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The collective effects of microswimmers in active suspensions result in active turbulence, a spatiotemporally chaotic dynamics at mesoscale, which is characterized by the presence of vortices and jets at scales much larger than the characteristic size of the individual active constituents. To describe this dynamics, Navier-Stokes-based one-fluid models driven by small-scale forces have been proposed. Here, we provide a justification of such models for the case of dense suspensions in two dimensions (2D). We subsequently carry out an in-depth numerical study of the properties of one-fluid models as a function of the active driving in view of possible transition scenarios from active turbulence to large-scale pattern, referred to as condensate, formation induced by the classical inverse energy cascade in Newtonian 2D turbulence. Using a one-fluid model it was recently shown [M. Linkmann et al., Phys. Rev. Lett 122, 214503 (2019)10.1103/PhysRevLett.122.214503] that two-dimensional active suspensions support two nonequilibrium steady states, one with a condensate and one without, which are separated by a subcritical transition. Here, we report further details on this transition such as hysteresis and discuss a low-dimensional model that describes the main features of the transition through nonlocal-in-scale coupling between the small-scale driving and the condensate.We consider the synchronization of oscillators in complex networks where there is an interplay between the oscillator dynamics and the network topology. Through a remarkable transformation in parameter space and the introduction of virtual frequencies we show that Kuramoto oscillators on annealed networks, with or without frequency-degree correlation, and Kuramoto oscillators on complete graphs with frequency-weighted coupling can be transformed to Kuramoto oscillators on complete graphs with a rearranged, virtual frequency distribution and uniform coupling. The virtual frequency distribution encodes both the natural frequency distribution (dynamics) and the degree distribution (topology). We apply this transformation to give direct explanations to a variety of phenomena that have been observed in complex networks, such as explosive synchronization and vanishing synchronization onset.About three-quarters of eukaryotic DNA is wrapped into nucleosomes; DNA spools with a protein core. The affinity of a given DNA stretch to be incorporated into a nucleosome is known to depend on the base-pair sequence-dependent geometry and elasticity of the DNA double helix. This causes the rotational and translational positioning of nucleosomes. In this study we ask the question whether the latter can be predicted by a simple coarse-grained DNA model with sequence-dependent elasticity, the rigid base-pair model. Whereas this model is known to be rather robust in predicting rotational nucleosome positioning, we show that the translational positioning is a rather subtle effect that is dominated by the guanine-cytosine content dependence of entropy rather than energy. A correct qualitative prediction within the rigid base-pair framework can only be achieved by assuming that DNA elasticity effectively changes on complexation into the nucleosome complex. With that extra assumption we arrive at a model which gives an excellent quantitative agreement to experimental in vitro nucleosome maps, under the additional assumption that nucleosomes equilibrate their positions only locally.We present a model which displays the Griffiths phase, i.e., algebraic decay of density with continuously varying exponents in the absorbing phase. In the active phase, the memory of initial conditions is lost with continuously varying complex exponents in this model. This is a one-dimensional model where a fraction r of sites obey rules leading to the directed percolation class and the rest evolve according to rules leading to the compact directed percolation class. For infection probability p≤p_c, the fraction of active sites ρ(t)=0 asymptotically. For p>p_c, ρ(∞)>0. At p=p_c, ρ(t), the survival probability from a single seed and the average number of active sites starting from single seed decay logarithmically. The local persistence P_l(∞)>0 for p≤p_c and P_l(∞)=0 for p>p_c. For p≥p_s, local persistence P_l(t) decays as a power law with continuously varying exponents. The persistence exponent is clearly complex as p→1. The complex exponent implies logarithmic periodic oscillations in persistence. The wavelength and the amplitude of the logarithmic periodic oscillations increase with p. learn more We note that the underlying lattice or disorder does not have a self-similar structure.In this paper, we study the robustness of interdependent networks with multiple-dependence (MD) relation which is defined that a node is interdependent on several nodes on another layer, and this node will fail if any of these dependent nodes are failed. We propose a two-layered asymmetric interdependent network (AIN) model to address this problem, where the asymmetric feature is that nodes in one layer may be dependent on more than one node in the other layer with MD relation, while nodes in the other layer are dependent on exactly one node in this layer. We show that in this model the layer where nodes are allowed to have MD relation exhibits different types of phase transitions (discontinuous and hybrid), while the other layer only presents discontinuous phase transition. A heuristic theory based on message-passing approach is developed to understand the structural feature of interdependent networks and an intuitive picture for the emergence of a tricritical point is provided. Moreover, we study the correlation between the intralayer degree and interlayer degree of the nodes and find that this correlation has prominent impact to the continuous phase transition but has feeble effect on the discontinuous phase transition. Furthermore, we extend the two-layered AIN model to general multilayered AIN, and the percolation behaviors and properties of relevant phase transitions are elaborated.The kinetics of oxidation is examined using a phase-field model of electrochemistry when the oxide film is smaller than the Debye length. As a test of the model, the phase-field approach recovers the results of classical Wagner diffusion-controlled oxide growth when the interfacial mobility of the oxide-metal interface is large and the films are much thicker than the Debye length. However, for small interfacial mobilities, where the growth is reaction controlled, we find that the film increases in thickness linearly in time, and that the phase-field model naturally leads to an electrostatic overpotential at the interface that affects the prefactor of the linear growth law. Since the interface velocity decreases with the distance from the oxide vapor, for a fixed interfacial mobility, the film will transition from reaction- to diffusion-controlled growth at a characteristic thickness. For thin films, we find that in the limit of high interfacial mobility we recover a Wagner-type parabolic growth law in the limit of a composition-independent mobility.
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