In this paper, the standard homotopy analysis method was applied to initial value problems of the second order with some types of discontinuities, for both linear and nonlinear cases. To show the high accuracy of the ...In this paper, the standard homotopy analysis method was applied to initial value problems of the second order with some types of discontinuities, for both linear and nonlinear cases. To show the high accuracy of the solution results compared with the exact solution, a comparison of the numerical results was made applying the standard homotopy analysis method with the iteration of the integral equation and the numerical solution with the Simpson rule. Also, the maximum absolute error, , the maximum relative error, the maximum residual error and the estimated order of convergence were given. The research is meaningful and I recommend it to be published in the journal.展开更多
Various applications of volume dielectric barrier discharges(DBDs)with airflows have attracted significant attention such as in the fields of plasma medicine,surface modification,ozone synthesis,etc.In this work,the n...Various applications of volume dielectric barrier discharges(DBDs)with airflows have attracted significant attention such as in the fields of plasma medicine,surface modification,ozone synthesis,etc.In this work,the nonlinearity characteristics of DBDs in initiating and extinguishing boundaries with airflows are experimentally investigated.It is found that the difference between initiating pulse repetition frequencies(PRFs)and extinguishing PRFs is affected by the addition of airflows.A hysteresis region is produced between these two PRFs.A topological rule of Thom's classification theorem is proposed to investigate the hysteresis phenomenon of discharges with airflows.It is concluded that the discharge state is dependent on the operation route.The discharge state would transit from initiating to extinguishing,or in the opposite direction,while passing along a specific operation route.Based on the topological method,two nonlinear laws of discharge structure transition under the typical operation routes are predicted and verified in the discharge experiments.展开更多
文摘In this paper, the standard homotopy analysis method was applied to initial value problems of the second order with some types of discontinuities, for both linear and nonlinear cases. To show the high accuracy of the solution results compared with the exact solution, a comparison of the numerical results was made applying the standard homotopy analysis method with the iteration of the integral equation and the numerical solution with the Simpson rule. Also, the maximum absolute error, , the maximum relative error, the maximum residual error and the estimated order of convergence were given. The research is meaningful and I recommend it to be published in the journal.
基金supported by National Natural Science Foundation of China(Nos.51676053 and 91741204)。
文摘Various applications of volume dielectric barrier discharges(DBDs)with airflows have attracted significant attention such as in the fields of plasma medicine,surface modification,ozone synthesis,etc.In this work,the nonlinearity characteristics of DBDs in initiating and extinguishing boundaries with airflows are experimentally investigated.It is found that the difference between initiating pulse repetition frequencies(PRFs)and extinguishing PRFs is affected by the addition of airflows.A hysteresis region is produced between these two PRFs.A topological rule of Thom's classification theorem is proposed to investigate the hysteresis phenomenon of discharges with airflows.It is concluded that the discharge state is dependent on the operation route.The discharge state would transit from initiating to extinguishing,or in the opposite direction,while passing along a specific operation route.Based on the topological method,two nonlinear laws of discharge structure transition under the typical operation routes are predicted and verified in the discharge experiments.
