential barrier that prevents crossing of rods. We thus find a clustering window with a maximum cluster size at medium propulsion strengths.

In this study we model population dynamics in a three-species food web with heterogeneous resources and intraguild predation by using a nonspatial Lotka-Volterra system with a density-dependent interaction of resource items. The model consists of two predators with an intraguild predation (IGP) relation competing for a common resource. The resource is subdivided into subpopulations of different quality that are distinguished by grazing rates of the two predators, contact rates between subpopulations and mortality rates. The proposed system describes an exchange of traits between species from distinct subpopulations by using a species interaction term. In particular, we examine the percentage of stable coexistence solutions versus resource carrying capacity and contact rates between distinct resource pools. We also present a numerical comparison of the percentage of stable food webs found for different numbers of subpopulations. While at high enrichment no stable coexistence was found in the IGP system with a single resource, our model predicts a stable coexistence of two IGP-related predators and resources at high and intermediate enrichment already at a low contact rate between subpopulations.

The dynamics of scroll waves with a variable orientation to a vertically oriented gradient of excitability is studied by optical tomography in the ferroin-catalyzed Belousov-Zhabotinsky reaction. An almost perpendicular orientation between the scroll wave and gradient induces a pair of twists of opposite handedness on the scroll wave. The position of the nodal plane formed between the twists is governed by the time delay of the twist formation and therefore leads to a symmetric or asymmetric twisted scroll wave. Larger inclinations between scroll wave and gradient cause a drift of the filament along the reactor wall until it reaches the bottom of the reaction container. In this case, the scroll wave does not twist, suggesting that a drift acts as an alternative mechanism of responding to the gradient.

We study how reliably generalized synchronization can be detected and characterized from time-series analysis. To that end, we analyze synchronization in a generalized sense of delay-coupled chaotic oscillators in unidirectional ring configurations. The generalized synchronization condition can be verified via the auxiliary system approach; however, in practice, this might not always be possible. Therefore, in this study, widely used indicators to directly quantify generalized and phase synchronization from noise-free time series of two oscillators are employed complementarily to the auxiliary system approach. In our analysis, none of the indices provide the consistent results of the auxiliary system approach. Our findings indicate that it is a major challenge to directly detect synchronization in a generalized sense between two oscillators that are connected via a chain of other oscillators, even if the oscillators are identical. This has major consequences for the interpretation of the dynamics of coupled systems and applications thereof.

We study analytically the instability of the subharmonic resonances in magnetogravity waves excited by a (vertical) time-periodic shear for an inviscid and nondiffusive unbounded conducting fluid. Due to the fact that the magnetic potential induction is a Lagrangian invariant for magnetohydrodynamic Euler-Boussinesq equations, we show that plane-wave disturbances are governed by a four-dimensional Floquet system in which appears, among others, the parameter $\varepsilon$ representing the ratio of the periodic shear amplitude to the vertical Brunt-Väisälä frequency $N_3$. For sufficiently small $\varepsilon$ and when the magnetic field is horizontal, we perform an asymptotic analysis of the Floquet system following the method of Lebovitz and Zweibel [Astrophys. J. 609, 301 (2004)]. We determine the width and the maximal growth rate of the instability bands associated with subharmonic resonances. We show that the instability of subharmonic resonance occurring in gravity shear waves has a maximal growth rate of the form ${\Delta }_m=(3\sqrt{3}/16)\varepsilon$. This instability persists in the presence of magnetic fields, but its growth rate decreases as the magnetic strength increases. We also find a second instability involving a mixing of hydrodynamic and magnetic modes that occurs for all magnetic field strengths. We also elucidate the similarity between the effect of a vertical magnetic field and the effect of a vertical Coriolis force on the gravity shear waves considering axisymmetric disturbances. For both cases, plane waves are governed by a Hill equation, and, when $\varepsilon$ is sufficiently small, the subharmonic instability band is determined by a Mathieu equation. We find that, when the Coriolis parameter (or the magnetic strength) exceeds $N_3/2$, the instability of the subharmonic resonance vanishes.

We investigate the evolution and stability of a decaying magnetohydrodynamic Taylor-Green flow, using pseudospectral simulations with resolutions up to ${2048}^3$. The chosen flow has been shown to result in a steep total energy spectrum with power law behavior $k^{-2}$. We study the symmetry breaking of this flow by exciting perturbations of different amplitudes. It is shown that for any finite amplitude perturbation there is a high enough Reynolds number for which the perturbation will grow enough at the peak of dissipation rate resulting in a nonlinear feedback into the flow and subsequently break the Taylor-Green symmetries. In particular, we show that symmetry breaking at large scales occurs if the amplitude of the perturbation is ${\sigma }_{\mathrm{crit}}\sim {\mathrm{Re}}^{-1}$ and at small scales occurs if ${\sigma }_{\mathrm{crit}}\sim {\mathrm{Re}}^{-3/2}$. This symmetry breaking modifies the scaling laws of the energy spectra at the peak of dissipation rate away from the $k^{-2}$ scaling and towards the classical $k^{-5/3}$ and $k^{-3/2}$ power laws.

Development of steady state thermodynamics and statistical mechanics depends crucially on our ability to extend the notions of equilibrium thermodynamics to nonequilibrium steady states (NESS). The present paper considers the extension of heat capacity. A modified definition is proposed which continues to maintain the same relation to steady state Shannon entropy as in equilibrium, thus providing a thermodynamically consistent treatment of NESS heat capacity.

We present a theoretical investigation of thermal fluctuation statistics in a molecular motor. Energy transfer in the motor is described using a multidimensional discrete master equation with nearest-neighbor hopping. In this theory, energy transfer leads to statistical correlations between thermal fluctuations in different degrees of freedom. For long times, the energy transfer is a multivariate diffusion process with constant drift and diffusion. The fluctuations and drift align in the strong-coupling limit enabling a one-dimensional description along the coupled coordinate. We derive formal expressions for the probability distribution and simulate single trajectories of the system in the near- and far-from-equilibrium limits both for strong and weak coupling. Our results show that the hopping statistics provide an opportunity to distinguish different operating regimes.

In this paper we consider a model of accelerated dynamics with the rules modified from those of the recently proposed [Dong et al., Phys. Rev. Lett. 109, 130602 (2012)] accelerated exclusion process (AEP) such that particle-vacancy symmetry is restored to facilitate a mapping to a solid-on-solid growth model in $1+1$ dimensions. In addition to kicking a particle ahead of the moving particle, as in the AEP, in our model another particle from behind is drawn, provided it is within the “distance of interaction” denoted by ${\ell }_{\max }$. We call our model the doubly accelerated exclusion process (DAEP). We observe accelerated transport and interface growth and widening of the cluster size distribution for cluster sizes above ${\ell }_{\max }$, when compared with the ordinary totally asymmetric exclusion process (TASEP). We also characterize the difference between the TASEP, AEP, and DAEP by computing a “staggered” order parameter, which reveals the local order in the steady state. This order in part explains the behavior of the particle current as a function of density. The differences of the steady states are also reflected by the behavior of the temporal and spatial correlation functions in the interface picture.

We study the entropy and information flow in a Maxwell-demon device based on a single-electron transistor with controlled gate potentials. We construct the protocols for measuring the charge states and manipulating the gate voltages, which minimizes irreversibility for (i) constant input power from the environment or (ii) given energy gain. Charge measurement is modeled by a series of detector readouts for time-dependent gate potentials, and the amount of information obtained is determined. The protocols optimize irreversibility that arises due to (i) enlargement of the configuration space on opening the barriers, and (ii) finite rate of operation. These optimal protocols are general and apply to all systems in which barriers between different regions can be manipulated.

We show that in order to describe the isotropic-nematic transition in stripe-forming systems with isotropic competing interactions of the Brazovskii class it is necessary to consider the next to leading order in a $1/N$ approximation for the effective Hamiltonian. This can be conveniently accomplished within the self-consistent screening approximation. We solve the relevant equations and show that the self-energy in this approximation is able to generate the essential wave vector dependence to account for the anisotropic character of a two-point correlation function characteristic of a nematic phase.

We investigate the approach to catastrophic failure in a model porous granular material undergoing uniaxial compression. A discrete element computational model is used to simulate both the microstructure of the material and the complex dynamics and feedbacks involved in local fracturing and the production of crackling noise. Under strain-controlled loading, microcracks initially nucleate in an uncorrelated way all over the sample. As loading proceeds the damage localizes into a narrow damage band inclined at 30${}^{\circ }$–45${}^{\circ }$ to the load direction. Inside the damage band the material is crushed into a poorly sorted mixture of mainly fine powder hosting some larger fragments. The mass probability density distribution of particles in the damage zone is a power law of exponent 2.1, similar to a value of 1.87 inferred from observations of the length distribution of wear products (gouge) in natural and laboratory faults. Dynamic bursts of radiated energy, analogous to acoustic emissions observed in laboratory experiments on porous sedimentary rocks, are identified as correlated trails or cascades of local ruptures that emerge from the stress redistribution process. As the system approaches macroscopic failure consecutive bursts become progressively more correlated. Their size distribution is also a power law, with an equivalent Gutenberg-Richter $b$ value of 1.22 averaged over the whole test, ranging from 3 to 0.5 at the time of failure, all similar to those observed in laboratory tests on granular sandstone samples. The formation of the damage band itself is marked by a decrease in the average distance between consecutive bursts and an emergent power-law correlation integral of event locations with a correlation dimension of 2.55, also similar to those observed in the laboratory (between 2.75 and 2.25).

We generate jammed disordered packings of $100\le N\le 2000$ monodisperse hard spheres in three dimensions whose strictly jammed backbones are demonstrated to be exactly isostatic with unprecedented numerical accuracy. This is accomplished by using the Torquato-Jiao (TJ) packing algorithm as a means of studying the maximally random jammed (MRJ) state. The rattler fraction of these packings converges towards $0.015$ in the infinite-system limit, which is markedly lower than previous estimates for the MRJ state using the Lubachevsky-Stillinger protocol. This is because the packings that the TJ algorithm creates are closer to the true MRJ state, as shown using bond-orientational and translational order metrics. The rattler pair correlation statistics exhibit strongly correlated behavior contrary to the conventional understanding that they be randomly (Poisson) distributed. Dynamically interacting “polyrattlers” may be found imprisoned in shared cages as well as interacting through “bottlenecks” in the backbone and these clusters are mainly responsible for the sharp increase in the rattler pair correlation function near contact. We discover the surprising existence of polyrattlers with cluster sizes of up to five rattlers (which is expected to increase with system size) and present a distribution of polyrattler occurrence as a function of cluster size and system size. We also enumerate all of the rattler interaction topologies we observe and present images of several examples, showing that MRJ packings of monodisperse spheres can contain large rattler cages while still obeying the strict jamming criterion. The backbone spheres that encage the rattlers are significantly hypostatic, implying that correspondingly hyperstatic regions must exist elsewhere in these isostatic packings. We also observe that rattlers in hard-sphere packings share an apparent connection with the low-temperature two-level system anomalies that appear in real amorphous insulators and semiconductors.

The parametric instability in nematic liquid crystal layers has been studied using linear stability theory. Using material parameters of typical nematics, the neutral stability curve and dispersion relation of a system that presents critical subharmonic waves is obtained. The critical acceleration and wave number of the unstable stationary waves are discontinuous at the nematic-isotropic transition temperature and conform to similar sharp changes experienced by the viscosities and surface tension as a function of temperature. Due to Marangoni flow the curve of the critical acceleration as a function of excitation frequency exhibits a minimum. If the Marangoni flow is neglected and the dynamical viscosity is increased, a monotonously increasing dependence of the acceleration in terms of oscillation frequency is observed. A bicritical instability is reached for a layer thickness of a few millimeters. A well-defined subharmonic wave is attained when the thickness of the layer is further increased. The dispersion relation of these waves displays a discontinuous shift at high frequencies due to alternating secondary thresholds of Faraday waves. At negligible external forcing we determined the dispersion relationship of thermal surface waves.

The dynamics of droplet spreading on two-dimensional wicking surfaces were studied using square arrays of Si nanopillars. It was observed that the wicking film always precedes the droplet edge during the spreading process causing the droplet to effectively spread on a Cassie-Baxter surface composed of solid and liquid phases. Unlike the continual spreading of the wicking film, however, the droplet will eventually reach a shape where further spreading becomes energetically unfavorable. In addition, we found that the displacement-time relationship for droplet spreading follows a power law that is different from that of the wicking film. A quantitative model was put forth to derive this displacement-time relationship and predict the contact angle at which the droplet will stop spreading. The predictions of our model were validated with experimental data and results published in the literature.

Adsorption thermodynamics of interacting particles adsorbed on icosahedral and truncated octahedral nanoparticles was studied by a detailed mean-field approximation and Monte Carlo simulations. The nanoparticle is tackled as a multivariate surface, where different types of adsorption sites occur according to coordination with nearest neighbors. In addition, lateral couplings between the adsorbed particles are considered. The analysis covers a wide range of interactions, extending from physical to strong chemical bonds, and different sizes and shapes of nanoparticles.

Based on a continuum theory, we investigate the manipulation of the nonequilibrium behavior of a sheared liquid crystal via closed-loop feedback control. Our goal is to stabilize a specific dynamical state, that is, the stationary “flow alignment,” under conditions where the uncontrolled system displays oscillatory director dynamics with in-plane symmetry. To this end we employ time-delayed feedback control (TDFC), where the equation of motion for the $i$th component $q_i\left(t\right)$ of the order parameter tensor is supplemented by a control term involving the difference $q_i\left(t\right)-q_i(t-\tau )$. In this diagonal scheme, $\tau$ is the delay time. We demonstrate that the TDFC method successfully stabilizes flow alignment for suitable values of the control strength $K$ and $\tau$; these values are determined by solving an exact eigenvalue equation. Moreover, our results show that only small values of $K$ are needed when the system is sheared from an isotropic equilibrium state, contrary to the case where the equilibrium state is nematic.

When nematic liquid crystals are embedded in random polymer networks, the disordered environment disrupts the long-range order, producing a glassy state. If an electric field is applied, it induces large and fairly temperature-independent orientational order. To understand the experiments, we simulate a liquid crystal in a disordered polymer network, visualize the domain structure, and calculate the response to a field. Furthermore, using an Imry-Ma-like approach we predict the domain size and estimate the field-induced order. The simulations and analytic results agree with each other, and suggest how the materials can be optimized for electro-optic applications.

We report an unusual temperature dependence of the elastic constants of a rodlike nematic liquid crystal (RLC) mixed with a highly kinked bent-core liquid crystal (BLC). On cooling through the nematic phase, the splay elastic constant ($K_{11}$) of the RLC-BLC mixture increased below the nematic-isotropic phase transition temperature, but started to decrease midway through the nematic phase. The decrease of $K_{11}$ was more prominent with a greater concentration of BLC. On the other hand, the bend elastic constant ($K_{33}$) of the RLC-BLC mixture monotonically increased through the nematic phase with decreasing temperature.

We employ nuclear magnetic resonance microimaging to study the kinetics of a high-swelling ionic polymer gel. This includes the time evolution of the sphere diameter and also the evolution of the swollen-unswollen boundary. The experimental results for spherical ionic polyacrylamide gels are compared with the predictions of a nonlinear poroelastic theory by numerically solving the equations for the evolution.