Deterministic and Stochastic Analysis of a New Rumor Propagation Model with Nonlinear Propagation Rate in Social Network

This paper presents a study on a new rumor propagation model with nonlinear propagation rate and secondary propagation rate. We divide the total population into three groups, the ignorant, the spreader and the aware. The nonlinear incidence rate describes the psychological impact of certain serious rumors on social groups when the number of individuals spreading rumors becomes larger. The main contributions of this work are the development of a new rumor propagation model and some results of deterministic and stochastic analysis of the rumor propagation model. The results show the influence of nonlinear propagation rate and stochastic fluctuation on the dynamic behavior of the rumor propagation model by using Lyapunov function method and stochastic related knowledge. Numerical examples and simulation results are given to illustrate the results obtained.

Studies on the Construction Parameter of an Artificial Occluded Cell for In-situ Inspection of the Propagation Rate of Localized Corrosion

An artificial localized corrosion system is assembled and some parameters related to the localized corrosion in active dissolution state (i.e., non-passive state) have been studied. The results showed that the developed electrochemical system can satisfactorily imitate a naturally formed localized corrosion and the coupling current can indicate the maximum localized propagating rate. In this artificial system, the anodic dissolution reaction followed the auto-catalytic mechanism. The localized corrosion current density was dependent on the area ratio R of the cathode to the occluded anode. While R was equal to or more than 6, the coupling current reached at a maximum value and did not alter with the increase in R-value. Therefore, R=7 is chosen as one of these optimum parameters used in constructing the system, with which the biggest galvanic current might be obtained. In contrast, the thickness of the polymer filler separating the occluded anode area from the bulk electrolyte solution and the volume of the occluded anode area did not affect the corrosion current obviously. They might affect the response time to approach a steady state.

Compliance-based testing method for fatigue crack propagation rates of mixed-modeⅠ-Ⅱcracks

Mixed-mode I-II crack-based fatigue crack propagation(FCPⅠ-Ⅱ)usually occurs in engineering structures;however,no theoretical formula or effective compliance test methods have been established for FCPI-IIto date.For mixed-mode I-II flawed components,based on the principle of mean-value energy equivalence,we propose a theoretical method to describe the relationship between material elastic parameters,geometrical dimensions,load(or displacement),and energy.Based on the maximum circumferential stress criterion,we propose a uniform compliance model for compact tensile shear(CTS)specimens with horizontal cracks deflecting and propagating(flat-folding propagation)under different loading angles,geometries,and materials.Along with an innovative design of the fixture of CTS specimens used for FCPI-IItests,we develop a new compliancebased testing method for FCPⅠ-Ⅱ.For the 30Cr2Ni4MoV rotor steel,the FCP rates of modeⅠ,modeⅡ,and mixed-modeⅠ-Ⅱcracks were obtained via FCP tests using compact tension,Arcan,and CTS specimens,respectively.The obtained da/d N versusΔJ curves of the FCP rates are close.The loading angleαand dimensionless initial crack length a0/W demonstrated negligible effects on the FCP rates.Hence,the FCP rates of mode I crack can be used to predict the residual life of structural crack propagation.