I. Gabatarwa
Fractals abubuwa ne na lissafi waɗanda ke nuna kaddarorin kama da kai a ma'auni daban-daban. Wannan yana nufin cewa lokacin da kuka zuƙowa / fita akan sifar fractal, kowane ɓangaren sa yayi kama da gaba ɗaya; wato, nau'ikan sifofi iri ɗaya ko sifofi iri ɗaya suna maimaitawa a matakan haɓaka daban-daban (duba misalan ɓarna a hoto na 1). Yawancin fractals suna da rikitattun siffofi, dalla-dalla, kuma maras iyaka.
siffa 1
Masanin ilimin lissafi Benoit B. Mandelbrot ne ya gabatar da manufar fractals a cikin 1970s, kodayake ana iya gano asalin jigogi na fractal zuwa farkon aikin masana lissafi da yawa, kamar Cantor (1870), von Koch (1904), Sierpinski (1915) ), Julia (1918), Fatou (1926), da Richardson (1953).
Benoit B. Mandelbrot yayi nazarin alakar da ke tsakanin fractals da yanayi ta hanyar bullo da sabbin nau'ikan fractals don kwaikwaya mafi hadaddun sifofi, kamar bishiyoyi, tsaunuka, da bakin teku. Ya ƙirƙiro kalmar “fractal” daga kalmar sifa ta Latin “fractus”, ma’ana “karye” ko “karya”, watau wanda ya ƙunshi ɓangarorin da ba su dace ba, don bayyana sifofin da ba daidai ba da rarrabuwa na geometric waɗanda ba za a iya rarraba su ta hanyar lissafi na Euclidean na gargajiya ba. Bugu da ƙari, ya ɓullo da ƙididdiga na lissafi da algorithms don samarwa da nazarin fractals, wanda ya haifar da ƙirƙirar sanannen saitin Mandelbrot, wanda tabbas shine mafi shahara kuma mai ban sha'awa na gani mai siffar fractal tare da hadaddun tsarin maimaitawa mara iyaka (duba Hoto 1d).
Ayyukan Mandelbrot ba wai kawai ya yi tasiri kan ilimin lissafi ba, har ma yana da aikace-aikace a fannoni daban-daban kamar kimiyyar lissafi, zane-zanen kwamfuta, ilmin halitta, tattalin arziki, da fasaha. A zahiri, saboda iyawarsu na yin ƙira da wakiltar sarƙaƙƙiya da tsarin kamanni na kansu, fractals suna da sabbin aikace-aikace masu yawa a fagage daban-daban. Misali, an yi amfani da su sosai a wuraren aikace-aikacen da ke gaba, waɗanda kaɗan ne kawai na faɗuwar aikace-aikacensu:
1. Zane-zane na kwamfuta da raye-raye, samar da yanayi na zahiri da kyan gani, bishiyoyi, gajimare, da laushi;
2. Fasahar matsawa bayanai don rage girman fayilolin dijital;
3. Hoton hoto da siginar sigina, fitar da sifofi daga hotuna, gano alamu, da kuma samar da ingantattun hanyoyin damtse hoto da sake ginawa;
4. Ilimin halitta, yana kwatanta ci gaban shuke-shuke da kuma tsarin neurons a cikin kwakwalwa;
5. Ka'idar Antenna da metamaterials, zayyana m / Multi-band eriya da m metasurfaces.
A halin yanzu, juzu'i na fractal yana ci gaba da samun sabbin amfani da sabbin abubuwa a fannonin kimiyya, fasaha da fasaha daban-daban.
A cikin fasahar lantarki (EM), siffofi na fractal suna da matukar amfani ga aikace-aikacen da ke buƙatar ƙaranci, daga eriya zuwa metamaterials da filayen zaɓin mita (FSS). Yin amfani da jumloli na fractal a cikin eriya na al'ada na iya ƙara tsayin wutar lantarki, ta haka rage girman girman tsarin resonant gabaɗaya. Bugu da ƙari, yanayin kamanni da kansu na sifofin fractal ya sa su dace don gane maɓalli da yawa ko sifofin resonant. Ƙaƙƙarfan ƙarancin ƙarancin ƙima na fractals suna da ban sha'awa musamman don ƙirar ƙira, eriya mai tsararru, masu ɗaukar metamaterial da metasurfaces don aikace-aikace daban-daban. A haƙiƙa, yin amfani da ƙananan abubuwan tsararru na iya kawo fa'idodi da yawa, kamar rage haɗin gwiwar juna ko samun damar yin aiki tare da tsararraki tare da ƙaramin tazara, don haka tabbatar da kyakkyawan aikin dubawa da manyan matakan kwanciyar hankali.
Don dalilan da aka ambata a sama, eriya fractal da metasurfaces suna wakiltar wuraren bincike guda biyu masu ban sha'awa a fagen na'urorin lantarki waɗanda suka ja hankalin mutane da yawa a cikin 'yan shekarun nan. Dukansu ra'ayoyi suna ba da hanyoyi na musamman don sarrafa da sarrafa raƙuman ruwa na lantarki, tare da aikace-aikace da yawa a cikin sadarwa mara waya, tsarin radar da ji. Kaddarorinsu masu kama da kansu suna ba su damar zama ƙanana a cikin girman yayin da suke riƙe kyakkyawar amsawar lantarki. Wannan ƙaƙƙarfan yana da fa'ida musamman a aikace-aikacen da ke da kuncin sararin samaniya, kamar na'urorin hannu, alamun RFID, da tsarin sararin samaniya.
Amfani da eriya na fractal da metasurfaces yana da yuwuwar inganta ingantaccen sadarwa mara waya, hoto, da tsarin radar, yayin da suke ba da ƙarfi, manyan na'urori tare da ingantattun ayyuka. Bugu da kari, fractal geometry ana ƙara yin amfani da shi wajen ƙirƙira na'urori masu auna firikwensin microwave don bincikar kayan abu, saboda ikonsa na aiki a cikin maɗauran mitar mitoci da yawa da kuma ikonsa na ɗan ƙaranci. Ci gaba da bincike a waɗannan yankuna na ci gaba da bincika sabbin ƙira, kayan aiki, da fasahohin ƙirƙira don gane cikakkiyar damar su.
Wannan takarda yana da nufin yin bitar bincike da ci gaban aikace-aikacen eriyar fractal da metasurfaces da kwatanta eriya na tushen fractal da metasurfaces, yana nuna fa'idodi da iyakokin su. A ƙarshe, an gabatar da cikakken bincike game da sabbin abubuwan nuna haske da raka'a metamaterial, kuma an tattauna ƙalubale da ci gaban waɗannan sifofin lantarki na gaba.
2. FractalEriyaAbubuwa
Za a iya amfani da mahimmin ra'ayi na fractals don tsara abubuwan eriya masu ban mamaki waɗanda ke ba da kyakkyawan aiki fiye da eriya na al'ada. Abubuwan eriya masu ɓarkewa na iya zama ƙanƙanta a girman kuma suna da madaukai da yawa da/ko damar watsa labarai.
Ƙirar eriya ta fractal ta ƙunshi maimaita takamaiman tsarin geometric a ma'auni daban-daban a cikin tsarin eriya. Wannan tsari mai kama da kai yana ba mu damar ƙara tsayin eriya gabaɗaya a cikin ƙayyadaddun sarari na zahiri. Bugu da kari, fractal radiators na iya cimma makada da yawa saboda sassa daban-daban na eriya sun yi kama da juna a ma'auni daban-daban. Don haka, abubuwan eriya na fractal na iya zama ƙanƙanta da maɓalli da yawa, suna ba da faffadar ɗaukar hoto fiye da eriya ta al'ada.
Tunanin eriya fractal za a iya gano su a ƙarshen 1980s. A cikin 1986, Kim da Jaggard sun nuna aikace-aikacen kamanni na fractal a cikin haɗar tsararrun eriya.
A cikin 1988, masanin kimiyya Nathan Cohen ya gina eriya ta farko ta fractal element a duniya. Ya ba da shawarar cewa ta hanyar haɗa nau'ikan lissafi mai kama da kai a cikin tsarin eriya, za a iya inganta aikin sa da ƙarancin ƙarfinsa. A cikin 1995, Cohen ya kafa Fractal Antenna Systems Inc., wanda ya fara samar da mafitacin eriya na tushen fractal na kasuwanci na farko a duniya.
A tsakiyar 1990s, Puente et al. ya nuna iyawar ƙungiyoyi masu yawa na fractals ta amfani da monopole na Sierpinski da dipole.
Tun daga aikin Cohen da Puente, abubuwan da suka dace na eriya na fractal sun jawo hankalin masu bincike da injiniyoyi a fagen sadarwa, wanda ke haifar da ƙarin bincike da haɓaka fasahar eriya ta fractal.
A yau, ana amfani da eriya ta fractal a cikin tsarin sadarwar mara waya, gami da wayoyin hannu, hanyoyin sadarwar Wi-Fi, da sadarwar tauraron dan adam. A haƙiƙa, eriya na fractal ƙananan ƙanana ne, multiband, kuma suna da inganci sosai, yana sa su dace da na'urori da cibiyoyin sadarwa iri-iri.
Alkaluman da ke biyo baya suna nuna wasu eriya na fractal dangane da sanannun sifofin fractal, waɗanda kaɗan ne kawai na ginshiƙai daban-daban da aka tattauna a cikin adabi.
Musamman, Hoto 2a yana nuna monopole na Sierpinski wanda aka gabatar a Puente, wanda ke da ikon samar da aiki mai tarin yawa. An kafa triangle Sierpinski ta hanyar cire triangle mai jujjuyawar tsakiya daga babban alwatika, kamar yadda aka nuna a hoto 1b da Hoto 2a. Wannan tsari ya bar triangles guda uku daidai gwargwado akan tsarin, kowanne yana da tsawon gefe na rabin na farkon triangle (duba hoto 1b). Hakanan za'a iya maimaita hanyar cirewa don ragowar triangles. Saboda haka, kowanne daga cikin manyan sassansa guda uku daidai yake da duka abu, amma a cikin ninki biyu, 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, Sierpinski monopole da aka tsara yana aiki a cikin ƙungiyoyi 5. Ana iya ganin cewa kowane ɗayan ƙananan gasket guda biyar (tsararrun da'ira) a cikin Hoto 2a sigar sikeli ce ta gabaɗayan tsarin, don haka tana ba da madaukai na mitar aiki daban-daban guda biyar, kamar yadda aka nuna a cikin ma'aunin bayanan shigar da ke cikin hoto na 2b. Har ila yau, adadi yana nuna ma'auni masu alaƙa da kowane rukunin mitar, gami da ƙimar mitar fn (1 ≤ n ≤ 5) a mafi ƙarancin ƙimar asarar dawo da shigarwar da aka auna (Lr), bandwidth dangi (Bwidth), da ƙimar mitar tsakanin Ƙungiyoyin mitar mitoci biyu (δ = fn +1/fn). Hoto na 2b yana nuna cewa makada na Sierpinski monopoles suna logarithm lokaci-lokaci ana yin tazarar su ta hanyar juzu'i na 2 (δ ≅ 2), wanda yayi daidai da sikelin sikeli iri ɗaya da ke cikin sifofi iri ɗaya a cikin siffa ta fractal.
siffa 2
Hoto na 3a yana nuna ƙaramin eriya mai tsayin waya dangane da lanƙwan ɓangarorin Koch. An gabatar da wannan eriya don nuna yadda ake yin amfani da kaddarorin masu cika sararin samaniya na sifofin fractal don tsara ƙananan eriya. A haƙiƙa, rage girman eriya shine manufa ta ƙarshe na adadin aikace-aikacen da yawa, musamman waɗanda suka shafi tashoshin wayar hannu. An ƙirƙiri monopole na Koch ta amfani da hanyar ginin fractal wanda aka nuna a cikin Hoto 3a. Farkon maimaitawar K0 shine madaidaiciyar monopole. Ana samun maimaitawar K1 na gaba ta hanyar amfani da canjin kamanni zuwa K0, gami da sikeli ta ɗaya bisa uku da juyawa ta 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 3a yana nuna nau'in juzu'i biyar na Koch monopole (watau K5) tare da tsayi h daidai da 6 cm, amma jimlar tsayin ana ba da shi ta hanyar dabara l = h · (4/3) 5 = 25.3 cm. An gano eriya biyar masu dacewa da na'urorin farko guda biyar na Koch curve (duba Hoto 3a). Duk gwaje-gwaje da bayanai sun nuna cewa Koch fractal monopole na iya inganta aikin monopole na gargajiya (duba Hoto 3b). Wannan yana ba da shawarar cewa yana iya yiwuwa a “rage” eriya na fractal, yana ba su damar dacewa da ƙaramin juzu'i yayin da suke riƙe ingantaccen aiki.
siffa 3
Hoto 4a yana nuna eriyar fractal dangane da saitin Cantor, wanda ake amfani da shi don tsara eriya mai faɗi don aikace-aikacen girbin makamashi. Ana amfani da keɓantaccen kayan eriya na fractal waɗanda ke gabatar da ƙararrawa da yawa kusa da su don samar da faffadan bandwidth fiye da eriya na al'ada. Kamar yadda aka nuna a cikin Hoto 1a, zane na Cantor fractal set yana da sauƙi: an kwafi layin madaidaiciya na farko kuma an raba shi zuwa kashi uku daidai, wanda aka cire sashin tsakiya; Hakanan ana amfani da wannan tsari akai-akai akan sabbin sassan da aka samar. Ana maimaita matakan jujjuyawar ɓarna har sai an sami bandwidth na eriya (BW) na 0.8–2.2 GHz (watau 98% BW). Hoto na 4 yana nuna hoton samfurin eriya da aka gane (Hoto 4a) da madaidaicin shigar da bayanan sa (Hoto na 4b).
siffa 4
Hoto na 5 yana ba da ƙarin misalan eriyar fractal, gami da eriyar monopole mai tushen Hilbert curve, eriyar facin microstrip na tushen Mandelbrot, da tsibirin Koch (ko “dusar ƙanƙara”) facin faci.
adadi 5
A ƙarshe, Hoto na 6 yana nuna shirye-shiryen ɓarna daban-daban na abubuwan tsararru, gami da Sierpinski carpet planar arrays, Cantor ring arrays, Cantor linear arrays, da fractal bishiyoyi. Waɗannan shirye-shiryen suna da amfani don samar da tsararrun tsararru da/ko cimma aikin ƙungiyoyi masu yawa.
siffa 6
Don ƙarin koyo game da eriya, da fatan za a ziyarci:
Lokacin aikawa: Yuli-26-2024
