Chimeras are complex spatiotemporal patterns that emerge as coexistence of both coherent and incoherent groups of coupled dynamical systems. Here, we investigate the emergence of chimera states in nonlocal networks of type-I Morris-Lecar neurons coupled via chemical synapses. This constitutes a more realistic neuronal modeling framework than previous studies of chimera states, since the Morris-Lecar model provides biophysically more relevant control parameters to describe the activity in actual neural systems. We explore systematically the transitions of dynamic behavior and find that different types of synchrony appear depending on the excitability level and nonlocal network features. Furthermore, we map the transitions between incoherent states, traveling waves, chimeras, coherent states, and global amplitude death in the parameter space of interest. This work contributes to a better understanding of biological conditions giving rise to the emergence of chimera states in neural medium.

The out-of-time-order correlator (OTOC), recently analyzed in several physical contexts, is studied for low-dimensional chaotic systems through semiclassical expansions and numerical simulations. The semiclassical expansion for the OTOC yields a leading-order contribution in ${\hslash }^2$ that is exponentially increasing with time within an intermediate, temperature-dependent, time window. The growth-rate in such a regime is governed by the Lyapunov exponent of the underlying classical system and scales with the square-root of the temperature.

Much research effort has been devoted to developing methods for reconstructing the links of a network from dynamics of its nodes. Many current methods require the measurements of the dynamics of all the nodes to be known. In real-world problems, it is common that either some nodes of a network of interest are unknown or the measurements of some nodes are unavailable. These nodes, either unknown or whose measurements are unavailable, are called hidden nodes. In this paper, we derive analytical results that explain the effects of hidden nodes on the reconstruction of bidirectional networks. These theoretical results and their implications are verified by numerical studies.

The design and implementation of genetic logic gates is a fundamental component of biological computation. In this article we show that the function of a common class of synthetic genetic AND and NAND gates is not completely dictated by the circuit connectivity, even if promoter leakage is very small. Rather, the logic function is strongly determined by a simple power law relationship between the promoter leakage rate and the binding affinity of the protein complex carrying the information from the input to the output of the gate. Depending on the value of the power law exponent, a circuit designed to be an AND gate can actually operate as a TRUE, OR, AND, or FALSE gate, even if the leakage rate is practically negligible. Surprisingly, all these functionalities are compatible with the physiological range of parameter values showing that the design of genetic logic gates which preserve functionality across cell types and conditions requires careful consideration of both circuit connectivity and parameter values.

Filamentous biomaterials such as fibrin or collagen networks exhibit an enormous stiffening of their elastic moduli upon large deformations. This pronounced nonlinear behavior stems from a significant separation between the stiffnesses scales associated with bending versus stretching the material's constituent elements. Here we study a simple model of such materials, floppy networks of hinged rigid bars embedded in an elastic matrix, in which the effective ratio of bending to stretching stiffnesses vanishes identically. We introduce a theoretical framework and build upon it to construct a numerical method with which the model's micro- and macromechanics can be carefully studied. Our model, numerical method and theoretical framework allow us to robustly observe and fully understand the critical properties of the athermal strain-stiffening transition that underlies the nonlinear mechanical response of a broad class of biomaterials.

We explore waves and entrainment in a model of coupled oscillators, inspired from the cellular oscillators in the presomitic mesoderm (PSM) of mice. The internal clock in each cell is based on a negative feedback loop which couples to the clocks of neighboring cells through a Notch mechanism. We investigate how a morphogen gradient in the mesoderm, which affects the period of oscillating cells, gives rise to phase waves traveling from the posterior to the anterior part of the PSM. We show that the phase waves can be entrained by an external periodic variation in this morphogen and also observe that multiple oscillatory solutions can coexist in the cell population. Together, these provide a way to potentially control phase waves and thereby manipulate somite patterning in embryos, based on entrainment properties of coupled nonlinear oscillators.

Gold nanoparticles moving in an aqueous solution under an optical vortex lattice are shown to present a complex collective optofluidic dynamics. Above a critical field intensity and concentration, the system presents a spontaneous transition toward synchronized motion, driven by the interplay between nonconservative optical forces, thermal fluctuations, and hydrodynamic pairing. Above criticality, the system exhibits swarm behavior with strong unidirectional currents of nanoparticles reaching speeds of centimeters per second. This relatively simple optofluidic setup offers an alternative way to control nanoparticle transport in aqueous environments.

A simplistic model of atomic dynamics in liquid, based on the concept of dynamic fluctuations in local atomic connectivity, is proposed to elucidate the temperature variation of the viscosity of a material in its liquid phase. Within the simplifications and hypothesis made to define the model, it is possible to explain the crossover from a simple liquid to a cooperative liquid and covariance of viscosity near the glass transition temperature. The model is a mechanical analog of the Drude model for the electric transport in metal.

The low-temperature properties of amorphous solids are widely believed to be controlled by the low-frequency quasilocalized modes. However, what governs their spatial structure and density is unclear. We study these questions numerically in very large systems as the jamming transition is approached and the pressure $p$ vanishes. We find that these modes consist of an unstable core and a stable far-field component. The length scale of the core diverges as $p^{-1/4}$ and its characteristic volume diverges as $p^{-1/2}$. These spatial features are precisely those of the anomalous modes that are known to cause the boson peak in the vibrational spectra of weakly coordinated materials. From this correspondence, we deduce that the density of quasilocalized modes must follow $g_{\mathrm{loc}}\left(\omega \right)\sim {\omega }^4/p^2$, which is in agreement with previous observations. Thus, our analysis demonstrates the nature of quasilocalized modes in a class of amorphous materials.

The behavior of the percolation threshold and the jamming coverage for isotropic random sequential adsorption samples has been studied by means of numerical simulations. A parallel algorithm that is very efficient in terms of its speed and memory usage has been developed and applied to the model involving large linear $k$-mers on a square lattice with periodic boundary conditions. We have obtained the percolation thresholds and jamming concentrations for lengths of $k$-mers up to $2^{17}$. A large $k$ regime of the percolation threshold behavior has been identified. The structure of the percolating and jamming states has been investigated. The theorem of Kondrat, Koza, and Brzeski [Phys. Rev. E 96, 022154 (2017)] has been generalized to the case of periodic boundary conditions. We have proved that any cluster at jamming is a percolating cluster and that percolation occurs before jamming.

In real magnets the tendency toward ferromagnetism—promoted by exchange coupling—is usually frustrated by dipolar interaction. As a result, the uniformly ordered phase is replaced by modulated (multidomain) phases, characterized by different order parameters rather than the global magnetization. The transitions occurring within those modulated phases and toward the disordered phase are generally not of second-order type. Nevertheless, strong experimental evidence indicates that a standard critical behavior is recovered when comparatively small fields are applied that stabilize the uniform phase. The resulting power laws are observed with respect to a putative critical point that falls in the portion of the phase diagram occupied by modulated phases, in line with an avoided-criticality scenario. Here we propose a generalization of the scaling hypothesis for ferromagnets, which explains this observation assuming that the dipolar interaction acts as a relevant field, in the sense of renormalization group. We corroborate this proposal with analytic and numerical calculations on the 2D Ising model frustrated by dipolar interaction (isotropic part). Our analysis is directly applicable to thin magnetic films with out-of-plane anisotropy.

We investigate the effect of noisy feed rates on the behavior of a cubic autocatalytic chemical reaction model. By combining the renormalization group and stoichiometric network analysis, we demonstrate how externally adjustable random perturbations (extrinsic noise) can be used to select reaction pathways and therefore control reaction yields. This method is general and provides the means to explore the impact that changing statistical parameters in a noisy external environment (such as noisy feed rates and fluctuating reaction rates induced by noisy light) has on chemical fluxes and pathways, thus demonstrating how external noise may be used to control, promote, direct, and optimize chemical progress through a given reaction pathway.

We use percolation theory to propose a strategy that increases the production yield of plants with high susceptibility to a pathogen plague. This strategy consists in sowing a second variety with a lower susceptibility. The percolation threshold is determined as a function of the plant density, the mixture of plants, the pathogen susceptibilities, and the initial percentage of inoculated soil. Moreover, we provide conditions to prevent the formation of a spanning cluster of infected plants. We present an application of this strategy to a particular chili plantation. Under controlled conditions, we measure the pathogen susceptibilities to different strains of Phytophthora capsici for three varieties of chili peppers with high commercial value in Mexico. Then we simulate the propagation process of the pathogen on nearest and next-to-nearest-neighbor square lattices. We find that the production yield of plantations with the highest susceptibility can be significantly increased as a result of this novel application of percolation theory.

One of the long-standing issues concerning the thermal properties of amorphous solids is the complex pattern of phonon transport. Recent advances in experiments and computer simulations have indicated a crossover from Rayleigh scattering to ${\mathrm{\Omega }}^2$ law (where $\mathrm{\Omega }$ is the propagation frequency). A number of theories have been proposed, yet critical tests are missing and the validity of these theories is unclear. In particular, the precise location of the crossover frequency remains controversial, and more critically, even the validity of the Rayleigh scattering has been seriously questioned. To settle these issues, we focus on a model amorphous solid, whose vibrational eigenmodes were recently clarified over a wide frequency regime: a mixture of phonon modes and soft localized modes in the continuum limit and disordered and extended modes in the boson peak regime. The present work demonstrates that Rayleigh scattering occurs in the continuum limit and ${\mathrm{\Omega }}^2$ damping occurs in the boson peak regime, and these behaviors are therefore linked to the underlying eigenmodes in the corresponding frequency regimes. Our results unambiguously determine the crossover frequency. Furthermore, we establish characteristic scaling laws of phonon transport near the jamming transition, which are consistent with the prediction of the mean-field theory at higher frequencies but inconsistent in the low-frequency, Rayleigh scattering regime. Our results therefore reveal crucial issues to be solved with regard to the current theory.

We study the dynamics of self-propelled chains with the excluded volume interaction via the Brownian dynamics simulation, in which the bending elasticity of chains is varied. The changes of the bending elasticity lead to various characteristics of the clustering behavior in the short-chain-only system. When a long self-propelled chain is mixed with these short chains, it can fold into the spiral coil, a steadily rotating spiral conformation, either at a high density of short chains or at a low density if the long chain itself is sufficiently flexible. Our results qualitatively support the speculation that the formation of the spiral coil in the swarm of Vibrio alginolyticus is triggered by collisions from the clusters of the shorter bacteria.

We derive the Green's function of unsteady Stokes equations near a plane boundary with no-slip boundary conditions. This provides flow due to an oscillating point force acting on fluid bounded by a wall. Our derivation is different from previous theories and resolves the apparent discrepancies of the reported results. Two-dimensional Fourier transform of the solution with respect to horizontal coordinates is given via elementary functions in a more compact form than by the previous theories. The tensorial Green's function in real space is reduced to two Hankel transforms of order zero. We derive a simple form for the real-space solution in the two limiting cases of a distance to the wall much larger and much smaller than the viscous penetration depth. We demonstrate the applicability of this form by obtaining results for the force exerted on a sphere oscillating near the wall. Using the integral equation on surface traction whose kernel is the fundamental solution, we derive the force in the limits of a distant wall and low frequency. The wall correction to the force decays as the inverse third power of the source to the wall separation distance, much faster than the inverse first power of the classical Lorentz solution for the time-independent problem. Our results significantly extend the range of parameters for which the force admits a simple closed-form solution. Small biological swimmers propelled by inherently unsteady swimming gait generate flows driven by derivatives of the point source and we provide an example of a wall-bounded solution of this type. We demonstrate that frequency expansion is an efficient way of studying the Green's functions in confined geometry that gives the complete series solution for channel geometry.

The two-dimensional natural convection of air in upper and a lower square cavities connected with a vertical vent is studied numerically and theoretically. At high Rayleigh numbers (Ra), it is revealed by the dynamic-mode-decomposition method that the plumes yield to a new sway mode, where the plumes oscillate in the azimuthal direction around the vent ends. In particular, when Ra is high enough, a reversal convection occurs, i.e., the dominating large-scale circulation changes its flow direction quasiperiodically. A van der Pol–type model is developed based on the momentum and the energy equations, and the reversal phenomenon is explained in terms of the relaxation oscillation caused by the competition between the nonlinear advection and the thermal diffusion.

We study the scalar one-component two-dimensional (2D) ${\varphi }^4$ model by computer simulations, with local Metropolis moves. The equilibrium exponents of this model are well established, e.g., for the 2D ${\varphi }^4$ model $\gamma =1.75$ and $\nu =1$. The model has also been conjectured to belong to the Ising universality class. However, the value of the critical dynamical exponent $z_c$ is not settled. In this paper, we obtain $z_c$ for the 2D ${\varphi }^4$ model using two independent methods: (a) by calculating the relative terminal exponential decay time $\tau$ for the correlation function $\langle \mathrm{\Phi }\left(t\right)\mathrm{\Phi }\left(0\right)\rangle$, and thereafter fitting the data as $\tau \sim L^{z_c}$, where $L$ is the system size, and (b) by measuring the anomalous diffusion exponent for the order parameter, viz., the mean-square displacement $\langle \mathrm{\Delta }{\mathrm{\Phi }}^2\left(t\right)\rangle \sim t^c$ as $c=\gamma /\left(\nu z_c\right)$, and from the numerically obtained value $c\approx 0.80$, we calculate $z_c$. For different values of the coupling constant $\lambda$, we report that $z_c=2.17\pm 0.03$ and $z_c=2.19\pm 0.03$ for the two methods, respectively. Our results indicate that $z_c$ is independent of $\lambda$, and is likely identical to that for the 2D Ising model. Additionally, we demonstrate that the generalized Langevin equation formulation with a memory kernel, identical to those applicable for the Ising model and polymeric systems, consistently captures the observed anomalous diffusion behavior.