Komplex rendszerek dinamikája = Dynamics of complex systems
2011
Terelmeleti modszerekkel vizsgaltuk a tulhűtott folyadekbol a kristalyos fazisba atvezető kritikus fluktuaciok tulajdonsagait. Megmutattuk, hogy a Ginzburg-Landau sorfejtesen alapulo modellek kielegitő pontossaggal adjak meg a nukleacios gat magassagat. A polikristalyos megszilardulas 3D leirasara a kristalytani orientacio kvaternio-reprezentaciojan alapulo fazismező elmeletet dolgoztunk ki, mellyel olyan komplex alakzatok kepződeset modelleztunk, mint az egymassal kolcsonhato dendritek, a szferolitok szeles skalaja, ill. a shish-kebab morfologia. Egyszerű dinamikus sűrűseg funkcional elmelet kereteben a kristalyos megszilardulas mikroszkopikus vonatkozasait vizsgaltuk a kristaly nukleaciot megelőző amorf prekurzor megjelenesetől, a diffuzios instabilitasokon at, a versengő diffuzio kontrollalt es diffuzio mentes modusok mintazatkepződesben jatszott szerepeig. Klasszikus es kvantum rendszerek nem-egyensulyi relaxaciojat vizsgaltuk gyorshűtesi folyamatok soran ahol a rendszer kezdő allapotat kulonboző feltetelekkel szabalyoztuk. Tanulmanyoztuk a dinamikai folyamat soran kialakulo furtok es a fazisokat elvalaszto hatarretegek tulajdonsagait es vizsgaltuk a mintaba befagyott rendezetlenseg szerepet is. | We have used field theoretic models to characterize the heterophase fluctuations that drive the system from un-dercooled liquid to the crystalline state. We have shown that models relying on Ginzburg-Landau expanded free energy predict the nucleation barrier fairly accurately. We have developed a phase-field theory relying on the qua-ternion representation when describing crystallographic orientation in 3D. Using this approach, formation of complex solidification patterns such as interacting dendrites, a variety of spherulites, and the shish-kebab mor-phology has been modeled. Using a simple dynamical density functional theory, we have explored the micro-scopic aspects of crystallization, including the formation of amorphous nucleation precursors, the diffusional in-stabilities, and the role competing diffusionless and diffusion controlled growth modes play in pattern formation. We have studied non-equilibrium relaxation of classical and quantum systems following a quench in which the initial state of the system is prepared in different forms. We have investigated the properties of the clusters, as well as the behavior of the interface which separates the evolving phases. We have also studied the role of quenched disorder in such processes.
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