The Poynting effect is a paragon of nonlinear soft matter mechanics. It is the tendency (found in all incompressible, isotropic, hyperelastic solids) exhibited by a soft block to expand vertically when sheared horizontally. It can be observed whenever the length of the cuboid is at least four times its thickness. Here we show that the Poynting effect can be easily reversed and the cuboid can shrink vertically, simply by reducing this aspect ratio. In principle, this discovery means that for a given solid, say one used as a seismic wave absorber under a building, an optimal ratio exists where vertical displacements and vibrations can be completely eliminated. Here we first recall the classical theoretical treatment of the positive Poynting effect, and then show experimentally how it can be reversed. Using finite-element simulations, we then investigate how the effect can be suppressed. We find that cubes always provide a reverse Poynting effect, irrespective of their material properties (in the third-order theory of weakly nonlinear elasticity).

Models of pulse formation in nerve conduction have provided manifold insight not only into neuronal dynamics but also the nonlinear dynamics of pulse formation in general. Recent observation of neuronal electrochemical pulses also driving mechanical deformation of the tubular neuronal wall, and thereby generating ensuing cytoplasmic flow, now question the impact of flow on the electrochemical dynamics of pulse formation. Here, we theoretically investigate the classical Fitzhugh-Nagumo model, now accounting for advective coupling between the pulse propagator typically describing membrane potential and triggering mechanical deformations, and thus governing flow magnitude, and the pulse controller, a chemical species advected with the ensuing fluid flow. Employing analytical calculations and numerical simulations, we find that advective coupling allows for a linear control of pulse width while leaving pulse velocity unchanged. We therefore uncover an independent control of pulse width by fluid flow coupling.

Self-organization is a ubiquitous phenomenon in Nature due to the permanent balance between injection and dissipation of energy. The wavelength selection process is the main issue of pattern formation. Stripe, hexagon, square, and labyrinthine patterns are observed in homogeneous conditions. In systems with heterogeneous conditions, a single wavelength is not the rule. Large-scale self-organization of vegetation in arid environments can be affected by heterogeneities, such as interannual precipitation fluctuations, fire occurrences, topographic variations, grazing, soil depth distribution, and soil-moisture islands. Here, we investigate theoretically the emergence and persistence of vegetation labyrinthine patterns in ecosystems under deterministic heterogeneous conditions. Based on a simple local vegetation model with a space-varying parameter, we show evidence of perfect and imperfect labyrinthine patterns, as well as disordered vegetation self-organization. The intensity level and the correlation of the heterogeneities control the regularity of the labyrinthine self-organization. The phase diagram and the transitions of the labyrinthine morphologies are described with the aid of their global spatial features. We also investigate the local spatial structure of labyrinths. Our theoretical findings qualitatively agree with satellite images data of arid ecosystems that show labyrinthinelike textures without a single wavelength.

Modular and hierarchical community structures are pervasive in real-world complex systems. A great deal of effort has gone into trying to detect and study these structures. Important theoretical advances in the detection of modular have included identifying fundamental limits of detectability by formally defining community structure using probabilistic generative models. Detecting hierarchical community structure introduces additional challenges alongside those inherited from community detection. Here we present a theoretical study on hierarchical community structure in networks, which has thus far not received the same rigorous attention. We address the following questions. (1) How should we define a hierarchy of communities? (2) How do we determine if there is sufficient evidence of a hierarchical structure in a network? (3) How can we detect hierarchical structure efficiently? We approach these questions by introducing a definition of hierarchy based on the concept of stochastic externally equitable partitions and their relation to probabilistic models, such as the popular stochastic block model. We enumerate the challenges involved in detecting hierarchies and, by studying the spectral properties of hierarchical structure, present an efficient and principled method for detecting them.

Discordant alternans, the spatially out-of-phase alternation of the durations of propagating action potentials in the heart, has been linked to the onset of fibrillation, a major cardiac rhythm disorder. The sizes of the regions, or domains, within which these alternations are synchronized are critical in this link. However, computer models employing standard gap junction-based coupling between cells have been unable to reproduce simultaneously the small domain sizes and rapid action potential propagation speeds seen in experiments. Here we use computational methods to show that rapid wave speeds and small domain sizes are possible when a more detailed model of intercellular coupling that accounts for so-called ephaptic effects is used. We provide evidence that the smaller domain sizes are possible, because different coupling strengths can exist on the wavefronts, for which both ephaptic and gap-junction coupling are involved, in contrast to the wavebacks, where only gap-junction coupling plays an active role. The differences in coupling strength are due to the high density of fast-inward (sodium) channels known to localize on the ends of cardiac cells, which are only active (and thus engage ephaptic coupling) during wavefront propagation. Thus, our results suggest that this distribution of fast-inward channels, as well as other factors responsible for the critical involvement of ephaptic coupling in wave propagation, including intercellular cleft spacing, play important roles in increasing the vulnerability of the heart to life-threatening tachyarrhythmias. Our results, combined with the absence of short-wavelength discordant alternans domains in standard gap-junction-dominated coupling models, also provide evidence that both gap-junction and ephaptic coupling are critical in wavefront propagation and waveback dynamics.

Using the exact enumeration technique, we have studied the force-induced melting of a DNA hairpin on the face centered cubic lattice for two different sequences which differ in terms of loop closing base pairs. The melting profiles obtained from the exact enumeration technique is consistent with the Gaussian network model and Langevin dynamics simulations. Probability distribution analysis based on the exact density of states revealed the microscopic details of the opening of the hairpin. We showed the existence of intermediate states near the melting temperature. We further showed that different ensembles used to model single-molecule force spectroscopy setups may give different force-temperature diagrams. We delineate the possible reasons for the observed discrepancies.

We extensively study the Toner-Tu-Swift-Hohenberg model of motile active matter by means of direct numerical simulations in a two-dimensional confined domain. By exploring the space of parameters of the model we investigate the emergence of a new state of active turbulence which occurs when the aligning interactions and the self-propulsion of the swimmers are strong. This regime of flocking turbulence is characterized by a population of few strong vortices, each surrounded by an island of coherent flocking motion. The energy spectrum of flocking turbulence displays a power-law scaling with an exponent which depends weakly on the model parameters. By increasing the confinement we observe that the system, after a long transient characterized by power-law-distributed transition times, switches to the ordered state of a single giant vortex.

We demonstrate the capability of flying focus (FF) laser pulses with $\ell =1$ orbital angular momentum (OAM) to transversely confine ultrarelativistic charged particle bunches over macroscopic distances while maintaining a tight bunch radius. A FF pulse with $\ell =1$ OAM creates a radial ponderomotive barrier that constrains the transverse motion of particles and travels with the bunch over extended distances. As compared with freely propagating bunches, which quickly diverge due to their initial momentum spread, the particles cotraveling with the ponderomotive barrier slowly oscillate around the laser pulse axis within the spot size of the pulse. This can be achieved at FF pulse energies that are orders of magnitude lower than required by Gaussian or Bessel pulses with OAM. The ponderomotive trapping is further enhanced by radiative cooling of the bunch resulting from rapid oscillations of the charged particles in the laser field. This cooling decreases the mean-square radius and emittance of the bunch during propagation.

The replicator equations are a family of ordinary differential equations that arise in evolutionary game theory, and are closely related to Lotka-Volterra. We produce an infinite family of replicator equations which are Liouville-Arnold integrable. We show this by explicitly providing conserved quantities and a Poisson structure. As a corollary, we classify all tournament replicators up to dimension 6 and most of dimension 7. As an application, we show that Fig. 1 of Allesina and Levine [Proc. Natl. Acad. Sci. USA 108, 5638 (2011)] produces quasiperiodic dynamics.

We present a semidefinite programming algorithm to find eigenvalues of Schrödinger operators within the bootstrap approach to quantum mechanics. The bootstrap approach involves two ingredients: a nonlinear set of constraints on the variables (expectation values of operators in an energy eigenstate), plus positivity constraints (unitarity) that need to be satisfied. By fixing the energy we linearize all the constraints and show that the feasibility problem can be presented as an optimization problem for the variables that are not fixed by the constraints and one additional slack variable that measures the failure of positivity. To illustrate the method we are able to obtain high-precision, sharp bounds on eigenenergies for arbitrary confining polynomial potentials in one dimension.

We derive a field theory for the two-dimensional classical dimer model by applying bosonization to Lieb's (fermionic) transfer-matrix solution. Our constructive approach gives results that are consistent with the well-known height theory, previously justified based on symmetry considerations, but also fixes coefficients appearing in the effective theory and the relationship between microscopic observables and operators in the field theory. In addition, we show how interactions can be included in the field theory perturbatively, treating the case of the double dimer model with interactions within and between the two replicas. Using a renormalization-group analysis, we determine the shape of the phase boundary near the noninteracting point, in agreement with results of Monte Carlo simulations.

The nonlinear dynamics of a one-dimensional molecular crystal in the form of a chain of planar coronene molecules is analyzed. Using molecular dynamics, it is shown that a chain of coronene molecules supports acoustic solitons, rotobreathers, and discrete breathers. An increase in the size of planar molecules in a chain leads to an increase in the number of internal degrees of freedom. This results in an increase in the rate of emission of phonons from spatially localized nonlinear excitations and a decrease in their lifetime. Presented results contribute to the understanding of the effect of the rotational and internal vibrational modes of molecules on the nonlinear dynamics of molecular crystals.

The paper is devoted to analytical and numerical studies of the effects of nonlinearity on the two-path phonon interference in the transmission through two-dimensional arrays of atomic defects embedded in a lattice. The emergence of transmission antiresonance (transmission node) in the two-path system is demonstrated for the few-particle nanostructures, which allow us to model both linear and nonlinear phonon transmission antiresonances. The universality of destructive-interference origin of transmission antiresonances of waves of different nature, such as phonons, photons, and electrons, in two-path nanostructures and metamaterials is emphasized. Generation of the higher harmonics as a result of the interaction of lattice waves with nonlinear two-path atomic defects is considered, and the full system of nonlinear algebraic equations is obtained to describe the transmission through nonlinear two-path atomic defects with an account for the generation of second and third harmonics. Expressions for the coefficients of lattice energy transmission through and reflection from the embedded nonlinear atomic systems are derived. It is shown that the quartic interatomic nonlinearity shifts the antiresonance frequency in the direction determined by the sign of the nonlinear coefficient and enhances in general the transmission of high-frequency phonons due to third harmonic generation and propagation. The effects of the quartic nonlinearity on phonon transmission are described for the two-path atomic defects with a different topology. Transmission through the nonlinear two-path atomic defects is also modeled with the simulation of the phonon wave packet, for which the proper amplitude normalization is proposed and implemented. It is shown that the cubic interatomic nonlinearity red shifts in general the antiresonance frequency for longitudinal phonons independently of the sign of the nonlinear coefficient, and the equilibrium interatomic distances (bond lengths) in the atomic defects are changed by the incident phonon due to cubic interatomic nonlinearity. For longitudinal phonons incident on a system with the cubic nonlinearity, the new narrow transmission resonance on the background of a broad antiresonance is predicted to emerge, which we relate to the opening of the additional transmission channel for the phonon second harmonic through the nonlinear defect atoms. Conditions of the existence of the new nonlinear transmission resonance are determined and demonstrated for different two-path nonlinear atomic defects. A two-dimensional array of embedded three-path defects with an additional weak transmission channel, in which a linear analog of the nonlinear narrow transmission resonance on the background of a broad antiresonance is realized, is proposed and modeled. The presented results provide better understanding and detailed description of the interplay between the interference and nonlinearity in phonon propagation through and scattering in two-dimensional arrays of two-path anharmonic atomic defects with a different topology.

Social units, such as households and schools, can play an important role in controlling epidemic outbreaks. In this work, we study an epidemic model with a prompt quarantine measure on networks with cliques (a clique is a fully connected subgraph representing a social unit). According to this strategy, newly infected individuals are detected and quarantined (along with their close contacts) with probability $f$. Numerical simulations reveal that epidemic outbreaks in networks with cliques are abruptly suppressed at a transition point $f_c$. However, small outbreaks show features of a second-order phase transition around $f_c$. Therefore, our model can exhibit properties of both discontinuous and continuous phase transitions. Next, we show analytically that the probability of small outbreaks goes continuously to 1 at $f_c$ in the thermodynamic limit. Finally, we find that our model exhibits a backward bifurcation phenomenon.

The gaits of undulating animals arise from a complex interaction of their central nervous system, muscle, connective tissue, bone, and environment. As a simplifying assumption, many previous studies have often assumed that sufficient internal force is available to produce observed kinematics, thus not focusing on quantifying the interconnection between muscle effort, body shape, and external reaction forces. This interplay, however, is critical to locomotion performance in crawling animals, especially when accompanied by body viscoelasticity. Moreover, in bioinspired robotic applications, the body's internal damping is indeed a parameter that the designer can tune. Still, the effect of internal damping is not well understood. This study explores how internal damping affects the locomotion performance of a crawler with a continuous, viscoelastic, nonlinear beam model. Crawler muscle actuation is modeled as a traveling wave of bending moment propagating posteriorly along the body. Consistent with the friction properties of the scales of snakes and limbless lizards, environmental forces are modeled using anisotropic Coulomb friction. It is found that by varying the crawler body's internal damping, the crawler's performance can be altered, and distinct gaits could be achieved, including changing the net locomotion direction from forward to back. We will discuss this forward and backward control and identify the optimal internal damping for peak crawling speed.

Colloidal spheres in weakly conductive fluids roll back and forth across the surface of a plane electrode when subject to strong electric fields. The so-called Quincke oscillators provide a basis for active matter based on self-oscillating units that can move, align, and synchronize within dynamic particle assemblies. Here, we develop a dynamical model for oscillations of a spherical particle and investigate the coupled dynamics of two such oscillators in the plane normal to the field. Building on existing descriptions of Quincke rotation, the model describes the dynamics of the charge, dipole, and quadrupole moments due to charge accumulation at the particle-fluid interface and particle rotation in the external field. The dynamics of the charge moments are coupled by the addition of a conductivity gradient, which describes asymmetries in the rates of charging near the electrode. We study the behavior of this model as a function of the field strength and gradient magnitude to identify the conditions required for sustained oscillations. We investigate the dynamics of two neighboring oscillators coupled by far field electric and hydrodynamic interactions in an unbounded fluid. Particles prefer to align and synchronize their rotary oscillations along the line of centers. The numerical results are reproduced and explained by accurate low-order approximations of the system dynamics based on weakly coupled oscillator theory. The coarse-grained dynamics of the oscillator phase and angle can be used to investigate collective behaviors within ensembles of many self-oscillating colloids.

We present a detailed analysis of $\mathit{c}$-director anchoring measurements on simple edge dislocations at the surface of smectic-$C_A$ films (steps). Indications show that the $\mathit{c}$-director anchoring on the dislocations originates from a local and partial melting of the dislocation core that depends on the anchoring angle. The $\mathrm{Sm}{C}_A$ films are induced on isotropic puddles of 1-(methyl)-heptyl-terephthalylidene-bis-amino cinnamate molecules by the surface field, while the dislocations are located at the isotropic-smectic interface. The experimental setup is based on the connection of a three-dimensional smectic film sandwiched between a one-dimensional edge dislocation on its lower surface, and a two-dimensional surface polarization spread over the upper surface. Applying an electric field produces a torque that balances the anchoring torque of the dislocation. The film distortion that results is measured under a polarizing microscope. Exact calculations on these data, anchoring torque versus director angle, yield the anchoring properties of the dislocation. A specificity of our sandwich configuration is to improve the measurement quality by a factor of $N^{3/2}\sim 600$, where $N=72$ is the number of smectic layers in the film. We fit a second-order Fourier series on the torque-anchoring angle data, which has the advantage of converging uniformly over the entire anchoring angle range, i.e., over more than ${70}^{\circ }$. The two corresponding Fourier coefficients, $k_{a1}^{F2}$ and $k_{a2}^{F2}$, are anchoring parameters that generalize the usual anchoring coefficient. When changing the electric field $\mathit{E}$, the anchoring state evolves along paths in a torque-anchoring angle diagram. Two cases occur depending on the angle ${\alpha }_{\infty }$ of $\mathit{E}$ relative to the unit vector $\mathit{S}$, perpendicular to the dislocation and parallel to the film. When ${\alpha }_{\infty }<{130}^{\circ }$, the operating point Q that represents the anchoring state in the diagram follows reversible and “at-equilibrium” paths. Its free displacement velocity is infinitely slow, so that we have to push it with electric torque steps smaller than the experimental error bar $\delta \mathrm{\Gamma }\sim {10}^{-14}\mathrm{N}$. On the other hand, for ${\alpha }_{\infty }>{130}^{\circ }$, Q describes a hysteresis loop similar to the usually encountered ones in solids. This loop connects two states that exhibit broken and nonbroken anchorings, respectively. The paths that join them in an out-of-equilibrium process are irreversible and dissipative. When coming back to a nonbroken anchoring state, both the dislocation and smectic film spontaneously heal back in the very same state they were before the anchoring broke. The process does not produce any erosion thanks to their liquid nature, including at the microscopic scale. The energy that is dissipated on these paths is roughly estimated in terms of the c-director rotational viscosity. Similarly, we can evaluate the maximum time of flight along the dissipative paths to be of the order of a few seconds, which is consistent with qualitative observations. In contrast, the paths located inside each domain of these anchoring states are reversible and can be followed in an “at equilibrium” manner all along. This analysis should provide a basis for understanding the structure of multiple edge dislocations in terms of parallel simple edge dislocations interacting with each other through pseudo-Casimir forces arising from $\mathit{c}$-director thermodynamic fluctuations between them.

We analyze the cluster formation in a nonergodic stochastic system as a result of counterflow, with the aid of an exactly solvable model. To illustrate the clustering, a two species asymmetric simple exclusion process with impurities on a periodic lattice is considered, where the impurity can activate flips between the two nonconserved species. Exact analytical results, supported by Monte Carlo simulations, show two distinct phases, free-flowing phase and clustering phase. The clustering phase is characterized by constant density and vanishing current of the nonconserved species, whereas the free-flowing phase is identified with nonmonotonic density and nonmonotonic finite current of the same. The $n$-point spatial correlation between $n$ consecutive vacancies grows with increasing $n$ in the clustering phase, indicating the formation of two macroscopic clusters in this phase, one of the vacancies and the other consisting of all the particles. We define a rearrangement parameter that permutes the ordering of particles in the initial configuration, keeping all the input parameters fixed. This rearrangement parameter reveals the significant effect of nonergodicity on the onset of clustering. For a special choice of the microscopic dynamics, we connect the present model to a system of run-and-tumble particles used to model active matter, where the two species having opposite net bias manifest the two possible run directions of the run-and-tumble particles, and the impurities act as tumbling reagents that enable the tumbling process.

Equilibrium molecular dynamics simulations are performed to study two-dimensional (2D) dusty plasma liquids. Based on the stochastic thermal motion of simulated particles, the longitudinal and transverse phonon spectra are calculated, and used to determine the corresponding dispersion relations. From there, the longitudinal and transverse sound speeds of 2D dusty plasma liquids are obtained. It is discovered that, for wavenumbers beyond the hydrodynamic regime, the longitudinal sound speed of a 2D dusty plasma liquid exceeds its adiabatic value, i.e., the so-called fast sound. This phenomenon appears at roughly the same length scale of the cutoff wavenumber for transverse waves, confirming its relation to the emergent solidity of liquids in the nonhydrodynamic regime. Using the thermodynamic and transport coefficients extracted from the previous studies, and relying on the Frenkel theory, the ratio of the longitudinal to the adiabatic sound speeds is derived analytically, providing the optimal conditions for fast sound, which are in quantitative agreement with the current simulation results.

A recent numerical treatment of data obtained by the Parker Solar Probe spacecraft describes the electron concentration in solar wind as a function of the heliocentric distance based on a Kappa distribution with spectral index $\kappa =5$. In this work, we derive and, subsequently, solve an entirely different class of nonlinear partial differential equations describing the one-dimensional diffusion of a suprathermal gas. The theory is applied to describe the aforementioned data and we find a spectral index $\kappa \gtrsim 1.5$ providing the widely acknowledged identification of Kappa electrons in solar wind. We also find that suprathermal effects increase the length scale of classical diffusion by one order of magnitude. Such a result does not depend on the microscopic details of the diffusion coefficient since our theory is based on a macroscopic formulation. Forthcoming extensions of our theory by including magnetic fields and relating our formulation to nonextensive statistics are briefly addressed.