A method is proposed for generalizing the equations obtained within the framework of the edge-based compartmental modeling approach for the case of non-Poissonian transmission and recovery processes. It is confirmed that non-Markovian systems of equations obtained in this manner, which describe the spread of epidemic diseases, can be represented as Markovian systems of equations. The application of the proposed method in particular types of edge-based compartmental models is considered. In particular, the analytical expressions for the basic reproductive number and the final size of an epidemic are derived for the non-Markovian dynamic variable-degree model.

Electrohydrodynamic (EHD) breakup phenomena for a leaky dielectric drop suspended in another immiscible viscous dielectric and subjected to a uniform electric field are examined using the leaky dielectric theory and the explicit forcing lattice Boltzmann method, by taking into account full nonlinear inertia effects. The breakup modes are first computed for varied conductivity of the drop fluid, as the viscosity ratio $\lambda$ $\left(={\mu }_{\mathrm{in}}/{\mu }_{\mathrm{out}}\right)$ is momentarily set to unity, that is, for the slightly conducting $\left(R={\sigma }_{\mathrm{in}}/{\sigma }_{\mathrm{out}}<10\right)$, moderately conducting $\left(10\le R\le 20\right)$, and highly conducting $\left(R>20\right)$ cases. For slightly conducting drops $\left(R=5\right)$ only one breakup mode via two symmetrical necks persists for permittivity ratios $0.05<Q={\varepsilon }_{\mathrm{in}}/{\varepsilon }_{\mathrm{out}}<3.0$ and electric capillary number ${\mathrm{Ca}}_E>\mathrm{C}{\mathrm{a}}_{E,\mathrm{critical}}$ (ratio of electric and surface tension forces), despite significant length-scale variation of mother and daughter drops. At higher $Q$ (for increased drop permittivity) two necks move closer to the bulbous midpart of the extended droplet, which helps enlarge two daughter drops. However, in the case of moderately conducting drops $\left(10\le R\le 20\right)$ the number of necks increased to four for increased ${\mathrm{Ca}}_E$. Accordingly two pairs of symmetrical daughter drops are created because of recurrent fluctuations of the electrical shear stress and centerline momentum flux. For highly conducting cases of $R>20$, depending on ${\mathrm{Ca}}_E$, three distinctly elongated droplet states are formed prior to breakup, which results in the onset of three different breakup modes, namely, via formations of lobed ends $\left({\mathrm{Ca}}_E\le 0.264\right)$, pointed ends $\left({\mathrm{Ca}}_E\le 0.68\right)$, and nonpointed ends $\left({\mathrm{Ca}}_E>0.83\right)$. While being consistent with past measurements, here we precisely characterize the associated breakup mechanisms and physics in terms of the interactive electric pressure, electric shear stress, and hydrodynamic pressure plus velocity gradients. Since the EHD drop breakup is a dynamic process, on an elongated slender drop the activated locally distinct driving forces, i.e., electric pressure at the end regions and tangential electric stress in the midsection, effectively lead to neck formations by virtue of the created high centerline velocity gradient. Accordingly, resulting variations of local extension rate and net mass flux toward drop ends or into intermediate bulbous regions facilitate the multiple-mode drop breakup via the inertia effect, whereas the developed negative curvature around a neck encourages capillary breakup. We also explicitly reveal the effect of the viscosity contrast $\lambda$, which particularly influences the breakup characteristics over a broader range of conductivity ratios.

Coordination of dynamical routes can alleviate traffic congestion and is essential for the coming era of autonomous self-driving cars. However, dynamical route coordination is difficult and many existing routing protocols are either static or without intervehicle coordination. In this paper, we first apply the cavity approach in statistical physics to derive the theoretical behavior and an optimization algorithm for dynamical route coordination, but they become computationally intractable as the number of time segments increases. We therefore map static spatial networks to space-time networks to derive a computational feasible message-passing algorithm compatible with arbitrary system parameters; it agrees well with the analytical and algorithmic results of the conventional cavity approach and outperforms multistart greedy search in saving total travel time by as much as 15% in simulations. The study sheds light on the design of dynamical route coordination protocols and the solution to other dynamical problems via static analytical approaches on space-time networks.

We study the statistical mechanics of a single active slider on a fluctuating interface, by means of numerical simulations and theoretical arguments. The slider, which moves by definition towards the interface minima, is active as it also stimulates growth of the interface. Even though such a particle has no counterpart in thermodynamic systems, active sliders may provide a simple model for ATP-dependent membrane proteins that activate cytoskeletal growth. We find a wide range of dynamical regimes according to the ratio between the timescales associated with the slider motion and the interface relaxation. If the interface dynamics is slow, the slider behaves like a random walker in a random environment, which, furthermore, is able to escape environmental troughs by making them grow. This results in different dynamic exponents to the interface and the particle: the former behaves as an Edward-Wilkinson surface with dynamic exponent 2, whereas the latter has dynamic exponent $3/2$. When the interface is fast, we get sustained ballistic motion with the particle surfing a membrane wave created by itself. However, if the interface relaxes immediately (i.e., it is infinitely fast), particle motion becomes symmetric and goes back to diffusive. Due to such a rich phenomenology, we propose the active slider as a toy model of fundamental interest in the field of active membranes and, generally, whenever the system constituent can alter the environment by spending energy.

We study the spatiotemporal dynamics of a conductance-based neuronal cable. The processes of one-dimensional (1D) and 2D diffusion are considered for a single variable, which is the membrane voltage. A 2D Morris-Lecar (ML) model is introduced to investigate the nonlinear responses of an excitable conductance-based neuronal cable. We explore the parameter space of the uncoupled ML model and, based on the bifurcation diagram (as a function of stimulus current), we analyze the 1D diffusion dynamics in three regimes: phasic spiking, coexistence states (tonic spiking and phasic spiking exist together), and a quiescent state. We show (depending on parameters) that the diffusive system may generate regular and irregular bursting or spiking behavior. Further, we explore a 2D diffusion acting on the membrane voltage, where striped and hexagonlike patterns can be observed. To validate our numerical results and check the stability of the existing patterns generated by 2D diffusion, we use amplitude equations based on multiple-scale analysis. We incorporate 1D diffusion in an extended 3D version of the ML model, in which irregular bursting emerges for a certain diffusion strength. The generated patterns may have potential applications in nonlinear neuronal responses and signal transmission.

We present a method for the construction of ensembles of random networks that consist of a single connected component with a given degree distribution. This approach extends the construction toolbox of random networks beyond the configuration model framework, in which one controls the degree distribution but not the number of components and their sizes. Unlike configuration model networks, which are completely uncorrelated, the resulting single-component networks exhibit degree-degree correlations. Moreover, they are found to be disassortative, namely, high-degree nodes tend to connect to low-degree nodes and vice versa. We demonstrate the method for single-component networks with ternary, exponential, and power-law degree distributions.

Pneumatic structures and actuators are found in a variety of natural and engineered systems such as dielectric actuators, soft robots, plants and fungi cells, or even the vocal sac of frogs. These structures are often subjected to mechanical instabilities arising from the thinning of their cross section and that may be harvested to perform mechanical work at a low energetic cost. While most of our understanding of this unstable behavior is for purely elastic membranes, real materials including lipid bilayers, elastomers, and connective tissues typically display a time-dependent viscoelastic response. This paper thus explores the role of viscous effects on the nature of this elastic instability when such membranes are dynamically inflated. For this, we first introduce an extension of the transient network theory to describe the finite strain viscoelastic response of membranes, enabling an elegant formulation while keeping a close connection with the dynamics of the underlying polymer network. We then combine experiments and simulations to analyze the viscoelastic behavior of an inflated blister made of a commercial adhesive tape (VHB 4905). Our results show that the viscous component induces a rich spectrum of behaviors bounded by two well-known elastic solutions corresponding to very high and very low inflation rates. We also show that membrane relaxation may induce unwanted buckling when it is subjected to cyclic inflations at certain frequencies. These results have clear implications for the inflation and mechanical work performed by time-dependent pneumatic structures and instability-based actuators.

The applicability to dense hard sphere colloidal suspensions of a general coarse-graining approach called Record Dynamics (RD) is tested by extensive molecular dynamics simulations. We reproduce known results as logarithmic diffusion and the logarithmic decay of the average potential energy per particle. We provide quantitative measures for the cage size and identify the displacements of single particles corresponding to intermittent cage breakings. We then partition the system into spatial domains and show that, within each domain, a subset of such intermittent events called quakes constitutes a log-Poisson process, as predicted by RD. Specifically, quakes are shown to be statistically independent and Poisson distributed with an average depending on the logarithm of time. Finally, we discuss the nature of the dynamical barriers surmounted by quakes and link RD to the phenomenology of aging hard sphere colloids.

The properties of a hinged floating elastic sheet of finite length under compression are considered. Numerical continuation is used to compute spatially localized buckled states with many spatially localized folds. Both symmetric and antisymmetric states are computed and the corresponding bifurcation diagrams determined. Weakly nonlinear analysis is used to analyze the transition from periodic wrinkles to singlefold and multifold states and to compute their energy. States with the same number of folds have energies that barely differ from each other and the energy gap decreases exponentially as localization increases. The stability of the different competing states is studied and the multifold solutions are all found to be unstable. However, the decay time into solutions with fewer folds can be so slow that multifolds may appear to be stable.

We put forward a quantum-optical model for a thermal diode based on heat transfer between two thermal baths through a pair of interacting qubits. We find that if the qubits are coupled by a Raman field that induces an anisotropic interaction, heat flow can become nonreciprocal and undergoes rectification even if the baths produce equal dissipation rates of the qubits, and these qubits can be identical, i.e., mutually resonant. The heat flow rectification is explained by four-wave mixing and Raman transitions between dressed states of the interacting qubits and is governed by a global master equation. The anisotropic two-qubit interaction is the key to the operation of this simple quantum thermal diode, whose resonant operation allows for high-efficiency rectification of large heat currents. Effects of spatial overlap of the baths are addressed. We discuss the possible realizations of the model in various platforms, including optomechanical setups, systems of trapped ions, and circuit QED.

The ferromagnetic transition in the Ising model is the paradigmatic example of ergodicity breaking accompanied by symmetry breaking. It is routinely assumed that the thermodynamic limit is taken with free or periodic boundary conditions. More exotic symmetry-preserving boundary conditions, like cylindrical antiperiodic, are less frequently used for special tasks, such as the study of phase coexistence or the roughening of an interface. Here we show, instead, that when the thermodynamic limit is taken with these boundary conditions, a novel type of transition takes place below $T_c$ (the usual Ising transition temperature) without breaking either ergodicity or symmetry. Then the low-temperature phase is characterized by a regime (condensation) of strong magnetization's fluctuations which replaces the usual ferromagnetic ordering. This is due to critical correlations perduring for all $T$ below $T_c$. The argument is developed exactly in the $d=1$ case and numerically in the $d=2$ case.

In improving the stability of complex dynamical systems, an outstanding problem is how to achieve the desired performance at a low cost. For engineering and biological complex systems whose performance and functionality rely on the synchronous motion of their units, an important question related to the performance-cost-balance problem is how to improve efficiently the system synchronizability when a small amount of additional coupling resource is available. Here, employing a complex network of coupled chaotic oscillators as the model, we address this question by introducing a small amount of coupling intensity to only a single oscillator and investigate how the improvement of the network synchronizability is dependent on the location of the target oscillator. Theoretical analysis shows that, to achieve the maximum network synchronizability, the target oscillator to be strengthened should be chosen according to the eigenvector of the most unstable mode. Based on the theoretical finding, we further propose a single-node-based scheme for improving synchronization: the eigenvector-centrality-based strengthening scheme. We describe in detail how to apply this scheme under different synchronization scenarios and justify its efficiency in various network models by numerical simulations. The performance of the new scheme is compared with the conventional ones based on betweenness, closeness, and degree centralities, and it is shown that the new scheme has a clear advantage over the conventional ones. Furthermore, by a brute-force search of the target oscillator over the network, it is verified numerically that the oscillator identified by the new scheme indeed gives the best synchronization performance.

We study mixing patterns in networks, meaning the propensity for nodes of different kinds to connect to one another. The phenomenon of assortative mixing, whereby nodes prefer to connect to others that are similar to themselves, has been widely studied, but here we go further and examine how and to what extent nodes that are otherwise similar can have different preferences. Many individuals in a friendship network, for instance, may prefer friends who are roughly the same age as themselves, but some may display a preference for older or younger friends. We introduce a network model that captures this behavior and a method for fitting it to empirical network data. We propose metrics to characterize the mean and variation of mixing patterns and show how to infer their values from the fitted model, either using maximum-likelihood estimates of model parameters or in a Bayesian framework that does not require fixing any parameters.

In this paper the small-amplitude motion of multiple superposed viscous fluids is studied as a linearized initial-value problem. The analysis results in a closed set of equations for the Laplace transformed amplitudes of the interfaces that can be inverted numerically. The derived equations also contain the general normal mode equations, which can be used to determine the asymptotic growth rates of the systems directly. After derivation, the equations are used to study two different problems involving three fluid layers. The first problem is the effect of initial phase difference on the development of a Rayleigh-Taylor instability and the second is the damping effect of a thin, highly viscous, surface layer.

We study the contact-angle hysteresis and morphology changes of a liquid drop sitting on a solid substrate inclined with respect to the horizontal at an angle $\alpha$. This one is always smaller than the critical angle, ${\alpha }_{\text{crit}}$, above which the drop would start to slide down. The hysteresis cycle is performed for positive and negative $\alpha$'s ($\left|\alpha \right|<{\alpha }_{\text{crit}}$), and a complete study of the changes in contact angles, free surface, and footprint shape is carried out. The drop shape is analyzed in terms of a solution of the equilibrium pressure equation within the long-wave model (lubrication approximation). We obtain a truncated analytical solution describing the static drop shapes that is successfully compared with experimental data. This solution is of practical interest since it allows for a complete description of all the drop features, such as its footprint shape or contact angle distribution around the drop periphery, starting from a very small set of relatively easy to measure drop parameters.

Systems kept out of equilibrium in stationary states by an external source of energy store an energy $\mathrm{\Delta }U=U-U_0$. $U_0$ is the internal energy at equilibrium state, obtained after the shutdown of energy input. We determine $\mathrm{\Delta }U$ for two model systems: ideal gas and a Lennard-Jones fluid. $\mathrm{\Delta }U$ depends not only on the total energy flux, $J_U$, but also on the mode of energy transfer into the system. We use three different modes of energy transfer where the energy flux per unit volume is (i) constant, (ii) proportional to the local temperature, and (iii) proportional to the local density. We show that $\mathrm{\Delta }U/J_U=\tau$ is minimized in the stationary states formed in these systems, irrespective of the mode of energy transfer. $\tau$ is the characteristic timescale of energy outflow from the system immediately after the shutdown of energy flux. We prove that $\tau$ is minimized in stable states of the Rayleigh-Benard cell.

We model a particulate flow of constant velocity through confined geometries, ranging from a single channel to a bundle of $N_c$ identical coupled channels, under conditions of reversible blockage. Quantities of interest include the exiting particle flux (or throughput) and the probability that the bundle is open. For a constant entering flux, the bundle evolves through a transient regime to a steady state. We present analytic solutions for the stationary properties of a single channel with capacity $N\le 3$ and for a bundle of channels each of capacity $N=1$. For larger values of $N$ and $N_c$, the system's steady state behavior is explored by numerical simulation. Depending on the deblocking time, the exiting flux either increases monotonically with intensity or displays a maximum at a finite intensity. For large $N$ we observe an abrupt change from a state with few blockages to one in which the bundle is permanently blocked and the exiting flux is due entirely to the release of blocked particles. We also compare the relative efficiency of coupled and uncoupled bundles. For $N=1$ the coupled system is always more efficient, but for $N>1$ the behavior is more complex.

The manipulation of the self-organized critical systems by repeatedly deliberate local relaxations (local smoothing) is considered. During a local smoothing, the grains diffuse to the neighboring regions, causing a smoothening of the height filed over the system. The local smoothings are controlled by a parameter $\zeta$ which is related to the number of local smoothening events in an avalanche. The system shows some new (mass and time) scales, leading to some oscillatory behaviors. A bifurcation occurs at some $\zeta$ value, above which some oscillations are observed for the mean number of grains, and also in the autocorrelation functions. These oscillations are associated with spanning avalanches which are due to the accumulation of grains in the smoothed system. The analysis of the rare event waiting time confirms also the appearance of a new time scale.

Effective connectivity embodied in transfer functions is derived from symmetric-network activity correlations under task-free conditions via a recent causal spectral factorization method. This generalizes previous covariance-based analyses to include frequency dependencies and time delays. Results are verified against analytic solutions of equations that have reproduced many aspects of experimental brain dynamics and against cases of more complex connectivity. Robustness to noise is also demonstrated.