In this paper we study the critical behavior of the fully connected $p$-color Potts spin glass at the dynamical transition. In the framework of mode coupling theory (MCT), the time autocorrelation function displays a two-step relaxation, with two exponents governing the approach to the plateau and the exit from it. Exploiting a relation between static and equilibrium dynamics which has been recently introduced, we are able to compute the critical slowing down exponents at the dynamical transition with arbitrary precision and for any value of the number of colors $p$. When available, we compare our exact results with numerical simulations. In addition, we present a detailed study of the dynamical transition in the large $p$ limit, showing that the system is not equivalent to a random energy model.

Ion channels are membrane proteins that open and close at random and play a vital role in the electrical dynamics of excitable cells. The stochastic nature of the conformational changes these proteins undergo can be significant, however current stochastic modeling methodologies limit the ability to study such systems. Discrete-state Markov chain models are seen as the “gold standard,” but are computationally intensive, restricting investigation of stochastic effects to the single-cell level. Continuous stochastic methods that use stochastic differential equations (SDEs) to model the system are more efficient but can lead to simulations that have no biological meaning. In this paper we show that modeling the behavior of ion channel dynamics by a reflected SDE ensures biologically realistic simulations, and we argue that this model follows from the continuous approximation of the discrete-state Markov chain model. Open channel and action potential statistics from simulations of ion channel dynamics using the reflected SDE are compared with those of a discrete-state Markov chain method. Results show that the reflected SDE simulations are in good agreement with the discrete-state approach. The reflected SDE model therefore provides a computationally efficient method to simulate ion channel dynamics while preserving the distributional properties of the discrete-state Markov chain model and also ensuring biologically realistic solutions. This framework could easily be extended to other biochemical reaction networks.

We analyze the dynamics of particles in two dimensions with constant speed and a stochastic switching angle dynamics defined by a correlated dichotomous Markov process (telegraph noise) plus Gaussian white noise. We study various cases of the asymptotic diffusional motion of the particle which is characterized by the effective diffusion coefficient. Expressions for this coefficient are derived and discussed in dependence on the correlation time and the intensity of the noise. The situation with a given mean curvature is of special interest since a nonmonotonic behavior of the effective diffusion coefficient as a function of the noise intensity and correlation time is found. A time scale matching condition for maximal diffusion is formulated.

Many edge prediction methods have been proposed, based on various local or global properties of the structure of an incomplete network. Community structure is another significant feature of networks: Vertices in a community are more densely connected than average. It is often true that vertices in the same community have “similar” properties, which suggests that missing edges are more likely to be found within communities than elsewhere. We use this insight to propose a strategy for edge prediction that combines existing edge prediction methods with community detection. We show that this method gives better prediction accuracy than existing edge prediction methods alone.

The dynamical properties of delay-coupled systems are currently of great interest. So far the analysis has concentrated primarily on identical synchronization properties. Here we study the dynamics of rings of delay-coupled nodes, a topology that cannot show identical synchronization, and compare its properties to those of linear stochastic maps. We find that, in the long delay limit, the correlation functions and spectra of delay-coupled rings of nonlinear systems obey the same scaling laws as linear systems, indicating that important properties of the emerging solution result from network topology.

The large-scale circulation of planetary atmospheres such as that of the Earth is traditionally thought of in a dynamical framework. Here we apply the statistical mechanics theory of turbulent flows to a simplified model of the global atmosphere, the quasigeostrophic model, leading to nontrivial equilibria. Depending on a few global parameters, the structure of the flow may be either a solid-body rotation (zonal flow) or a dipole. A second-order phase transition occurs between these two phases, with associated spontaneous symmetry breaking in the dipole phase. This model allows us to go beyond the general theory of marginal ensemble equivalence through the notion of Goldstone modes.

When an intense and short laser pulse propagates in a dielectric material, significant production of conduction electrons through multiphoton absorption (MPA) may occur. In addition to the laser intensity, the MPA process depends mainly on the laser frequency spectrum which may evolve significantly during the course of laser propagation in the material. Simple models for MPA accounting for possible time-dependent evolution of the laser frequency spectrum (as harmonic generation, chirping or broadening) are addressed. The first model is based on Bloch-Volkov states whereas the second approach relies on the density matrix formalism which has been adapted for the present study. Both models are well adapted for their introduction in a propagation code and are shown to correctly account for the MPA process whatever the characteristics of the laser frequency spectrum. The reliability of these approaches has been studied in two cases of practical interest. First, in the case where a second harmonic is present within the fundamental pulse, calculations show that the ionization rate may be significantly enhanced. Second, in the case of a chirped pulse, models are shown to correctly account for possible change in the multiphoton order during the course of interaction.

A two-dimensional model of microwave-induced plasma (field frequency 2.45 GHz) in argon at atmospheric pressure is presented. The model describes in a self-consistent manner the gas flow and heat transfer, the in-coupling of the microwave energy into the plasma, and the reaction kinetics relevant to high-pressure argon plasma including the contribution of molecular ion species. The model provides the gas and electron temperature distributions, the electron, ion, and excited state number densities, and the power deposited into the plasma for given gas flow rate and temperature at the inlet, and input power of the incoming TEM microwave. For flow rate and absorbed microwave power typical for analytical applications (200–400 ml/min and 20 W), the plasma is far from thermodynamic equilibrium. The gas temperature reaches values above 2000 K in the plasma region, while the electron temperature is about 1 eV. The electron density reaches a maximum value of about 4 $\times {10}^{21}{\mathrm{m}}^{-3}$. The balance of the charged particles is essentially controlled by the kinetics of the molecular ions. For temperatures above 1200 K, quasineutrality of the plasma is provided by the atomic ions, and below 1200 K the molecular ion density exceeds the atomic ion density and a contraction of the discharge is observed. Comparison with experimental data is presented which demonstrates good quantitative and qualitative agreement.

Finite two-dimensional dust clusters are systems of a small number of charged grains. The self-confinement of dust clusters in isotropic plasmas is studied using the particle-in-cell method. The energetically favorable configurations of grains in plasma are found that are due to the kinetic effects of plasma ions and electrons. The self-confinement phenomenon is attributed to the change in the plasma composition within a dust cluster resulting in grain attraction mediated by plasma ions. This is a self-consistent state of a dust cluster in which grain's repulsion is compensated by the reduced charge and floating potential on grains, overlapped ion clouds, and depleted electrons within a cluster. The common potential well is formed trapping dust clusters in the confined state. These results provide both valuable insights and a different perspective to the classical view on the formation of boundary-free dust clusters in isotropic plasmas.

We study networks of noisy phase oscillators whose nodes are characterized by random degrees counting the number of their connections. Both these degrees and the natural frequencies of the oscillators are distributed according to a given probability density. Replacing the randomly connected network by an all-to-all coupled network with weighted edges allows us to formulate the dynamics of a single oscillator coupled to the mean field and to derive the corresponding Fokker-Planck equation. From the latter we calculate the critical coupling strength for the onset of synchronization as a function of the noise intensity, the frequency distribution, and the first two moments of the degree distribution. Our approach is applied to a dense small-world network model, for which we calculate the degree distribution. Numerical simulations prove the validity of the replacement. We also test the applicability to more sparsely connected networks and formulate homogeneity and absence of correlations in the degree distribution as limiting factors of our approach.

We argue that thermal machines can be understood from the perspective of “virtual qubits” at “virtual temperatures”: The relevant way to view the two heat baths which drive a thermal machine is as a composite system. Virtual qubits are two-level subsystems of this composite, and their virtual temperatures can take on any value, positive or negative. Thermal machines act upon an external system by placing it in thermal contact with a well-selected range of virtual qubits and temperatures. We demonstrate these claims by studying the smallest thermal machines. We show further that this perspective provides a powerful way to view thermodynamics, by analyzing a number of phenomena. This includes approaching Carnot efficiency (where we find that all machines do so essentially by becoming equivalent to the smallest thermal machines), entropy production in irreversible machines, and a way to view work in terms of negative temperature and population inversion. Moreover we introduce the idea of “genuine” thermal machines and are led to considering the concept of “strength” of work.

Based on self-consistent equations of the order parameter $P_{\infty }$ and the mean cluster size $S$, we develop a self-consistent simulation method for arbitrary percolation on the Bethe lattice (infinite homogeneous Cayley tree). By applying the self-consistent simulation to well-known percolation models, random bond percolation, and bootstrap percolation, we obtain prototype functions for continuous and discontinuous phase transitions. By comparing key functions obtained from self-consistent simulations for Achlioptas models with a product rule and a sum rule to the prototype functions, we show that the percolation transition of Achlioptas models on the Bethe lattice is continuous regardless of details of growth rules.

We investigate the dynamical scaling behavior of the static diffusive epidemic process and a fixed-energy Manna sandpile model, undergoing nonequilibrium absorbing phase transitions in one dimension. These models belong to the so-called conserved directed-percolation or Manna universality class characterized by the conservation of the total particle number, activity coupled to a nondiffusive conserved field and infinitely many absorbing states. We measure the dynamical exponents of these models in one dimension by using the critical spreading simulation of a localized activity in absorbing configurations. In the spreading simulations, boundaries are never touched, so the results are free from the finite-size effects. In contrast to the scattered results for the different models from the previous finite-size scaling analyses, we obtain consistent estimates of the dynamical exponents for both models.

A density functional perturbation theory, which is based both on the modified fundamental-measure theory and on the first-order mean-spherical approximation for long-range attractive and repulsive interactions, has been developed for studying the structure and phase behaviors of a competing system restricted to slit pores. The hysteresis loop for the adsorption and desorption curves indicates that the system exhibits vapor-cluster and cluster-liquid transitions which depend on the pair potential parameters and the slit width ($H$). The periodic spacing ($D$) of the cluster is commensurate with the periodicity of modulation in the particle density distribution and more closely related to the vapor-cluster and cluster-liquid phase transitions of the system. For the cluster phase, we find the transition from a single liquidlike slab to a multi-liquidlike slab with increasing the slit width. The multi-liquidlike slab is formed depending on the periodicity of modulation by finite-size artifacts. The cluster-related phase transitions, such as the vapor-cluster or cluster-liquid transitions occur for $H>D$, while for $H<D$ the system only exhibits the vapor-liquid transition. At a low amplitude, the vapor-liquid transition disappears and the cluster-liquid transition only occurs for $H<D$. The coexistence curves for the confined phase diagram are contained within the corresponding bulk liquid-vapor coexistence curve. For a wide slit pore ($H>D$), the system exhibits two tricritical points, joined to one another by the line of second-order transition. The results support the conclusion that the confinement effect plays an important role in determining the equilibrium phase transition.

We present a Brownian dynamics model of driven polymer translocation, in which nonequilibrium memory effects arising from tension propagation (TP) along the cis side subchain are incorporated as a time-dependent friction. To solve the effective friction, we develop a finite chain length TP formalism, based on the idea suggested by Sakaue [Phys. Rev. E 76, 021803 (2007)]. We validate the model by numerical comparisons with high-accuracy molecular dynamics simulations, showing excellent agreement in a wide range of parameters. Our results show that the dynamics of driven translocation is dominated by the nonequilibrium TP along the cis side subchain. Furthermore, by solving the model for chain lengths up to ${10}^{10}$ monomers, we show that the chain lengths probed by experiments and simulations are typically orders of magnitude below the asymptotic limit. This explains both the considerable scatter in the observed scaling of translocation time with respect to chain length, and some of the shortcomings of present theories. Our study shows that for a quantitative theory of polymer translocation, explicit consideration of finite chain length effects is required.

Nonlinear interaction of membrane proteins with cytoskeleton and membrane leads to non-Gaussian structure of their displacement probability distribution. We propose a statistical analysis technique for learning the characteristics of the nonlinear potential from the time dependence of the cumulants of the displacement distribution. The efficiency of the approach is demonstrated on the analysis of the kurtosis of the displacement distribution of the particle traveling on a membrane in a cage-type potential. Results of numerical simulations are supported by analytical predictions. We show that the approach allows robust identification of some characteristics of the potential for the much lower temporal resolution compared with the mean-square displacement analysis and we demonstrate robustness to experimental errors in determining the particle positions.

Membrane curvature of a biological cell is actively involved in various fundamental cell biological functions. It has been discovered that membrane curvature and binding of peripheral membrane proteins follow a symbiotic relationship. The exact mechanism behind this interplay of protein binding and membrane curvature has not yet been properly understood. To improve understanding of the mechanism, we study curvature sorting of proteins in a model system consisting of a tether pulled from a giant unilamellar vesicle using mechanical-thermodynamic models. The concentration of proteins bound to the membrane changes significantly due to curvature. This has also been observed in experiments by other researchers. We also find that there is a phase transition based on protein concentration and we discuss the coexistence of phases and stability of solutions. Furthermore, when sorting is favorable, the increase in protein concentration stabilizes the tether in the sense that less pulling force is required to maintain the tether. A similar mechanism may be in place, when motor proteins pull tethers from donor membranes.

Given the adjacency matrix $A$ of a network, we present a second-order mean-field expansion that improves on the first-order $N$-intertwined susceptible-infected-susceptible (SIS) epidemic model. Unexpectedly, we found that, in contrast to first-order, second-order mean-field theory is not always possible: the network size $N$ should be large enough. Under the assumption of large $N$, we show that the crucial and characterizing quantity, the SIS epidemic threshold ${\tau }_c$, obeys an eigenvalue equation, more complex than the one in the first-order $N$-intertwined model. However, the resulting epidemic threshold is more accurate: ${\tau }_c^{\left(2\right)}={\tau }_c^{\left(1\right)}+O\left(\frac{{\tau }_c^{\left(1\right)}}{N}\right)$, where the first-order epidemic threshold is ${\tau }_c^{\left(1\right)}=\frac{1}{{\lambda }_1\left(A\right)}$ and where ${\lambda }_1\left(A\right)$ is the spectral radius of the adjacency matrix $A$.

A system of phase oscillators with repulsive global coupling and periodic external forcing undergoing asynchronous rotation is considered. The synchronization rate of the system can exhibit persistent fluctuations depending on parameters and initial phase distributions, and the amplitude of the fluctuations scales with the system size for uniformly random initial phase distributions. Using the Watanabe-Strogatz transformation that reduces the original system to low-dimensional macroscopic equations, we show that the fluctuations are collective dynamics of the system corresponding to low-dimensional trajectories of the reduced equations. It is argued that the amplitude of the fluctuations is determined by the inhomogeneity of the initial phase distribution, resulting in system-size scaling for the random case.

New tools for analysis of oscillatory networks using phase response theory (PRT) under the assumption of pulsatile coupling have been developed steadily since the 1980s, but none have yet allowed for analysis of mixed systems containing nonoscillatory elements. This caveat has excluded the application of PRT to most real systems, which are often mixed. We show that a recently developed tool, the functional phase resetting curve (fPRC), provides a serendipitous benefit: it allows incorporation of nonoscillatory elements into systems of oscillators where PRT can be applied. We validate this method in a model system of neural oscillators and a biological system, the pyloric network of crustacean decapods.