We study the coupling between backward- and forward-propagating wave modes, with the same group velocity, in a composite right- and left-handed nonlinear transmission line. Using an asymptotic multiscale expansion technique, we derive a system of two coupled nonlinear Schrödinger equations governing the evolution of the envelopes of these modes. We show that this system supports a variety of backward- and forward-propagating vector solitons of the bright-bright, bright-dark, and dark-bright type. Performing systematic numerical simulations in the framework of the original lattice that models the transmission line, we study the propagation properties of the derived vector soliton solutions. We show that all types of the predicted solitons exist, but differ on their robustness: Only bright-bright solitons propagate undistorted for long times, while the other types are less robust, featuring shorter lifetimes. In all cases, our analytical predictions are in very good agreement with the results of the simulations, at least up to times of the order of the solitons’ lifetimes.

We formulate a phase-field, or diffuse-interface, model for the evolution of stepped surfaces under surface diffusion in the presence of distinct material parameters across nanoscale terraces. In the sharp-interface limit, our model reduces to a Burton-Cabrera-Frank (BCF)-type theory for the motion of noninteracting steps separating inhomogeneous terraces. This setting aims to capture features of reconstructed semiconductor, e.g., Si surfaces below the roughening transition. Our work forms an extension of the phase-field construction by Hu et al. [Physica D 241, 77 (2012)].

We investigate the relaxation time of magnetization or the lifetime of the metastable state for a spin $S=1$ square-lattice ferromagnetic Blume-Capel model with distribution of magnetic anisotropy (with small variances), using two different dynamics such as Glauber and phonon-assisted dynamics. At each lattice site, the Blume-Capel model allows three spin projections ($+$1, 0, $-$1) and a site-dependent magnetic anisotropy parameter. For each dynamic, we examine the low-temperature lifetime in two dynamic regions with different sizes of the critical droplet and at the boundary between the regions, within the single-droplet regime. We compute the average lifetime of the metastable state for a fixed lattice size, using both kinetic Monte Carlo simulations and the absorbing Markov chains method in the zero-temperature limit. We find that for both dynamics the lifetime obeys a modified Arrhenius-like law, where the energy barrier of the metastable state depends on the temperature and standard deviation of the distribution of magnetic anisotropy for a given field and magnetic anisotropy and that an explicit form of this dependence differs in different dynamic regions for different dynamics. Interestingly, the phonon-assisted dynamic prevents transitions between degenerate states, which results in a large increase in the energy barrier at the region boundary compared to that for the Glauber dynamic. However, the introduction of a small distribution of magnetic anisotropy allows the spin system to relax via lower-energy pathways such that the energy barrier greatly decreases. In addition, for the phonon-assisted dynamic, even the prefactor of the lifetime is substantially reduced for a broad distribution of magnetic anisotropy in both regions considered, in contrast to the Glauber dynamic. Our findings show that overall the phonon-assisted dynamic is more significantly affected by the distribution of magnetic anisotropy than the Glauber dynamic.

We investigate the density decay in the pair-annihilation process $A+A\to \varnothing$ in the case when the particles perform anomalous diffusion on a cubic lattice. The anomalous diffusion is realized via Lévy flights, which are characterized by long-range jumps and lead to superdiffusive behavior. As a consequence, the critical dimension depends continuously on the control parameter of the Lévy flight distribution. This instance is used to study the system close to the critical dimension by means of the nonperturbative renormalization group theory. Close to the critical dimension, the assumption of well-stirred reactants is violated by anticorrelations between the particles, and the law of mass action breaks down. The breakdown of the law of mass action is known to be caused by long-range fluctuations. We identify three interrelated consequences of these fluctuations. First, despite being a nonuniversal quantity and thus depending on the microscopic details, the renormalized reaction rate ${\lambda }_0$ can be approximated by a universal law close to the critical dimension. The emergence of universality relies on the fact that long-range fluctuations suppress the influence of the underlying microscopic details. Second, as criticality is approached, the macroscopic reaction rate decreases such that the law of mass action loses its significance. And third, additional nonanalytic power law corrections complement the analytic law of mass action term. An increasing number of those corrections accumulate and give an essential contribution as the critical dimension is approached. We test our findings for two implementations of Lévy flights that differ in the way they cross over to the normal diffusion in the limit $\sigma \to 2$.

We show via counterexamples that relative entropy between the solution of a Markovian master equation and the steady state is not a convex function of time. We thus disprove the hypotheses that a general evolution principle of thermodynamics based on the decrease of the nonadiabatic entropy production could hold. However, we argue that a large separation of typical decay times is necessary for nonconvex solutions to occur, making concave transients extremely short lived with respect to the main relaxation modes. We describe a general method based on the Fisher information matrix to discriminate between generators that admit nonconvex solutions and those that do not. While initial conditions leading to concave transients are shown to be extremely fine-tuned, by our method we are able to select nonconvex initial conditions that are arbitrarily close to the steady state. Convexity does occur when the system is close to satisfying detailed balance or, more generally, when certain normality conditions of the decay modes are satisfied. Our results circumscribe the range of validity of a conjecture by Maes et al. [Phys. Rev. Lett. 107, 010601 (2011)] regarding monotonicity of the large deviation rate functional for the occupation probability, showing that while the conjecture might hold in the long-time limit, the conditions for Lyapunov's second criterion for stability are not met.

We present statistics on granular avalanches in a rotating drum with and without imposed vertical vibration. The experiment consists of a quasi-two-dimensional, vertical drum containing pentagonal particles and rotated at a constant angular velocity. The drum rests on an electromagnetic shaker to allow vibration of the assembly as it rotates. We measure time series of the slope of the interface and find that the critical angle for slope failure ${\theta }_c$ and the resulting angle of repose ${\theta }_r$ are broadly distributed with an approximate power-law distribution of avalanches ${\theta }_c-{\theta }_r$ for large avalanches. The faceted pentagonal grains used lead to significant interlocking with critical and repose angles (${\theta }_c\approx {45}^{\circ }$ and ${\theta }_r\approx {39}^{\circ }$) larger than experiments using spherical grains, even with vibration, and avalanche magnitudes correlated with the prior build-up and anti-correlated with the prior avalanche. We find that the stability of the assembly increases with small vibrations and is destabilized at vibration amplitudes above a dimensionless acceleration (peak acceleration divided by acceleration due to gravity) of $\Gamma =0.2$. We also study history dependence of the avalanches by periodically oscillating the drum to compare the initial avalanche upon reversal of shear to steady-state distributions for avalanches during continuous rotation. We observe history dependence as an initial decrease in critical angle upon reversal of the drum rotation direction, indicating that a texture is induced to resist continued shear such that the surface is weaker to reversals in shear direction. Memory of this history is removed by sufficient external vibration ($\Gamma \ge 0.8$), which leads to compaction and relaxation of the surface layer grains responsible for avalanching dynamics, as initial and steady-state avalanche distributions become indistinguishable.

A connection between the dynamics of a sine-Gordon chain and a certain static membrane folding problem was recently found. The one-dimensional membrane profile is a cross section of the position-time sine-Gordon amplitude profile. Here we show that when one system is embedded in a higher-dimensional system in this way, obvious symmetries in the larger system can lead to nontrivial symmetries in the embedded system. In particular, a thin buckled membrane on a fluid substrate has a continuous degeneracy that interpolates between a symmetric and an antisymmetric fold. We find the Hamiltonian generator of this symmetry and the corresponding conserved momentum by interpreting the simple translational symmetries of the sine-Gordon chain in terms of the embedded coordinates. We discuss possible extensions to other embedded dynamical systems.

The fundamental parameter of the uniaxial liquid crystalline state that governs nearly all of its physical properties is the primary orientational order parameter ($S$) for the long axes of molecules with respect to the director. The biaxial liquid crystals (LCs) possess biaxial order parameters depending on the phase symmetry of the system. In this paper we show that in the first approximation a biaxial orthogonal smectic phase can be described by two primary order parameters: $S$ for the long axes and $C$ for the ordering of the short axes of molecules. The temperature dependencies of $S$ and $C$ are obtained by the Haller's extrapolation technique through measurements of the optical birefringence and biaxiality on a nontilted polar antiferroelectric (Sm-$A{P}_A$) phase of a homologous series of LCs built from the bent-core achiral molecules. For such a biaxial smectic phase both $S$ and $C$, particularly the temperature dependency of the latter, are being experimentally determined. Results show that $S$ in the orthogonal smectic phase composed of bent cores is higher than in Sm-$A$ calamatic LCs and $C$ is also significantly large.

Winnerless competition is analyzed in coupled maps with discrete temporal evolution of the Lotka-Volterra type of arbitrary dimension. Necessary and sufficient conditions for the appearance of structurally stable heteroclinic cycles as a function of the model parameters are deduced. It is shown that under such conditions winnerless competition dynamics is fully exhibited. Based on these conditions different cases characterizing low, intermediate, and high dimensions are therefore computationally recreated. An analytical expression for the residence times valid in the $N$-dimensional case is deduced and successfully compared with the simulations.

Bistability in periodically paced cardiac tissue is relevant to cardiac arrhythmias and its control. In the present paper, one-dimensional tissue of the phase I Luo-Rudy model is numerically investigated. The effects of various parameters of pacing signals on bistability width are studied. The following conclusions are obtained: (i) Pacing can be classified into two types: pulsatile and sinusoidal types. Pulsatile pacing reduces bistability width as its magnitude is increased. Sinusoidal pacing increases the width as its amplitude is increased. (ii) In a pacing period the hyperpolarizing part plays a more important role than the depolarizing part. Variations of the hyperpolarizing ratio in a period evidently change the width of bistability and its variation tendency. (iii) A dynamical mechanism is proposed to qualitatively explain the phenomena, which reveals the reason for the different effects of pulsatile and sinusoidal pacing on bistability. The methods for changing bistability width by external pacing may help control arrhythmias in cardiology.

Spontaneous neural activity has been increasingly recognized as a subject of key relevance in neuroscience. It exhibits nontrivial spatiotemporal structure reflecting the organization of the underlying neural network and has proved to be closely intertwined with stimulus-induced activity patterns. As an additional contribution in this regard, we report computational studies that strongly suggest that a stimulus-free feature rules the behavior of an important psychophysical measure of the sensibility of a sensory system to a stimulus, the so-called dynamic range. Indeed in this paper we show that the entropy of the distribution of avalanche lifetimes (information efficiency, since it can be interpreted as the efficiency of the network seen as a communication channel) always accompanies the dynamic range in the benchmark model for sensory systems. Specifically, by simulating the Kinouchi-Copelli (KC) model on two broad families of model networks, we generically observed that both quantities always increase or decrease together as functions of the average branching ratio (the control parameter of the KC model) and that the information efficiency typically exhibits critical optimization jointly with the dynamic range (i.e., both quantities are optimized at the same value of that control parameter, that turns out to be the critical point of a nonequilibrium phase transition). In contrast with the practice of taking power laws to identify critical points in most studies describing measured neuronal avalanches, we rely on data collapses as more robust signatures of criticality to claim that critical optimization may happen even when the distribution of avalanche lifetimes is not a power law, as suggested by a recent experiment. Finally, we note that the entropy of the size distribution of avalanches (information capacity) does not always follow the dynamic range and the information efficiency when they are critically optimized, despite being more widely used than the latter to describe the computational capabilities of a neural network. This strongly suggests that dynamical rules allowing a proper temporal matching of the states of the interacting neurons is the key for achieving good performance in information processing, rather than increasing the number of available units.

An inhomogeneous distribution of species density over physical space is a widely observed scenario in plankton systems. Understanding the mechanisms resulting in these spatial patterns is a central topic in plankton ecology. In this paper we explore the impact of time delay on spatiotemporal patterns in a prey-predator plankton system. We find that time delay can trigger the emergence of irregular spatial patterns via a Hopf bifurcation. Moreover, a phase transition from a regular spiral pattern to an irregular one was observed and the latter gradually replaced the former and persisted indefinitely. The characteristic length of the emergent spatial pattern is consistent with the scale of plankton patterns observed in field studies.

This study aims to provide a better understanding of recently identified transition scenarios exhibited by traveling wave solutions in pipe flow. This particular family of solutions are invariant under certain reflectional symmetry transformations and they emerge from saddle-node bifurcations within a two-dimensional parameter space characterized by the length of the pipe and the Reynolds number. The present work precisely provides a detailed analysis of a codimension-two saddle-node bifurcation arising in discrete dynamical systems (maps) with ${\mathbb{Z}}_2$ symmetry. Normal form standard techniques are applied in order to obtain the reduced map up to cubic order. All possible bifurcation scenarios exhibited by this normal form are analyzed in detail. Finally, a qualitative comparison of these scenarios with the ones observed in the aforementioned hydrodynamic problem is provided.

The Becker-Döring (BD) nucleation equation is known to predict a narrow double-exponential front (DEF) in the distribution of growing particles over sizes, which is due to early transient effects. When mass conservation is included, nucleation is eventually exhausted while independent growth is replaced by ripening. Despite the enormous difference in the associated time scales, and the resulting demand on numerics, within the generalized BD model the early DEF is shown to be crucial for the selection of the unique self-similar Lifshitz-Slyozov-Wagner asymptotic regime. Being preserved till the latest stages of growth, the DEF provides a universal part of the initial conditions for the ripening problem, regardless of the mass exchange mechanism between the nucleus and the matrix.

Bouncing droplets can self-propel laterally along the surface of a vibrated fluid bath by virtue of a resonant interaction with their own wave field. The resulting walking droplets exhibit features reminiscent of microscopic quantum particles. Here we present the results of an experimental investigation of droplets walking in a circular corral. We demonstrate that a coherent wavelike statistical behavior emerges from the complex underlying dynamics and that the probability distribution is prescribed by the Faraday wave mode of the corral. The statistical behavior of the walking droplets is demonstrated to be analogous to that of electrons in quantum corrals.

In microgravity, the gathering of granular material can be achieved by a dynamical clustering whose existence depends on the geometry of the cell that contains the particles and the energy that is injected into the system. By compartmentalizing the cell in several subcells of smaller volume, local clustering is triggered and the so formed dense regions act as stable traps. In this paper, molecular dynamics simulations were performed in order to reproduce the phenomenon and to analyze the formation and the stability of such traps. Depending on the total number $N$ of particles present in the whole system, several clustering modes are encountered and a corresponding bifurcation diagram is presented. Moreover, an iterative model based on the measured particle flux $F$ as well as a theoretical model giving the asymptotical steady states are used to validate our results. The obtained results are promising and can provide ways to manipulate grains in microgravity.

The measured viscoelastic properties of biological tissues is the result of the passive and active response of the cells. We propose an evolution law of the remodeling process in the cytoskeleton which is able to mimic the viscous properties of biological cellular tissues. Our model is based on dynamical changes of the resting length. We show that under the small strain regime, the linear rheology models are recovered, with the relaxation time being replaced by the cell resistance to remodel. We implement the one-dimensional model into network systems of two and three dimensions, and show that the same conclusions may be drawn for those systems.

We study a system of interacting self-propelled particles whose walking velocity depends on the stage of the locomotion cycle. The model introduces a phase equation in the optimal velocity model for vehicular traffic. We find that the system exhibits novel types of flow: synchronized free flow, phase-anchoring free flow, orderly jam flow, and disordered jam flow. The first two flows are characterized by synchronization of the phase, while the others do not have the global synchronization. Among these, the disordered jam flow is very complex, although the underlying model is simple. This phenomenon implies that the crowd behavior of moving particles can be destabilized by coupling their velocity to the phase of their motion. We also focus on “phase-anchoring” phenomena. They strongly affect particle flow in the system, especially when the density of particles is high.

The statistics of a neutral point-vortex gas in an arbitrary two-dimensional simply connected and bounded container are investigated in the framework of the microcanonical ensemble, following the cumulant expansion method of Pointin and Lundgren [Phys. Fluids 19, 1459 (1976)]. The equation for vorticity fluctuations, obtained when a thermodynamic scaling limit is taken, is solved explicitly. The solution depends on an infinite sequence of negative “domain inverse temperatures,” determined by the domain shape, which are obtained from solutions of a “vorticity mode” eigenvalue problem. An explicit expression for the thermodynamic curve relating inverse temperature and energy is found and is shown to depend on the geometry and not on the scale of the domain. Explicit formulas are then obtained for the time variance of the projection of the vorticity field onto each vorticity mode. The results are verified by two methods. First, for a chosen single-parameter family of domains, direct sampling of the microcanonical ensemble is used to demonstrate the accuracy of the formula for the thermodynamic curve. Second, direct numerical simulations are used to verify the formulas for the variance of the projections of the vorticity field, with convincing results.