Numerical evidence of persisting surface roughness when deposition stops

Do evolving surfaces become flat or not with time evolving when material deposition stops? As one qualitative exploration of this interesting issue, modified stochastic models for persisting roughness have been proposed by Schwartz and Edwards (2004 Phys. Rev. E 70 061602). In this work, we perform numerical simulations on the modified versions of Edwards–Wilkinson (EW) and Kardar–Parisi–Zhang (KPZ) systems when the angle of repose is introduced. Our results show that the evolving surface always presents persisting roughness during the flattening process, and sand dune-like morphology could gradually appear, even when the angle of repose is very small. Nontrivial scaling properties and differences of evolving surfaces between the modified EW and KPZ systems are also discussed.

Comment on ‘Out-of-equilibrium Frenkel–Kontorova model’ (Imparato A 2021 J. Stat. Mech. 013214)

We explain the ‘phases’ of a Frenkel–Kontorova chain of atoms in a different way to the commented article. We reject the decision of states of the chain into commensurate and incommensurate states introduced by Aubry.

Effects of homophily and heterophily on preferred-degree networks: mean-field analysis and overwhelming transition

We investigate the long-time properties of a dynamic, out-of-equilibrium network of individuals holding one of two opinions in a population consisting of two communities of different sizes. Here, while the agents’ opinions are fixed, they have a preferred degree which leads them to endlessly create and delete links. Our evolving network is shaped by homophily/heterophily, a form of social interaction by which individuals tend to establish links with others having similar/dissimilar opinions. Using Monte Carlo simulations and a detailed mean-field analysis, we investigate how the sizes of the communities and the degree of homophily/heterophily affect the network structure. In particular, we show that when the network is subject to enough heterophily, an ‘overwhelming transition’ occurs: individuals of the smaller community are overwhelmed by links from the larger group, and their mean degree greatly exceeds the preferred degree. This and related phenomena are characterized by the network’s total and joint degree distributions, as well as the fraction of links across both communities and that of agents having fewer edges than the preferred degree. We use our mean-field theory to discuss the network’s polarization when the group sizes and level of homophily vary.

Grand canonical partition function of a serial metallic island system

We present a calculation of the grand canonical partition function of a serial metallic island system by the imaginary-time path integral formalism. To this purpose, all electronic excitations in the lead and island electrodes are described using Grassmann numbers. The Coulomb charging energy of the system is represented in terms of phase fields conjugate to the island charges. By the large channel approximation, the tunneling action phase dependence can also be determined explicitly. Therefore, we represent the partition function as a path integral over phase fields with a path probability given in an analytically known effective action functional. Using the result, we also propose a calculation of the average electron number of the serial island system in terms of the expectation value of winding numbers. Finally, as an example, we describe the Coulomb blockade effect in the two-island system by the average electron number and propose a method to construct the quantum stability diagram.

Steady-state thermodynamics for population dynamics in fluctuating environments with side information

Steady-state thermodynamics (SST) is a relatively newly emerging subfield of physics, which deals with transitions between steady states. In this paper, we find an SST-like structure in population dynamics of organisms that can sense their fluctuating environments. As heat is divided into two parts in SST, we decompose population growth into two parts: housekeeping growth and excess growth. Then, we derive the Clausius equality and inequality for excess growth. Using numerical simulations, we demonstrate how the Clausius inequality behaves depending on the magnitude of noise and strategies that organisms employ. Finally, we discuss the novelty of our findings and compare them with a previous study.

Large deviations for metastable states of Markov processes with absorbing states with applications to population models in stable or randomly switching environment

The large deviations at level 2.5 are applied to Markov processes with absorbing states in order to obtain the explicit extinction rate of metastable quasi-stationary states in terms of their empirical time-averaged density and of their time-averaged empirical flows over a large time-window T. The standard spectral problem for the slowest relaxation mode can be recovered from the full optimization of the extinction rate over all these empirical observables and the equivalence can be understood via the Doob generator of the process conditioned to survive up to time T. The large deviation properties of any time-additive observable of the Markov trajectory before extinction can be derived from the level 2.5 via the decomposition of the time-additive observable in terms of the empirical density and the empirical flows. This general formalism is described for continuous-time Markov chains, with applications to population birth–death model in a stable or in a switching environment, and for diffusion processes in dimension d.

Optimal control of complex networks with conformity behavior

Despite the significant advances in identifying the driver nodes and energy requiring in network control, a framework that incorporates more complicated dynamics remains challenging. Here, we consider the conformity behavior into network control, showing that the control of undirected networked systems with conformity will become easier as long as the number of external inputs beyond a critical point. We find that this critical point is fundamentally determined by the network connectivity. In particular, we investigate the nodal structural characteristic in network control and propose optimal control strategy to reduce the energy requiring in controlling networked systems with conformity behavior. We examine those findings in various synthetic and real networks, confirming that they are prevailing in describing the control energy of networked systems. Our results advance the understanding of network control in practical applications.

Dispersion chain of Vlasov equations

On the basis of the Vlasov chain of equations, a new infinite dispersion chain of equations is obtained for the distribution functions of mixed higher order kinematical values. In contrast to the Vlasov chain, the dispersion chain contains distribution functions with an arbitrary set of kinematical values and has a tensor form of writing. For the dispersion chain, new equations for mixed Boltzmann functions and the corresponding chain of conservation laws for fluid dynamics are obtained. The probability is proved to be a constant value for a particle to belong the region where the quasi-probability density is negative (Wigner function).

Active Brownian motion with speed fluctuations in arbitrary dimensions: exact calculation of moments and dynamical crossovers

We consider the motion of an active Brownian particle with speed fluctuations in d-dimensions in the presence of both translational and orientational diffusion. We use an Ornstein–Uhlenbeck process for active speed generation. Using a Laplace transform approach, we describe and use a Fokker–Planck equation-based method to evaluate the exact time dependence of all relevant dynamical moments. We present explicit calculations of several such moments and compare our analytical predictions against numerical simulations to demonstrate and analyze the dynamical crossovers, determined by the orientational persistence of activity, speed fluctuation and relaxation. The kurtosis of displacement shows positive and negative deviations from a Gaussian behavior at intermediate times depending on the dominance of speed and orientational fluctuations, respectively.