Temporal percolation of a susceptible adaptive network

In the past decades, many authors have used the susceptible–infected–recovered model to study the impact of the disease spreading on the evolution of the infected individuals. However, few authors focused on the temporal unfolding of the susceptible individuals. In this paper, we study the dynamic of the susceptible–infected–recovered model in an adaptive network that mimics the transitory deactivation of permanent social contacts, such as friendship and work-ship ties. Using an edge-based compartmental model and percolation theory, we obtain the evolution equations for the fraction susceptible individuals in the susceptible biggest component. In particular, we focus on how the individual’s behavior impacts on the dilution of the susceptible network. We show that, as a consequence, the spreading of the disease slows down, protecting the biggest susceptible cluster by increasing the critical time at which the giant susceptible component is destroyed. Our theoretical results are fully supported by extensive simulations.     

Epidemic prevalence on random mobile dynamical networks: individual heterogeneity and correlation

In this paper, we extend the susceptible-infected-susceptible (SIS) epidemiological model on a random dynamical network composed of mobile individuals, in which the infection is caused by the collisions between susceptible and infected individuals at the spreading rate proportional to their susceptibilities and infectivities. We analytically study the criticality of spreading dynamics under different distributions of individual susceptibility and infectivity, and numerically verify the cases of power-law and (or) Gaussian distributions. Our findings show that the heterogeneity of individual susceptibility and infectivity increases the epidemic threshold, and the positive correlation of individual susceptibility and infectivity avails to the epidemic prevalence.     

Message Spreading and Forget--Remember Mechanism on a Scale-Free Network

We study message spreading on a scale-free network, by introducing a novel forget-remember mechanism. Message, a general term which can refer to email, news, rumor or disease, etc, can be forgotten and remembered by its holder. The way the message is forgotten and remembered is governed by the forget and remember function, F and R, respectively. Both F and R are functions of history time t concerning individual's previous states, namely being active (with message) or inactive (without message). Our systematicsimulations show at the low transmission rate whether or not the spreading can be efficient is primarily determined by the corresponding parameters for F and R.     

Hybrid phase transitions of spreading dynamics in multiplex networks

In this paper, we study the spreading dynamics of social behaviors and focus on heterogenous responses of individuals depending on whether they realize the spreading or not. We model the system with a two-layer multiplex network, in which one layer describes the spreading of social behaviors and the other layer describes the diffusion of the awareness about the spreading. We use the susceptible-infected-susceptible (SIS) model to describe the dynamics of an individual if it is unaware of the spreading of the behavior. While when an individual is aware of the spreading of the social behavior its dynamics will follow the threshold model, in which an individual will adopt a behavior only when the fraction of its neighbors who have adopted the behavior is above a certain threshold. We find that such heterogenous reactions can induce intriguing dynamical properties. The dynamics of the whole network may exhibit hybrid phase transitions with the coexistence of continuous phase transition and bi-stable states. Detailed study of how the diffusion of the awareness influences the spreading dynamics of social behavior is provided. The results are supported by theoretical analysis.     

Analytic-numerical description of asymptotic solutions of a Cauchy problem in a neighborhood of singularities for a linearized system of shallow-water equations

S. Yu. Dobrokhotov, B. Tirozzi, S. Ya. Sekerzh-Zenkovich, A. I. Shafarevich, and their co-authors suggested new effective asymptotic formulas for solving a Cauchy problem with localized initial data for multidimensional linear hyperbolic equations with variable coefficients and, in particular, for a linearized system of shallow-water equations over an uneven bottom in their cycle of papers. The solutions are localized in a neighborhood of fronts on which focal points and self-intersection points (singular points) occur in the course of time, due to the variability of the coefficients. In the present paper, a numerical realization of asymptotic formulas in a neighborhood of singular points of fronts is presented in the case of the system of shallow-water equations, gluing problems for these formulas together with formulas for regular domains are discussed, and also a comparison of asymptotic solutions with solutions obtained by immediate numerical computations is carried out.     

Phase dynamics modeling of parallel stacks of Josephson junctions

The phase dynamics of two parallel connected stacks of intrinsic Josephson junctions (JJs) in high temperature superconductors is numerically investigated. The calculations are based on the system of nonlinear differential equations obtained within the CCJJ + DC model, which allows one to determine the general current-voltage characteristic of the system, as well as each individual stack. The processes with increasing and decreasing base currents are studied. The features in the behavior of the current in each stack of the system due to the switching between the states with rotating and oscillating phases are analyzed.     

Generic two-phase coexistence, relaxation kinetics, and interface propagation in the quadratic contact process: Analytic studies

The quadratic contact process is implemented as an adsorption-desorption model on a two-dimensional square lattice. The model involves random adsorption at empty sites, and correlated desorption requiring diagonal pairs of empty neighbors. A simulation study of this model [D.-J. Liu, X. Guo, J.W. Evans, Phys. Rev. Lett. 98 (2007) 050601] revealed the existence of generic two-phase coexistence between a low-coverage active steady-state and a completely covered absorbing state. Here, an analytic treatment of model behavior is developed based on truncation approximations to the exact master equations. Applying this approach for spatially homogeneous states, we characterize steady-state behavior as well as the kinetics of relaxation to the steady-states. Extending consideration to spatially inhomogeneous states, we obtain discrete reaction-diffusion type equations characterizing evolution. These are employed to analyze an orientation-dependence of the propagation of planar interfaces between active and absorbing states which underlies the generic two-phase coexistence. We also describe the dynamics and critical forms of planar perturbations of the active state and of droplets of one phase embedded in the other.     

Disease spreading in structured scale-free networks

We study the spreading of a disease on top of structured scale-free networks recently introduced. By means of numerical simulations we analyze the SIS and the SIR models. Our results show that when the connectivity fluctuations of the network are unbounded whether the epidemic threshold exists strongly depends on the initial density of infected individuals and the type of epidemiological model considered. Analytical arguments are provided in order to account for the observed behavior. We conclude that the peculiar topological features of this network and the absence of small-world properties determine the dynamics of epidemic spreading. Received 16 October 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: yamir@ictp.trieste.it     

Autowaves in an active two-wire line with exponential current-voltage characteristics

Nonlinear wave processes in two-wire lines containing an active element with an exponential current-voltage characteristic (CVC) similar to that of a p-n junction are investigated. These lines are models of systems that are encountered in various physical and biological applications, such as biological membranes and semiconductor devices. It is shown that such systems may operate in different modes each of which has different dispersion and dissipation properties and, as a consequence, is described by autowave processes of different types. The behavior of a system in all basic modes is analyzed. For each mode, exact solutions to relevant equations are found and their differential conservation laws and intrinsic symmetries are investigated. One of common properties of such equations is the presence of a special superposition principle that describes the discrete structure of excitations in a line that consist of individual elementary excitations. It is shown that autopulses may be generated in such systems.     

Epidemiological impact of waning immunization on a vaccinated population

This is an epidemiological SIRV model based study that is designed to analyze the impact of vaccination in containing infection spread, in a 4-tiered population compartment comprised of susceptible, infected, recovered and vaccinated agents. While many models assume a lifelong protection through vaccination, we focus on the impact of waning immunization due to conversion of vaccinated and recovered agents back to susceptible ones. Two asymptotic states exist, the “disease-free equilibrium” and the “endemic equilibrium” and we express the transitions between these states as function of the vaccination and conversion rates and using the basic reproduction number. We find that the vaccination of newborns and adults have different consequences on controlling an epidemic. Also, a decaying disease protection within the recovered sub-population is not sufficient to trigger an epidemic at the linear level. We perform simulations for a parameter set mimicking a disease with waning immunization like pertussis. For a diffusively coupled population, a transition to the endemic state can proceed via the propagation of a traveling infection wave, described successfully within a Fisher-Kolmogorov framework.     

Finite temperature investigations of a two dimensional electron liquid

We investigate the spin dependent local field corrections and correlation functions of an electron layer at intermediate degeneracies. The results are obtained within the Singwi-Tosi-Land-Sjølander approximation by solving the corresponding set of coupled integral equations. Analytic expressions are given for the asymptotic limiting behavior. In addition, the free exchange-and correlation energy, which is in good agreement with Monte Carlo results at full degeneracy, is calculated for various temperatures.     

Impact of film thickness on threshold voltage of polysilicon TFTs

The threshold voltage is a key parameter in the silicon MOSFETS design and operation. In this paper, we study the factors that contribute to the changes of threshold voltage of thin-film LPCVD polysilicon transistors when varying the thickness of the active layer.The results show that the threshold voltage depends strongly on the film thickness. For high thicknesses, the threshold voltage is shown to be determined by the trapped holes at grain boundaries. The variation of this parameter with film thickness can be attributed to inter-granular trap states density variation in the film.For low thicknesses, a simple electrostatic model of the study structure, associated with a numerical method of solving 2D-Poisson's equations, shows that the changes of threshold voltage of polysilicon TFT depends on grain-boundary properties and charge-coupling between the front and back gates. Based on this consideration, the usual threshold voltage expression is modified. The results so obtained are compared with the available experimental data, which show a satisfactory match thus justifying the validity of the proposed relation.     

Chaos out of internal noise in the collective dynamics of diffusively coupled cells

We study the transition from stochasticity to determinism in calcium oscillations via diffusive coupling of individual cells that are modeled by stochastic simulations of the governing reaction-diffusion equations. As expected, the stochastic solutions gradually converge to their deterministic limit as the number of coupled cells increases. Remarkably however, although the strict deterministic limit dictates a fully periodic behavior, the stochastic solution remains chaotic even for large numbers of coupled cells if the system is set close to an inherently chaotic regime. On the other hand, the lack of proximity to a chaotic regime leads to an expected convergence to the fully periodic behavior, thus suggesting that near-chaotic states are presently a crucial predisposition for the observation of noise-induced chaos. Our results suggest that chaos may exist in real biological systems due to intrinsic fluctuations and uncertainties characterizing their functioning on small scales.     

Asymptotic results for a persistent diffusion model of Taylor dispersion of particles

We study Taylor diffusion for the case when the diffusion transverse to the bulk motion is a persistent random walk on a one-dimensional lattice. This is mapped onto a Markovian walk where each lattice site has two internal states. For such a model we find the effective diffusion coefficient which depends on the rate of transition among internal states of the lattice. The Markovian limit is recovered in the limit of infinite rate of transitions among internal states; the initial conditions have no role in the leading-order time-dependent term of the effective dispersion, but a strong effect on the constant term. We derive a continuum limit of the problem presented and study the asymptotic behavior of such limit.     

Different Epidemic Models on Complex Networks

Models for diseases spreading are not just limited to SIS or SIR. For instance, for the spreading of AIDS/HIV, the susceptible individuals can be classified into different cases according to their immunity, and similarly, the infected individuals can besorted into different classes according to their infectivity. Moreover, some diseases may develop through several stages. Many authors have shown that the individuals' relation can be viewed as a complex network. So in this paper, in order to better explain the dynamical behavior of epidemics, we consider different epidemicmodels on complex networks, and obtain the epidemic threshold for each case. Finally, we present numerical simulations for each case to verify our results.     

Self-similar factor approximants for evolution equations and boundary-value problems

The method of self-similar factor approximants is shown to be very convenient for solving different evolution equations and boundary-value problems typical of physical applications. The method is general and simple, being a straightforward two-step procedure. First, the solution to an equation is represented as an asymptotic series in powers of a variable. Second, the series are summed by means of the self-similar factor approximants. The obtained expressions provide highly accurate approximate solutions to the considered equations. In some cases, it is even possible to reconstruct exact solutions for the whole region of variables, starting from asymptotic series for small variables. This can become possible even when the solution is a transcendental function. The method is shown to be more simple and accurate than different variants of perturbation theory with respect to small parameters, being applicable even when these parameters are large. The generality and accuracy of the method are illustrated by a number of evolution equations as well as boundary value problems.     

The relative importance of structure and dynamics on node influence in reversible spreading processes

The reversible spreading processes with repeated infection widely exist in nature and human society, such as gonorrhea propagation and meme spreading. Identifying influential spreaders is an important issue in the reversible spreading dynamics on complex networks, which has been given much attention. Except for structural centrality, the nodes’ dynamical states play a significant role in their spreading influence in the reversible spreading processes. By integrating the number of outgoing edges and infection risks of node’s neighbors into structural centrality, a new measure for identifying influential spreaders is articulated which considers the relative importance of structure and dynamics on node influence. The number of outgoing edges and infection risks of neighbors represent the positive effect of the local structural characteristic and the negative effect of the dynamical states of nodes in identifying influential spreaders, respectively. We find that an appropriate combination of these two characteristics can greatly improve the accuracy of the proposed measure in identifying the most influential spreaders. Notably, compared with the positive effect of the local structural characteristic, slightly weakening the negative effect of dynamical states of nodes can make the proposed measure play the best performance. Quantitatively understanding the relative importance of structure and dynamics on node influence provides a significant insight into identifying influential nodes in the reversible spreading processes.     

Yang-Mills potentials and the van der Waals force between hadrons

The colour-induced magnetic dipole interaction between hadrons is discussed. Fermion motion in a gauge field obtained by solving the classical Yang-Mills equations is considered. It is shown that the spectrum of stationary fermion states is discrete and bound states are colourless. The long range asymptotic behaviour of the gauge potential results in the van der Waals interaction of hadrons.