Thesis supervisor: Imre Ferenc Barna
Location of studies (in Hungarian): Wigner Research Centre for Physics Abbreviation of location of studies: BME
Description of the research topic:
There are numerous fields in physics which deal with highly non-linear phenomena,and take place in space and time decribed by non-linear partialdifferential equations (PDE)such as wave phenomena, transport processes like fluid dynamics, plasma physics, high-energyphysics or grativation. There is no existing general mathematical theory of non-linear PDEs,however there are some trial functions (Ansätze) like self-similar solutions, travelingwaves which give us physically relevant reasonable solutions helping to get a deeper insight into the internal properties of such systems.In the last decades we investigated numerous PDEs, most of them wereproblems fromviscous hydrodynamics [1], but heat conduction [2], non-linear electrodynamics [3] orquantum mechanical problems [4] were addressed as well.The candidate should have a solid knowledge in basic theoretical physics andordinary differential equations. We can offer problems in fluid dynamics --which is under ourpresent interest --, but the research field of could be slightly changed and definedtogether with the PhD candidate.For background information see papers at: http://www.kfki.hu/~barnai[1]I.F. Barna, M.A. Pocsai, S. Lökös and L. Mátyás"Rayleigh-Benard convection in the generalized Oberbeck-Boussinesq system"Chaos Solitons and Fractals. 103, (2017) 336[2] I.F. Barna and R. Kersner"Heat conduction: a telegraph-type model with self-similar behavior of solutions"J. Phys. A: Math. Theor. 43, (2010) 375210[3] I.F. Barna"Self-similar shock wave solutions of the non-linear Maxwell equations"Laser Phys. 24, (2014) 086002[4]Understanding the Schrödinger Equation: Some [Non]Linear PerspectivesEditor: Valentino SimpaoI.F. Barna and L. Mátyás"Self-similar And Travelling-Wave Analysis Of The Madelung Equations ObtainedFrom the Free Schrödinger Equation an accepted book ChapterNova Science Publishers 2020
Required language skills: English Further requirements: Solid knowledge of basic theoretical physics and ordinary differential equationsGood communication skills in EnglishBasic knowledge of the Latex, Maple and Mathematica softwares
Number of students who can be accepted: 1
Deadline for application: 2023-01-31
2024. IV. 17. ODT ülés Az ODT következő ülésére 2024. június 14-én, pénteken 10.00 órakor kerül sor a Semmelweis Egyetem Szenátusi termében (Bp. Üllői út 26. I. emelet).
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