Zlámalův seminář

Jan FRANCŮ
V letním semestru 2017/18
Zlámalův seminář

Seminář se koná v seminární místnosti 1842 v 18. podlaží budovy A1 Fakulty strojního inženýrství VUT v Brně, Technická 2. v 13 hodin.

Program:

  • středa 4. dubna 2018
    Prof. RNDr. Ing. Tomáš Březina, CSc. 
    (Ústav matematiky FSI VUT v Brně)

    Tři příklady semisymbolických výpočtů 
    Semisymbolické výpočty jsou
    (a) výpočty symbolické (strojové získání symbolických výrazů) s následným dosazením numerických hodnot a vyčíslením výrazů,
    (b) výpočty s použitím racionální aritmetiky. 
    Uvedeny budou tyto příklady: 
    (1) Fyzikální modelování: L-obrazy veličin a jejich citlivosti
    (2) Tlumení vibrací systémů vysokého řádu
    (3) Rozšíření aplikací metody umístění pólů
  • středa 11. dubna 2018  (10 – 12 hodin) 
    10:00 Prof. Eugenia N. Petropoulou 
    (University of Patras Department of Civil Engineering)

    A nonstandard “discretization” technique for the solution of ODEs 
    Abstract: A nonstandard “discretization” technique for the solution of ordinary differential equations (ODEs) will be presented. This technique is based on the transformation of the original ODE into an equivalent difference equation, through an operator equation of an abstract Banach space. The technique will be demonstrated by applying it to initial or boundary value problems regarding the Duffing equation, the Duffing-van der Pol equation, the logistic equation and the Blasius equation. The obtained computed solutions are both real and complex. 
    11:00 E.E. Tzirtzilakis
    (Department of Mechanical Engineering, Technological Educational Institute of Western Greece, Patras, Greece)
    Modelling of Biomagnetic Fluid Flows and Applications
    Abstract: We will present the mathematical formulation of Biomagnetic Fluid Dynamics (BFD). The mathematical model is consistent with both principles of ferrohydrodynamics (FHD) and Magnetohydrodynamics (MHD). Blood is considered as a homogeneous non isothermal Newtonian fluid and is treated as an electrically conducting magnetic fluid which simultaneously exhibits polarization [1].
    As an application we consider two basic configuration physical problems. The BFD stretching sheet flow and the BFD fully developed flow in a 3D rectangular channel. The first physical problem of BFD stretching sheet flow, is described by a coupled, nonlinear system of ordinary differential equations subject to appropriate boundary conditions. This solution is obtained numerically by applying an efficient numerical technique based on finite differences method [2]. The second physical problem is that of the BFD flow in a 3D rectangular channel. The flow is considered as laminar, incompressible, three–dimensional, fully developed, taking place in a straight rectangular duct. The numerical results are obtained using a finite differences numerical technique based on a pressure–linked pseudotransient method on a collocated grid [1, 3].
    The obtained results for both physical problems are presented graphically for different values of the parameters entering into the problem under consideration. Emphasis is given to the study of the effect of the MHD and FHD interaction parameters on the flow field. It is apparent that both parameters effect significantly on various characteristics of the flow and consequently neither electrical conductivity nor magnetization of blood could be neglected. 
    [1] E.E. Tzirtzilakis, A mathematical model for blood flow in magnetic field, Physics of Fluids, Vol. 17, 077103, 2005.
    [2] M.G.Murtaza, E.E. Tzirtzilakis and M. Ferdows, Effect of electrical conductivity and magnetization on the biomagnetic fluid flow over a stretching sheet, ZAMP, 68:93, DOI 10.1007/s00033-017-0839-z, (15 pages), 2017.
    [3] E.E. Tzirtzilakis, V.D. Sakalis, N.G. Kafoussias, P.M. Hatzikonstantinou, Biomagnetic Fluid Flow in a 3D Rectangular Duct, International Journal for Numerical Methods in Fluids, Vol 44, pp. 1279–1298, 2004.

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