
fermi-pasta-ulam-singou samasya

bhouthika saastramlo, fermi-pasta-ulam-singou samasya ledhaa gatamlo fermi-pasta-ulam samasya anedi gandaragola siddhaantamlo spashtamaina vairudhyam, aneka sanklishtamaina bhouthika vyavasthalu daadaapu khachitamgaa aavartana pravartananu pradarsinchaayi-dheenini fermi-pasta-ulam-singou punaraavrutam (ledhaa fermi-pasta-ulam punaraavrutam) anie pilustaaru-oohinchina ergodic pravartanaku badulugaa. idhi aascharyakaramgaa vachindi, endukante fermi, khachitamgaa, chaalaa takkuva samayamlo vyavastha ushnam avtundani bhaavinchaaru. antey, anni kampana reetulu chivariki samaana saktitoe kanipistaayani, equipartition siddhaantam prakaram, ledhaa, marinta saadhaaranamgaa, ergodic parikalpana prakaram, anchanaa veyabadindi. inca ikkada ergodic parikalpananu tappinchukovadaaniki kanipinchina vyavastha undhi. punaraavrutaanni sulabhamgaa gamaninchinappatikii, chaalaa ekkuva kaalam paatu, vyavastha chivariki ushnataram avtundani chivariki spashtamaindi. vyavastha yokka pravartananu vivarinchadaaniki bahula pootii siddhaantaalu pratipaadinchabaddaayi, mariyu idhi kriyaaseela parisoedhana amsamgaa migilipoyindi.
appati kotta unmaada computerlo sankhya anukaranaku arhamaina bhouthika samasyanu kanugonadam asalu uddesam. thermalisation atuvanti savaalunu kaligistundani fermi bhaavinchaadu. anduvalla, idhi ganita parisoedhanaloo digital computerla yokka mottamodati upayogaalalo okatigaa suuchistumdi; adhe samayamlo, oohinchani phalitaalu naan leanier systems adhyayananni praarambhinchaayi.
fput prayogam.
1953 vesavilo enrico fermi, zaan pasta, stanisla ulam mariyu maerii singou oka kampinche string yokka computer anukaranalanu nirvahinchaaru, indulo naan-leanier padam (oka pareekshalo quadratic, maroka pareekshalo cubic, mariyu moodava pareekshalo cubic kuu peacewise leanier ujjaayimpu) unnaayi. vyavastha yokka pravartana antar drushti vaaru aasinche daanikante chaalaa bhinnamgaa undani vaaru kanugonnaru. aneka punaraavruttula taruvaata, vyavastha ushneekarananu pradarsistundani fermi bhaavinchaadu, idhi oka ergodic pravartana, dheenilo kampanam yokka prarambha reetula prabhavam masakabaarutundi mariyu vyavastha anni reetulato ekkuva ledhaa takkuva samanamga uttejitamavutundi. badulugaa, vyavastha chaalaa sanklishtamaina pakshika-kaala pravartananu pradarsinchindi. vaaru 1955loe laas alamos saanketika nivedikalo tama phalitaalanu prachurinchaaru. (enrico fermi 1954loe maraninchaadu, anduvalla eee saanketika nivedika fermi maranam taruvaata prachurinchabadindi.) 
2020loe, jaateeya bhadrata shaastra patrika singoupai oka kathanaanni prachurinchindi, indulo aame vyakhyanam mariyu putt samasyapai chaaritraka pratibimbaalu unnaayi. vyaasamlo, "okaroju pasta mariyu ulamtho akkada koorchovadam naaku gurtundi" anie, vaaru "computerlo manam cheyagala konni samasyalu, konni nijamgaa ganita samasyalu" anie medadu tuphaanu chesaaru.vaaru aneka vishayalanu prayatninchaaru, conny, chivariki, vaaru eee kampinche theegatho munduku vacchaaru."
naan leanier system pravartana yokka sanklishtata mariyu vislaeshanha vyavasthalalo computer anukarana viluvanu choopinchadamlo fput prayogam mukhyamainadi.
paeru maarpu.
asalu kaagitam paerlaloo fermi, pasta mariyu ulam rachayitalugaa (nivedika vraayabadataaniki mundhe fermi maraninchinappatikii), unmaada anukaranalanu prograaming cheyadamlo aame chesina krushiki singouku angeekaaramtho. abhivruddhi gurinchi adanapu samacharanni prachurinche varaku, mariyu aame aapaadimpunu manjuru cheyadaaniki samasya paeru maarchaalani pilupunicche varaku, fput samasyaku maerii singou chesina sahakaranni samajam ekkuvagaa vismarinchindi.
fput jaalaka vyavastha.
fermi, pasta, ulam mariyu singou sameepa-porugu janta ausilatorla yokka krindi vivikta vyavasthanu parishkarinchadam dwara kampinche stringnu anukarinchaaru. richard palis vyaasamlo icchina vivarananu memu anusaristaamu. samathoulya sthaanaala suutram _ 2 thoo podavaina suutram _ 1 yokka stringnu soochinche "n" aasiletarlu undanivvandi, ikkada suutram _ 3 anedi jaalaka antaram. appudu samayam yokka functionga "zhe"-va ausilator yokka sthaanam suutram _ 4, kabatti aaa suutram _ 5 samathoulyam nundi sthaanabhramsham istundi. fput eee krindi chalana sameekaranaalanu upayoginchindih
idhi "zhe"-va kanaaniki neuton yokka rendava niyamam matrame. modati kaaraka suutram _ 7 anedi balam kosam saadhaarana hook yokka chattam roopam. suutram _ 8 thoo unna karakam naan leanier fores. suutram _ 9 nuu taranga vaegamgaa nirvachinchadam dwara nirantara parimaanaala paramgaa manam dheenini tirigi vraayavacchu, ikkada suutram _ 10 anedi stringku yuva modulus, mariyu suutram _ 11 anedi saandrata.
kdv sameekaranaaniki anusandhanam.
string kosam paalaka sameekaranaala konasagimpu parimiti (quadratic fores padamtho) anedi courteveg-dii vrees sameekaranam (kdv sameekaranam).) eee sambandhaanni mariyu 1965loe martin david cruscal mariyu norman zabuski dwara kdv sameekaranam yokka solitan parishkaralanu kanugonadam naan leanier system parisoedhanaloo oka mukhyamaina mundadugu. palis vyaasamlo kanipinche vidhamgaa, eee parimiti yokka utpannam krinda memu punarutpatti chestaamu, idhi chaalaa gammattainadi. paina unna jaalaka sameekaranaala yokka "nirantara roopam" nundi praarambhinchi, manam modata "x" mariyu samayam "t" sthaanam vadda string yokka sthaanabhramsham anie "u" ("x", "t") nii nirvachistaamu. appudu manaku oka correspondence kaavaali, tadwara suutram _ 13 suutram _ 5 avutundi.
chinna suutram _ 16 ("u" yokka subscripts pakshika utpannaalanu suuchistaayi) kosam rendava karakanni tirigi vraayadaaniki manam taylor siddhaantaanni upayoginchavachhuh
adevidhamgaa, moodava kaarakamlo rendava padam
anduvalla, fput vyavastha
okavela okaru "o" ("h") varaku matrame nibandhanalanu unchi, suutram _ 20 oka parimitini cherukuntundani bhaavisthe, phalitamgaa vachhe sameekaranam shacklanu abhivruddhi chestundi, idhi gamaninchabadadu. eee vidhamgaa okaru "oo" ("hetch" 2) padaanni kooda unchutaru
ippudu manam eee krindi pratyaamnaayaalanu chestaamu, prayaana-taranga parishkarala kullipovadam dwara prerepinchabadi (saadhaarana taranga sameekaranam, idhi suutram _ 22 adrusyamainappudu taggutundi) edama mariyu kudi-kadile taramgaalugaa maarutundi, tadwara manam kudi-kadile taramgaanni matrame pariganistaamu. suutram _ 23. eee akshaamsaala maarpu kinda, sameekaranam avutundi
konasagimpu parimitini teesukoovadaaniki, suutram _ 25 sthiramgaa untundi, mariyu suutram _ 22 sunnaki velutundani anukundam. manam suutram _ 27 teesukunte, appudu
suutram _ 29 teesukunte kdv sameekaranamlo phalitaalu
kdv sameekaranam yokka solitan parishkaralu, fput prayogamlo taramgaala yokka pakshika-aavartanaanni vivarinche lakshanarahita aakaralanu prabhaavitam cheyakunda okadaanikokati daatagalavu anae vaastavam anie zabuski mariyu cruscal vaadinchaaru. sankshiptamgaa, vyavasthalo oka nirdishta "solitan cemetry" kaaranamgaa ushneekarana jaragaledu, idhi ergodicityni vichchinnam chesindi.
ilanti sardubatla samiti (mariyu sumaru) toda latis kuu daariteestundi, idhi puurtigaa samagra vyavasthagaa kooda prasiddhi chendindi. idhi kooda saliton parishkaralanu kaligi undhi, shidhilamaina jatalanu kaligi undhi, kabatti fput namoonaalo ergodicity lekapovadam kosam vaadinchadaaniki kooda upayoginchavacchu.
ushneekaranaku margalu.
1966loe, isrilev mariyu chirikov taginanta prarambha saktini andinchinatlayithe, vyavastha ushnamavutundi anie pratipaadinchaaru. ikkada aalochana emitante, naan-linearity dispersion relationnu maarustundi, idhi pratidhvani paraspara charyalanu jaragadaniki anumatistundi, idhi oka mode nundi maroka modku saktini raktasraavam chestundi. atuvanti namuunaala sameekshanu livi "ett all" loe chudavachu. ayinappatikee, 1970loe, ford mariyu lunsford ekapakshamgaa chinna prarambha saktulatoe kooda mixingnu gamaninchavacchani nokki chepparu. samasyaku sambandhinchina vidhaanaala sudeergha mariyu sanklishtamaina charitra undhi, (pakshika) survey kosam doxois (2008) chudandi.
onorato mariyu itarula iteevali pani."ushneekaranaku chaalaa aasaktikaramaina marganni pradarsistundi. saadhaarana reetula paramgaa fput namuunaanu tirigi vrayadam, naan-leanier padam moodu-mode paraspara charyaga vyakteekaristundi (ganaanka yantrasaastram yokka bhashanu upayoginchi, dheenini "moodu-phonen paraspara charya" anie pilustaaru.) ayithe, idhi pratidhvani paraspara charya kaadu, anduvalla oka mode nundi maroka modku saktini vyaapti cheyalemu; idhi kevalam input punaraavrutaanni matrame utpatti cheyagaladu. moodu-phonen paraspara charya vyavasthanu ushnaparachadu.
ayithe, eee reetulu "uchita" mariyu "kattubadi" reetula kalayika anie oka mukhya antardrushti. antey, adhika samarasyalu praadhamikaaniki "kattubadi untaayi", adhe vidhamgaa kdv sameekaranaaniki parishkaralalo adhika samarasyalu praadhamikaaniki kattubadi untaayi. vaariki vaari swantha dynamics ledhu, badulugaa praathamika dasaku dasha-lock cheyabadi untaayi. ushneekarana, unte, uchita reetulalo matrame untundi.
uchita reetulanu pondadaaniki, uchitam kaani (pratidhvani paraspara charyalalo paalgonani) anni reetulanu tolaginche canonical parivartananu vartimpajeyavachu. fput vyavastha kosam alaa cheyadam valla naalugu-taranga paraspara charyanu kaligi unna ausilator modlalo phalitaalu vastaayi (moodu-taranga paraspara charya tolaginchabadindi). eee quartetlu pratidhvanistuu sankarshana chendutaayi, "i.ii."oka samayamlo naalugu modlanu kalapandi. vichitramgaa, ayithe, fput golusulo 16,32 ledhaa 64 nodes matrame unnappudu, eee quartetlu okadaanikokati nundi verucheyabadataayi. edainaa mode oka quartetku matrame chendinadi, mariyu shakti oka quartet nundi maroka quartetku raktasraavam cheyadu. paraspara charya yokka adhika kramaalaku konasaagutuu, pratidhvanicche aaru-taranga paraspara charya untundi; inca, prati mode kaneesam rendu ververu aaru-taranga paraspara charyalalo paalgontundi. maroe maatalo cheppalante, anni reetulu parasparam anusandhaaninchabadi untaayi, mariyu shakti anni vibhina reetula madhya badilee avutundi.
moodu-taranga paraspara charya balam suutram _ 31 (paina perkonna munupati vibhagalalo unna adhe suutram _ 8). naalugu-taranga paraspara charya balam suutram _ 33 mariyu aaru-taranga paraspara charya balam suutram _ 34. paraspara charyala sahasambandham nundi saadhaarana suutraala aadhaaramgaa (bbgky sopanakramam nundi udbhavinchindi) ushneekarana samayam paraspara charya yokka chaturasramgaa nadustundani okaru aasistaaru. anduvalla, asalu fput jaalakam (parimaanam 16,32 ledhaa 64) chivariki thermalise avutundi, arder formula _ 35 yokka samaya sthaayiloh spashtamgaa, balaheena paraspara charya suutram _ 36 kosam idhi chaalaa ekkuva samayam avutundi; intalo, fput punaraavrutam nirantaraayamgaa nadustunnatlu kanipistundi. eee pratyeka phalitam eee nirdishta jaalaka parimaanaalaku vartistundi; vividha jaalaka parimaanaala kosam pratidhvani naalugu-taramgaalu ledhaa aaru-taranga paraspara charyalu kalisi modlanu kalapavacchu ledhaa kalapakapovachhu (endukante brilloin mandalaalu vaerae parimaanamlo untaayi, kabatti taranga-vahakalu sunnaki jama cheyagala misramaalu maarchabadataayi.) kattubadi unna vidhaanaalanu saralikrutam chese canonical parivartanalanu pondadaaniki saadhaarana vidhanalu kriyaaseela parisoedhana amsamgaa untaayi.

