We consider random geometric graphs on the plane characterized by a nonuniform density of vertices. In particular, we introduce a graph model where $n$ vertices are independently distributed in the unit disk with positions, in polar coordinates $(l,\theta )$, obeying the probability density functions $\rho \left(l\right)$ and $\rho \left(\theta \right)$. Here we choose $\rho \left(l\right)$ as a normal distribution with zero mean and variance $\sigma \in (0,\infty )$ and $\rho \left(\theta \right)$ as a uniform distribution in the interval $\theta \in [0,2\pi )$. Then, two vertices are connected by an edge if their Euclidean distance is less than or equal to the connection radius $\ell$. We characterize the topological properties of this random graph model, which depends on the parameter set $(n,\sigma ,\ell )$, by the use of the average degree $\langle k\rangle$ and the number of nonisolated vertices $V_{\times }$, while we approach their spectral properties with two measures on the graph adjacency matrix: the ratio of consecutive eigenvalue spacings $r$ and the Shannon entropy $S$ of eigenvectors. First we propose a heuristic expression for $\langle k(n,\sigma ,\ell )\rangle$. Then, we look for the scaling properties of the normalized average measure $\langle \overline{X}\rangle$ (where $X$ stands for $V_{\times }$, $r$, and $S$) over graph ensembles. We demonstrate that the scaling parameter of $\langle \overline{V_{\times }}\rangle =\langle V_{\times }\rangle /n$ is indeed $\langle k\rangle$, with $\langle \overline{V_{\times }}\rangle \approx 1-exp(-\langle k\rangle )$. Meanwhile, the scaling parameter of both $\langle \overline{r}\rangle$ and $\langle \overline{S}\rangle$ is proportional to $n^{-\gamma }\langle k\rangle$ with $\gamma \approx 0.16$.

Centrality measures identify and rank the most influential entities of complex networks. In this paper, we generalize matrix function-based centrality measures, which have been studied extensively for single-layer and temporal networks in recent years to layer-coupled multiplex networks. The layers of these networks can reflect different relationships and interactions between entities or changing interactions over time. We use the supra-adjacency matrix as network representation, which has already been used to generalize eigenvector centrality to temporal and multiplex networks. With a suitable choice of edge weights, the definition of single-layer matrix function-based centrality measures in terms of walks on networks carries over naturally to the multilayer case. In contrast to other walk-based centralities, matrix function-based centralities are parameterized measures, which have been shown to interpolate between (local) degree and (global) eigenvector centrality in the single-layer case. As the explicit evaluation of the involved matrix function expressions becomes infeasible for medium to large-scale networks, we present highly efficient approximation techniques from numerical linear algebra, which rely on Krylov subspace methods, Gauss quadrature, and stochastic trace estimation. We present extensive numerical studies on synthetic and real-world multiplex transportation, communication, and collaboration networks. The comparison with established multilayer centrality measures shows that our framework produces meaningful rankings of nodes, layers, and node-layer pairs. Furthermore, our experiments corroborate the linear computational complexity of the employed numerical methods in terms of the network size that is theoretically indicated under the assumption of sparsity in the supra-adjacency matrix. This excellent scalability allows the efficient treatment of large-scale networks with the number of node-layer pairs of order ${10}^7$ or higher.

In this paper, we use a long-wave model to examine how the curvature elasticity modifies the famous Plateau-Rayleigh mechanism and the formation of viscous beads on a vertically placed fiber. By blending the analyses of linear stability, weakly nonlinear stability, exact nonlinear solutions, and numerical simulations, the effects of spontaneous curvature, surface bending rigidity, Gaussian curvature, and Van der Waals forces on the Plateau-Rayleigh mechanism and breakup of the liquid film are examined. The spontaneous curvature and surface bending rigidity are stabilizing the interface, which can reduce the amplitude and wave speed of nonlinear traveling waves and retard the breakup of film caused by Van der Waals attractions. However, the Gaussian curvature effect reinforces the Plateau-Rayleigh mechanism, which accelerates the rupture of film.

We investigate the phase-ordering dynamics of the incompressible Toner-Tu equation in three dimensions. We show that the phase ordering proceeds via defect merger events and the dynamics is controlled by the Reynolds number $\text{Re}$. At low $\text{Re}$, the dynamics is similar to that of the Ginzburg-Landau equation. At high $\text{Re}$, turbulence controls phase ordering. In particular, we observe a forward energy cascade from the coarsening length scale to the dissipation scale, clustering of defects, and multiscaling in velocity correlations.

In 1994, Jansen and Oerding predicted an interesting anomalous tricritical dynamic behavior in three-dimensional models via renormalization group theory. However, we highlight the lack of literature about the computational verification of this universal behavior. Here, we use some tricks to capture the log corrections and the parameters predicted by these authors using the three-dimensional Blume-Capel model. We quantify the crossover phenomena by computing the critical exponents near the tricritical point. In addition, we also perform a more detailed study of the dynamic localization of the phase diagram via power-law optimization.

Recently, some general relations have been intensively investigated in nonequilibrium mesoscopic systems. In particular, the thermodynamic uncertainty relation (TUR) provides a general bound of the precision for the fluctuation of some currents in terms of the corresponding entropy production. On the other hand, the fluctuation of the work performed is also a significant quantity, which is supposed to satisfy TUR under some conditions, such as symmetric driving protocol. In this paper, we analytically show that the TUR holds for the work performed on an externally perturbed quantum harmonic oscillator interacting with multiple reservoirs in full quantum regime. In this manner, we evaluate how the noncommutativity affects the thermodynamic precision. We also explore its experimental accessibility.

The statistics of first-passage times of random walks to target sites has proved to play a key role in determining the kinetics of space exploration in various contexts. In parallel, the number of distinct sites visited by a random walker and related observables has been introduced to characterize the geometry of space exploration. Here, we address the question of the joint distribution of the first-passage time to a target and the number of distinct sites visited when the target is reached, which fully quantifies the coupling between the kinetics and geometry of search trajectories. Focusing on one-dimensional systems, we present a general method and derive explicit expressions of this joint distribution for several representative examples of Markovian search processes. In addition, we obtain a general scaling form, which holds also for non-Markovian processes and captures the general dependence of the joint distribution on its space and time variables. We argue that the joint distribution has important applications to various problems, such as a conditional form of the Rosenstock trapping model, and the persistence properties of self-interacting random walks.

In this work we present an analytical and numerical study of rogue and solitary waves in a coupled one-dimensional nonlinear lattice that involves both axial and rotational degrees of freedom. Using a multiple-scale analysis, we derive a system of coupled nonlinear Schrödinger-type equations in order to approximate solitary waves and rogue waves of the coupled lattice model. Numerical simulations are found to agree with the analytical approximations. We also consider generic initialization data in the form of a Gaussian profile and observe that they can result in the spontaneous formation of rogue-wave-like patterns in the lattice. The solitary and rogue waves in the lattice demonstrate both energy isolation and exchange between the axial and rotational degrees of freedom of the system. This suggests that the studied coupled lattice has the potential to be an efficient energy isolation, transfer, and focusing medium.

Disaster propagation in complex, interdependent, and multilayered networks has attracted considerable research interest in recent years. In this paper, we propose a model that combines two dynamic mechanisms, i.e., the spreading of failure in layer-dependent networks, where each node in a layer depends on one in another layer. We first investigate the robustness of the Erdős-Rényi (ER)-ER, scale-free (sf)-ER, and sf-sf pattern of interdependent networks against cascading failure with different probabilities of triggering, and then use the random link, assortative link, and disassortative link patterns between the networks to analyze the scope of propagation of failure. The numerical results show that with increasing probability of triggering, the number of damaged nodes in both layers increased and the robustness of the scale-free network to random failures decreased due to the interdependence. Regardless of the topological structure, the two layers eventually tended to have similar failure characteristics due to their interdependence. In addition, the different link patterns had a significant effect on enhancing disaster propagation in interdependent networks.

Evolutionary game theory and the concept of an evolutionarily stable strategy have been not only extensively developed and successfully applied to explain the evolution of animal behavior, but also widely used in economics and social sciences. Recently, in order to reveal the stochastic dynamical properties of evolutionary games in randomly fluctuating environments, the concept of stochastic evolutionary stability based on conditions for stochastic local stability for a fixation state was developed in the context of a symmetric matrix game with two phenotypes and random payoffs in pairwise interactions [Zheng et al., Phys. Rev. E 96, 032414 (2017)]. In this paper, we extend this study to more general situations, namely, multiphenotype symmetric as well as asymmetric matrix games with random payoffs. Conditions for stochastic local stability and stochastic evolutionary stability are established. Conditions for a fixation state to be stochastically unstable and almost everywhere stochastically unstable are distinguished in a multiphenotype setting according to the initial population state. Our results provide some alternative perspective and a more general theoretical framework for a better understanding of the evolution of animal behavior in a stochastic environment.

In a biochemical assay that converts fan-in networks into feed-forward loops (FFLs), we show that the inter-regulator redundant information about the output gene product can be decomposed into finer components, mediated by the constituent pathways. Variance-based information within the linear noise regime facilitates quantifying these submodular redundancies. Contrary to the conventional wisdom on information decomposition, we report that information redundancy depends nontrivially on inter-regulator correlation. For the type-1 coherent (C1) and incoherent (I1) FFLs, the direct regulatory path-mediated redundancy is certainly correlation independent. However, components induced by the indirect regulatory path and interpathway interference are correlation dependent in (non)linear fashion. The trade-off between information redundancy and similarly decomposable extrinsic noise from input to output node has been demonstrated for the pathways and full motifs. Our analyses suggest that the interpathway cross redundancy positively and negatively influences the superposition of elementary redundancies in the C1- and I1-FFLs, respectively. Their corresponding total extrinsic noise is produced by the weighted sum and difference of the pathway-specific components. We find that the I1-FFL is able to manufacture more varied redundancy and extrinsic noise responses compared to the C1-FFL. Underlying the differing characteristics of the composite metrics across FFL variants, there exist uniformly behaving pathway-dependent elements. The decomposition framework has been meticulously explored in biologically rational parametric realizations through analytical estimates and stochastic simulations.

The Metropolis Monte Carlo (MMC) method is used to extract reaction kinetics from a given equilibrium distribution of states of a complex system. The approach is illustrated by the folding/unfolding reaction for two proteins: a model $\beta$-hairpin and $\alpha$-helical protein ${\alpha }_3\mathrm{D}$. For the $\beta$-hairpin, the free energy surfaces (FESs) and free energy profiles (FEPs) are employed as the equilibrium distributions of states, playing a role of the potentials of mean force to determine the acceptance probabilities of new states in the MMC simulations. Based on the FESs and PESs for a set of temperatures that were simulated with the molecular dynamics (MD) method, the MMC simulations are performed to extract folding/unfolding rates. It has been found that the rate constants and first-passage time (FPT) distributions obtained in the MMC simulations change with temperature in good agreement with those from the MD simulations. For ${\alpha }_3\mathrm{D}$ protein, whose equilibrium folding/unfolding was studied with the single-molecule FRET method [Chung et al., J. Phys. Chem. A 115, 3642 (2011)], the FRET-efficiency histograms at different denaturant concentrations were used as the equilibrium distributions of protein states. It has been found that the rate constants for folding and unfolding obtained in the MMC simulations change with denaturant concentration in reasonable agreement with the constants that were extracted from the photon trajectories on the basis of theoretical models. The simulated FPT distributions are single-exponential, which is consistent with the assumption of two-state kinetics that was made in the theoretical models. The promising feature of the present approach is that it is based solely on the equilibrium distributions of states, without introducing any additional parameters to perform simulations, which suggests its applicability to other complex systems.

In this work, we report a quenching of oscillations observed upon coupling two chemomechanical oscillators. Each one of these oscillators consists of a drop of liquid metal submerged in an oxidizing solution. These pseudoidentical oscillators have been shown to exhibit both periodic and aperiodic oscillatory behavior. In the experiments performed on these oscillators, we find that coupling two such oscillators via an attenuated resistive coupling leads the coupled system towards an oscillation quenched state. To further comprehend these experimental observations, we numerically explore and verify the presence of similar oscillation quenching in a model of coupled Hindmarsh-Rose (HR) systems. A linear stability analysis of this HR system reveals that attenuated coupling induces a change in eigenvalues of the relevant Jacobian, leading to stable quenched oscillation states. Additionally, the analysis yields a threshold of attenuation for oscillation quenching that is consistent with the value observed in numerics. So this phenomenon, demonstrated through experiments, as well as simulations and analysis of a model system, suggests a powerful natural mechanism that can potentially suppress periodic and aperiodic oscillations in coupled nonlinear systems.

This work investigates the entropy production rate, $\mathrm{\Pi }$, of the run-and-tumble model with a focus on scaling of $\mathrm{\Pi }$ as a function of the persistence time $\tau$. It is determined that (i) $\mathrm{\Pi }$ vanishes in the limit $\tau \to \infty$, marking it as an equilibrium. Stationary distributions in this limit are represented by a superposition of Boltzmann functions in analogy to a system with quenched disorder. (ii) Optimal $\mathrm{\Pi }$ is attained in the limit $\tau \to 0$, marking it as a system maximally removed from equilibrium. Paradoxically, the stationary distributions in this limit have the Boltzmann form. The value of $\mathrm{\Pi }$ in this limit is that of an unconfined run-and-tumble particle and is related to the dissipation energy of a sedimenting particle. In addition to these general conclusions, this work derives an exact expression of $\mathrm{\Pi }$ for the run-and-tumble particles in a harmonic trap.

Molecular motors convert chemical potential energy into mechanical work and perform a great number of critical biological functions. Examples include the polymerization and manipulation of nucleic acids, the generation of cellular motility and contractility, the formation and maintenance of cell shape, and the transport of materials within cells. The mechanisms underlying these molecular machines are varied, but are almost always considered in the context of a single kinetic pathway that describes motor stepping. However, the multidimensional nature of protein energy landscapes suggests the possibility of multiple reaction pathways connecting two states. Here we investigate the properties of a hypothetical molecular motor able to utilize parallel translocation mechanisms. We explore motor velocity and force dependence as a function of the energy landscape of each path and reveal the potential for such a mechanism to result in negative differential conductance. More specifically, regimes exist where increasing opposing force leads to increased velocity and an optimum load for motor function. We explore how the presence of this optimum depends on the rates of the individual paths and show that the distribution of stepping times characterized by the randomness parameter may be used to test for parallel path mechanisms. Last, we caution that experimental data consisting solely of measurements of velocity as a function of ATP concentration and force cannot be used to eliminate the possibility of such a parallel path mechanism.

Langevin dynamical simulations are performed to study the elastic behaviors of two-dimensional (2D) solid dusty plasmas under the periodic shear deformation. The frequency- and strain-dependent shear moduli $G(\omega ,\gamma )$ of our simulated 2D Yukawa solid are calculated from the ratio of the shear stress to strain in different orientations. The shear-softening and -hardening properties in different lattice orientations are discovered from the obtained $G(\omega ,\gamma )$. The component of the elastic constant tensor corresponding to the shear deformation is also calculated, whose variation trend exactly agrees with the discovered shear-softening and -hardening features in different shear directions. It is also found that the shear modulus of the 2D Yukawa solid always increases monotonically with the frequency.

Molecular expressions for thermodynamic properties of fluids and derivatives of the entropy up to third order in the isoenthalpic-isobaric ensemble are derived by using the methodology developed by Lustig for the microcanonical and canonical ensembles [J. Chem. Phys. 100, 3048 (1994); Mol. Phys. 110, 3041 (2012)]. They are expressed in a systematic way by phase-space functions, which represent derivatives of the phase-space volume with respect to enthalpy and pressure. The expressions for thermodynamic properties contain only ensemble averages of combinations of the kinetic energy and volume of the system. Thus, the calculation of thermodynamic properties in the isoenthalpic-isobaric ensemble does not require volume derivatives of the potential energy. This is particularly advantageous in Monte Carlo simulations when the interactions between molecules are described by very accurate ab initio pair and nonadditive three-body potentials. The derived expressions are validated by Monte Carlo simulations for the simple Lennard-Jones model fluid as a test case.

We study the performance of three-level quantum absorption refrigerators, paradigmatic autonomous quantum thermal machines, and reveal central impacts of strong couplings between the working system and the thermal baths. Using the reaction coordinate quantum master equation method, which treats system-bath interactions beyond weak coupling, we demonstrate that in a broad range of parameters the cooling window at strong coupling can be captured by a weak-coupling theory, albeit with parameters renormalized by the system-bath coupling energy. As a result, at strong system-bath couplings the window of cooling is significantly reshaped compared to predictions of weak-coupling treatments. We further show that strong coupling admits direct transport pathways between the thermal reservoirs. Such beyond-second-order transport mechanisms are typically detrimental to the performance of quantum thermal machines. Our study reveals that it is inadequate to claim for either a suppression or an enhancement of the cooling performance as one increases system-bath coupling—when analyzed against a single parameter and in a limited domain. Rather, a comprehensive approach should be adopted so as to uncover the reshaping of the operational window.

In this paper we analyze the relaxation to steady state of intracellular diffusion in a pair of cells with gap-junction coupling. Gap junctions are prevalent in most animal organs and tissues, providing a direct diffusion pathway for both electrical and chemical communication between cells. Most analytical models of gap junctions focus on the steady-state diffusive flux and the associated effective diffusivity. Here we investigate the relaxation to steady state in terms of the so-called local accumulation time. The latter is commonly used to estimate the time to form a protein concentration gradient during morphogenesis. The basic idea is to treat the fractional deviation from the steady-state concentration as a cumulative distribution for the local accumulation time. One of the useful features of the local accumulation time is that it takes into account the fact that different spatial regions can relax at different rates. We consider both static and dynamic gap junction models. The former treats the gap junction as a resistive channel with effective permeability $\mu$, whereas the latter represents the gap junction as a stochastic gate that randomly switches between an open and closed state. The local accumulation time is calculated by solving the diffusion equation in Laplace space and then taking the small-$s$ limit. We show that the accumulation time is a monotonically increasing function of spatial position, with a jump discontinuity at the gap junction. This discontinuity vanishes in the limit $\mu \to \infty$ for a static junction and $\beta \to 0$ for a stochastically gated junction, where $\beta$ is the rate at which the gate closes. Finally, our results are generalized to the case of a linear array of cells with nearest-neighbor gap junction coupling.