The Kuramoto model exhibits different types of synchronization transitions depending on the type of natural frequency distribution. To obtain these results, the Kuramoto self-consistency equation (SCE) approach has been used successfully. However, this approach affords only limited understanding of more detailed properties such as the stability. Here we extend the SCE approach by introducing an effective potential, that is, an integral version of the SCE. We examine the landscape of this effective potential for second-order, first-order, and hybrid synchronization transitions in the thermodynamic limit. In particular, for the hybrid transition, we find that the minimum of effective potential displays a plateau across the region in which the order parameter jumps. This result suggests that the effective potential can be used to determine a type of synchronization transition.

We simulate a tug-of-war (TOW) scenario for a model double-stranded DNA threading through a double nanopore (DNP) system. The DNA, simultaneously captured at both pores, is subject to two equal and opposite forces $-{\vec{f}}_L={\vec{f}}_R$ (TOW), where ${\vec{f}}_L$ and ${\vec{f}}_R$ are the forces applied to the left and the right pore, respectively. Even though the net force on the DNA polymer $\mathrm{\Delta }{\vec{f}}_{LR}={\vec{f}}_L+{\vec{f}}_R=0$, the mean first passage time (MFPT) $\langle \tau \rangle$ depends on the magnitude of the TOW forces $\left|f_L\right|=\left|f_R\right|=f_{LR}$. We qualitatively explain this dependence of $\langle \tau \rangle$ on $f_{LR}$ from the known results for the single-pore translocation of a triblock copolymer A-B-A with ${\ell }_{pB}>{\ell }_{pA}$, where ${\ell }_{pA}$ and ${\ell }_{pB}$ are the persistence length of the A and B segments, respectively. We demonstrate that the time of flight of a monomer with index $m \left[\langle {\tau }_{LR}\left(m\right)\rangle \right]$ from one pore to the other exhibits quasiperiodic structure commensurate with the distance between the pores $d_{LR}$. Finally, we study the situation where we offset the TOW biases so that $\mathrm{\Delta }{\vec{f}}_{LR}={\vec{f}}_L+{\vec{f}}_R\ne 0$, and qualitatively reproduce the experimental result of the dependence of the MFPT on $\mathrm{\Delta }{\vec{f}}_{LR}$. We demonstrate that, for a moderate bias, the MFPT for the DNP system for a chain length $N$ follows the same scaling ansatz as that for the single nanopore, $\langle \tau \rangle =\left(A{N}^{1+\nu }+{\eta }_{\mathrm{pore}}N\right){\left(\mathrm{\Delta }{f}_{LR}\right)}^{-1}$, where ${\eta }_{\mathrm{pore}}$ is the pore friction, which enables us to estimate $\langle \tau \rangle$ for a long chain. Our Brownian dynamics simulation studies provide fundamental insights and valuable information about the details of the translocation speed obtained from $\langle {\tau }_{LR}\left(m\right)\rangle$, and accuracy of the translation of the data obtained in the time domain to units of genomic distances.

In a recent paper [Wang, Huang, and Feng, Phys. Rev. E 99, 063206 (2019)], Langevin dynamical simulation results related to the shear modulus $G$ of a two-dimensional liquid dusty plasma were reported. The purpose of this Comment is to provide a comparison with available theoretical models to calculate $G$ and to indicate the correct way of interpreting the numerical results.

In the preceding Comment [Khrapak and Klumov, preceding Comment, Phys. Rev. E 101, 057201 (2020)], a completely different method is used to calculate the shear modulus of two-dimensional Yukawa solids. Here the results of the shear modulus of two-dimensional Yukawa solids obtained in a previous work [Wang et al., Phys. Rev. E 99, 063206 (2019)] are compared with the results in the preceding Comment. It is found that the two empirical fits from the two methods are in extremely close agreement, supporting the consistency of these two methods.

We introduce and numerically study the branching annihilating random walks with long-range attraction (BAWL). The long-range attraction makes hopping biased in such a manner that particle's hopping along the direction to the nearest particle has larger transition rate than hopping against the direction. Still, unlike the Lévy flight, a particle only hops to one of its nearest-neighbor sites. The strength of bias takes the form $x^{-\sigma }$ with non-negative $\sigma$, where $x$ is the distance to the nearest particle from a particle to hop. By extensive Monte Carlo simulations, we show that the critical decay exponent $\delta$ varies continuously with $\sigma$ up to $\sigma =1$ and $\delta$ is the same as the critical decay exponent of the directed Ising (DI) universality class for $\sigma \ge 1$. Investigating the behavior of the density in the absorbing phase, we argue that $\sigma =1$ is indeed the threshold that separates the DI and non-DI critical behavior. We also show by Monte Carlo simulations that branching bias with symmetric hopping exhibits the same critical behavior as the BAWL.

The Kardar-Parisi-Zhang (KPZ) equation is a paradigmatic model of nonequilibrium low-dimensional systems with spatiotemporal scale invariance, recently highlighting universal behavior in fluctuation statistics. Its space derivative, namely the noisy Burgers equation, has played a very important role in its study, predating the formulation of the KPZ equation proper, and being frequently held as an equivalent system. We show that, while differences in the scaling exponents for the two equations are indeed due to a mere space derivative, the field statistics behave in a remarkably different way: while the KPZ equation follows the Tracy-Widom distribution, its derivative displays Gaussian behavior, hence being in a different universality class. We reach this conclusion via direct numerical simulations of the equations, supported by a dynamic renormalization group study of field statistics.

Growing graphs describe a multitude of developing processes from maturing brains to expanding vocabularies to burgeoning public transit systems. Each of these growing processes likely adheres to proliferation rules that establish an effective order of node and connection emergence. When followed, such proliferation rules allow the system to properly develop along a predetermined trajectory. But rules are rarely followed. Here we ask what topological changes in the growing graph trajectories might occur after the specific but basic perturbation of permuting the node emergence order. Specifically, we harness applied topological methods to determine which of six growing graph models exhibit topology that is robust to randomizing node order, termed global reorderability, and robust to temporally local node swaps, termed local reorderability. We find that the six graph models fall upon a spectrum of both local and global reorderability, and furthermore we provide theoretical connections between robustness to node pair ordering and robustness to arbitrary node orderings. Finally, we discuss real-world applications of reorderability analyses and suggest possibilities for designing reorderable networks.

Whereas knowledge of a crystalline material's unit cell is fundamental to understanding the material's properties and behavior, there are no obvious analogs to unit cells for disordered materials despite the frequent existence of considerable medium-range order. This article views a material's structure as a collection of local atomic environments that are sampled from some underlying probability distribution of such environments, with the advantage of offering a unified description of both ordered and disordered materials. Crystalline materials can then be regarded as special cases where the underlying probability distribution is highly concentrated around the traditional unit cell. The $H_1$ barcode is proposed as a descriptor of local atomic environments suitable for disordered bond networks and is applied with three other descriptors to molecular dynamics simulations of silica glasses. Each descriptor reliably distinguishes the structure of glasses produced at different cooling rates, with the $H_1$ barcode and coordination profile providing the best separation. The approach is generally applicable to any system that can be represented as a sparse graph.

The cortical microtubule array of dark-grown hypocotyl cells of plant seedlings undergoes a striking, and developmentally significant, reorientation on exposure to light. This process is driven by the exponential amplification of a population of longitudinal microtubules, created by severing events localized at crossovers with the microtubules of the pre-existing transverse array. We present a dynamic one-dimensional model for microtubule amplification through this type of templated severing. We focus on the role of the probability of immediate stabilization-after-severing of the newly created lagging microtubule, observed to be a characteristic feature of the reorientation process. Employing stochastic simulations, we show that in the dynamic regime of unbounded microtubule growth, a finite value of this probability is not required for amplification to occur but does strongly influence the degree of amplification and hence the speed of the reorientation process. In contrast, in the regime of bounded microtubule growth, we show that amplification only occurs above a critical threshold. We construct an approximate analytical theory, based on a priori limiting the number of crossover events considered, which allows us to predict the observed critical value of the stabilization-after-severing probability with reasonable accuracy.

We discuss the experimental and modeling results for the x-ray heating and temperature of laboratory photoionized plasmas. A method is used to extract the electron temperature based on the analysis of transmission spectroscopy data that is independent of atomic kinetics modeling. The results emphasized the critical role of x-ray heating and radiation cooling in determining the energy balance of the plasma. They also demonstrated the dramatic impact of photoexcitation on excited-state populations, line emissivity, and radiation cooling. Modeling calculations performed with astrophysical codes significantly overestimated the measured temperature.

We show that Hermitian matrix models support the occurrence of a phase transition characterized by dispersive regularization of the order parameter near the critical point. Using the identification of the partition function with a solution of the reduction of the Toda hierarchy known as the Volterra system, we argue that the singularity is resolved by the onset of a multidimensional dispersive shock of the order parameter in the space of coupling constants. This analysis explains the origin and mechanism leading to the emergence of chaotic behaviors observed in $M^6$ matrix models and extends its validity to even nonlinearity of arbitrary order.

Solid-liquid interfacial properties out of equilibrium provide the essential information required for understanding and controlling solidification microstructures in metallic materials. However, few studies have attempted to reveal all interfacial properties out of equilibrium in detail. The present study proposes an approach for simultaneously estimating all interfacial properties in a pure metal below the melting point on the basis of the Bayesian inference theory. The solid-liquid interfacial energy, interfacial mobility, and anisotropy parameters in pure Fe are estimated by combining molecular dynamics simulation with phase-field simulation using an ensemble Kalman filter, which is a data assimilation technique. Furthermore, the temperature dependences of all interfacial parameters are computed and discussed. In summary, the proposed multiscale approach integrates atomistic and microstructural simulations within the framework of data science and it has considerable potential for a wide variety of applications in materials engineering.

Recent theories of nucleation that go beyond classical nucleation theory predict that diffusion-limited nucleation of both liquid droplets and of crystals from a low-density vapor (or weak solution) begins with long-wavelength density fluctuations. This means that in the early stages of nucleation, “clusters” can have low density but large spatial extent, which is at odds with the classical picture of arbitrarily small clusters of the condensed phase. We present the results of kinetic Monte Carlo simulations using forward flux sampling to show that these predictions are confirmed, namely, that on average, nucleation begins in the presence of low-amplitude, but spatially extended density fluctuations thus confirming a significant prediction of the nonclassical theory.

We study the overdamped Brownian dynamics of particles moving in piecewise-defined potential energy landscapes $U\left(x\right)$, where the height $Q$ of each section is obtained from the exponential distribution $p\left(Q\right)=a\beta \text{exp}(-a\beta Q)$, where $\beta$ is the reciprocal thermal energy, and $a>0$. The averaged effective diffusion coefficient $\langle D_{\text{eff}}\rangle$ is introduced to characterize the diffusive motion: $\langle x^2\rangle =2\langle D_{\text{eff}}\rangle t$. A general expression for $\langle D_{\text{eff}}\rangle$ in terms of $U\left(x\right)$ and $p\left(Q\right)$ is derived and then applied to three types of energy landscape: flat sections, smooth maxima, and sharp maxima. All three cases display a transition between subdiffusive and diffusive behavior at $a=1$, and a reduction to free diffusion as $a\to \infty$. The behavior of $\langle D_{\text{eff}}\rangle$ around the transition is investigated and found to depend heavily upon the shape of the maxima: Energy landscapes made up of flat sections or smooth maxima display power-law behavior, while for landscapes with sharp maxima, strongly divergent behavior is observed. Two aspects of the subdiffusive regime are studied: the growth of the mean squared displacement with time and the distribution of mean first-passage times. For the former, agreement between Brownian dynamics simulations and a coarse-grained equivalent was observed, but the results deviated from the random barrier model's predictions. The discrepancy could be a finite-time effect. For the latter, agreement between the characteristic exponent calculated numerically and that predicted by the random barrier model is observed in the large-amplitude limit.

We analytically derive maximum efficiency at given cooling power for Carnot-type low-dissipation refrigerators. The corresponding optimal cycle duration depends on a single parameter, which is a specific combination of irreversibility parameters and bath temperatures. For a slight decrease in power with respect to its maximum value, the maximum efficiency exhibits an infinitely fast nonlinear increase, which is standard in heat engines, only for a limited range of parameters. Otherwise, it increases only linearly with the slope given by ratio of irreversibility parameters. This behavior can be traced to the fact that maximum power is attained for vanishing duration of the hot isotherm. Due to the lengthiness of the full solution for the maximum efficiency, we discuss and demonstrate these results using simple approximations valid for parameters yielding the two different qualitative behaviors. We also discuss relation of our findings to those obtained for minimally nonlinear irreversible refrigerators.

In this paper, we broaden the master stability function approach to study the stability of the synchronization manifold in complex networks of stochastic dynamical systems. We provide necessary and sufficient conditions for exponential stability that allow us to discriminate the impact of noise. We observe that noise can be beneficial for synchronization when it diffuses evenly in the network. On the contrary, an excessively large amount of noise only acting on a subset of the node state variables might have disruptive effects on the network synchronizability. To demonstrate our findings, we complement our theoretical derivations with extensive simulations on paradigmatic examples of networks of noisy systems.

Game A $+$ Game B = Game C. Parrondo's games follow this basic structure where A and B are losing games and C is a winning game—a phenomenon called Parrondo's paradox. These games can take on a wider class of definitions and exhibit these paradoxical results. In this paper, we show three paradoxical cases. (i) The successive “tossing” of a single fair quantum coin gives a biased result, a previously known result. (ii) The random tossing of two quantum coins, each with successive biased expectations, gives an average random walk position of approximately zero. (iii) The sequential periodic tossing of two quantum coins, each with successive negative biased expectations, gives an average random walk with positive expectation. Using these results, we then propose a protocol for identifying and classifying quantum operations that span the same Hilbert space for a two-level quantum system.

The average fraction of infected nodes, in short the prevalence, of the Markovian $\varepsilon$-SIS (susceptible-infected-susceptible) process with small self-infection rate $\varepsilon >0$ exhibits, as a function of time, a typical “two-plateau” behavior, which was first discovered in the complete graph $K_N$. Although the complete graph is often dismissed as an unacceptably simplistic approximation, its analytic tractability allows to unravel deeper details, that are surprisingly also observed in other graphs as demonstrated by simulations. The time-dependent mean-field approximation for $K_N$ performs only reasonably well for relatively large self-infection rates, but completely fails to mimic the typical Markovian $\varepsilon$-SIS process with small self-infection rates. While self-infections, particularly when their rate is small, are usually ignored, the interplay of nodal self-infection and spread over links may explain why absorbing processes are hardly observed in reality, even over long time intervals.