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[{"key": "dc.contributor.author", "value": "Solanp\u00e4\u00e4, Janne", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2013-08-27T11:43:16Z", "language": "", "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2013-08-27T11:43:16Z", "language": "", "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2013", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.other", "value": "oai:jykdok.linneanet.fi:1278516", "language": null, "element": "identifier", "qualifier": "other", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/42033", "language": "", "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Chaos and nonlinear dynamics of single-particle Hamiltonian systems have\r\nbeen extensively studied in the past; however, less is known about interacting\r\nmany-body systems in this respect even though all physical systems include particle-particle interactions in one way or another. To study Hamiltonian chaos, two-dimensional billiards are usually employed, and due to the realization of billiards in semiconductor\r\nquantum dots, the electrostatic Coulomb interaction is the natural choice for the interparticle interaction. Yet, surprisingly little is known about chaos and nonlinear dynamics of Coulomb-interacting many-body billiards.\r\n\r\nTo address the challenging problems of interacting many-body billiards,\r\nwe have developed a flexible and expandable code implementing methods\r\npreviously used in molecular dynamics simulations. The code is \\emph{generic} in sense\r\nthat it is readily applicable to most two-dimensional billiards -- including periodic systems -- with different types of interparticle interactions. In this work, insights into Coulomb-interacting billiards are gained by applying the methods to two relevant systems:\r\na two-particle circular billiards and a few-particle diffusion, the latter of which is studied only as a closed system. Also general implications of the results for other systems are discussed.\r\n\r\nThe circular billiards is studied with the interaction strength varying\r\nfrom the weak to the strong-interaction limit. Bouncing maps show quasi-regular\r\nfeatures in the weak and strong-interacting limits. In the strong-interaction\r\nregime an analytical model for the phase space trajectory is derived,\r\nand the model is found to agree with the simulated data. At intermediate interaction strengths the bouncing maps get filled.\r\n\r\nTo obtain a quantitative view on the hyperbolicity and stickiness of the circular billiards, we calculate escape-time distributions of open circular billiards.\r\nAt weak interactions the escape-time distributions show a power-law tail owing to\r\nthe quasi-regular dynamics arising from the integrable non-interacting limit. At intermediate interaction strengths the distributions are exponential implying hyperbolicity within the studied time-scales.\r\n\r\nAs the second application, the diffusion process between two square containers connected by\r\na short channel is studied under a homogeneous magnetic field perpendicular to the table.\r\nDuring the propagation, over half of the particles -- all initially in the same container -- travel from one container to the other. The time this process takes is defined here as the relaxation time.\r\n\r\nThe average relaxation times are calculated as a function of the effective Larmor radius, which describes the average effect of the magnetic field on the particles. The behavior of the average relaxation times as a function of the effective Larmor radius is studied thoroughly for different interaction strengths and channel widths. Interestingly, the graphs show a universal minimum for all interaction strengths, and in the weak-interaction limit also other extrema appear. The new extrema in the weak-interaction limit are explained by calculating properties of open single-particle magnetic square billiards for different Larmor radii.", "language": "en", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Hamiltonisten yksihiukkasj\u00e4rjestelmien kaoottisuus ja dynaaminen ep\u00e4lineaarisuus tunnetaan suhteellisen hyvin. Vuorovaikuttavien monihiukkasj\u00e4rjestelmien kaoottisuus puolestaan tunnetaan suhteellisen heikosti, vaikka kaikki fysikaaliset j\u00e4rjestelm\u00e4t ovat tavalla tai toisella vuorovaikuttavia. Hamiltonisen kaaoksen tutkimiseen k\u00e4ytet\u00e4\u00e4n tyypillisesti biljardij\u00e4rjestelmi\u00e4. Biljardeissa s\u00e4hk\u00f6staattinen Coulomb-vuorovaikutus on luonnollinen valinta hiukkasten v\u00e4liselle vuorovaikutukselle, sill\u00e4 biljardit toimivat my\u00f6s malleina kokeellisesti toteutettaville puolijohdekvanttipisteille. Kuitenkin erityisesti Coulomb-vuorovaikuttavien biljardien kaoottisuus tunnetaan yll\u00e4tt\u00e4v\u00e4n huonosti.\r\n\r\nP\u00e4\u00e4st\u00e4ksemme k\u00e4siksi vuorovaikuttavien monihiukkasj\u00e4rjestelmien haastaviin kaaosongelmiin\r\nkehitimme joustavan ja laajennettavan laskentakoodin, joka k\u00e4ytt\u00e4\u00e4 aiemmin molekyylidynamiikan simuloinnissa k\u00e4ytettyj\u00e4 menetelmi\u00e4. Koodi on yleisp\u00e4tev\u00e4 siin\u00e4 mieless\u00e4, ett\u00e4 sit\u00e4 voi k\u00e4ytt\u00e4\u00e4 suoraan useimpien biljardij\u00e4rjestelmien -- mukaanlukien periodisten j\u00e4rjestelmien -- simulointiin erilaisilla hiukkasten v\u00e4lisill\u00e4 vuorovaikutuksilla. Menetelmi\u00e4 sovellettiin kahteen kaaostutkimuksen kannalta oleelliseen j\u00e4rjestelm\u00e4\u00e4n: kahden hiukkasen ympyr\u00e4biljardiin ja muutaman hiukkasen diffuusioon suljetussa j\u00e4rjestelm\u00e4ss\u00e4. Tuloksilla saatiin uutta tietoa Coulomb-vuorovaikuttavien j\u00e4rjestelmien kaoottisuudesta ja dynamiikasta. Lis\u00e4ksi ty\u00f6ss\u00e4 arvioitiin tuloksista saatujen johtop\u00e4\u00e4t\u00f6sten soveltuvuutta muihin j\u00e4rjestelmiin.\r\n\r\nYmpyr\u00e4biljardia tutkittiin eri vuorovaikutusvoimakkuuksilla heikon vuorovaikutuksen rajalta vahvan vuorovaikutuksen rajalle. T\u00f6rm\u00e4yskartoissa n\u00e4htiin n\u00e4enn\u00e4isesti s\u00e4\u00e4nn\u00f6llisi\u00e4 rakenteita sek\u00e4 heikoilla ett\u00e4 vahvoilla vuorovaikutuksilla. Lis\u00e4ksi vahvasti vuorovaikuttavan j\u00e4rjestelm\u00e4n faasiavaruusradoille johdettiin analyyttinen malli, joka t\u00e4sm\u00e4si numeerisesti laskettujen ratojen kanssa. Keskivahvoilla vuorovaikutuksilla t\u00f6rm\u00e4yskartat t\u00e4yttyiv\u00e4t.\r\n\r\nYmpyr\u00e4biljardin hyperbolisuuden ja tahmaisuuden kvantitatiiviseen tutkimiseen k\u00e4ytettiin avointa ympyr\u00e4biljardia, jonka pakoaikajakaumia laskettiin eri vuorovaikutusvoimakkuuksille. Heikon vuorovaikutuksen rajalla pakoaikajakaumat noudattivat asymptoottisesti potenssilakia, mik\u00e4 johtui n\u00e4enn\u00e4isesti s\u00e4\u00e4nn\u00f6llisist\u00e4 radoista pienill\u00e4 vuorovaikutusvoimakkuuksilla. Keskivahvoilla vuorovaikutusvoimakkuuksilla jakaumat olivat eksponentiaalisia, mihin perustuen j\u00e4rjestelm\u00e4n p\u00e4\u00e4teltiin olevan hyperbolinen tutkitulla aikaskaalalla.\r\n\r\nToinen tutkittava ilmi\u00f6 oli muutaman hiukkasen diffuusioprosessi kahden kanavalla yhdistetyn neli\u00f6s\u00e4ili\u00f6n v\u00e4lill\u00e4 magneettikent\u00e4ss\u00e4. Aluksi hiukkaset olivat samassa s\u00e4ili\u00f6ss\u00e4, mutta ajan kuluessa ne liikkuivat kohti tilannetta, jossa yli puolet hiukkasista oli siirtynyt toiseen s\u00e4ili\u00f6\u00f6n. Prosessiin kuluva aika nimettiin relaksaatioajaksi.\r\n\r\nRelaksaatioaikojen ensemble-keskiarvot laskettiin hiukkasten tehollisen syklotronis\u00e4teen (magneettikent\u00e4n keskim\u00e4\u00e4r\u00e4inen vaikutus hiukkasten ratoihin) funktiona useille eri vuorovaikutusvoimakkuuksille ja kanavan leveyksille. Syklotronis\u00e4de-relaksaatioaika-kuvaajissa havaittiin universaali minimi kaikille vuorovaikutusvoimakkuuksille. Lis\u00e4ksi heikon vuorovaikutuksen rajalla Syklotronis\u00e4de-relaksaatioaika-kuvaajiin ilmestyi my\u00f6s muita \u00e4\u00e4riarvoja, jotka selitettiin laskemalla avoimen magneettisen neli\u00f6biljardin ominaisuuksia eri syklotronis\u00e4teille.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted using Plone Publishing form by Janne Solanp\u00e4\u00e4 (jasasola) on 2013-08-27 11:43:14.401115. Form: Pro gradu -lomake (1 tekij\u00e4) (https://kirjasto.jyu.fi/julkaisut/julkaisulomakkeet/pro-gradu-lomake-1-tekijae). JyX data:", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by jyx lomake-julkaisija (jyx-julkaisija@noreply.fi) on 2013-08-27T11:43:16Z\r\nNo. of bitstreams: 2\r\nURN:NBN:fi:jyu-201308272200.pdf: 10709013 bytes, checksum: 39b132b25dae9ca968c58b2b81c3e9c1 (MD5)\r\nlicense.html: 107 bytes, checksum: a7d86e598caa500b1b433bbb9dc8ef1c (MD5)", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2013-08-27T11:43:16Z (GMT). No. of bitstreams: 2\r\nURN:NBN:fi:jyu-201308272200.pdf: 10709013 bytes, checksum: 39b132b25dae9ca968c58b2b81c3e9c1 (MD5)\r\nlicense.html: 107 bytes, checksum: a7d86e598caa500b1b433bbb9dc8ef1c (MD5)\r\n Previous issue date: 2013", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "1 verkkoaineisto.", "language": null, "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.format.mimetype", "value": "application/pdf", "language": null, "element": "format", "qualifier": "mimetype", "schema": "dc"}, {"key": "dc.language.iso", "value": "eng", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "chaos", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Nonlinear dynamics and chaos in classical Coulomb-interacting many-body billiards", "language": null, "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-201308272200", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.dcmitype", "value": "Text", "language": "en", "element": "type", "qualifier": "dcmitype", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Fysiikan laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Physics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Teoreettinen fysiikka", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Theoretical Physics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.date.updated", "value": "2013-08-27T11:43:16Z", "language": "", "element": "date", "qualifier": "updated", "schema": "dc"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": "fi", "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.oppiainekoodi", "value": "4024", "language": null, "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "fysiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "hiukkaset", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "kaaos", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.format.content", "value": "fulltext", "language": null, "element": "format", "qualifier": "content", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}, {"key": "dc.type.okm", "value": "G2", "language": null, "element": "type", "qualifier": "okm", "schema": "dc"}]
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