Animal locomotion activity relies on the generation and control of coordinated periodic actions in a central pattern generator (CPG). A core element of many CPGs responsible for the rhythm generation is a pair of reciprocally coupled neuron populations. Recent interest in the development of highly reduced models of CPG networks is motivated by utilization of CPG models in applications for biomimetic robotics. This paper considers the use of a reduced model in the form of a discrete time system to study the emergence of antiphase bursting activity in two reciprocally coupled populations evoked by the postinhibitory rebound effect.

We report a fluid system which exhibits chaotic dynamics under creeping flow conditions. A droplet in a uniform dc electric field deforms into an ellipsoid that can undergo irregular rotational motions. The nonlinear drop electrohydrodynamics is explained by a theoretical model which includes anisotropy in the polarization relaxation due to drop asphericity and charge convection due to rotational drop flow.

Magnetoelectric coupling—the ability of a material to magnetize upon application of an electric field and, conversely, to polarize under the action of a magnetic field—is rare and restricted to a rather small set of exotic hard crystalline materials. Intense research activity has recently ensued on materials development, fundamental scientific issues, and applications related to this phenomenon. This tantalizing property, if present in adequate strength at room temperature, can be used to pave the way for next-generation memory devices such as miniature magnetic random access memories and multiple state memory bits, sensors, energy harvesting, spintronics, among others. In this Rapid Communication, we prove the existence of an overlooked strain mediated nonlinear mechanism that can be used to universally induce the giant magnetoelectric effect in all (sufficiently) soft dielectric materials. For soft polymer foams—which, for instance, may be used in stretchable electronics—we predict room-temperature magnetoelectric coefficients that are comparable to the best known (hard) composite materials created. We also argue, based on a simple quantitative model, that magnetoreception in some biological contexts (e.g., birds) most likely utilizes this very mechanism.

Following our numerical work [Phys. Rev. Lett. 109, 170602 (2012)] focused upon the $2+1$ Kardar-Parisi-Zhang (KPZ) equation with flat initial condition, we return here to study, in depth, the three-dimensional (3D) radial KPZ problem, comparing common scaling phenomena exhibited by the pt-pt directed polymer in a random medium (DPRM), the stochastic heat equation (SHE) with multiplicative noise in three dimensions, and kinetic roughening phenomena associated with 3D Eden clusters. Examining variants of the 3D DPRM, as well as numerically integrating, via the Itô prescription, the constrained SHE for different values of the KPZ coupling, we provide strong evidence for universality within this 3D KPZ class, revealing shared values for the limit distribution skewness and kurtosis, along with universal first and second moments. Our numerical analysis of the 3D SHE, well flanked by the DPRM results, appears without precedent in the literature. We consider, too, the $2+1$ KPZ equation in the deeply evolved kinetically roughened stationary state, extracting the essential limit distribution characterizing fluctuations therein, revealing a higher-dimensional relative of the $1+1$ KPZ Baik-Rains distribution. Complementary, corroborative findings are provided via the Gaussian DPRM, as well as the restricted-solid-on-solid model of stochastic growth, stalwart members of the $2+1$ KPZ class. Next, contact is made with a recent nonperturbative, field-theoretic renormalization group calculation for the key universal amplitude ratio in this context. Finally, in the crossover from transient to stationary-state statistics, we observe a higher dimensional manifestation of the skewness minimum discovered by Takeuchi [Phys. Rev. Lett. 110, 210604 (2013)] in $1+1$ KPZ class liquid-crystal experiments.

The determination of the transport properties of heterogeneous porous rocks, such as an effective hydraulic conductivity, arises in a range of geoscience problems, from groundwater flow analysis to hydrocarbon reservoir modeling. In the presence of formation-scale heterogeneities, nonstationary flows, induced by pumping tests or propagating elastic waves, entail localized pressure diffusion processes with a characteristic frequency depending on the pressure diffusivity and size of the heterogeneity. Then, on a macroscale, a homogeneous equivalent medium exists, which has a frequency-dependent effective conductivity. The frequency dependence of the conductivity can be analyzed with Biot's equations of poroelasticity. In the quasistatic frequency regime of this framework, the slow compressional wave is a proxy for pressure diffusion processes. This slow compressional wave is associated with the out-of-phase motion of the fluid and solid phase, thereby creating a relative fluid-solid displacement vector field. Decoupling of the poroelasticity equations gives a diffusion equation for the fluid-solid displacement field valid in a poroelastic medium with spatial fluctuations in hydraulic conductivity. Then, an effective conductivity is found by a Green's function approach followed by a strong-contrast perturbation theory suggested earlier in the context of random dielectrics. This theory leads to closed-form expressions for the frequency-dependent effective conductivity as a function of the one- and two-point probability functions of the conductivity fluctuations. In one dimension, these expressions are consistent with exact solutions in both low- and high-frequency limits for arbitrary conductivity contrast. In 3D, the low-frequency limit depends on the details of the microstructure. However, the derived approximation for the effective conductivity is consistent with the Hashin-Shtrikman bounds.

We study a one-dimensional totally asymmetric simple exclusion process with one special site from which particles fly to any empty site (not just to the neighboring site). The system attains a nontrivial stationary state with a density profile varying over the spatial extent of the system. The density profile undergoes a nonequilibrium phase transition when the average density passes through the critical value $1-{\left[4(1-\ln 2)\right]}^{-1}=0.185277...,$ viz., in addition to the discontinuity in the vicinity of the special site, a shock wave is formed in the bulk of the system when the density exceeds the critical density.

We couple the recently developed self-learning metabasin escape algorithm, which enables efficient exploration of the potential energy surface (PES), with shear deformation to elucidate strain-rate and temperature effects on the shear transformation zone (STZ) characteristics in two-dimensional amorphous solids. In doing so, we report a transition in the STZ characteristics that can be obtained through either increasing the temperature or decreasing the strain rate. The transition separates regions having two distinct STZ characteristics. Specifically, at high temperatures and high strain rates, we show that the STZs have characteristics identical to those that emerge from purely strain-driven, athermal quasistatic atomistic calculations. At lower temperatures and experimentally relevant strain rates, we use the newly coupled PES $+$ shear deformation method to show that the STZs have characteristics identical to those that emerge from a purely thermally activated state. The specific changes in STZ characteristics that occur in moving from the strain-driven to thermally activated STZ regime include a 33% increase in STZ size, faster spatial decay of the displacement field, a change in the deformation mechanism inside the STZ from shear to tension, a reduction in the stress needed to nucleate the first STZ, and finally a notable loss in characteristic quadrupolar symmetry of the surrounding elastic matrix that has previously been seen in athermal, quasistatic shear studies of STZs.

When thin films are grown on a substrate by chemical vapor deposition, the evolution of the first deposited layers may be described, on mesoscopic scales, by dynamical models of the reaction-diffusion type. For monatomic layers, such models describe the evolution of atomic coverage due to the combined effect of reaction terms representing adsorption-desorption and chemical processes and nonlinear diffusion terms that are of the Cahn-Hilliard type. This combination may lead, below a critical temperature, to the instability of uniform deposited layers. This instability triggers the formation of nanostructures corresponding to regular spatial variations of substrate coverage. Patterns wavelengths and symmetries are selected by dynamical variables and not by variational arguments. According to the balance between reaction- and diffusion-induced nonlinearities, a succession of nanostructures including hexagonal arrays of dots, stripes, and localized structures of various types may be obtained. These structures may initiate different growth mechanisms, including Volmer-Weber and Frank–Van der Merwe types of growth. The relevance of this approach to the study of deposited layers of different species is discussed.

The interplay between liquid crystallinity and microphase separation in comblike liquid-crystalline diblock copolymers is examined via a Brazovskii-type phenomenological model using both analytical and numerical calculations. For symmetric diblock copolymers we determine a critical electric field that is required to tilt the orientation of the constituent liquid crystals of the polymer side chains in the microphase-separated lamellar state. Such electrically induced reorientation of the liquid-crystal molecules can lead to substantially large changes of lamellar periodicity. Our numerical results show that highly aligned polymer lamellar domains can self-assemble when the liquid-crystal ordering precedes microphase separation, and that weak electric fields can be used to direct the self-assembly process due to the dielectric anisotropy of the liquid-crystal side chains. We also find that phase separation of asymmetric diblock copolymers can coexist with a network of liquid-crystal nematic orientations, with domain morphology depending on the details of copolymer and liquid-crystal coupling.

We study the effects of cisplatin on the circular configuration of DNA using atomic force microscopy (AFM) and observe that the DNA gradually transforms to a complex configuration with an intersection and interwound structures from a circlelike structure. An algorithm is developed to extract the configuration profiles of circular DNA from AFM images and the radius of gyration is used to describe the flexibility of circular DNA. The quantitative analysis of the circular DNA demonstrates that the radius of gyration gradually decreases and two processes on the change of flexibility of circular DNA are found as the cisplatin concentration increases. Furthermore, a model is proposed and discussed to explain the mechanism for understanding the complicated interaction between DNA and cisplatin.

Time-varying networks play an important role in the investigation of the stochastic processes that occur on complex networks. The ability to formulate the development of the network topology on the same time scale as the evolution of the random process is important for a variety of applications, including the spreading of diseases. Past contributions have investigated random processes on time-varying networks with a purely random attachment mechanism. The possibility of extending these findings towards a time-varying network that is driven by mutual attractiveness is explored in this paper. Mutual attractiveness models are characterized by a linking function that describes the probability of the existence of an edge, which depends mutually on the attractiveness of the nodes on both ends of that edge. This class of attachment mechanisms has been considered before in the fitness-based complex networks literature but not on time-varying networks. Also, the impact of mutual selection is investigated alongside opinion formation and epidemic outbreaks. We find closed-form solutions for the quantities of interest using a factorizable linking function. The voter model exhibits an unanticipated behavior as the network never reaches consensus in the case of mutual selection but stays forever in its initial macroscopic configuration, which is a further piece of evidence that time-varying networks differ markedly from their static counterpart with respect to random processes that take place on them. We also find that epidemic outbreaks are accelerated by uncorrelated mutual selection compared to previously considered random attachment.

Recent progress in Kalman filters to estimate states and parameters in nonlinear systems has provided the possibility of applying such approaches to neural systems. We here apply the nonlinear method of unscented Kalman filters (UKFs) to observe states and estimate parameters in a neural mass model that can simulate distinct rhythms in electroencephalography (EEG) including dynamical evolution during epilepsy seizures. We demonstrate the efficiency of the UKF in estimating states and parameters. We also develop an UKF-based control strategy to modulate the dynamics of the neural mass model. In this strategy the UKF plays the role of observing states, and the control law is constructed via the estimated states. We demonstrate the feasibility of using such a strategy to suppress epileptiform spikes in the neural mass model.

We introduce a method to obtain steady-state uniaxial exponential-stretching flow of a fluid (akin to extensional flow) in the incompressible limit, which enables us to study the response of suspended macromolecules to the flow by computer simulations. The flow field in this flow is defined by $v_x=\epsilon x$, where $v_x$ is the velocity of the fluid and $\epsilon$ is the stretch flow gradient. To eliminate the effect of confining boundaries, we produce the flow in a channel of uniform square cross section with periodic boundary conditions in directions perpendicular to the flow, but simultaneously maintain uniform density of fluid along the length of the tube. In experiments a perfect elongational flow is obtained only along the axis of symmetry in a four-roll geometry or a filament-stretching rheometer. We can reproduce flow conditions very similar to extensional flow near the axis of symmetry by exponential-stretching flow; we do this by adding the right amounts of fluid along the length of the flow in our simulations. The fluid particles added along the length of the tube are the same fluid particles which exit the channel due to the flow; thus mass conservation is maintained in our model by default. We also suggest a scheme for possible realization of exponential-stretching flow in experiments. To establish our method as a useful tool to study various soft matter systems in extensional flow, we embed (i) spherical colloids with excluded volume interactions (modeled by the Weeks-Chandler potential) as well as (ii) a bead-spring model of star polymers in the fluid to study their responses to the exponential-stretched flow and show that the responses of macromolecules in the two flows are very similar. We demonstrate that the variation of number density of the suspended colloids along the direction of flow is in tune with our expectations. We also conclude from our study of the deformation of star polymers with different numbers of arms $f$ that the critical flow gradient ${\epsilon }_c$ at which the star undergoes the coil-to-stretch transition is independent of $f$ for $f=2,5,10$, and 20.

We propose a simple and analytically solvable model for a motor that generates mechanical motion by exploiting an entropic force arising from the topology of the underlying phase space. We show that the generation of mechanical forces in our system is surprisingly robust to local changes in kinetic and topological parameters. Furthermore, we find that the efficiency at maximum power of the motor may show discontinuities.

Despite the fact that the localization-delocalization transition (LDT) widely exists in wave systems, quantitative studies on its critical and multifractal properties are mainly focused on solids. In this work, these properties are investigated on the vibrational motions of liquid water. Simulations of up to $18000$ molecules on the flexible extended simple point charge water model provide nearly ${10}^6$ instantaneous normal modes. They are shown to undergo an LDT close to the translational transition and exhibit multifractal fluctuations while approaching the LDT. In combination with finite-size scaling, multifractal analysis predicts the critical frequency Im$\left({\omega }_c\right)\approx -131.6$ cm${}^{-1}$ for unstable modes at room temperature. The estimated critical exponent $\nu \approx 1.60$ is close to those of other calculated systems in the same Wigner-Dyson class. At the LDT, the fractal spectrum $f\left(\alpha \right)$ and the most probable local vibrational intensity ${\alpha }_{mc}\approx 4.04$ coincide with those of the Anderson model, which might be additional universal properties of LDT in more general wave systems. The results extend the validity of the multifractal scaling approach beyond Andersonian systems to a Hessian system.

Many critical properties of the Hintermann-Merlini model are known exactly through the mapping to the eight-vertex model. Wu [J. Phys. C 8, 2262 (1975)] calculated the spontaneous magnetizations of the model on two sublattices by relating them to the conjectured spontaneous magnetization and polarization of the eight-vertex model, respectively. The latter conjecture remains unproved. In this paper we numerically study the critical properties of the model by means of a finite-size scaling analysis based on transfer matrix calculations and Monte Carlo simulations. All analytic predictions for the model are confirmed by our numerical results. The central charge $c=1$ is found for the critical manifold investigated. In addition, some unpredicted geometric properties of the model are studied. Fractal dimensions of the largest Ising clusters on two sublattices are determined. The fractal dimension of the largest Ising cluster on the sublattice $A$ takes a fixed value $D_a=1.888\left(2\right)$, while that for sublattice $B$ varies continuously with the parameters of the model.

We present a new mode of transport of spherical particles in a horizontally vibrated channel with sawtooth-shaped side walls. The underlying driving mechanism is based on an interplay of directional energy injection transformed by the sidewall collisions and density-dependent interparticle collisions. Experiments and matching numerics show that the average particle velocity reaches a maximum at 60% of the maximal filling density. Introducing a spatial phase shift between the channel boundaries increases the transport velocity by an order of magnitude.

Various dynamical systems with many degrees of freedom display avalanche dynamics, which is characterized by scale invariance reflected in power-law statistics. The superposition of avalanche processes in real systems driven at a finite velocity may influence the experimental determination of the underlying power law. The present paper reports results of an investigation of this effect using the example of acoustic emission (AE) accompanying plastic deformation of crystals. Indeed, recent studies of AE did not only prove that the dynamics of crystal defects obeys power-law statistics, but also led to a hypothesis of universality of the scaling law. We examine the sensitivity of the apparent statistics of AE to the parameters applied to individualize AE events. Two different alloys, MgZr and AlMg, both displaying strong AE but characterized by different plasticity mechanisms, are investigated. It is shown that the power-law indices display a good robustness in wide ranges of parameters even in the conditions leading to very strong superposition of AE events, although some deviations from the persistent values are also detected. The totality of the results confirms the scale-invariant character of deformation processes on the scale relevant to AE, but uncovers essential differences between the power-law exponents found for two kinds of alloys.

Creasing and wrinkling are different types of instabilities on material surfaces characterized by localized singular folds and continuously smooth undulation, respectively. While it is known that electric fields can induce both types of instabilities in elastomer films bonded on substrates, the relation and transition between the field-induced instabilities have not been analyzed or understood. We show that the surface energy, modulus, and thickness of the elastomer determine the types, critical fields, and wavelengths of the instabilities. By independently varying these parameters of elastomers under electric fields, our experiments demonstrate transitions between creases with short wavelengths and wrinkles with long wavelengths. We further develop a unified theoretical model that accounts for both creasing and wrinkling instabilities induced by electric fields and predicts their transitions. The experimental data agree well with the theoretical model.