An operator splitting scheme for the fractional kinetic Fokker-Planck equation

In this paper, we develop an operator splitting scheme for the fractional kinetic Fokker-Planck equation (FKFPE). The scheme consists of two phases: a fractional diffusion phase and a kinetic transport phase. The first phase is solved exactly using the convolution operator while the second one is solved approximately using a variational scheme that minimizes an energy functional with respect to a certain Kantorovich optimal transport cost functional. We prove the convergence of the scheme to a weak solution to FKFPE. As a by-product of our analysis, we also establish a variational formulation for a kinetic transport equation that is relevant in the second phase. Finally, we discuss some extensions of our analysis to more complex systems

Current Situation and Measures of Environment Affected by Mine Water in Hunan Limin Coal Mine

The pump drainage of mine water in Hunan Limin Coal Mine has caused various problems including huge depression cone and collapse of goaf roof, resulting in serious leakage of surface water. Therefore, a great need of measures should be conducted. In this paper, the mine water properties and the hydrogeological characteristics were studied. The results indicate that the PH value of main shaft water of Limin Well is 2.21-3.81 (average: 2.90), Fe2+ is 178-1,308 mg/L, Mn2+ is 3.93-8.65 mg/L; the PH value of auxiliary shaft water is 3.45-4.08, Fe2+ is 876-1,264 mg/L, Mn2+ is 6.27-8.71 mg/L; the PH value of Shuikoushan old pithead water is 2.33-3.91, Fe2+ is 1,059-2,207 mg/L and Mn2+ is 23.00-34.00 mg/L, which indicates that the mine water in the area is strongly acidic, and Fe2+ and Mn2+ exceed the standard seriously. Based on the characteristics of mining tunnel in the area, the wellhead of artesian water in Limin Well should be closed with shaft without pressure so as to ensure that the mine water can be discharged out in a concentrated and orderly way. The sewage treatment facilities at the main shaft of Limin Well need to be expanded, and new sewage treatment facilities should be built at Shuikoushan old pithead. Through hydrologic survey and water balance analysis, Zhoutou Reservoir can be used as a water source to construct drinking water project, which can completely solve the problem of drinking water safety in the area. The study would solve the bad situation of Limin Coal mine by providing the corresponding measures, which could provide the references for the similar mines when facing these problems