Application of novel relaxation time approximation for the Boltzmann equation in relativistic fluid dynamics

Ultrarelativistic heavy-ion collisions are modelled with relativistic fluid dynamics. Since quark-gluon plasma formed in collider experiments cannot be directly measured, the investigation of the substance is heavily based on comparing experimental data to predictions of theoretical models. In this...

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Bibliografiset tiedot
Päätekijä: Piipponen, Mika
Muut tekijät: Faculty of Sciences, Matemaattis-luonnontieteellinen tiedekunta, Department of Physics, Fysiikan laitos, University of Jyväskylä, Jyväskylän yliopisto
Aineistotyyppi: Pro gradu
Kieli:eng
Julkaistu: 2024
Aiheet:
Linkit: https://jyx.jyu.fi/handle/123456789/95848
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author Piipponen, Mika
author2 Faculty of Sciences Matemaattis-luonnontieteellinen tiedekunta Department of Physics Fysiikan laitos University of Jyväskylä Jyväskylän yliopisto
author_facet Piipponen, Mika Faculty of Sciences Matemaattis-luonnontieteellinen tiedekunta Department of Physics Fysiikan laitos University of Jyväskylä Jyväskylän yliopisto Piipponen, Mika Faculty of Sciences Matemaattis-luonnontieteellinen tiedekunta Department of Physics Fysiikan laitos University of Jyväskylä Jyväskylän yliopisto
author_sort Piipponen, Mika
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description Ultrarelativistic heavy-ion collisions are modelled with relativistic fluid dynamics. Since quark-gluon plasma formed in collider experiments cannot be directly measured, the investigation of the substance is heavily based on comparing experimental data to predictions of theoretical models. In this thesis we review a novel relaxation time approximation for the relativistic Boltzmann equation, which is fully compatible with the macroscopic conservation laws. We calculate approximations for the temperature dependence of bulk viscosity, particle diffusion coefficient and shear viscosity of a fluid employing this model. The calculation is carried out by matching the fluid dynamical quantities with the underlying microscopic theory, where the single particle momentum distribution function is expressed using first order Chapman–Enskog expansion. In this way, even with energy-dependent relaxation times, we achieve consistent approximations for the fluid dynamical transport coefficients that are in full agreement with the second law of thermodynamics. The novel relaxation time approximation can be utilized to construct effective kinetic descriptions for matter in heavy-ion collisions. Ultrarelativististen raskasionitörmäysten mallintamisessa hyödynnetään relativistista virtausmekaniikkaa. Törmäyskokeissa syntyvän kvarkkigluoniplasman viskositeettia ei voida suoraan mitata, joten tämän tutkimus painottuu kokeellisen datan vertaamiseen teoriamallin ennustukseen. Tässä tutkielmassa tutustaan uudenlaiseen relaksaatioaika-approksimaatioon relativistiselle Boltzmannin yhtälölle, joka on yhteensopiva makroskooppisten säilymislakien kanssa. Tämän avulla lasketaan teoreettiset arviot fluidin puristusviskositeetin, diffuusiovakion ja leikkausviskositeetin lämpötilariippuvuudelle. Lasku toteutetaan sovittamalla virtausmekaniikan suureet taustalla olevaan mikroskooppiseen teoriaan, jossa yksihiukkastiheysfunktio esitetään ensimmäisen kertaluokan Chapman–Enskog -ekspansion avulla. Näin saadaan energiariippuvilla relaksaatioajoilla tuotettua virtausmekaniikan kuljetuskertoimille johdonmukaisia arvioita, jotka ovat yhteensopivia termodynamiikan toisen lain kanssa. Uuden relaksaatioaika-approksimaation avulla on mahdollista luoda efektiivisiä kineettisiä malleja kuvaamaan materiaa raskasionitörmäyksissä.
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In this thesis we review a novel relaxation time\napproximation for the relativistic Boltzmann equation, which is fully compatible with\nthe macroscopic conservation laws. We calculate approximations for the temperature\ndependence of bulk viscosity, particle diffusion coefficient and shear viscosity of a\nfluid employing this model. The calculation is carried out by matching the fluid\ndynamical quantities with the underlying microscopic theory, where the single particle\nmomentum distribution function is expressed using first order Chapman\u2013Enskog\nexpansion. In this way, even with energy-dependent relaxation times, we achieve\nconsistent approximations for the fluid dynamical transport coefficients that are in\nfull agreement with the second law of thermodynamics. The novel relaxation time\napproximation can be utilized to construct effective kinetic descriptions for matter\nin heavy-ion collisions.", "language": "en", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Ultrarelativististen raskasionit\u00f6rm\u00e4ysten mallintamisessa hy\u00f6dynnet\u00e4\u00e4n relativistista\nvirtausmekaniikkaa. T\u00f6rm\u00e4yskokeissa syntyv\u00e4n kvarkkigluoniplasman viskositeettia\nei voida suoraan mitata, joten t\u00e4m\u00e4n tutkimus painottuu kokeellisen datan vertaamiseen teoriamallin ennustukseen. T\u00e4ss\u00e4 tutkielmassa tutustaan uudenlaiseen\nrelaksaatioaika-approksimaatioon relativistiselle Boltzmannin yht\u00e4l\u00f6lle, joka on\nyhteensopiva makroskooppisten s\u00e4ilymislakien kanssa. T\u00e4m\u00e4n avulla lasketaan\nteoreettiset arviot fluidin puristusviskositeetin, diffuusiovakion ja leikkausviskositeetin l\u00e4mp\u00f6tilariippuvuudelle. Lasku toteutetaan sovittamalla virtausmekaniikan\nsuureet taustalla olevaan mikroskooppiseen teoriaan, jossa yksihiukkastiheysfunktio esitet\u00e4\u00e4n ensimm\u00e4isen kertaluokan Chapman\u2013Enskog -ekspansion avulla. N\u00e4in\nsaadaan energiariippuvilla relaksaatioajoilla tuotettua virtausmekaniikan kuljetuskertoimille johdonmukaisia arvioita, jotka ovat yhteensopivia termodynamiikan toisen\nlain kanssa. 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spellingShingle Piipponen, Mika Application of novel relaxation time approximation for the Boltzmann equation in relativistic fluid dynamics relaxation time relativistic Boltzmann equation kinetic theory fluid dynamics Navier-Stokes Theoretical Physics Teoreettinen fysiikka 4024 suhteellisuus hydrodynamiikka fysiikka viskositeetti kvarkki-gluoniplasma relativity hydrodynamics physics viscosity quark-gluon plasma
title Application of novel relaxation time approximation for the Boltzmann equation in relativistic fluid dynamics
title_full Application of novel relaxation time approximation for the Boltzmann equation in relativistic fluid dynamics
title_fullStr Application of novel relaxation time approximation for the Boltzmann equation in relativistic fluid dynamics Application of novel relaxation time approximation for the Boltzmann equation in relativistic fluid dynamics
title_full_unstemmed Application of novel relaxation time approximation for the Boltzmann equation in relativistic fluid dynamics Application of novel relaxation time approximation for the Boltzmann equation in relativistic fluid dynamics
title_short Application of novel relaxation time approximation for the Boltzmann equation in relativistic fluid dynamics
title_sort application of novel relaxation time approximation for the boltzmann equation in relativistic fluid dynamics
title_txtP Application of novel relaxation time approximation for the Boltzmann equation in relativistic fluid dynamics
topic relaxation time relativistic Boltzmann equation kinetic theory fluid dynamics Navier-Stokes Theoretical Physics Teoreettinen fysiikka 4024 suhteellisuus hydrodynamiikka fysiikka viskositeetti kvarkki-gluoniplasma relativity hydrodynamics physics viscosity quark-gluon plasma
topic_facet 4024 Boltzmann equation Navier-Stokes Teoreettinen fysiikka Theoretical Physics fluid dynamics fysiikka hydrodynamics hydrodynamiikka kinetic theory kvarkki-gluoniplasma physics quark-gluon plasma relativistic relativity relaxation time suhteellisuus viscosity viskositeetti
url https://jyx.jyu.fi/handle/123456789/95848 http://www.urn.fi/URN:NBN:fi:jyu-202406134614
work_keys_str_mv AT piipponenmika applicationofnovelrelaxationtimeapproximationfortheboltzmannequationinrelativistic