Cator and Van Mieghem [Phys. Rev. E 89, 052802 (2014)] stated that the correlation of infection at the same time between any pair of nodes in a network is non-negative for the Markovian susceptible-infected-susceptible (SIS) and susceptible-infected-removed (SIR) epidemic models. The arguments used to obtain this result rely strongly on the graphical construction of the stochastic process, as well as the Fortuin, Kasteleyn, and Ginibre (FKG) inequality. In this Comment, we show that although the approach used by the authors applies to the SIS model, it cannot be used for the SIR model as stated in their work. In particular, we observe that monotonicity in the process is crucial for invoking the FKG inequality. Moreover, we provide an example of a simple graph for which the nodal infection in the SIR Markovian model is negatively correlated.

We emphasize that correlations between infection states in both the SIS and SIR model are always positive and that the title of the article “Nodal infection in Markovian susceptible-infected-susceptible and susceptible-infected-removed epidemics on networks are non-negatively correlated” [Phys. Rev. E 89, 052802 (2014)] is correct. The history and motivation that led to the proof is placed in perspective.

The irreversible currents and entropy production rate of a dilute colloidal suspension are calculated using linear irreversible thermodynamics and the linear response theory. The “anomalous” or “hidden” entropy that has been the subject of recent discussion in the context of stochastic thermodynamics is fully accounted for in these classical frameworks. We show that the two distinct formulations lead to identical results as long as the local equilibrium assumption, or equivalently, the linear response theory, is valid.

Recently, Antonioni and Cardillo proposed a coevolutionary model based on the intertwining of oscillator synchronization and evolutionary game theory [Phys. Rev. Lett. 118, 238301 (2017)], in which each Kuramoto oscillator can decide whether to interact or not with its neighbors, and all oscillators can receive some benefits from the local synchronization, but those who choose to interact must pay a cost. Oscillators are allowed to update their strategies according to payoff difference, wherein the strategy of an oscillator who has obtained higher payoff is more likely to be followed. Utilizing this coevolutionary model, we find that the global synchronization level reaches the highest level when the average degree of the underlying interaction network is moderate. We also study how synchronization is affected by the individual rationality in choosing strategy.

Granular systems confined in vertically vibrated shallow horizontal boxes (quasi-two-dimensional geometry) present a liquid-to-solid phase transition when the frequency of the periodic forcing is increased. An effective model, where grains move and collide in two-dimensions is presented, which reproduces the aforementioned phase transition. The key element is that besides the two-dimensional degrees of freedom, each grain has an additional variable $\varepsilon$ that accounts for the kinetic energy stored in the vertical motion in the real quasi-two-dimensional motion. This energy grows monotonically during free flight, mimicking the energy gained by collisions with the vibrating walls and, at collisions, this energy is instantaneously transferred to the horizontal degrees of freedom. As a result, the average values of $\varepsilon$ and the kinetic temperature are decreasing functions of the local density, giving rise to an effective pressure that can present van der Waals loops. A kinetic theory approach predicts the conditions that must satisfy the energy growth function to obtain the phase separation, which are verified with molecular dynamics simulations. Notably, the effective equation of state and the critical points computed considering the velocity–time-of-flight correlations differ only slightly from those obtained by simple kinetic theory calculations that neglect those correlations.

It has been shown that contact aging due to chemical reactions in single asperity contacts can have a significant effect on friction. However, it is currently unknown how chemically induced contact aging of friction depends on roughness that is typically encountered in macroscopic rough contacts. Here we develop an approach that brings together a kinetic Monte Carlo model of chemical aging with a contact mechanics model of rough surfaces based on the boundary element method to determine the magnitude of chemical aging in silica-silica contacts with random roughness. Our multiscale model predicts that chemical aging for randomly rough contacts has a logarithmic dependence on time. It also shows that friction aging switches from a linear to a nonlinear dependence on the applied load as the load increase. We discover that surface roughness affects the aging behavior primarily by modifying the real contact area and the local contact pressure, whereas the effect of contact morphology is relatively small. Our results demonstrate how understanding of chemical aging can be translated from studies of single asperity contacts to macroscopic rough contacts.

When a swollen, thermoresponsive polymer gel is heated in a solvent bath, it expels solvent and deswells. When this heating is slow, deswelling proceeds homogeneously, as observed in a toroid-shaped gel that changes volume while maintaining its toroidal shape. By contrast, if the gel is heated quickly, an impermeable layer of collapsed polymer forms and traps solvent within the gel, arresting the volume change. The ensuing evolution of the gel then happens at fixed volume, leading to phase separation and the development of inhomogeneous stress that deforms the toroidal shape. We observe that this stress can cause the torus to buckle out of the plane, via a mechanism analogous to the bending of bimetallic strips upon heating. Our results demonstrate that thermodynamic instabilities, i.e., phase transitions, can be used to actuate mechanical deformation in an extreme thermodynamics of materials.

In bistable reaction–diffusion systems, transitions between stable states typically occur on timescales orders of magnitude longer than the chemical equilibration time. Estimation of transition rates within explicit Brownian dynamics simulations is computationally prohibitively costly. We present a method that exploits a single trajectory, generated by a prior simulation of diffusive motions of molecules, to sample chemical kinetic processes on timescales several orders of magnitude longer than the duration of the diffusive trajectory. In this approach, we “loop” the diffusive trajectory by transferring chemical states of the molecules from the last to the first time step of the trajectory. Trajectory looping can be applied to enhance sampling of rare events in biochemical systems in which the number of reacting molecules is constant, as in cellular signal transduction pathways. As an example, we consider a bistable system of autophosphorylating kinases, for which we calculate state-to-state transition rates and traveling wave velocities. We provide an open-source implementation of the method.

We study the mean velocity and diffusion constant in three related models of molecular Brownian ratchets. Brownian ratchets can be used to describe translocation of biopolymers like DNA through nanopores in cells in the presence of chaperones on the trans side of the pore. Chaperones can bind to the polymer and prevent it from sliding back through the pore. First, we study a simple model that describes the translocation in terms of an asymmetric random walk. It serves as an introductory example but already captures the main features of a Brownian ratchet. We then provide an analytical expression for the diffusion constant in the classical model of a translocation ratchet that was first proposed by Peskin et al. [C. S. Peskin, G. M. Odell, and G. F. Oster, Cellular motions and thermal fluctuations: The Brownian ratchet, Biophys. J. 65, 316 (1993)]. This model is based on the assumption that the binding and unbinding of the chaperones are much faster than the diffusion of the DNA strand. To remedy this shortcoming, we propose a modified model that is also applicable if the (un)binding rates are finite. We calculate the force-dependent mean velocity and diffusivity for this model and compare the results to the original one. Our analysis shows that for large pulling forces the predictions of both models can differ strongly even if the (un)binding rates are large in comparison to the diffusion timescale but still finite. Furthermore, implications of the thermodynamic uncertainty relation on the efficiency of Brownian ratchets are discussed.

A rigorous microscopic treatment of a nematic fluid system based on a pairwise interaction potential is immensely complex. For studying such systems molecular field theories are often the standard method of choice. In this paper we have chosen a simple effective potential $U=\frac{u_4}{v^4}-\frac{u_2}{v^2}-\frac{A{u}_2}{v^2}〈P_2〉P_2(cos\vartheta )$ to study an isothermal-isobaric ensemble describing a liquid crystalline system. Using this we have studied in particular the pressure dependence of liquid crystalline phase transitions.

Transient properties of the one-dimensional washboard potential are investigated in order to understand observed modulations in the statistics of escape events. Specifically, we analyze the effects of different kinds of initial conditions on the escape distribution obtained by linearly increasing the tilt of the potential. Despite the complexity of the dynamics leading up to the eventual escape, we find that the overall statistics can be interpreted in terms of the system parameters, which offers illuminating perspectives for driven one-dimensional systems with washboard potentials. We choose parameters sets relevant for Josephson junctions, a commonly studied system due to both its applications and its use as a model system in condensed matter physics.

The robustness of quantum transport under various perturbations is analyzed in disordered interacting many-body systems, which are constructed from the embedded Gaussian random matrix ensembles (EGEs). The transport efficiency can be enhanced drastically, if centrosymmetry (csEGE) is imposed. When the csEGE is perturbed with an ordinary EGE, the transport efficiency in the optimal cases is reduced significantly, while in the suboptimal cases the changes are less pronounced. Qualitatively the same behavior is observed, when parity and centrosymmetry are broken by block perturbations. Analyzing the influence of the environment coupling, optimal transport is observed at a certain coupling strength, while too weak and too strong coupling reduce the transport. Taking into account the effects of decoherence, in the EGE the transport efficiency approaches its maximum at a finite nonzero decoherence strength (environment-assisted transport). In the csEGE the efficiency decays monotonically with the decoherence but is always larger than in the EGE.

This paper revisits the well-known transition fronts (kinks) in chains of coupled oscillators with nondegenerate on-site potentials. Usually, such transition fronts are considered in terms of traveling-wave solutions. We explore the loss of stability of such traveling waves. Generically, it corresponds to one of the common scenarios for fixed points of discrete maps. For example, one can encounter the quasiperiodic kink propagation (due to Hopf bifurcation), or the Feigenbaum cascade of period doublings, leading to a chaoticlike propagation pattern. The aforementioned scenarios show up, for instance, for triparabolic and ${\phi }^4$ on-site potentials. Numeric evidence suggests that the loss of stability occurs due to resonances between the frequency associated with the kink propagation, and the linear band gaps of the chain. Particular resonance mechanisms are model dependent. For the classical Atkinson-Cabrera model with a biparabolic on-site potential, the stability threshold is estimated by the simple means of linear algebra. The loss of stability in this model occurs through Hopf bifurcation. The results are in good agreement with numerical simulations.

We study the dynamics of sets of independent systems, all of which are coupled to the same time-dependent external force. Using optimal control theory, we compute the most efficient temporal pulse shape for this force that can maximize simultaneously the collective response of these systems. This response can be a weighted sum of all amplitudes at the final interaction time. Remarkably, it turns out that for certain systems this optimal force for the collective response can be related to the individual forces that would optimize each system separately. We illustrate this superposition principle for the simultaneous optimization of collective responses with numerical and also analytical solutions for sets of damped linear and nonlinear oscillators. We also apply this principle to predict the optimal temporal profile of a laser pulse that can maximize the final macroscopic polarization (total dipole moment) of a set of quantum mechanical two-level atoms.

We study continuum percolation with disks, a variant of continuum percolation in two-dimensional Euclidean space, by applying tools from topological data analysis. We interpret each realization of continuum percolation with disks as a topological subspace of ${[0,1]}^2$ and investigate its topological features across many realizations. Specifically, we apply persistent homology to investigate topological changes as we vary the number and radius of disks, and we observe evidence that the longest persisting invariant is born at or near the percolation transition.

Identification and quantification of the structural dissimilarities between complex networks is a very important and challenging problem in network science. A simple and efficient way to quantify network differences remains unexplored. Although the methods for network comparison based on the probability distribution of a network descriptor have been shown to be effective for specific purposes, the information they provide is often limited or incomplete. In order to overcome the defect of the methods, here we use the communicability between two nodes to define the communicability sequence entropy of networks, and on the basis of this entropy measure, we propose a Jensen-Shannon divergence of two networks which can be used as natural distance measure between complex networks. By the extensive experiments, we find that the measure can accurately quantify the structural dissimilarities between synthetic networks. Most importantly, the measure can be able to identify the critical percolation probability of the random network in the evolution process, and it can also effectively guide us to choose a more suitable model to simulate real systems.

We study how the interaction between hydrodynamics and chemotaxis affects the colonization of nutrient sources by microorganisms. We use an individual-based model and perform probabilistic simulations to ascertain the impact of important environmental and motility characteristics on the spatial distribution of microorganisms around a spherical nutrient source. In general, we unveil four distinct regimes based on the distribution of the microorganisms: (i) strong surface colonization, (ii) rotary-diffusion-induced “off-surface” accumulation, (iii) a depletion zone in the spatial distribution, and (iv) no appreciable aggregation, with their occurrence being contingent on the relative strengths of hydrodynamic and chemotactic effects. More specifically, we show that the extent of surface colonization first increases, then reaches a plateau, and finally decreases as the nutrient availability is increased. We also show that surface colonization reduces monotonically as the mean run length of the chemotactic microorganisms increases. Our study provides insight into the interplay of two important mechanisms governing microorganism behavior near nutrient sources, isolates each of their effects, and thus offers greater predictability of this nontrivial phenomenon.

Steady thermocapillary droplet migration in a uniform temperature gradient combined with a radiation energy source at large Reynolds and Marangoni numbers is studied. To reach a terminal quasisteady process, the magnitude of the radiation energy source is required to preserve the conservative integral thermal flux across the surface. Under a quasisteady state assumption, an analytical result for the steady thermocapillary migration of a droplet at large Reynolds and Marangoni numbers is derived by using the method of matched asymptotic expansions. It is shown that the thermocapillary droplet migration speed increases as the Marangoni number increases, while a radiation energy source with a sine square dependence is provided.

Numerical simulations of lattice quantum field theories whose continuum counterparts possess classical solutions with nontrivial topology face a severe critical slowing down as the continuum limit is approached. Standard Monte Carlo algorithms develop a loss of ergodicity, with the system remaining frozen in configurations with fixed topology. We analyze the problem in a simple toy model, consisting of the path integral formulation of a quantum mechanical particle constrained to move on a circumference. More specifically, we implement for this toy model various techniques which have been proposed to solve or alleviate the problem for more complex systems, like non-Abelian gauge theories, and compare them both in the regime of low temperature and in that of very high temperature. Among the various techniques, we propose an alternative algorithm which completely solves the freezing problem, but unfortunately is specifically tailored for this particular model and not easily exportable to more complex systems.

We present an analytical and numerical study of the Ising model on a bilayer honeycomb lattice including interlayer frustration and coupling with an external magnetic field. First, we discuss the exact $T=0$ phase diagram, where we find finite entropy phases for different magnetizations. Then, we study the magnetic properties of the system at finite temperature using complementary analytical techniques (Bethe lattice) and two types of Monte Carlo algorithms (Metropolis and Wang-Landau). We characterize the phase transitions and discuss the phase diagrams. The system presents a rich phenomenology: There are first- and second-order transitions, low-temperature phases with extensive degeneracy, and order-by-disorder state selection.