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Polskiej Akademii Nauk

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Włodzimierz Bielski

Institute of Geophysics (PL)


Ostatnie publikacje
1.  Wojnar R., Bielski W., Laminar flow past the bottom with obstacles – a suspension approximation, BULLETIN OF THE POLISH ACADEMY OF SCIENCES: TECHNICAL SCIENCES, ISSN: 0239-7528, DOI: 10.1515/bpasts-2015-0080, Vol.63, No.3, pp.685-695, 2015

Streszczenie:
From Albert Einstein’s study (1905) it is known that suspension introduced to a fluid modifies its viscosity. We propose to describe the influence of obstacles on the Stokesian flow as a such modification. Hence, we treat the fluid flow through small obstacles as a flow with suspension. The flow is developing past the plane bottom under the gravity force. The spatial distribution of suspension concentration is treated as given, and is regarded as an approximation of different obstacles which modify the fluid flow and change its viscosity. The different densities of suspension are considered, beginning of small suspension concentration until 40%. The influence of suspension concentration on fluid viscosity is analyzed, and Brinkman’s formula as fitting best to experimental data is applied.

Słowa kluczowe:
Stokes’ flow, Einstein’s suspension, Brinkman’s suspension, non-uniform viscosity, velocity distribution, wastes, plants on the bottom

Afiliacje autorów:
Wojnar R. - IPPT PAN
Bielski W. - Institute of Geophysics (PL)
20p.
2.  Gambin B., Bielski W., Incompressible limit for a magnetostrictive energy functional, BULLETIN OF THE POLISH ACADEMY OF SCIENCES: TECHNICAL SCIENCES, ISSN: 0239-7528, DOI: 10.2478/bpasts-2013-0110, Vol.61, No.4, pp.320-326, 2013

Streszczenie:
The modern materials undergoing large elastic deformations and exhibiting strong magnetostrictive effect are modelled here by free energy functionals for nonlinear and non-local magnetoelastic behaviour. The aim of this work is to prove a new theorem which claims that a sequence of free energy functionals of slightly compressible magnetostrictive materials with a non-local elastic behaviour, converges to an energy functional of a nearly incompressible magnetostrictive material. This convergence is referred to as a Γ -convergence. The non-locality is limited to non-local elastic behaviour which is modelled by a term containing the second gradient of deformation in the energy functional.

Słowa kluczowe:
gamma-convergence, incompressibility, magnetostrictive material, second gradient of deformation, existence of minimizers

Afiliacje autorów:
Gambin B. - IPPT PAN
Bielski W. - Institute of Geophysics (PL)
25p.
3.  Bielski W., Gambin B., Relationship between existence of energy minimizers of incompressible and nearly incompressible magnetostrictive materials, REPORTS ON MATHEMATICAL PHYSICS, ISSN: 0034-4877, Vol.66, No.2, pp.147-157, 2010

Streszczenie:
Models of incompressible and slightly compressible magnetostrictive materials are introduced. They are given by the free energy functionals which depend on magnetization and elastic deformation as well as on their gradients. We demonstrate the existence of minimum of an energy functional for a slightly compressible material. We also prove a theorem on convergence of a sequence of minimizers of less and less compressible material energy functionals to a minimize of energy of incompressible material. Besides the existence of solution of the incompressible magnetostrictive problem is obtained.

Słowa kluczowe:
micromagnetics, magnetostrictive material, incompressible, nearly incompressible materials, existence problem

Afiliacje autorów:
Bielski W. - Institute of Geophysics (PL)
Gambin B. - IPPT PAN
13p.
4.  Bielski W., Telega J.J., A non-linear elastic plate model of moderate thickness: Existence, uniquenness and duality, JOURNAL OF ELASTICITY, ISSN: 0374-3535, DOI: 10.1007/BF00041792, Vol.42, No.3, pp.243-273, 1996

Streszczenie:
Three problems are solved for a nonlinear model of elastic plates with transverse shear deformations. The material of the plate may be anisotropic. An existence theorem is formulated and proved for a class of boundary conditions. A uniqueness theorem is given for small loadings. The dual problem is derived and the minimax or Lagrangian approach is discussed.

Afiliacje autorów:
Bielski W. - Institute of Geophysics (PL)
Telega J.J. - IPPT PAN
5.  Bielski W., Telega J.J., Tarcie na uskokach geologicznych: modelowanie i wariacyjne sformułowanie zagadnień brzegowo-początkowych, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.31, pp.1-30, 1994
6.  Bielski W., Telega J.J., On Existence of Solutions and Duality for a Model of Non-linear Elastic Plates with Transverse Shear Deformations, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.35, pp.1-26, 1992

Lista rozdziałów w ostatnich monografiach
1. 
Bielski W., Wojnar R., Applicable Solutions in Nonlinear Dynamical Systems, rozdział: Gravity waves in channels with corrugated bottom: asymptotic approaches, Wydawnictwo Politechniki Łódzkiej, Łódź, pp.75-86, 2019
2. 
Wojnar R., Bielski W., Modern Problems in Applied Analysis. Trends in Mathematics, rozdział: Gravity Driven Flow Past the Bottom with Small Waviness, Birkhauser – Springer International Publishing AG, part of Springer Nature 2018, Piotr Drygaś and Sergei Rogosin (Eds.), pp.181-202, 2018
3. 
Bielski W., Wojnar R., Dynamical Systems in Theoretical Perspective. Springer Proceedings in Mathematics & Statistics, rozdział: Stokes Flow Through a Tube with Wavy Wall, Springer International Publishing AG, part of Springer Nature 2018, Jan Awrejcewicz (Ed.), 248, pp.379-390, 2018
4. 
Bielski W., Wojnar R., Vibration, Control and Stability of Dynamical Systems - DSTA 2017, rozdział: Stokes flow through a tube with wavy wall, Jan Awrejcewicz, Marek Kaźmierczak, Jerzy Mrozowski, Paweł Olejnik (Eds.), Department of Automation, Biomechanics and Mechatronics, ARSA Druk i Reklama, Łódź, pp.83-94, 2017
5. 
Bielski W., Kowalczyk P., Wojnar R., The Book of Abstracts of the Numerical Heat Transfer 2015 - Eurotherm Seminar No. 109, rozdział: Two-temperature heat transfer in metal films, Institute of Thermal Technology, Silesian University of Technology, Gliwice, Poland and Institute of Heat Engineering, Warsaw University of Technology, Warsaw, Poland, Editors: Andrzej J. Nowak, Jerzy Banaszek, and Bozidar Sarler, pp.29-30, 2015
6. 
Bielski W., Kowalczyk P., Wojnar R., The Conference Proceedings of the Numerical Heat Transfer 2015 - Eurotherm Seminar No. 109, rozdział: Two-temperature heat transfer in metal films, Institute of Thermal Technology, Silesian University of Technology, Gliwice, Poland and Institute of Heat Engineering, Warsaw University of Technology, Warsaw, Poland, Editors: Andrzej J. Nowak, Jerzy Banaszek, and Bozidar Sarler, pp.57-67, 2015
7. 
Bielski W., Wojnar R., PCM-CMM-2015 - 3rd Polish Congress of Mechanics & 21st Computer Methods in Mechanics, rozdział: Laminar flow past the bottom with obstacles - from suspension to porous medium, Polish Society of Theoretical and Applied Mechanics, Drukarnia WIB Piotr Winczewski, Gdańsk, Poland, Editors: Michał Kleiber, Tadeusz Burczyński, Krzysztof Wilde, Jarosław Górski, Karol Winkelmann, and Łukasz Smakosz, Vol. 1, 1, pp.207-208, 2015
8. 
Wojnar R., Bielski W., Complex Analysis and Potential Theory with Applications, rozdział: Flow in the canal with plants on the bottom, Cambridge Scientific Publishers, T. Aliev Azerogly, A. Golberg, S.V. Rogosin (Eds.), pp.167-183, 2014
9. 
Bielski W., Wojnar R., Analytic Methods of Analysis and Differential Equations, rozdział: Homogenisation of flow through double scale porous medium, Cambridge Scientific Publishers, Cambridge UK, Kilbas A.A., Rogosin S.V. (Eds.), pp.27-43, 2008
10. 
Kruglenko E., Gambin B., Bielski W., Elektromagnetyczne techniki w ochronie zdrowia, rozdział: Materiały nieściśliwe magnetosprężyste jako model tkanek z mikromagnetycznymi cząstkami, CIOP PIB (Warszawa), Krawczyk A., Duraj A. (Eds.), pp.96-109, 2007
11. 
Bielski W., Gambin B., Kruglenko E., Nonsmooth/Nonconvex Mechanics with applications in Engineering II. NNMAE206, A volume dedicated to the memory of Professor P.D.Panagiotopoulos, rozdział: Selected problems of rigid and deformable micromagnetics, ZITI, Baniotopoulos C.C. (Ed.), pp.69-76, 2006

Abstrakty konferencyjne
1.  Bielski W., Wojnar R., Brinkman's regulatization of Darcian seepage, PCM-CMM, 4th Polish Congress of Mechanics, 23rd International Conference on Computer Methods in Mechanics, 2019-09-08/09-12, Kraków (PL), pp.396-MS12-CR, 2019
2.  Bielski W., Wojnar R., Plane flow through the porous medium with chessboard-like distribution of permeability, 2nd Workshop on Porous Media, 2018-06-28/06-30, Olsztyn (PL), pp.7, 2018
3.  Bielski W., Kowalczyk P., Wojnar R., Thermal stresses and two temperature heat transfer, SolMech 2018, 41st SOLID MECHANICS CONFERENCE, 2018-08-27/08-31, Warszawa (PL), pp.234-235, 2018
4.  Bielski W., Gambin B., An estimation of wave velocities in geomaterials, SolMech 2010, 37th Solid Mechanics Conference, 2010-09-06/09-10, Warszawa (PL), pp.240-241, 2010

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