Daidaitawar yawan jama'a

An gabatar da daidaitattun-daidaitattun jama'a (PBEs) a cikin rassa da yawa na kimiyya ta zamani, galibi a cikin Injiniyan Chemical,  don bayyana juyin halitta na yawan barbashi. Wannan ya haɗa da batutuwa kamar crystallization,  leaching (metallurgy),  cire ruwa-ruwa, rarraba gas-ruwa kamar ruwa electrolysis,  halayen ruwa-ruwan ruwa, raguwa, Injiniyan aerosol, ilmin halitta (inda ƙungiyoyi daban-daban sune sel bisa ga girman su ko sunadarai na intracellular ), polymerization, da dai sauransu. Za'a iya cewa ana iya samun daidaitattun daidaitattun ma'aunin Smoluchowski wanda ke bayyana kawai haɗin barbashi. PBEs, gabaɗaya, suna bayyana yadda yawan jama'a na ƙungiyoyi daban-daban ke tasowa a cikin takamaiman kaddarorin a tsawon lokaci. Su ne saiti na daidaitattun bambance-bambance na Integro-partial wanda ke ba da halayyar matsakaicin filin yawan barbashi daga nazarin halayyar barbashi guda ɗaya a cikin yanayin gida. Tsarin ƙwayoyin cuta ana nuna su ta hanyar haihuwa da mutuwar ƙwayoyin. Misali, la'akari da tsarin hazo (tsarin ƙarfi daga maganin ruwa) wanda ke da subprocesses nucleation, agglomeration, ƙarya, da dai sauransu, wanda ke haifar da karuwa ko raguwar yawan barbashi na wani radius (yana ɗaukar samar da barbashi na spherical). Ma'aunin yawan jama'a ba komai bane face ma'auni akan yawan barbashi na wani jiha (a cikin wannan misali, girman).

 Tsarin PBE 
Yi la'akari da matsakaita adadin barbashi tare da barbashi Properties nuna ta wani barbashi jihar vector (x, r) (inda x yayi dace da barbashi Properties kamar size, yawa, da dai sauransu kuma aka sani da ciki daidaitawa da, r yayi dace da sarari matsayi ko waje daidaitawa) tarwatsa a cikin wani m lokaci ayyana ta wani lokaci vector Y (r,t) (wanda kuma shi ne wani nau'i na vector na duk wani nau'i na daban-daban na wurare dabam dabam).  f(x,r,t) ya nuna.  Don haka yana ba da halayen barbashi a cikin dukiya da yankunan sararin samaniya.  Bari h(x,r,Y,t) ya nuna adadin haihuwar barbashi kowace juzu'in juzu'in barbashi, don haka za'a iya rubuta lambar kiyayewa kamar haka. 

 Maganin PBE 
Hanyoyin Monte Carlo  ,  hanyoyin rarrabewa  da hanyoyin lokaci   [3]  ana amfani da su galibi don warware waɗannan daidaitattun. Zaɓin ya dogara da aikace-aikace da kayan aikin lissafi.
Rukuni:Shafuka masu fassarorin da ba'a duba ba