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The propagation of a dissipative soliton was experimentally studied in a two-dimensional binary complex plasma. The crystallization was suppressed in the center of the particle suspension where two types of particles were mixed. The motions of individual particles were recorded using video microscopy, and the macroscopic properties of the solitons were measured in the amorphous binary mixture in the center and in the plasma crystal in the periphery. Although the overall shape and parameters of solitons propagating in amorphous and crystalline regions were quite similar, their velocity structures at small scales as well as the velocity distributions were profoundly distinct. Moreover, the local structure rearranged drastically in and behind the soliton, which was not observed in the plasma crystal. Langevin dynamics simulations were performed, and the results agreed with the experimental observations.

The phase transition of epidemic spreading model on networks is one of the most important concerns of physicists to theoretical epidemiology. In this paper, we present an analytical expression of epidemic threshold for interplay between epidemic spreading and human behavior on multiplex networks. The threshold formula proposed in this paper reveals the relation between the threshold on single-layer networks and that on multiplex networks, which means that the theoretical conclusions of single-layer networks can be used to improve the threshold accuracy of multiplex networks. To verify how well our formula works in different networks, we build a network model with constant total number of edges but gradually changing the heterogeneity of the network, from scale-free network to Erdős-Rényi random network. By use of theoretical analysis and computer simulations, we find that the heterogeneity of information layer behaves as a "double-edged sword" on the epidemic threshold: The strong heterogeneity can effectively improve the epidemic threshold (which means the disease outbreak requires a higher infection probability) when the awareness probability α is low, while the opposite effect takes place for high α. Meanwhile, the weak heterogeneity of the information layer is effective in suppressing the epidemic prevalence when the awareness probability is neither too high nor too low.

Theoretical results are given in the present paper, which can well explain the experimental observations performed under microgravity conditions in the PK-3 Plus Laboratory on board the International Space Station about the propagation of a solitary wave across an interface in a binary complex plasma. By using the traditional reductive perturbation method and the continuity conditions of both the electric potential and the momentum at the interface, we obtain the equivalent "initial conditions" for both the transmitted wave and the reflected waves from the incident wave. Then we obtain the numbers of the reflected and the transmitted solitary waves as well as all the wave amplitudes by using the inverse scattering method. The ripples of both reflection and transmission have also been given by using the Fourier series. The number of the reflected and the transmitted solitary waves produced by interface, as well as all the solitary wave amplitudes, depend on the system parameters such as the number density, electric charge, mass of the dust particles, and the effective temperature in both regions. The analytical results agree with observations in the experiments.

We develop a theory for the susceptible-infected-susceptible (SIS) epidemic model on networks that incorporate both network structure and dynamic correlations. This theory can account for the multistage onset of the epidemic phase in scale-free networks. This phenomenon is characterized by multiple peaks in the susceptibility as a function of the infection rate. It can be explained by that, even under the global epidemic threshold, a hub can sustain the epidemics for an extended period. Moreover, our approach improves theoretical calculations of prevalence close to the threshold in heterogeneous networks and also can predict the average risk of infection for neighbors of nodes with different degree and state on uncorrelated static networks.

The penetration of a supersonic particle at the interface is studied in a binary complex plasma. Inspired by the experiments performed in the PK-3 Plus Laboratory on board the International Space Station, Langevin dynamics simulations were carried out. A Mach cone structure forms in the lateral wave behind the supersonic extra particle, where the kink of the cone flanks is observed at the interface. The propagation of the pulse-like perturbation along the interface is demonstrated by the evolution of the radial and axial velocity of the small particles in the vicinity of the interface. The decay of the pulse strength is determined by the friction, where the propagation distance can reach several interparticle distances for small damping rate. The dependence of the dynamics of the background particles in the vicinity of the interface on the penetration direction implies that the disparity of the mobility may be the cause of various interfacial effects.

Whenever a dynamical process unfolds on static networks, the dynamical state of any focal individual will be exclusively influenced by directly connected neighbors, rather than by those unconnected ones, hence the arising of the dynamical correlation problem, where mean-field-based methods fail to capture the scenario. The dynamic correlation coupling problem has always been an important and difficult problem in the theoretical field of physics. The explicit analytical expressions and the decoupling methods often play a key role in the development of corresponding field. In this paper, we study the cyclic three-state dynamics on static networks, which include a wide class of dynamical processes, for example, the cyclic Lotka-Volterra model, the directed migration model, the susceptible-infected-recovered-susceptible epidemic model, and the predator-prey with empty sites model. We derive the explicit analytical solutions of the propagating size and the threshold curve surface for the four different dynamics. We compare the results on static networks with those on annealed networks and made an interesting discovery: for the symmetrical dynamical model (the cyclic Lotka-Volterra model and the directed migration model, where the three states are of rotational symmetry), the macroscopic behaviors of the dynamical processes on static networks are the same as those on annealed networks; while the outcomes of the dynamical processes on static networks are different with, and more complicated than, those on annealed networks for asymmetric dynamical model (the susceptible-infected-recovered-susceptible epidemic model and the predator-prey with empty sites model). We also compare the results forecasted by our theoretical method with those by Monte Carlo simulations and find good agreement between the results obtained by the two methods.