Spreading behavior of SIS epidemic model on networks with dynamical topology

Based on the two-dimensional regular lattice,a modified SIS(Susceptible-Infected-Susceptible)epidemic model with motion rules is presented to study the spreading behavior on networks with dynamical topology.The mean-field theory is utilized to analyze the critical threshold(λc)of epidemic spreading under the randomly mixing conditions.It is found that λc is only related with the population density within the lattice.Large-scale numerical simulations are carried out to verify the mean-field results,and it is observed that the long-range probability p largely affects the epidemic spreading behavior.In addition,the effect of the dual time scales on epidemic spreading is also investigated by the simulations,and it is shown that the dual time scales accelerate the dynamic spreading behavior.The results indicate that the model with motion can help us to further understand the real epidemics.

A dual timescale model for micro-mixing and its application in LES-TPDF simulations of turbulent nonpremixed flames

The numerical simulation of modern aero-engine combustion chamber needs accurate description of the interaction between turbulence and chemical reaction mechanism. The Large Eddy Simulation(LES) method with the Transported Probability Density Function(TPDF) turbulence combustion model is promising in engineering applications. In flame region, the impact of chemical reaction should be considered in TPDF molecular mixing model. Based on pioneer research, three new TPDF turbulence-chemistry dual time scale molecular mixing models were proposed tentatively by adding the chemistry time scale in molecular mixing model for nonpremixed flame. The Aero-Engine Combustor Simulation Code(AECSC) which is based on LES-TPDF method was combined with the three new models. Then the Sandia laboratory's methane-air jet flames: Flame D and Flame E were simulated. Transient simulation results show that all the three new models can predict the instantaneous combustion flow pattern of the jet flames. Furthermore,the average scalar statistical results were compared with the experimental data. The simulation result of the new TPDF arithmetic mean modification model is the closest to the experimental data:the average error in Flame D is 7.6% and 6.6% in Flame E. The extinction and re-ignition phenomena of the jet flames especially Flame E were captured. The turbulence time scale and the chemistry time scale are in different order in the whole flow field. The dual time scale TPDF combustion model has ability to deal with both the turbulence effect and the chemistry reaction effect, as well as their interaction more accurately for nonpremixed flames.