In this paper, we introduce stochasticity into a model of SIR with density dependent birth rate. We show that the model possesses non-negative solutions as desired in any population dynamics. We also carry out the globally asymptotical stability of the equilibrium through the stochastic Lyapunov functional method if R 0 ≤ 1. Furthermore, when R 0 > 1, we give the asymptotic behavior of the stochastic system around the endemic equilibrium of the deterministic model and show that the solution will oscillate around the endemic equilibrium. We consider that the disease will prevail when the white noise is small and the death rate due to disease is limited.

Due to the nonsmoothness of the small-signal stability constraint, calculating the available transfer capability (ATC) limited by small-signal stability rigorously through the nonlinear programming is quite difficult. To tackle this challenge, this paper proposes a sequential quadratic programming (SQP) method combined with gradient sampling (GS) in a dual formulation. The highlighted feature is the sample size of the gradient changes dynamically in every iteration, yielding an adaptive gradient sampling (AGS) process. Thus, the computing efficiency is greatly improved owing to the decrease and the parallelization of gradient evaluation, which dominates the computing time of the whole algorithm. Simulations on an IEEE 10-machine 39-bus system and an IEEE 54-machine 118-bus system prove the effectiveness and high efficiency of the proposed method.

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In this paper, we study a stochastic non-autonomous logistic system with feedback control. Sufficient conditions for stochastic asymptotically bounded, extinction, non-persistence in the mean, weak persistence, and persistence in the mean are established. The critical number between weak persistence and extinction is obtained. A very important fact is found in our results, that is, the feedback control is harmless to the permanence of species under the randomized environment.

A numerical model of multiphase flow was developed to investigate the heat and mass transfer mechanisms in refueling process. The two-dimensional model takes into account the effects of surface tension, gravity, and viscosity. The heat and mass exchange process of free surface was defined to study isooctane liquid evaporation in refueling process. The reliability of the model was verified by the theoretical solution of the Stephan problem. The evolution of the flow field, temperature field, pressure field, concentration field, and evaporation rate was discussed in detail. It shows that there is a strong turbulence and gas entrainment phenomenon. The volume-averaged temperature of the fuel tank is lower than the ambient temperature, and the maximum difference is about 4°C resulting from evaporation; the curve of evaporation rate versus time is very similar to that of the volume-averaged pressure versus time. Besides, the change in evaporation rate is negligible after 1.75 s.