21. Buşe, Constantin; Jitiau, Oprea: A new theorem on exponential stability of periodic evolution families on Banach spaces. - Electron. J. Differ. Equ. 2003, Paper no. 14, 10 p., electronic only (2003). [ISSN 1072-6691]Miklavž Mastinšek, 2004, recenzija, prikaz knjige, kritika Ključne besede: matematika, analiza, skoraj periodične funkcije, eksponentna stabilnost, integralska neenakost, diferencialna neenakost, Banachov prostor, mathematics, analysis, almost periodic functions, exponential stability, periodic evolution families of operators, integral inequality, differential inequality on Banach spaces
Objavljeno v DKUM: 10.07.2015; Ogledov: 1338; Prenosov: 37
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23. Integrabilnost in lokalne bifurkacije v polinomskih sistemih navadnih diferencialnih enačbBrigita Ferčec, 2013, doktorska disertacija Opis: V tej doktorski disertaciji obravnavamo naslednje probleme kvalitativne teorije navadnih diferencialnih enačb (NDE): problem centra in fokusa, problem cikličnosti, problem izohronosti in problem bifurkacij kritičnih period. V prvem poglavju vpeljemo nekaj glavnih pojmov kvalitativne teorije NDE in opišemo nekaj temeljnih metod in algoritmov komutativne računske algebre, ki so potrebni za našo študijo. V drugem poglavju obravnavamo problem razlikovanja med centrom in fokusom, ki je ekvivalenten problemu obstoja prvega integrala določene oblike za dan sistem. To je vzrok, zakaj problemu centra in fokusa pravimo tudi problem integrabilnosti. Poiskali smo potrebne pogoje za integrabilnost (pogoje za center) za družino dvodimenzionalnih kubičnih sistemov, za Lotka-Volterrov sistem v obliki linearnega centra, motenega s homogenimi polinomi četrte stopnje in za nekatere polinomske družine v obliki linearnega centra, motenega s homogenimi polinomi pete stopnje. Z uporabo različnih metod smo za večino teh pogojev dokazali njihovo zadostnost za integrabilnost. Nadalje smo v tretjem poglavju z uporabo metod računske algebre pridobili zgornjo mejo za cikličnost (t.j. število limitnih ciklov, ki bifurcirajo iz izhodišča pri majhnih motnjah) družine kubičnih sistemov, obravnavane v drugem poglavju. Izračune premaknemo v polinomsko podalgebro, ki je povezana s časovno rezerzibilnimi sistemi družine in se na tak način izognemo problemu neradikalnosti Bautinovega ideala, povezanega s tem sistemov. Prav tako določimo število limitnih ciklov, ki bifurcirajo iz vsake komponente raznoterosti centra. V zadnjem poglavju disertacije obravnavamo problem izohronosti in problem bifurkacij kritičnih period za tridimenzionalne sisteme s centralnimi mnogoterostmi, na katerih vse trajektorije ustrezajo periodičnim rešitvam sistema. Za koeficiente sistema podamo kriterije za koeficiente sistema za razlikovanje med primeri izohronih in primeri neizohronih nihanj in za določitev zgornje meje števila kritičnih period.
Ključne besede: sistem NDE, integrabilnost, problem centra, časovna reverzibilnost, Darbouxov integral, linearizabilnost, raznoterost centra, fokusna količina, limitni cikel, problem cikličnosti, bifurkacije kritičnih period, funkcija periode, problem izohronosti
Objavljeno v DKUM: 08.07.2013; Ogledov: 2560; Prenosov: 261
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25. Computational fluid dynamics by boundary-domain integral methodLeopold Škerget, Matjaž Hriberšek, G. Kuhn, 1999, izvirni znanstveni članek Opis: A boundary-domain integral method for the solution of general transport phenomena incompressible fluid motion given by the Navier-Stokes equation set is presented. Velocity-vorticity formulation of the conservations is employed. Different integral representations for conservation field functions based on different fundamental solutions are developed. Special attention is given to the use of subdomain technique and Krylov subspace iterative solvers. The computed solutions of several benchmark problems agree well with available experimental and other computational results.
Ključne besede: fluid mechanics, fluid dynamics, numerical methods, boundary domain integral method, viscous fluid, heat transfer, diffusion-convective solution
Objavljeno v DKUM: 01.06.2012; Ogledov: 2443; Prenosov: 88
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27. Boundary element method for natural convection in non-Newtonian fluid saturated square porous cavityRenata Jecl, Leopold Škerget, 2003, izvirni znanstveni članek Opis: The main purpose of this work is to present the use of the Boundary Element Method (BEM) in the analysis of the natural convection in the square porous cavity saturated by the non-Newtonian fluid. The results of hydrodynamic and heat transfer evaluations are reported for the configuration in which the enclosure is heated from a side wall while the horizontal walls are insulated.The flow in the porous medium is modelled using the modified Brinkman extended Darcy model taking into account the non-Darcy viscous effects. The governing equations are transformed by the velocity-vorticity variables formulation enabling the computation scheme to be partitioned into kinematic and kinetic parts. To analyse the effects of the available non-Newtonian viscosity and to evaluate the presented approach, the power law model for shear thinning fluids (n<1), for shear thickening fluids (n>1) and in the limit for the Newtonian fluids (n=1) is considered. Numerical model is tested also for the Carreau model adequate for many non-Newtonian fluids. Solutions for the flow and temperature fields and Nusselt numbers are obtainedin terms of a modified Rayleigh number Ra*, Darcy number Da, and the non-Newtonian model parameters. The agreement between the results obtained with finite difference method is very good indicating that BEM can be efficiently used for solving transport phenomena in saturated porous medium.
Ključne besede: natural convection, non-Newtonian fluid, porous medium, cavity flow, boundary element method, boundary domain integral method
Objavljeno v DKUM: 01.06.2012; Ogledov: 1928; Prenosov: 99
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28. Experimental models of medium break loss of coolant accidents with and without steam generator tube ruptureJure Marn, Marjan Delić, Leopold Škerget, 2003, izvirni znanstveni članek Opis: This paper reports model experiments simulating medium break loss of coolant accidents, with and without steam generator tube rupture (SGTR), in pressurized water reactors. Apart from a significant influence on the pressure in the reactor coolant system in the early parts of the accident, SGTR generally has only a small effect on the pressures and temperatures during the accident. The initial reactor conditions are found to be more significant. Some results of preliminary numerical models are briefly presented and these are broadly in agreement with the experimental measurements.
Ključne besede: nuclear engineering, nuclear accidents, steam generator tube rupture, loss of coolant, medium break loss of coolant accident, computer program, Melcor, MELCOR computer code, integral test facility
Objavljeno v DKUM: 01.06.2012; Ogledov: 1864; Prenosov: 118
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29. On fracture behaviour of inhomogeneous materials - a case study for elastically inhomogeneous bimaterialsOtmar Kolednik, Jožef Predan, G.X. Shan, N.K. Simha, Franz Dieter Fischer, 2005, izvirni znanstveni članek Opis: This paper presents a case study, examining the influence of a sharp bimaterial interface on the effective crack driving force in a fracture mechanics specimen. The inhomogeneity of the elastic modulus in linear elasticand non-hardening and hardening elastic-plastic bimaterials is considered. The interface is perpendicular to the crack plane. The material properties and the distance between the crack tip and the interface are systematically varied. The effect of the material inhomogeneity is captured in form of a quantity called "material inhomogeneity term",▫$C_inh$▫. This term can be evaluated either by a simple post-processing procedure, following a conventional finite element stress analysis, or by computing the J-integral along a contour around the interface, ▫$J_int$▫. The effective crack driving force,▫$J_tip$▫, can be determined as the sum of ▫$C_inh$▫ and the nominally applied far-field crack driving force, ▫$J_far$▫. The results show that ▫$C_inh$▫ can be accurately determined by both methods even in cases where ▫$J_tip$▫-values are inaccurate. When a crack approaches a stiff/compliant interface,▫$C_inh$▫ is positive and ▫$J_tip$▫ becomes larger than ▫$J-far$▫. A compliant/stiff transition leads to a negative ▫$C_inh$▫, and ▫J_tip$▫ becomes smaller than ▫$J_far$▫. The material inhomogeneity term, ▫$C_inh$▫, can have the same order of magnitude as ▫$J_far$▫. Based on the numerical results, the dependencies of ▫$C_inh$▫ on the material parameters and the geometry are derived. Simple expressions are obtained to estimate ▫$C_inh$▫.
Ključne besede: mechanics of structures, fracture toughness, inhomogeneous materials, J-integral, crack driving force, interface, material force
Objavljeno v DKUM: 01.06.2012; Ogledov: 1720; Prenosov: 37
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30. Boundary domain integral method for high Reynolds viscous fluid flows in complex planar geometriesMatjaž Hriberšek, Leopold Škerget, 2005, izvirni znanstveni članek Opis: The article presents new developments in boundary domain integral method (BDIM) for computation of viscous fluid flows, governed by the Navier-Stokes equations. The BDIM algorithm uses velocity-vorticity formulation and is basedon Poisson velocity equation for flow kinematics. This results in accurate determination of boundary vorticity values, a crucial step in constructing an accurate numerical algorithm for computation of flows in complex geometries, i.e. geometries with sharp corners. The domain velocity computations are done by the segmentation technique using large segments. After solving the kinematics equation the vorticity transport equation is solved using macro-element approach. This enables the use of macro-element based diffusion-convection fundamental solution, a key factor in assuring accuracy of computations for high Reynolds value laminar flows. The versatility and accuracy of the proposed numerical algorithm is shown for several test problems, including the standard driven cavity together with the driven cavity flow in an L shaped cavity and flow in a Z shaped channel. The values of Reynolds number reach 10,000 for driven cavity and 7500 for L shapeddriven cavity, whereas the Z shaped channel flow is computed up to Re = 400. The comparison of computational results shows that the developed algorithm is capable of accurate resolution of flow fields in complex geometries.
Ključne besede: fluid mechanics, numerical methods, boundary domain integral method, algorithms, incompressible fluid flow, Navier-Stokes equations, velocity vorticity formulation, segmentation technique, driven cavity flow
Objavljeno v DKUM: 01.06.2012; Ogledov: 2229; Prenosov: 92
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