简介:Inthisnote,weobtainanasymptoticestimateforthetimederivativeoftheΦ-entropyintermsofthelowerboundoftheBakry–EmeryΓ2curvature.InthecasesofhyperbolicspaceandtheHeisenberggroup(moregenerally,thenilpotentLiegroupofranktwo),weshowthatthetimederivativeoftheΦ-entropyisnon-increasingandconcaveintimet,alsowegetasharpasymptoticboundforthetimederivativeoftheentropyinthesecases.
简介:Anexperimentaladvancedsuperconductingtokamak(EAST)operationwindowwiththelowerhybridcurrentdrive(LHCD)inH-modeisestimatedbyusingacore-SOL-divertor(C-S-D)modelvalidatedbythepresentEASTdivertorexperiments.Theoperationwindowconsistsoffourlimitsincludingtwousuallimits,oneofwhichisthemaximumallowableheatloadontothedivertorplate,andtwoadditionallimitsassociatedwiththeLHCD.ThepredictiveEASToperationwindowisnotqualifiedtofulfillitsmissionforhighinputpower.Toextendtheoperationwindow,gaspuffingandimpurityseedingarepresentedastwoeffectivemethods.Inaddition,theeffectoftheLHCDcurrentontheoperationwindowisalsodiscussed.OurnumericalanalysisresultsprovideareferenceforthesafeoperationofEASTexperimentswithLHCDinfuture.