TURAWAR INJIN HASKE, AN LISSAFA TA HAR ZUWA GEFE

Radiometer ta Crookes, wadda Crookes ya bayyana a 1874, ita ce misalin gargajiya na abin da masana kimiyyar lissafi ke kira tasirin radiometer. Siririn fiffike wanda fuskokinsa biyu ke da yanayin zafi daban-daban, idan aka sanya shi a cikin gas mara yawa, yana jin wani ƙarfi kuma yana motsawa da gefensa mafi zafi a baya. Bayanin da marubutan suka bayar: fuskar mai zafi tana mayar da ƙwayoyin gas da sauri, a matsakaici, fiye da fuskar mai sanyi, don haka gas ɗin yana ƙara turawa a gefen mai zafi.

Wannan tasiri yana sake samun kulawa don ƙananan na’urorin ruwa da iska, don ƙurar iska (aerosols) da kuma don tashi a cikin iska mara yawa sosai ta sararin sama na sama. Halinsa ya dogara sosai da yadda gas ɗin ba shi da yawa, wanda ake auna shi da lambar Knudsen: rabo tsakanin matsakaicin hanya mara cikas (mean free path) — matsakaicin nisan da ƙwaya ke tafiya tsakanin karo biyu — da girman fiffiken. A cikin gas mara yawa sosai ƙarfin yana bazuwa a duk saman; a cikin gas mai yawa yana taruwa kusa da gefe.

Fiffike mafi sauƙi

Takuma Tomita, Satoshi Taguchi da Tetsuro Tsuji, a Makarantar Digiri ta Informatics ta Jami’ar Kyoto, sun yi niyyar bayyana wannan ƙarfi a duk faɗin matakan rashin yawan gas, tare da kulawa ta musamman ga gefe. Fiffiken samfurinsu shi ne mafi sauƙi da ke riƙe gefe: faifai mai da’ira siriri mara iyaka, mai ’yancin motsawa a kan tsakiyarsa cikin gas mara iyaka, fuska ɗaya ta fi ɗaya ɗumi kaɗan.

Ba sa ɗaukar gas a matsayin ruwa mai gudana, sai dai a matsayin tarin ƙwayoyi, suna amfani da sigar lissafin Boltzmann da aka sauƙaƙa (samfurin BGK), wanda aka mayar madaidaici ga ƙananan bambance-bambancen zafi da motsi a hankali. Abu mai wuya shi ne kaifin gefe: yana haifar da tsalle-tsalle na ba-zata a rarraba saurin ƙwayoyi, waɗanda ke bazuwa cikin gas kuma suna da wahala musamman a girma uku. Ƙungiyar tana amfani da hanyar lissafi da ke bin ƙwayoyi a kan hanyoyi madaidaita kuma tana kula da waɗannan tsalle-tsalle a fili, an gudanar da ita a kan babban kwamfutar Jami’ar Kyoto.

Saboda layin madaidaici, matsalar tana rabuwa gida-gida: ƙarfin radiometric a kan faifai mai fuska ɗaya mai zafi, da ja-baya (drag) a kan faifan da ke motsi. Ana kai ga iyakar saurin faifan lokacin da su biyun suka daidaita.

Abin da lissafin ya nuna

(a) Ƙarfin radiometric idan aka kwatanta da rashin yawan gas (da’irori), tare da ma’aunin argon na Selden da abokan aiki (alwatika); (b) iyakar saurin faifan, mai ɗan ƙololuwa (ƙaramin zane a ciki). — Hoto na 3, Tomita, Taguchi da Tsuji (2026), arXiv:2610.02896.

• A siga mara ma’auni, ƙarfin yana ƙaruwa a hankali kuma a ci gaba tare da rashin yawan gas. A cikin gas mai yawa yana tafiya daidai da Kn^(3/2); a cikin gas mara yawa sosai yakan daidaita a wani ƙima mai ɗorewa, −π/2.
• Wannan ya bayyana dalilin da ya sa gwaje-gwaje, waɗanda galibi ke sauya matsin iska, ke samun ainihin ƙarfin mafi girma a matsin tsaka-tsaki. An zana ƙimomin da aka samo daga ma’aunin argon na Selden da abokan aikinsa tare da lissafin.
• Iyakar sauri ba ta ƙaruwa a ci gaba: tana kai ƙololuwa a matakin tsaka-tsaki na rashin yawan gas, ɗan sama kaɗan da ƙimarta a gas mafi rashin yawa. Ƙara rage yawan gas ba koyaushe ke sa faifan ya ƙara sauri ba.
• Kewaye da faifan, gas ɗin ya fi ɗumi kuma ya fi rashin yawa kusa da fuskar mai zafi, akwai tsallen zafi tsakanin wannan fuska da gas ɗin da ke kusa, gudana tare da saman mai zafi, da gudana mai ƙarfi da ta taru a ƙaramin yanki kewaye da gefen.

Gefen da ke yin aikin

Sakamako mafi ban mamaki ya shafi bambancin matsin lamba tsakanin fuskokin biyu. Ga faifan da aka riƙe a tsaye, duk fuskar tana turawa, kuma tana ƙara turawa a gefe yayin da gas ɗin ke ƙara yawa. Ga faifan da ke motsi kyauta a iyakar saurinsa cikin gas mai yawa, hoton yana rabuwa: ƙaramin zirin a gefe yana tura faifan gaba, yayin da sauran fuskar ke birkice shi, kuma su biyun suna daidaita.

Faɗin wannan zirin gefe yana ƙaruwa daidai da matsakaicin hanya mara cikas, don haka a cikin gas mai yawa yana kusan girman takun ƙwaya guda. Marubutan sun lura cewa wannan ya yi daidai da zaton da Einstein ya yi a wata takarda ta 1924 kan ƙarfin radiometer, wanda ƙididdiga na baya-bayan nan har yanzu ke amfani da shi.

An tabbatar ta wata hanya

Don gwada lambobinsu, marubutan sun yi amfani da wata daidaituwa (symmetry) ta lissafin Boltzmann da ke da alaƙa da dangantakar musayar Onsager: dole ƙarfin radiometric ya yi daidai da kwararar zafi da aka lissafa a wata matsala daban, faifai mai motsi mai yanayin zafi iri ɗaya. Su biyun sun yi daidai aƙalla zuwa lambobi uku masu ma’ana a kowane hali — wanda kuma ke goyon bayan wannan daidaituwa idan akwai kaifin gefe.

Samfurin bai haɗa da kaurin ainihin fikafikai ba kuma yana amfani da dokar karo da aka sauƙaƙa. Marubutan suna ganin teburansu a matsayin bayanan tunani ga matsalolin motsin ƙwayoyi masu kaifin gefe da kuma ga ƙurar iska mara siffar ƙwallo, kuma suna shirin amfani da cikakken lissafin Boltzmann da faifai masu kauri na gaba.