BME Fizikai Tudományok Doktori Iskola
PhD témajavaslat
| A témavezető neve:
Barna Imre Ferenc - munkahelye: Wigner Fizikai Kutatóközpont - beosztása: tudományos főmunkatárs - tudományos fokozata: PhD - email címe: barna.imre@wigner.hu |
A konzulens neve:
Prof. Dr. Apagyi Barnabás - tanszéke: Fizikai Intézet - beosztása: Címzetes Egyetemi Tanár - tudományos fokozata: MTA Doktora - email címe: apagyi@phy.bme.hu |
| A doktori munka készítésénak helye és címe: Wigner FK Konkoly Thege Miklós út 29 - 33, Budapest, 1121 |
| A kidolgozandó feladat címe: Searching for analytic solutions of physically relevant non-linear partial differential equations |
A téma rövid leírása, a megoldandó legfontosabb feladatok felsorolása:
Searching for analytic solutions of physically relevant non-linear partial differential equations
There are numerous fields in physics which deal with highly non-linear phenomena,
and take place in space and time decribed by non-linear partial differential equations (PDE)
such as wave phenomena, transport processes like fluid dynamics, plasma physics, high-energy
physics or grativation. There is no existing general mathematical theory of non-linear PDEs,
however there are some trial functions (Ansätze) like self-similar solutions, traveling
waves 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 were problems from
viscous hydrodynamics [1], but difusion [2], non-linear electrodynamics [3] or
dark fluid [4] were addressed as well.
The candidate should have a solid knowledge in basic theoretical physics and
ordinary differential equations. We can offer problems in fluid dynamics -- which is under our
present interest --, but the research field of could be slightly changed and defined
together with the PhD candidate.
For background information see papers at: http://www.kfki.hu/~barnai
[1] I.F. Barna, G. Bognár, L. Mátyás and K. Hriczó,
"Self-similar analysis of the time-dependent compressible and incompressible boundary
layer including heat condution"
Journal of Thermal Analysis and Calorimetry 147 (2022) 13625
[2] I.F. Barna and l. Mátyás
"Advanced Analytic Self-Similar Solutions of Regular and Irregular Diffusion Equations"
Mathematics 10, (2022) 3281
[3] I.F. Barna
"Self-similar shock wave solutions of the non-linear Maxwell equations"
Laser Phys. 24, (2014) 086002
[4] I.F. Barna, M.A. Pocsai and G.G. Barnaföldi
"Self-similar solutions of a gravtitating dark fluid"
Mathematics 10 (2022) 3220
|
A jelentkezővel szemben támasztott elvárások: Solid knowledge of basic theoretical physics and ordinary differential equations Good communication skills in English Basic knowledge of the Latex, Maple and Mathematica softwares |
| Nyilatkozat: A fenti munkahelyen a javasolt témában kutatás feltételei biztosítottak, a téma meghirdetését a munkahelyi vezető jóváhagyta. |
| Budapesti Műszaki és Gazdaságtudományi Egyetem Természettudományi Kar |
 |
1111 Budapest, Műegyetem rakpart 3. K épület I. em. 18. www.ttk.bme.hu |