taarakiya spandan

taarakiya spandan baahari paraton mein vistaar aur sankuchan key kaaran hotey hain kyonki ack taaraa santulan banaae rakhna chaahata haye. taarakiya trijya mein yeye utaar-chadhaav taaron kii chamak mein sambandhit parivartanon kaa kaaran banate hain. khagolvid varnakram koo mapkar aur doppler prabhaav kaa avalokan karke iss tantra kaa anuman lagaane mein saksham hain. kaee aantarik charr taare joe badey aayamon key saath spandit hotey hain, jaise kii shaastriya seyfeeds, rr lyre sitaare aur badey-ayam delta scooty sitaare niyamit prakaash vakr dikhaate hain.
yeh niyamit vyavhaar taaron kii parivartansheelta key vipareet haye joe heartzsprung-russell aarekh mein shaastriya charr taaron key uchch-chamak/cumm-tapman vaale paksh key samanantar aur samanantar haye. inn vishal taaron koo kamjor aniyamitata seey laker, jaba koee abhee bhee ausat saikil chalaane key samay yaa avadhi (adhikansh aarvi tauri aur ardh-rekhiya charr key roop mein) koo paribhaashit curr sakata haye, aniyamit charr mein punaravritti kii anupasthiti key nikat honey taka, spandan seey gujarate hue dekhaa jaataa haye. virginis charr interfaces parr hotey hain; alpaavadhi vaale niyamit hotey hain aur lambi avadhi vaale pahale apekshaakrit niyamit parivartan koo spandan mein dikhaate hain.
chakr, jisake baad aar. vee. tauri sitaaron mein halki aniyamitata kii shuruat hoti haye, jisamen way dheere-dheere apani avadhi key lambe honey key saath parivartit hoe jaate hain. taarakiya vikas aur spandan siddhant bataate hain kii inn aniyamit sitaaron mein dravyamaan (ell/aim) anupaat key liye bahut adhik chamak hoti haye.
kaee taare gair-radial pulsator hotey hain, jinaki chamak mein maanak mombattiyon key roop mein upayog kiye jaane vaale niyamit charr kii tulanaa mein cumm utaar-chadhaav hotaa haye.
niyamit charr.
aniyamit parivartansheelta key liye ack poorv shart yeh haye kii taaraa ack avadhi key samay paimaane parr apane ayam koo badalane mein saksham hoe. dusare shabdon mein, iss tarah key parivartanon kii anumati dene key liye spandan aur garmi key pravaah key beach kaa yugman paryaapt roop seey badaa honah chaahiye. iss yugman koo ack spandan chakr (avadhi) mein diye gaye samanya mode key ayam key saapeksh raikhik vriddhi-yaa kshay darr κ (kappa) dwara maapa jaataa haye. niyamit charr (sayfed, rr lyre, aadi) key liye.) sankhyaatmak taarakiya pratiroopan aur raikhik sthirata vishleshan seey pataa chalata haye kii κ praasangik, uttejit spandan mode key liye kuchh pratishat key crum mein haye. doosari or, usee prakaar key vishleshan seey pataa chalata haye kii uchch ell/aim model key liye κ kaafee badaa (30 pratishat yaa adhik) haye.
niyamit charr key liye chhoti saapeksh vriddhi darr kaa arth haye kii dou alag-alag samay paimaane hain, arthaat dolan kii avadhi aur ayam bhinnata key saath judaa lamba samay. ganitiya roop seey, gatishilata mein ack kendra manifold, yaa adhik sateek roop seey ack nikat kendra manifold hotaa haye. isake alawa, yeh paaya gayaa haye kii taarakiya spand kewal iss arth mein kamjor gair-raikhik hain kii unakaa vivaran spandan ayam kii seemit shaktiyaan hoe sakati hain. yeye dou guna bahut samanya hain aur jansankhya gatishilata, samudra vigyaan, plasma bhautiki aadi jaise kaee anya kshetron mein dolan pranaliyon key liye hotey hain.
kamjor araikhikta aur ayam bhinnata key lambe samay key paimaane seey spandan pranali key asthaayi vivaran koo kewal spandan aayamon key roop mein saral banaaya jaa sakata haye, iss prakaar avadhi key cumm samay paimaane parr gati koo samaapt curr diyaa jaataa haye. parinam ayam samikaranon key sandarbh mein pranali kaa vivaran haye joe aayamon kii cumm shaktiyon mein kataa huaa haye. iss tarah key ayam sameekaran vibhinn takneekon dwara praapt kiye gaye hain, ee.jee. dharmnirpeksh shabdon key unmoolan kii poinkere-lindstead vidhi, yaa bahu-samay asymptotic vikshobh vidhi, aur adhik aam taur parr, samanya roop siddhant.
udaaharan key liye, dou gair-pratidhvani mode key mamle mein, aam taur parr rr lyre charr mein ack sthiti kaa saamana karna padata haye, dou samanya mode 1 aur 2 key ayam a1 aur a2 kaa asthaayi vikas haye
samanya vibhedak samikaranon key nimnalikhit samooh dwara shaasit
jahan qij gair-anuranan yugman gunank hain.
yeye ayam sameekaran sabse nichale crum kii gair-tuchchh gair-raikhiktaon taka seemit rahey hain. taarakiya spandan siddhant mein ruchi key samadhan asymptotic samadhan hain (kyonki samay anant kii or jaataa haye) kyonki ayam bhinnataon key liye samay paimana aamtaur parr taare key vikas samay paimaane kii tulanaa mein bahut cumm hotaa haye joe paramanu jalate samay paimaane haye. uparokt samikaranon mein sthir aayamon key saath nishchit bindu samadhan hain, joe ekal-mode key anuroop hain.
हैं। _ 3 0, a2 = 0) yaa
(a1 = 0, 0 _ 3 0) aur double-mode
samadhan. yeye taaron key ekal aavadhik aur dogune aavadhik spandanon key anuroop hain. iss baat parr jore denaa mahatvapurna haye kii bhautik (i) key liye uparokt samikaranon kaa koee anya asymptotic samadhan maujood naheen haye.ee., nakaratmak) yugman gunank.
anunaad mode key liye upayukt ayam samikaranon mein atirikt shabd hotey hain joe mode key beach anunaad yugman kaa varnan karate hain. shaastriya (ekal aavadhik) sephide key prakaash vakr rupiki mein heartzsprung pragati maulik spandan mode aur dusare overtone mode key beach ack prasiddh 2:1 anunaad kaa parinam haye. ayam sameekaran koo aage gair-vikiran taarakiya spandanon taka badhaaya jaa sakata haye.
spandit taaron key samagr vishleshan mein, ayam sameekaran sambhaavit spandaniya avasthaon key beach dwibhajan aarekh koo maanchitrit karane kii anumati dete hain. iss chitra mein, asthirta patti kii seemaaen jahan taare key vikas key dauran spandan sett hotaa haye, ack hopp vibhajan key anuroop hoti hain.
ack kendra kaa astitva arajak (i.ee. aniyamit) avadhi key samay paimaane parr spandan. yadyapi anunaad ayam sameekaran paryaapt roop seey jatil hain joe arajak samadhanon kii anumati dete hain, yeh ack bahut hii alag arajakta haye kyonki yeh aayamon kii asthaayi bhinnata mein haye aur lambe samay key paimaane parr hotaa haye.
jabaki spandan aayamon key asthaayi parivartanon mein deerghakaalik aniyamit vyavhaar sambhav haye jaba ayam sameekaran lagu hotey hain, yeh samanya sthiti naheen haye. vaastav mein, adhikansh tippaniyon aur modeling key liye, inn sitaaron kii spandan nirantar fourier aayamon key saath hoti haye, jisase niyamit spandan hotey hain joe aavadhik yaa bahu-aavadhik (ganitiya saahitya mein ardh-aavadhik) hoe sakate hain.
aniyamit spandan.
badey aayamon vaale aantarik charr taaron key prakaash vakr sadiyon seey aise vyavhaar koo pradarshit karane key liye jaane jaate hain joe atyadhik niyamitata seey, jaise kii shaastriya seyfeeds aur rr lyre sitaaron key liye, atyadhik aniyamitata taka jaataa haye, jaisa kii tathaakathit aniyamit charr key liye. jansankhya mein yeh aniyamitata dheere-dheere cumm avadhi key virginis charr seey aarvi tauri charr key madhyam seey ardh-paridhiya charr key shasson mein badh jaati haye. taarakiya spandanon mein nimn-ayami arajakta iss sthaapit ghatana kii vartamaan vyakhya haye.
seyfeeds kaa niyamit vyavhaar.
seyfeeds key niyamit vyavhaar koo 1960 key dashak seey sankhyaatmak hydrodynamics key saath safaltapurvak model kiya gayaa haye, aur ack saiddhaantik drishtikon seey ise aasaani seey kendra kii upasthiti key kaaran samajha jaataa haye joe gatishil pranali kii kamjor apvyayakaari prakriti key kaaran utpann hotaa haye. yeh, aur yeh tathya kii spandanaaen kamjor roop seey araikhik hain,
ayam samikaranon key sandarbh mein pranali kaa vivaran detaa haye
 aur sambhaavit prakaar key spandan (yaa seema chakr) key dwibhajan aarekh (dwibhajan siddhant bhee dekhein) kaa nirmaan, iss tarah key maulik mode spandan, pahale yaa dusare overtone spandan, yaa adhik jatil, double-mode spandan jisamen kaee mode nirantar ayam key saath uttejit hotey hain. asthirta patti kii seemaaen jahan taare key vikas key dauran spandan sett hotaa haye, ack hopp vibhajan key anuroop hoti hain.
jansankhya kii aniyamitata II sitaare.
isake vipareet, badee ayam aabaadi II sitaaron kii aniyamitata koo samajhaana adhik chunautipurna haye.
ack avadhi mein spandan ayam kii bhinnata kaa tatparya haye "badaa" apavyay, aur isaliye koee kendra bahugunit naheen haye.
vibhinn tantra prastaavit kiye gaye hain, lekin unamen kamee paaee gaee haye. ack, kaee nikat doori kii spandan aavrittiyon kii upasthiti kaa sujhaav detaa haye joe beat karenge
ack dusare key khilaf, lekin upayukt taarakiya model mein aisee koee aavritti maujood naheen haye. ack aur, adhik dilchasp sujhaav yeh haye kii vividhataaen yaadrichhik prakriti kii hain, lekin koee tantra prastaavit yaa maujood naheen haye joe itane badey avalokan ayam bhinnataon key liye oorjaa pradaan curr sakey. abb yeh sthaapit hoe gayaa haye kii aniyamit prakaash vakron key peechhe kaa tantra ack antarnihit nimn ayami arajak gatishilata haye (arajakta siddhant bhee dekhein). yeh nishkarsh dou prakaar key adhyayanon parr adharit haye.
see. aff. dee. simulation.
virginis taarakiya model key "anukramon" key spandan key liye computational drav gatishilata sankhyaatmak purvanuman aniyamit vyavhaar key liye dou drishtikon pradarshit karate hain joe cumm ayami arajakta key spasht hastakshar hain. pahala sanket "pahale vaapsee maanchitra" seey aataa haye jisamen ack adhikatam trijya, yaa kissy anya upayukt charr, banaam agale ack koo plot kartaa haye.
model kaa anukram dwigunit honey kii avadhi, yaa cascade koo darshaata haye, jisase arajakta paida hoti haye.
maanchitra kaa lagbhag dwighaat aakar arajakta kaa sanket haye aur ack antarnihit ghode kii naal kaa maanchitra darshaata haye. model key anya anukram kuchh alag maarg kaa anusaran karate hain, lekin arajakta key liye bhee,
arthaat pomeu-manville yaa "sparshrekha vibhajan" maarg.
nimnalikhit taarakiya model key ack anukram key liye arajakta key liye cascade koo doguna karane kii avadhi key samaan drishya koo darshaata haye joe unake ausat satah key tapman tii seey bhinn hotaa haye.
graph taarakiya trijya key maanon key tiguna koo darshaata haye (rii, rii + 1, rii + 2)
jahan soochkaank i, i + 1, i + 2 kramik samay antaral koo ingit karate hain.
nimn ayami arajakta kii upasthiti kii pushti model spandanon key ack anya, adhik parishkrit, vishleshan dwara bhee kii jaati haye joe sabse cumm asthir aavadhik kakshaon koo nikaalata haye aur unake sthalvaigyaanik sangathan (mudanaa) kii jaanch kartaa haye. antarnihit aakarshan rossler aakarshan kii tarah bunded paaya jaataa haye, halanki baind mein ack atirikt modd hotaa haye.
avalokan kiye gaye prakaash vakron seey vaishvik pravaah punarnirmaan.
vaishvik pravaah punarnirmaan" kii vidhi ack ekal avalokan sanket {aiss. aaee.) kaa upayog karati haye joe ise utpann karane vaali gatishil pranali key gunon kaa anuman lagaane key liye haye. pahale aine-ayami 'vactor' sootra _ 7 kaa nirmaan kiya jaataa haye.
agale charan mein araikhik vikas prachaalak sootra _ 8 key liye ack abhivyakti khojana shamil haye joe pranali koo samay sootra _ 9 seey samay sootra _ 10, i taka leey jaataa haye.ee., sootra _ 11.
takens kii pramey iss baat kii guaranti detee haye kii bahut samanya paristhitiyon mein iss punarnirmit vikas prachaalak key sthalvaigyaanik guna bhautik pranali key samaan hain, basharte kii embedding ayam n paryaapt badaa hoe.
iss prakaar "ack ekal avalokan charr key gyaan seey" koee bhee vaastavik bhautik pranali key baare mein gunon kaa anuman lagaa sakata haye joe kaee swatantra charon dwara shaasit haye.
iss drishtikon koo starr aar scooty key liye aavaso detta parr lagu kiya gayaa haye.
yeh anuman lagaaya jaa sakata haye kii iss taare kii aniyamit spandan ack antarnihit 4-ayami gatishilata seey utpann hoti haye. alag tareeke seey yeh kahata haye kii kissy bhee 4 padosi tippaniyon seey koee bhee agale avalokan kii bhavishyavani curr sakata haye. bhautik drishtikon seey yeh kahata haye kii 4 swatantra charr hain joe pranali kii gatishilata kaa varnan karate hain. jhoothe nikatatam padosiyon kii vidhi 4 key ack embedding ayam kii pushti karati haye.
sanganit lyapunov ghaatankon seey anumaanit aar scooty kii gatishilata kaa asthi-vibhaajak ayam 3.1 aur 3.2 key beach haye.
vikas prachaalak key nishchit binduon key vishleshan seey ack achchi bhautik tasveer kaa anuman lagaaya jaa sakata haye, arthaat "ack asthir spandan mode key uttejana seey spandan utpann hotey hain joe ack dusare, sthir spandan mode mein gair-raikhik roop seey jode jaate hain joe pahale key saath 2:1 anunaad mein hotaa haye", ack paridrishya jise shilnikov pramey dwara varnit kiya gayaa haye.
yeh anunaad tantra aar scooty taka seemit naheen haye, lekin kaee anya sitaaron key liye pakad mein paaya gayaa haye jinake liye avalokan detta paryaapt roop seey achchha haye.

