Jos_von_Asmuth_Thesis.pdf - repository

`Ü~éíÉê=P=TU=òÉêç=~åÇ=íÜÉ=ÄÉííÉê=íÜÉ=~ééêçñáã~íáçå=çÑ= p( τ ) =EïáíÜ=10.9dt = 0dt = 50dt = 100ìåáíë=xiq JN dt = 150zF=ïáää=ÄÉK=kçíÉ=íÜ~í=íÜÉ= 0.8dt = 200Éêêçê=ã~ÇÉ=Äó=íÜáë=~ëëìãéíáçå=ïáää=0.7î~êó=áå=íáãÉ=ïÜÉå=åçåJÉèìáÇáëí~åí=éêÉÅáéáí~íáçå=ëìêéäìë=çÄëÉêî~íáçåë=~êÉ=ìëÉÇI=ïÜáÅÜ=ïáää=áåíêçÇìÅÉ=åçåJëí~íáçå~êáíó=áå=íÜÉ=ãçÇÉä=êÉëáÇì~äëK=eçïÉîÉêI=ïÉ=~ëëìãÉ=íÜ~íI=ïÜÉå=íÜÉ=íáãÉ=ëíÉéë=~êÉ=åçí=íçç=ä~êÖÉ=~åÇ=áêêÉÖìä~êI=íÜáë=ÉÑÑÉÅí=áë=ëã~ää=ïÜÉå=Åçãé~êÉÇ=íç=íÜÉ=0.60.50.40.30.20.1çíÜÉê=ëçìêÅÉë=çÑ=ãçÇÉä=Éêêçê=~åÇ=0Å~å=íÜÉêÉÑçêÉ=ÄÉ=åÉÖäÉÅíÉÇK==0 50 100 150 200 250 300time (in days)===pÉÅçåÇI=~ë=Éèì~íáçå=EPKSF=~åÇ= figure 3.3: Example BR functions of a single linearEPKTF=Åçåí~áå=íáãÉ=Ñêçã= −∞ I=ïÉ= reservoir ( ∆ t = [0,50,100,150,200] , n = 1 ,Ü~îÉ=íç=ÇÉÑáåÉ=~å=áåáíá~ä=î~äìÉ=íç=A = 100 , a = 0.01 ), illustrating the effect of differentÄÉ=~ÄäÉ=íç=Éî~äì~íÉ=íÜÉ=Éèì~íáçåë=time steps on the shape of the BR function.ïáíÜ=çÄëÉêî~íáçåë=ëí~êíáåÖ=Ñêçã=t = 0 K=eÉêÉ=ïÉ=ÇÉÑáåÉ=íÜÉ=áåáíá~ä=î~äìÉ=çÑ= p =Ñêçã= t = −∞ íç= t = 0 íç=ÄÉ= p I=íÜÉ=íÉãéçê~ä=~îÉê~ÖÉ=çÑ=íÜÉ=éêÉÅáéáí~íáçå=ëìêéäìë=ëÉêáÉë=ìëÉÇ=Ñçê=íÜÉ=ëáãìä~íáçåë=EÄìí=ïÜÉå=~î~áä~ÄäÉ=~=ÜáëíçêáÅ~ä=~îÉê~ÖÉ=ÅçìäÇ=~äëç=ÄÉ=ìëÉÇFK=táíÜ=íÜÉ=~áÇ=çÑ=Éèì~íáçå=EPKNQFI=íÜÉ=íê~åëÑÉê=ãçÇÉä=EÉèì~íáçå=EPKSFF=Å~å=åçï=ÄÉ=Éî~äì~íÉÇ=ìëáåÖ=íÜÉ=ÄäçÅâ=êÉëéçåëÉ=E_oF=ÑìåÅíáçåK=qÜÉ=_o=ÑìåÅíáçå= Θ( t)Å~å=ÄÉ=çÄí~áåÉÇ=Äó=ÅçåîçäìíáåÖ=íÜÉ=fo=ÑìåÅíáçå=ïáíÜ=~=ÚÄäçÅâÛ=çÑ=éêÉÅáéáí~íáçå=ëìêéäìë=ïáíÜ=ìåáí=áåíÉåëáíó=çîÉê=~=éÉêáçÇ= ∆tI=ïÜáÅÜ=Éèì~äëW==tΘ ( t) = ∫ θ ( τ )dτ(3.15)t−∆tresponse (−)=qç=ã~âÉ=íÜÉ=_o=ÑìåÅíáçå=Éèìáî~äÉåí=íç=íÜÉ=ÇáëÅêÉíÉ=íê~åëÑÉê=ÑìåÅíáçåI=áí=Ü~ë=íç=ÄÉ=ÇáîáÇÉÇ=Äó= ∆ t =áå=çêÇÉê=íç=ëÅ~äÉ=áí=íç=~=ÄäçÅâ=áåéìí=ïáíÜ=ìåáí=~êÉ~K=få=ÑáÖìêÉ=PKP=ëçãÉ=Éñ~ãéäÉ=_o=ÑìåÅíáçåë=çÑ=~=ëáåÖäÉ=äáåÉ~ê=êÉëÉêîçáê=~êÉ=éäçííÉÇ=Ñçê=ÇáÑÑÉêÉåí=íáãÉ=ëíÉéëK=*qÜÉ=éêÉÇáÅíÉÇ=ÖêçìåÇï~íÉê=äÉîÉä=ëÉêáÉë= h Å~å=ÄÉ=çÄí~áåÉÇ=Äó=~ÇÇáåÖ=íÜÉ=êÉëéçåëÉë=çÑ=~ää=ÚÄäçÅâëÛ=çÑ=éêÉÅáéáí~íáçåK=_ÉÅ~ìëÉ= Θ =áë=~=Åçåíáåìçìë=ÑìåÅíáçåI= h =áë=~äëç=Åçåíáåìçìë=~åÇ=Ñçê=ÉîÉêó=çÄëÉêî~íáçå=çÑ= h =~=ë~ãéäÉ=çÑ=íÜÉ=êÉëáÇì~ä=ëÉêáÉë= n =áë=çÄí~áåÉÇK===kÉñíI=íÜÉ=åçáëÉ=ãçÇÉä=EÉèì~íáçå=EPKTFF=áë=Éî~äì~íÉÇ=áå=çêÇÉê=íç=çÄí~áå=~=ëÉêáÉë=çÑ=áååçî~íáçåë=ν K=qç=Éî~äì~íÉ=íÜÉ=åçáëÉ=ãçÇÉä=ïáíÜçìí=Ü~îáåÖ=íç=ìëÉ=~=h~äã~å=cáäíÉê=EïÜáÅÜ=áë=Åçãéìí~íáçå~ääó=ÉñéÉåëáîÉF=ïÉ=ïáää=ÇÉêáîÉ=~=ÇáêÉÅí=êÉä~íáçå=ÄÉíïÉÉå=íÜÉ=êÉëáÇì~äë= n ~åÇ=íÜÉ=áååçî~íáçåë=ν K=`çåëáÇÉê=íÜÉ=áååçî~íáçå=ëÉêáÉë=ν =~ë=íÜÉ=åçåJÉèìáÇáëí~åíäó=ë~ãéäÉÇ=ÅÜ~åÖÉ=áå=íÜÉ=ëçäìíáçå=íç=íÜÉ=ëíçÅÜ~ëíáÅ=áåíÉÖê~ä=ÇÉëÅêáÄáåÖ=íÜÉ=*..…………………………………………………………………………………………….….