I. Gabatarwa
Fractals abubuwa ne na lissafi waɗanda ke nuna halaye iri ɗaya a ma'auni daban-daban. Wannan yana nufin cewa lokacin da ka yi zuƙowa/fita a kan siffar fractal, kowanne daga cikin sassansa yana kama da gaba ɗaya; wato, alamu na geometric ko tsari iri ɗaya suna maimaitawa a matakan girma daban-daban (duba misalan fractal a Hoto na 1). Yawancin fractals suna da siffofi masu rikitarwa, cikakkun bayanai, kuma marasa iyaka.
siffa ta 1
Masanin lissafi Benoit B. Mandelbrot ne ya gabatar da manufar fractals a shekarun 1970, kodayake asalin tsarin lissafi na fractal za a iya samo asali ne daga ayyukan da masana lissafi da yawa suka yi a baya, kamar Cantor (1870), von Koch (1904), Sierpinski (1915), Julia (1918), Fatou (1926), da Richardson (1953).
Benoit B. Mandelbrot ya yi nazarin alaƙar da ke tsakanin fractals da yanayi ta hanyar gabatar da sabbin nau'ikan fractals don kwaikwayon gine-gine masu rikitarwa, kamar bishiyoyi, duwatsu, da bakin teku. Ya ƙirƙiro kalmar "fractal" daga siffa ta Latin "fractus", ma'ana "karyewa" ko "karyewa", watau wanda ya ƙunshi guntu-guntu masu karyewa ko marasa tsari, don bayyana siffofi na geometric marasa tsari da marasa tsari waɗanda ba za a iya rarraba su ta hanyar tsarin Euclidean na gargajiya ba. Bugu da ƙari, ya ƙirƙiro samfuran lissafi da algorithms don ƙirƙirar da nazarin fractals, wanda ya haifar da ƙirƙirar sanannen saitin Mandelbrot, wanda wataƙila shine mafi shahara kuma mafi ban sha'awa na siffar fractal tare da siffofi masu rikitarwa da maimaitawa marasa iyaka (duba Hoto na 1d).
Ayyukan Mandelbrot ba wai kawai sun yi tasiri ga lissafi ba, har ma sun yi amfani da su a fannoni daban-daban kamar kimiyyar lissafi, zane-zanen kwamfuta, ilmin halitta, tattalin arziki, da fasaha. A gaskiya ma, saboda iyawarsu ta yin ƙira da kuma wakiltar tsare-tsare masu rikitarwa da kama da juna, fractals suna da aikace-aikace masu yawa na kirkire-kirkire a fannoni daban-daban. Misali, an yi amfani da su sosai a fannoni masu zuwa na aikace-aikacen, waɗanda kaɗan ne daga cikin misalan aikace-aikacensu:
1. Zane-zanen kwamfuta da zane-zanen motsi, waɗanda ke samar da shimfidar wurare na halitta masu ban sha'awa da kuma na gani, bishiyoyi, gajimare, da kuma laushi;
2. Fasahar matse bayanai don rage girman fayilolin dijital;
3. Sarrafa hoto da sigina, cire fasaloli daga hotuna, gano alamu, da kuma samar da ingantattun hanyoyin matse hoto da sake gina shi;
4. Ilimin halittu, wanda ke bayyana girman tsirrai da kuma tsarin jijiyoyi a cikin kwakwalwa;
5. Ka'idar eriya da kayan metamaterials, tsara ƙananan eriya/masu haɗakar tashoshi da kuma sabbin hanyoyin metasurfaces.
A halin yanzu, tsarin lissafi na fractal yana ci gaba da samun sabbin amfani da sabbin abubuwa a fannoni daban-daban na kimiyya, fasaha da fasaha.
A cikin fasahar lantarki (EM), siffofi na fractal suna da matuƙar amfani ga aikace-aikacen da ke buƙatar ƙaramin aiki, daga eriya zuwa metamaterials da saman zaɓaɓɓen mita (FSS). Yin amfani da tsarin fractal a cikin eriya na gargajiya na iya ƙara tsawon wutar lantarki, ta haka rage girman tsarin resonant gabaɗaya. Bugu da ƙari, yanayin kama da na fractal yana sa su zama masu dacewa don aiwatar da tsarin resonant mai yawa ko broadband. Ƙarfin miniaturization na fractals yana da kyau musamman don ƙirƙirar reflectarrays, eriya mai tsari mai matakai, masu ɗaukar metamaterial da metasurfaces don aikace-aikace daban-daban. A zahiri, amfani da ƙananan abubuwan array na iya kawo fa'idodi da yawa, kamar rage haɗin gwiwa ko samun damar yin aiki tare da arrays tare da ƙaramin tazara na abubuwa, don haka tabbatar da kyakkyawan aikin dubawa da matakan kwanciyar hankali na kusurwa.
Saboda dalilan da aka ambata a sama, eriya da metasurfaces suna wakiltar fannoni biyu masu ban sha'awa na bincike a fannin electromagnetics waɗanda suka jawo hankali sosai a cikin 'yan shekarun nan. Dukansu ra'ayoyi suna ba da hanyoyi na musamman don sarrafa da sarrafa raƙuman lantarki, tare da aikace-aikace iri-iri a cikin sadarwa mara waya, tsarin radar da ji. Sifofinsu masu kama da juna suna ba su damar zama ƙanana a girma yayin da suke riƙe da kyakkyawan amsawar electromagnetic. Wannan ƙanƙantar yana da fa'ida musamman a cikin aikace-aikacen sararin samaniya da aka iyakance, kamar na'urorin hannu, alamun RFID, da tsarin sararin samaniya.
Amfani da eriya da kuma metasurfaces na da yuwuwar inganta sadarwa mara waya, daukar hoto, da tsarin radar sosai, domin suna ba da damar ƙananan na'urori masu aiki mai ƙarfi tare da ingantaccen aiki. Bugu da ƙari, ana ƙara amfani da tsarin fractal wajen ƙirar na'urori masu auna sigina na microwave don gano abubuwa, saboda ikonsa na aiki a cikin madaukai da yawa da kuma ikon rage girmansa. Bincike da ake ci gaba da yi a waɗannan fannoni yana ci gaba da bincika sabbin ƙira, kayan aiki, da dabarun ƙera don cimma cikakken ƙarfinsu.
Wannan takarda tana da nufin yin bitar bincike da ci gaban aikace-aikacen eriya da metasurfaces da kuma kwatanta eriya da metasurfaces da ke tushen fractal, tare da nuna fa'idodi da iyakokinsu. A ƙarshe, an gabatar da cikakken bincike na sabbin na'urori masu haskakawa da na'urorin metamaterial, kuma an tattauna ƙalubalen da ci gaban waɗannan tsarin lantarki na gaba.
2. FractalEriyaAbubuwa
Ana iya amfani da manufar gabaɗaya ta fractals don tsara abubuwan eriya na waje waɗanda ke ba da aiki mafi kyau fiye da eriya na gargajiya. Abubuwan eriya na fractal na iya zama ƙanana a girma kuma suna da ƙarfin multiband da/ko broadband.
Tsarin eriya na fractal ya ƙunshi maimaita takamaiman tsare-tsare na geometric a ma'auni daban-daban a cikin tsarin eriya. Wannan tsari mai kama da kansa yana ba mu damar ƙara tsawon eriya gaba ɗaya a cikin sarari mai iyaka. Bugu da ƙari, radiators na fractal na iya cimma madaukai da yawa saboda sassa daban-daban na eriya suna kama da juna a ma'auni daban-daban. Saboda haka, abubuwan eriya na fractal na iya zama ƙanana da yawa, suna ba da faɗin mita fiye da eriya na al'ada.
An iya gano manufar eriya ta fractal tun daga ƙarshen shekarun 1980. A shekarar 1986, Kim da Jaggard sun nuna amfani da kamannin kai na fractal a cikin tsarin haɗa antenna.
A shekarar 1988, masanin kimiyyar lissafi Nathan Cohen ya gina eriya ta farko ta fractal element a duniya. Ya ba da shawarar cewa ta hanyar haɗa tsarin eriya mai kama da juna a cikin tsarin eriya, za a iya inganta aikinta da ƙarfinta na ƙarami. A shekarar 1995, Cohen ya haɗu ya kafa Fractal Antenna Systems Inc., wanda ya fara samar da mafita ta eriya ta kasuwanci ta farko a duniya ta fractal.
A tsakiyar shekarun 1990, Puente da abokan aikinsa sun nuna ƙarfin fractals masu yawa ta amfani da monopole da dipole na Sierpinski.
Tun bayan aikin Cohen da Puente, fa'idodin da ke tattare da eriya ta fractal sun jawo hankalin masu bincike da injiniyoyi a fannin sadarwa, wanda hakan ya haifar da ƙarin bincike da haɓaka fasahar eriya ta fractal.
A yau, ana amfani da eriya ta fractal sosai a tsarin sadarwa ta waya, ciki har da wayoyin hannu, na'urorin sadarwa na Wi-Fi, da kuma sadarwa ta tauraron dan adam. A gaskiya ma, eriya ta fractal ƙanana ne, masu amfani da yawa, kuma suna da inganci sosai, wanda hakan ya sa suka dace da nau'ikan na'urori da hanyoyin sadarwa iri-iri.
Hotunan da ke ƙasa suna nuna wasu eriya na fractal bisa ga sanannun siffofi na fractal, waɗanda kaɗan ne daga cikin misalai na tsare-tsare daban-daban da aka tattauna a cikin adabi.
Musamman ma, Hoto na 2a yana nuna madaidaicin Sierpinski da aka gabatar a Puente, wanda ke da ikon samar da aiki mai yawa. An samar da alwatika na Sierpinski ta hanyar cire alwatika mai juyawa ta tsakiya daga babban alwatika, kamar yadda aka nuna a Hoto na 1b da Hoto na 2a. Wannan tsari yana barin alwatika guda uku daidai a kan tsarin, kowannensu yana da tsawon gefe na rabin alwatika na farko (duba Hoto na 1b). Ana iya maimaita tsarin ragewa iri ɗaya ga sauran alwatika. Saboda haka, kowanne daga cikin manyan sassansa guda uku daidai yake da dukkan abu, amma a ninka rabon, da sauransu. Saboda waɗannan kamanceceniya na musamman, Sierpinski na iya samar da madaukai masu yawa saboda sassa daban-daban na eriya suna kama da juna a ma'auni daban-daban. Kamar yadda aka nuna a Hoto na 2, madaidaicin Sierpinski da aka gabatar yana aiki a cikin madaukai 5. Ana iya ganin cewa kowanne daga cikin ƙananan gaskets guda biyar (tsarin da'ira) a Hoto na 2a sigar sikelin dukkan tsarin ne, don haka yana samar da madaukai masu aiki guda biyar daban-daban, kamar yadda aka nuna a cikin ma'aunin nunin shigarwa a Hoto na 2b. Wannan adadi kuma yana nuna sigogi da suka shafi kowace mitar, gami da ƙimar mitar fn (1 ≤ n ≤ 5) a mafi ƙarancin ƙimar asarar dawowar shigarwa da aka auna (Lr), bandwidth mai dangantaka (Bwidth), da rabon mitar tsakanin mitar guda biyu da ke maƙwabtaka (δ = fn +1/fn). Hoto na 2b ya nuna cewa madaurin Sierpinski monopoles suna da logarithmically tazara lokaci-lokaci ta hanyar factor na 2 (δ ≅ 2), wanda ya yi daidai da ma'aunin sikelin iri ɗaya da ke cikin sifofi iri ɗaya a cikin siffar fractal.
siffa ta 2
Hoto na 3a yana nuna ƙaramin eriya mai tsayi bisa lanƙwasa fractal na Koch. An gabatar da wannan eriya don nuna yadda ake amfani da kaddarorin cike sararin samaniya na siffofi na fractal don tsara ƙananan eriya. A zahiri, rage girman eriya shine babban burin aikace-aikace da yawa, musamman waɗanda suka shafi tashoshin hannu. An ƙirƙiri monopole na Koch ta amfani da hanyar gina fractal da aka nuna a Hoto na 3a. Koyarwar farko K0 monopole ce madaidaiciya. Ana samun koyarwar K1 ta gaba ta hanyar amfani da canjin kamanceceniya zuwa K0, gami da aunawa da kashi ɗaya bisa uku da juyawa da 0°, 60°, −60°, da 0°, bi da bi. Ana maimaita wannan tsari akai-akai don samun abubuwan da ke gaba Ki (2 ≤ i ≤ 5). Hoto na 3a yana nuna sigar maimaitawa biyar na Koch monopole (watau, K5) tare da tsayi h daidai da 6 cm, amma jimlar tsawon an bayar da ita ta hanyar dabarar l = h ·(4/3) 5 = 25.3 cm. An cimma eriya biyar da suka yi daidai da maimaitawa biyar na farko na lanƙwasa Koch (duba Hoto na 3a). Duk gwaje-gwaje da bayanai sun nuna cewa monopole na fractal na Koch zai iya inganta aikin monopole na gargajiya (duba Hoto na 3b). Wannan yana nuna cewa yana yiwuwa a "rage" eriya na fractal, wanda zai ba su damar shiga cikin ƙananan girma yayin da suke ci gaba da aiki mai inganci.
siffa ta 3
Hoto na 4a yana nuna eriya ta fractal bisa saitin Cantor, wanda ake amfani da shi don tsara eriya mai faɗi don amfani da tattara makamashi. An yi amfani da keɓantaccen ikon eriya na fractal waɗanda ke gabatar da resonances da yawa da ke maƙwabtaka don samar da bandwidth mai faɗi fiye da eriya na gargajiya. Kamar yadda aka nuna a Hoto na 1a, ƙirar saitin Cantor fractal abu ne mai sauƙi: ana kwafi layin madaidaiciya na farko kuma an raba shi zuwa sassa uku daidai, daga inda aka cire ɓangaren tsakiya; sannan ana amfani da wannan tsari akai-akai ga sabbin sassan da aka samar. Ana maimaita matakan maimaita fractal har sai an cimma bandwidth na eriya (BW) na 0.8–2.2 GHz (watau, 98% BW). Hoto na 4 yana nuna hoton samfurin eriya da aka gano (Hoto na 4a) da ma'aunin nunin shigarwarsa (Hoto na 4b).
siffa ta 4
Siffa ta 5 ta ba da ƙarin misalai na eriya masu kama da fractal, gami da eriya mai kama da fractal mai kama da Hilbert lankwasa, eriya mai kama da fractal mai kama da Mandelbrot, da kuma facin fractal na tsibirin Koch (ko "snowflake").
siffa ta 5
A ƙarshe, Hoto na 6 yana nuna shirye-shiryen fractal daban-daban na abubuwan array, gami da arrays ɗin Sierpinski planar arrays, arrays ɗin zobe na Cantor, arrays ɗin layi na Cantor, da bishiyoyin fractal. Waɗannan shirye-shiryen suna da amfani don samar da arrays masu faɗi da/ko cimma aikin multi-band.
siffa ta 6
Don ƙarin koyo game da eriya, da fatan za a ziyarci:
Lokacin Saƙo: Yuli-26-2024
