The emergent dynamics in networks of recurrently coupled spiking neurons depends on the interplay between single-cell dynamics and network topology. Most theoretical studies on network dynamics have assumed simple topologies, such as connections that are made randomly and independently with a fixed probability (Erdös-Rényi network) (ER) or all-to-all connected networks. However, recent findings from slice experiments suggest that the actual patterns of connectivity between cortical neurons are more structured than in the ER random network. Here we explore how introducing additional higher-order statistical structure into the connectivity can affect the dynamics in neuronal networks. Specifically, we consider networks in which the number of presynaptic and postsynaptic contacts for each neuron, the degrees, are drawn from a joint degree distribution. We derive mean-field equations for a single population of homogeneous neurons and for a network of excitatory and inhibitory neurons, where the neurons can have arbitrary degree distributions. Through analysis of the mean-field equations and simulation of networks of integrate-and-fire neurons, we show that such networks have potentially much richer dynamics than an equivalent ER network. Finally, we relate the degree distributions to so-called cortical motifs.

We examine the phase behavior of a quasi-one-dimensional system of hard squares with side-length $\sigma$, where the particles are confined between two parallel walls and only nearest-neighbor interactions occur. As in our previous work [Gurin, Varga, and Odriozola, Phys. Rev. E 94, 050603 (2016)], the transfer operator method is used, but here we impose a restricted orientation and position approximation to yield an analytic description of the physical properties. This allows us to study the parallel fluid-like to zigzag solid-like structural transition, where the compressibility and heat capacity peaks sharpen and get higher as $H\to H_c=2\sqrt{2}-1\approx 1.8284$ and $p\to p_c=\infty$. Here $H$ is the width of the channel measured in $\sigma$ units and $p$ is the pressure. We have found that this structural change becomes critical at the $(p_c,H_c)$ point. The obtained critical exponents belong to the universality class of the one-dimensional Ising model. We believe this behavior holds for the unrestricted orientational and positional case.

We examined the influence of internal noise on the irregular switching of the shape of the free surface of fluids in an open cylindrical vessel driven by a bottom disk rotating at constant speed [Suzuki, Iima, and Hayase, Phys. Fluids 18, 101701 (2006)]. A slight increase in the disk-rim gap (less than 3% of the disk radius) was established experimentally to cause significant changes in this system, specifically, frequent appearance of the surface descending event connecting a nonaxisymmetric shape in strong mixing flow (turbulent flow) and an axisymmetric shape in laminar flow, as well as a shift in critical Reynolds number that define the characteristic states. The physical mechanism underlying the change is analyzed in terms of flow characteristics in the disk-rim gap, which acts as a noise source, and a mathematical model established from measurements of the surface height fluctuations with noise term.

In this paper, the thermohydrodynamics of an evaporating droplet is investigated by using a single-component pseudopotential lattice Boltzmann model. The phase change is applied to the model by adding source terms to the thermal lattice Boltzmann equation in such a way that the macroscopic energy equation of multiphase flows is recovered. In order to gain an exhaustive understanding of the complex hydrodynamics during evaporation, a single droplet is selected as a case study. At first, some tests for a stationary (non-)evaporating droplet are carried out to validate the method. Then the model is used to study the thermohydrodynamics of a falling evaporating droplet. The results show that the model is capable of reproducing the flow dynamics and transport phenomena of a stationary evaporating droplet quite well. Of course, a moving droplet evaporates faster than a stationary one due to the convective transport. Our study shows that our single-component model for simulating a moving evaporating droplet is limited to low Reynolds numbers.

Because the standard lattice Boltzmann (LB) method is proposed for Cartesian Navier-Stokes (NS) equations, additional source terms are necessary in the axisymmetric LB method for representing the axisymmetric effects. Therefore, the accuracy and applicability of the axisymmetric LB models depend on the forcing schemes adopted for discretization of the source terms. In this study, three forcing schemes, namely, the trapezium rule based scheme, the direct forcing scheme, and the semi-implicit centered scheme, are analyzed theoretically by investigating their derived macroscopic equations in the diffusive scale. Particularly, the finite difference interpretation of the standard LB method is extended to the LB equations with source terms, and then the accuracy of different forcing schemes is evaluated for the axisymmetric LB method. Theoretical analysis indicates that the discrete lattice effects arising from the direct forcing scheme are part of the truncation error terms and thus would not affect the overall accuracy of the standard LB method with general force term (i.e., only the source terms in the momentum equation are considered), but lead to incorrect macroscopic equations for the axisymmetric LB models. On the other hand, the trapezium rule based scheme and the semi-implicit centered scheme both have the advantage of avoiding the discrete lattice effects and recovering the correct macroscopic equations. Numerical tests applied for validating the theoretical analysis show that both the numerical stability and the accuracy of the axisymmetric LB simulations are affected by the direct forcing scheme, which indicate that forcing schemes free of the discrete lattice effects are necessary for the axisymmetric LB method.

We investigate the influence of time-delayed coupling in a ring network of nonlocally coupled Stuart-Landau oscillators upon chimera states, i.e., space-time patterns with coexisting partially coherent and partially incoherent domains. We focus on amplitude chimeras, which exhibit incoherent behavior with respect to the amplitude rather than the phase and are transient patterns, and we show that their lifetime can be significantly enhanced by coupling delay. To characterize their transition to phase-lag synchronization (coherent traveling waves) and other coherent structures, we generalize the Kuramoto order parameter. Contrasting the results for instantaneous coupling with those for constant coupling delay, for time-varying delay, and for distributed-delay coupling, we demonstrate that the lifetime of amplitude chimera states and related partially incoherent states can be controlled, i.e., deliberately reduced or increased, depending upon the type of coupling delay.

In spite of the vast literature on spreading dynamics on complex networks, the role of local synergy, i.e., the interaction of elements that when combined produce a total effect greater than the sum of the individual elements, has been studied but only for irreversible spreading dynamics. Reversible spreading dynamics are ubiquitous but their interplay with synergy has remained unknown. To fill this knowledge gap, we articulate a model to incorporate local synergistic effect into the classical susceptible-infected-susceptible process, in which the probability for a susceptible node to become infected through an infected neighbor is enhanced when the neighborhood of the latter contains a number of infected nodes. We derive master equations incorporating the synergistic effect, with predictions that agree well with the numerical results. A striking finding is that when a parameter characterizing the strength of the synergy reinforcement effect is above a critical value, the steady-state density of the infected nodes versus the basic transmission rate exhibits an explosively increasing behavior and a hysteresis loop emerges. In fact, increasing the synergy strength can promote the spreading and reduce the invasion and persistence thresholds of the hysteresis loop. A physical understanding of the synergy promoting explosive spreading and the associated hysteresis behavior can be obtained through a mean-field analysis.

We present Monte Carlo data of the stress-strain diagrams obtained using two different triangulated surface models. The first is the canonical surface model of Helfrich and Polyakov (HP), and the second is a Finsler geometry (FG) model. The shape of the experimentally observed stress-strain diagram is called J-shaped. Indeed, the diagram has a plateau for the small strain region and becomes linear in the relatively large strain region. Because of this highly nonlinear behavior, the J-shaped diagram is far beyond the scope of the ordinary theory of elasticity. Therefore, the mechanism behind the J-shaped diagram still remains to be clarified, although it is commonly believed that the collagen degrees of freedom play an essential role. We find that the FG modeling technique provides a coarse-grained picture for the interaction between the collagen and the bulk material. The role of the directional degrees of freedom of collagen molecules or fibers can be understood in the context of FG modeling. We also discuss the reason for why the J-shaped diagram cannot (can) be explained by the HP (FG) model.

Cells may control fluctuations in protein levels by means of negative autoregulation, where transcription factors bind DNA sites to repress their own production. Theoretical studies have assumed a single binding site for the repressor, while in most species it is found that multiple binding sites are arranged in clusters. We study a stochastic description of negative autoregulation with multiple binding sites for the repressor. We find that increasing the number of binding sites induces regular bursting of gene products. By tuning the threshold for repression, we show that multiple binding sites can also suppress fluctuations. Our results highlight possible roles for the presence of multiple binding sites of negative autoregulators.

We investigate the size distribution of damage clusters in concrete under uniaxial tension loading conditions. Using the finite-element method, the concrete is modeled at the mesoscale by a random distribution of elastic spherical aggregates within an elastic mortar paste. The propagation and coalescence of damage zones are then simulated by means of dynamically inserted cohesive elements. Dynamic failure analysis shows that the size distribution of damage clusters follows a power law when a system-spanning cluster is first observed, with an exponent close to that of percolation theory. This is found for a range of selected mesostructural parameters, material defects, and applied strain rates. In all cases, the system-spanning cluster occurs prior to the onset of local decohesion, a regime of crack nucleation and propagation, and eventual material failure. The resulting fully damaged crack surfaces after failure are found to be only weakly correlated with the percolated damage region structures.

Although redistribution of red blood cells at bifurcated vessels is highly dependent on flow rate, it is still challenging to quantitatively express the dependence of flow rate in plasma skimming due to nonlinear cellular interactions. We suggest a plasma skimming model that can involve the effect of fractional blood flow at each bifurcation point. To validate the model, it is compared with in vivo data at single bifurcation points, as well as microvascular network systems. In the simulation results, the exponential decay of the plasma skimming parameter $M$ along fractional flow rate shows the best performance in both cases.

Numerical simulations are performed to demonstrate that proportional-integral control, one of the most commonly used feedback schemes in control engineering, can stabilize propagating wave segments in excitable media to a desired size. The proportional-integral controller measures the size of a wave segment and applies a spatially uniform signal to the medium. This controller has the following features: difficult trial-and-error adjustment is not necessary, wave segments can be stabilized to different sizes without readjusting the controller, and the wave segment size can be maintained even in media having position-dependent parameters.

In this paper, we construct a special kind of breather solution of the nonlinear Schrödinger (NLS) equation, the so-called breather-positon (b-positon for short), which can be obtained by taking the limit ${\lambda }_j\to {\lambda }_1$ of the Lax pair eigenvalues in the order-$n$ periodic solution, which is generated by the $n$-fold Darboux transformation from a special “seed” solution–plane wave. Further, an order-$n$ b-positon gives an order-$n$ rogue wave under a limit ${\lambda }_1\to {\lambda }_0$. Here, ${\lambda }_0$ is a special eigenvalue in a breather of the NLS equation such that its period goes to infinity. Several analytical plots of order-2 breather confirm visually this double degeneration. The last limit in this double degeneration can be realized approximately in an optical fiber governed by the NLS equation, in which an injected initial ideal pulse is created by a frequency comb system and a programable optical filter (wave shaper) according to the profile of an analytical form of the b-positon at a certain position $z_0$. We also suggest a new way to observe higher-order rogue waves generation in an optical fiber, namely, measure the patterns at the central region of the higher-order b-positon generated by above ideal initial pulses when ${\lambda }_1$ is very close to the ${\lambda }_0$. The excellent agreement between the numerical solutions generated from initial ideal inputs with a low signal-to-noise ratio and analytical solutions of order-2 b-positon supports strongly this way in a realistic optical fiber system. Our results also show the validity of the generating mechanism of a higher-order rogue waves from a multibreathers through the double degeneration.

We present a numerical framework to simulate pedestrian dynamics in highly competitive conditions by means of a force-based model implemented with spherocylindrical particles instead of the traditional, symmetric disks. This modification of the individuals' shape allows one to naturally reproduce recent experimental findings of room evacuations through narrow doors in situations where the contact pressure among the pedestrians was rather large. In particular, we obtain a power-law tail distribution of the time lapses between the passage of consecutive individuals. In addition, we show that this improvement leads to new features where the particles' rotation acquires great significance.

Mammals not only can be synchronized to the natural 24-h light-dark cycle, but also to a cycle with a non-24-h period. The range of the period of the external cycle, for which the animals can be entrained to, is called the entrainment range, which differs among species. The entrainment range as a characteristic of the animal is determined by the main circadian clock, i.e., the suprachiasmatic nucleus (SCN) in the brain. The SCN is composed of $\sim 10000$ heterogeneous neurons, which can be divided into two subgroups, i.e., the ventrolateral subgroup (VL) directly receiving the light information from the retina and relaying the information to the dorsomedial subgroup (DM). Among the SCN neurons, the amplitudes are different; however, it is unclear that the amplitude is related to the location of the neurons in experiments. In the present study, we examined the effect of the difference in the neuronal amplitude between the VL and the DM on the entrainment range of the SCN, based on a mathematical model, i.e., the Poincaré model, which is used to describe the circadian clock. We find that the maximal entrainment range is obtained when the difference is equal to a critical point. If the difference of the amplitudes of the VL neurons to the amplitudes of the DM neurons is smaller than a critical point, with the increase of the difference, the entrainment range of the SCN increases, while if the difference is larger than the critical point, the entrainment range decreases with the increase of the difference. Our finding may give a potential explanation for the diversity of the entrainment range among species.

A physiologically based corticothalamic model of large-scale brain activity is used to analyze critical dynamics of transitions from normal arousal states to epileptic seizures, which correspond to Hopf bifurcations. This relates an abstract normal form quantitatively to underlying physiology that includes neural dynamics, axonal propagation, and time delays. Thus, a bridge is constructed that enables normal forms to be used to interpret quantitative data. The normal form of the Hopf bifurcations with delays is derived using Hale's theory, the center manifold theorem, and normal form analysis, and it is found to be explicitly expressed in terms of transfer functions and the sensitivity matrix of a reduced open-loop system. It can be applied to understand the effect of each physiological parameter on the critical dynamics and determine whether the Hopf bifurcation is supercritical or subcritical in instabilities that lead to absence and tonic-clonic seizures. Furthermore, the effects of thalamic and cortical nonlinearities on the bifurcation type are investigated, with implications for the roles of underlying physiology. The theoretical predictions about the bifurcation type and the onset dynamics are confirmed by numerical simulations and provide physiologically based criteria for determining bifurcation types from first principles. The results are consistent with experimental data from previous studies, imply that new regimes of seizure transitions may exist in clinical settings, and provide a simplified basis for control-systems interventions. Using the normal form, and the full equations from which it is derived, more complex dynamics, such as quasiperiodic cycles and saddle cycles, are discovered near the critical points of the subcritical Hopf bifurcations.

We experimentally investigated the self-assembly of chemically active colloidal Janus spheres into dimers. The trans-dimer conformation, in which the two active sites are oriented roughly in opposite directions and the particles are osculated at their equators, becomes dominant as the hydrogen peroxide fuel concentration increases. Our observations suggest high spinning frequency combined with little translational motion is at least partially responsible for the stabilization of the trans-dimer as activity increases.

Traditional Darcy theory for two-phase flow in porous media is shown to predict the propagation of nonmonotone saturation profiles, also known as saturation overshoot. The phenomenon depends sensitively on the constitutive parameters, on initial conditions, and on boundary conditions. Hysteresis in relative permeabilities is needed to observe the effect. Two hysteresis models are discussed and compared. The shape of overshoot solutions can change as a function of time or remain fixed and time independent. Traveling-wave-like overshoot profiles of fixed width exist in experimentally accessible regions of parameter space. They are compared quantitatively against experiment.