Instytut Podstawowych Problemów Techniki
Polskiej Akademii Nauk

Pracownicy

dr Ryszard Wojnar

Zakład Teorii Ośrodków Ciągłych i Nanostruktur (ZTOCiN)
Pracownia Mechaniki Analitycznej i Teorii Pola (PMAiTP)
emeryt, zlecenie
telefon: (+48) 22 826 12 81 wewn.: 433
pokój: 116
e-mail:
ORCID: 0000-0001-5927-3087

Doktorat
1973 Liniowa mechanika statystyczna uogólnionej dyfuzji 
promotor -- prof. dr hab. Jan Stecki, IChF
 

Ostatnie publikacje
1.  Wojnar R., Kinetic equation for the dilute Boltzmann gas in an external field, ACTA PHYSICA POLONICA B, ISSN: 0587-4254, DOI: 10.5506/APhysPolB.49.905, Vol.49, No.5, pp.905-920, 2018

Streszczenie:
We report a kinetic equation for an auxiliary distribution function f(k,v1,t) which yields the intermediate scattering function Is(k,t). To this end, the projection operator proposed by Stecki was applied. The scattering operator was given in explicit form in the limit of low density gas. The general kinetic equation was next specialized for the case of Lorentz gas.

Afiliacje autorów:
Wojnar R. - IPPT PAN
20p.
2.  Wojnar R., Heuristic derivation of Brinkman's seepage equation, Technical Sciences, ISSN: 1505-4675, Vol.20, No.4, pp.359-374, 2017

Streszczenie:
Brinkman's law is describing the seepage of viscous fluid through a porous medium and is more acuratethan the classicalDarcy's law.Namely, Brinkman's law permitsto conform the flow through a porous medium to the free Stokes' flow. However, Brinkman's law, similarly as Schro¨dinger's equation was only devined. Fluid in its motion through a porous solid is interacting at every point with the walls of pores, but the interactions of the fluid particles inside pores are different than the interactions at the walls, and are described by Stokes' equation. Here, we arrive at Brinkman's law from Stokes' flow equation making use of successive iterations, in type of Born's approximation method, and using Darcy's law as a zero-th approximation.

Słowa kluczowe:
porosity, Darcy's law, Stokes' equation, successive iterations, Born's approximation

Afiliacje autorów:
Wojnar R. - IPPT PAN
11p.
3.  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.
4.  Gambin B., Kruglenko E., Gałka A.A., Wojnar R., Macroscopic thermal properties of quasi-linear cellular medium on example of the liver tissue, COMPUTER ASSISTED METHODS IN ENGINEERING AND SCIENCE, ISSN: 2299-3649, Vol.22, No.4, pp.329-346, 2015

Streszczenie:
There are two main topics of this research: (i) one topic considers overall properties of a nonlinear cellular composite, treated as a model of the liver tissue, and (ii) the other topic concerns the propagation of heat in the nonlinear medium described by the homogenised coefficient of thermal conductivity.

For (i) we give a method and find the effective thermal conductivity for the model of the liver tissue, and for the point (ii) we present numerical and analytical treatment of the problem, and indicate the principal difference of heat propagation in linear and nonlinear media. In linear media, as it is well known, the range of the heat field is infinite for all times t > 0, and in nonlinear media it is finite.

Pennes’ equation, which should characterize the heat propagation in the living tissue, is in general a quasi-nonlinear partial differential equation, and consists of three terms, one of which describes Fourier’s heat diffusion with conductivity being a function of temperature T. This term is just a point of our analysis.

We show that a nonlinear character of the medium (heat conductivity dependent on the temperature) changes in qualitative manner the nature of heat transfer. It is proved that for the heat source concentrated initially (t = 0) at the space point, the range of heated region (for t > 0) is finite. The proof is analytical, and illustrated by a numerical experiment.

Słowa kluczowe:
heat transport, asymptotic homogenisation, effective heat conductivity

Afiliacje autorów:
Gambin B. - IPPT PAN
Kruglenko E. - IPPT PAN
Gałka A.A. - inna afiliacja
Wojnar R. - IPPT PAN
14p.
5.  Wojnar P., Zieliński M., Janik E., Zaleszczyk W., Wojciechowski T., Wojnar R., Szymura M., Kłopotowski Ł., Baczewski L.T., Pietruchik A., Wiater M., Kret S., Karczewski G., Wojtowicz T., Kossut J., Strain-induced energy gap variation in ZnTe/ZnMgTe core/shell nanowires, APPLIED PHYSICS LETTERS, ISSN: 0003-6951, DOI: 10.1063/1.4873355, Vol.104, pp.163111-1-5, 2014

Streszczenie:
Strain-induced changes of ZnTe energy gap in ZnTe/ZnMgTe core/shell nanowires arising from lattice mismatch between the core and the shell semiconductor are studied by means of optical methods. It is shown that the increase of the Mg content in the shell, as well as the increase of the shell thickness result in an effective redshift of the near band edge photoluminescence from ZnTe nanowire cores, which reflects directly the decrease of energy gap under tensile strain conditions. The conclusions are supported by theoretical calculations in terms of the valence force field model. The observed change of ZnTe energy gap can be as large as 120 meV with respect to the unstrained conditions and can be tuned in a continuous manner by adjusting shell parameters, which open a path towards an effective band gap engineering in these structures.

Słowa kluczowe:
Nanowires, II-VI semiconductors, Magnesium, Band gap, Quantum effects

Afiliacje autorów:
Wojnar P. - Institute of Physics, Polish Academy of Sciences (PL)
Zieliński M. - inna afiliacja
Janik E. - inna afiliacja
Zaleszczyk W. - inna afiliacja
Wojciechowski T. - Institute of Physics, Polish Academy of Sciences (PL)
Wojnar R. - IPPT PAN
Szymura M. - inna afiliacja
Kłopotowski Ł. - inna afiliacja
Baczewski L.T. - Institute of Physics, Polish Academy of Sciences (PL)
Pietruchik A. - Institute of Physics, Polish Academy of Sciences (PL)
Wiater M. - Institute of Physics, Polish Academy of Sciences (PL)
Kret S. - Institute of Physics, Polish Academy of Sciences (PL)
Karczewski G. - inna afiliacja
Wojtowicz T. - Institute of Physics, Polish Academy of Sciences (PL)
Kossut J. - Institute of Physics, Polish Academy of Sciences (PL)
40p.
6.  Wojnar R., Flow of Stokesian fluid through a cellular medium and thermal effects, BULLETIN OF THE POLISH ACADEMY OF SCIENCES: TECHNICAL SCIENCES, ISSN: 0239-7528, DOI: 10.2478/bpasts-2014-0031, Vol.62, No.2, pp.321-329, 2014

Streszczenie:
The thermal effects of a stationary Stokesian flow through an elastic micro-porous medium are compared with the entropy produced by Darcy’s flow. A micro-cellular elastic medium is considered as an approximation of the elastic porous medium. It is shown that after asymptotic two-scale analysis these two approaches, one analytical, starting from Stoke’s equation and the second phenomenological, starting from Darcy’s law give the same result. The incompressible and linearly compressible fluids are considered, and it is shown that in micro-porous systems the seepage of both types of fluids is described by the same equations.

Słowa kluczowe:
porous media, Onsager’s principle, entropy, heat production

Afiliacje autorów:
Wojnar R. - IPPT PAN
25p.
7.  Wojnar R., Wojnar P., Kret S., Elastic State Induced Energy Gap Variation in ZnTe/ZnMgTe Core/Shell Nanowires, TECHNISCHE MECHANIK, ISSN: 0232-3869, Vol.34, pp.233-245, 2014

Streszczenie:
The zinc telluride (ZnTe) nanowires grown recently are covered with the ZnMgTe shell. As a result of addition of magnesium the ZnMgTe lattice is expanded with respect to pure ZnTe lattice. From the lattice mismatch between the ZnMgTe shell and ZnTe nanowire core the internal strain and stress are created. Depending on the shell thickness and the Mg content in the shell the optical emission exhibits a considerable energy shift. To estimate this effect, at least qualitatively, the elastic state of the nanowire is calculated.

An analysis of the state of strain and stress in the core-shell nanowire within linear elasticity, using an analogy with thermal stresses is presented, in the similar way as it is applied, e.g. in hygro-mechanics. The suitable system of the differential Lame-Navier’s type equations is derived, and its solution for the axially symmetric problem is given. The jump of stress at the core-shell boundary is determined.

Afiliacje autorów:
Wojnar R. - IPPT PAN
Wojnar P. - Institute of Physics, Polish Academy of Sciences (PL)
Kret S. - Institute of Physics, Polish Academy of Sciences (PL)
8.  Wojnar R., Random Walk, Diffusion and Wave Equation, ACTA PHYSICA POLONICA B, ISSN: 0587-4254, DOI: 10.5506/APhysPolB.44.1067, Vol.44, No.5, pp.1067-1084, 2013

Streszczenie:
One-dimensional random walk is analyzed. First, it is shown that the classical interpretation of random walk reaching Lord Rayleigh’s analysis should be completed. Further, an attention is called to the fact that the parabolic diffusion is not an unique interpretation, but also the wave (or hyperbolic) equation can be deduced. It depends on the accepted scale of the length of step h and duration of the step τ in the walk, whether Fick–Smoluchowski’s diffusion or a wave process is obtained. Only additional arguments, such as positivity of distribution function or positivity of the entropy growth, can help to choose the proper physical model. Also, the infinite diffusion velocity paradox in connection with Einstein’s formula is explained.

Afiliacje autorów:
Wojnar R. - IPPT PAN
20p.
9.  Wojnar R., Random walk, Rayleigh-Kac’ scheme and diffusion equation, REPORTS ON MATHEMATICAL PHYSICS, ISSN: 0034-4877, Vol.72, No.3, pp.321-332, 2013

Streszczenie:
Nonsymmetric random walk is studied and amelioration of existing schemes of its interpretation is proposed. It is shown that for a nonsymmetric random walk not only the analog of the drift force appears, but in comparison with the symmetric random walk the diffusion coefficient is modified. The infinite velocity paradox is also discussed.

Słowa kluczowe:
difference-differential limit, diffusion coefficient, Smoluchowski’s equation, Einstein’s formula, limit transitions, infinite velocity paradox

Afiliacje autorów:
Wojnar R. - IPPT PAN
15p.
10.  Wojnar R., Rayleigh's Distribution, Wigner's Surmise and Equation of the Diffusion, ACTA PHYSICA POLONICA A, ISSN: 0587-4246, DOI: 10.12693/APhysPolA.123.624, Vol.123, No.3, pp.624-628, 2013

Streszczenie:
After summaries on Rayleigh's distribution and Wigner's surmise, the time evolution of Rayleigh Wigner's statistics is studied and a suitable diffusion type equation is proposed. Also the variance and kurtosis of time evolution of Rayleigh's distribution are calculated. Obtained results maybe useful in description of physical, social and biological processes.

Afiliacje autorów:
Wojnar R. - IPPT PAN
15p.
11.  Wojnar R., Student’s t-distribution versus Zeldovich–Kompaneets solution of diffusion problem, ACTA PHYSICA POLONICA A, ISSN: 0587-4246, Vol.121, No.2-B, pp.133-136, 201215p.
12.  Wojnar R., Two-level diffusion, random walk and uniqueness, REPORTS ON MATHEMATICAL PHYSICS, ISSN: 0034-4877, Vol.68, No.1, pp.85-96, 201120p.
13.  Wojnar R., Boussinesq equation for flow in an aquifer with time dependent porosity, BULLETIN OF THE POLISH ACADEMY OF SCIENCES: TECHNICAL SCIENCES, ISSN: 0239-7528, Vol.58, No.1, pp.165-170, 20109p.
14.  Wojnar R., Kinetic equation for a gas with attractive forces as a functional equation, Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica, ISSN: 2081-545X, Vol.8, pp.91-116, 2009
15.  Wojnar R., Structural control in tissue development, JOURNAL OF THEORETICAL AND APPLIED MECHANICS, ISSN: 1429-2955, Vol.43, No.4, pp.805-812, 2005
16.  Telega J.J., Wojnar R., Piezoelectric effects in biological tissues, JOURNAL OF THEORETICAL AND APPLIED MECHANICS, ISSN: 1429-2955, Vol.40, No.3, pp.723-759, 2002

Streszczenie:
The aim of this paper is to analyze different contributions and differents points of view concerning the meaning of the piezoelectric effect in the bone. It is now obvious that this effect is overhelming in dry bone. In wet bone more important are streaming potentials.

Słowa kluczowe:
bone, piezoelectricity

Afiliacje autorów:
Telega J.J. - IPPT PAN
Wojnar R. - IPPT PAN
17.  Wojnar R., Homogenization of piezoelectric solid and thermodynamics, REPORTS ON MATHEMATICAL PHYSICS, ISSN: 0034-4877, DOI: 10.1016/S0034-4877(97)85908-3, Vol.40, No.3, pp.585-598, 1997

Streszczenie:
The problem of homogenization of a piezoelectric periodic composite in which thermal effects are taken into account is treated by a method of 2-scale asymptotic expansions. Albeit a nonlinear entropy-temperature relation is used, the local problems are formulated in a way similar to that of a linear theory. Also, effective material coefficients are in majority the same as those obtained in a linearized theory. The difference appears in the homogenized thermoelastic, thermoelectric and specific heat coefficients only. A Francfort type result on shift of the initial conditions for a homogenized problem is also obtained.

Afiliacje autorów:
Wojnar R. - IPPT PAN
18.  Gałka A., Telega J.J., Wojnar R., Some computational aspects of homogenization of thermopiezoelectric composites, Computer Assisted Mechanics and Engineering Sciences, ISSN: 1232-308X, Vol.3, No.2, pp.133-154, 1996

Streszczenie:
On the basis of the paper [1] two topics are discussed. Firstly, exact formulae for the homogenized coeffi-cients of a layered thermopiezoelectric composite are derived. Secondly, by applying the Ritz method, the local problems are solved approximately. Specific cases are also examined and illustrated.

Afiliacje autorów:
Gałka A. - inna afiliacja
Telega J.J. - IPPT PAN
Wojnar R. - IPPT PAN
19.  Telega J.J., Wojnar R., Main Polish Historical and Modern Sources on Applied Mechanics, Applied Mechanics Reviews, ISSN: 0003-6900, DOI: 10.1115/1.3101933, Vol.49, No.8, pp.401-432, 1996

Streszczenie:
The aim of thikocvzeń article is to present the list of books by Polish scientists on applied mechanics in a rather broad sense. An effort was made to cover the last century. Previous Polish sources, until 1874, were collected by Kucharzewski (1894). A list of the main journals in applied mechanics is also given, essentially covering the period starting after the Second World War.

Afiliacje autorów:
Telega J.J. - IPPT PAN
Wojnar R. - IPPT PAN
20.  Gałka A., Wojnar R., Dynamiczne naprężenia cieplne w półprzestrzeni sprężystej wywołane przez impuls laserowy, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.25, pp.1-53, 1993
21.  Gałka A., Telega J.J., Wojnar R., Thermodiffusion in Heterogeneous Elastic Solids and Homogenization, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.14, pp.1-76, 1993
22.  Gałka A., Telega J.J., Wojnar R., Homogenization and thermopiezoelectricity, Mechanics Research Communications, ISSN: 0093-6413, DOI: 10.1016/0093-6413(92)90050-K, Vol.19, No.4, pp.315-324, 1992

Streszczenie:
In [9] the formulae were derived for the effective moduli of a piezoelectric composite exhibiting fine periodic structure. The static case considered was studied by the method of F-convergence, cf.[l]. Next, in [10] these results were extended by investigating the dynamic behaviour. The same formulae for the effective moduli were obtained by using the method of Bloch expansions. The aim of this contribution is to present our preliminary results concerning homogenization of the equations of the linear thermopiezoelectricity. To such a problem the method of F-convergence is not applicable. Therefore the relevant analysis was performed by using the method of two-scale asymptotic developments. Our analysis leads to interesting conclusions related to the effective moduli and to the change of the initial condition for the temperature of the homogenized body.

Afiliacje autorów:
Gałka A. - inna afiliacja
Telega J.J. - IPPT PAN
Wojnar R. - IPPT PAN
23.  Wojnar R., Uniqueness of displacement-heat flux and stress-temperature problems in thermoelasticity with one relaxation time, JOURNAL OF THERMAL STRESSES, ISSN: 0149-5739, DOI: 10.1080/01495738508942242, Vol.8, No.4, pp.351-364, 1985

Streszczenie:
Two uniqueness theorems of linear thermoelasticity with one relaxation time corresponding to natural initial boundary value problems described in terms of two different pairs of thermoelastic variables: displacement-heat flux and stress-temperature are proved.

Afiliacje autorów:
Wojnar R. - IPPT PAN
24.  Wojnar R., Twierdzenie o jednoznaczności dla pewnego układu naprężeniowych równań ruchu liniowej teorii sprężystości, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.70, pp.1-10, 1972
25.  Wojnar R., O jednoznaczności rozwiązań naprężeniowych równań ruchu typu Beltramiego-Michella, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.63, pp.1-11, 1972
26.  Wojnar R., O wyznaczeniu naprężeń zmiennych w czasie z obrazów elastooptycznych, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.33, pp.1-12, 1970

Lista rozdziałów w ostatnich monografiach
1. 
Wojnar R., Postępy w badaniach fizykochemicznych - wybrane zagadnienia, rozdział: Helisa Boerdijka-Coxetera - w geometrii, biologii, fizyce, ..., Wydawnictwo Naukowe TYGIEL Sp. z o.o., Lublin, pp.180-197, 2019
2. 
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
3. 
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
4. 
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
5. 
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
6. 
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
7. 
Rylko N., Wojnar R., Geometry, Integrability, Mechanics and Quantization, rozdział: Resurgence edge effects in composites: fortuity and geometry, Ivailo M. Mladenov, Mariana Hadzhilazova and Vasyl Kovalchuk (Editors), Avangard Prima, Sofia, pp.342-349, 2015
8. 
Wojnar R., Geometry, Integrability, Mechanics and Quantization, rozdział: Bohmian picture of the wave function and the gauge invariance, Ivailo M. Mladenov, Mariana Hadzhilazova and Vasyl Kovalchuk (Editors), Avangard Prima, Sofia, pp.411-424, 2015
9. 
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
10. 
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
11. 
Wojnar R., PCM-CMM-2015 - 3rd Polish Congress of Mechanics & 21st Computer Methods in Mechanics, rozdział: Modelling polycrystalline structure of collagen fibrils dense packing by the most uniform concentric pattern, 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.269-270, 2015
12. 
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
13. 
Wojnar R., Piezoelectric nanomaterials for biomedical applications. Nanomedicine and Nanotoxicology, rozdział: Piezoelectric phenomena in biological tissues, Springer, Gianni Ciofani and Arianna Menciassi (Eds.), pp.173-185, 2012
14. 
Wojnar R., Biomechanics of hard tissues: Modeling, testing and materials, rozdział: Bone and cartilage - its structure and physical properties, Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim, pp.1-76, 2010
15. 
Wojnar R., More Progresses In Analysis: Proceedings of the 5th International Isaac Congres, rozdział: Strains in tissue development: a vortex description, World Scientific Publishing Co., Begehr H.G.W., Nicolosi F. (Eds.), pp.1271-1281, 2009
16. 
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

Prace konferencyjne
1.  Wojnar R., Complex dielectric coefficients and maxwell’s averaging, 8th International ISAAC Congress, 2011-08-22/08-27, Moscow (RU), pp.1-7, 2011

Abstrakty konferencyjne
1.  Wojnar R., Kapsydy wirusów jako wielościany, XII Interdyscyplinarna Konferencja Naukowa TYGIEL 2020. Interdyscyplinarność kluczem do rozwoju., 2020-09-24/09-27, Lublin (PL), pp.60-60, 2020
2.  Wojnar R., Moments of the Van Hove dynamic scattering law, Symposium on Statistical Physics, 2020-12-03/12-04, Kraków (PL), pp.64-64, 2020
3.  Wojnar R., Rozkład Bosego-Einsteina i prawo Pareta, XII Interdyscyplinarna Konferencja Naukowa TYGIEL 2020. Interdyscyplinarność kluczem do rozwoju., 2020-09-24/09-27, Lublin (PL), pp.225, 2020
4.  Wojnar R., Helisy i piezoelektryczność, XII Interdyscyplinarna Konferencja Naukowa TYGIEL 2020. Interdyscyplinarność kluczem do rozwoju., 2020-09-24/09-27, Lublin (PL), pp.89, 2020
5.  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
6.  Wołowicz J., Lissowski A., Wojnar R., How to Construct BC Helix From the Simplest Children's Toy: The Equilateral Triangle, World Congress on Physics, 2019-10-17/10-18, Berlin (DE), pp.14, 2019
7.  Wojnar R., Kinetic equation for the pair distribution function in the Boltzmann gas, 32nd Marian Smołuchowski Symposium on Statistical Physics, 2019-09-18/09-20, Kraków (PL), pp.35, 2019
8.  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
9.  Wojnar R., Movement of coincidence grain boundaries with sigma = 7,13,19,...,49,...,91,...: from isotropy to anisotropy, SolMech 2018, 41st SOLID MECHANICS CONFERENCE, 2018-08-27/08-31, Warszawa (PL), pp.250-251, 2018
10.  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
11.  Gambin B., Kruglenko E., Wojnar R., Macroscopic thermal properties of quasi-linear cellular medium on example of the liver tissue, NHT 2015, Numerical Heat Transfer 2015 – Eurotherm Seminar No. 109, 2015-09-27/09-30, Warszawa (PL), pp.177-178, 2015

Streszczenie:
After discovery of strong sonar systems, it was realized that the high intensity ultrasound waves can be dangerous for biological organisms. This observation led to research in tissue heating effects. The liver tissue from mathematical point of view can be considered as a micro-periodic cellular medium, and in circumstances justified by biological reasons, the mathematical methods of homogenisation developed for micro-periodic media can be applied to determine some overall properties of the tissue. Fourier’s heat diffusion term in Pennes’ equation is the point of departure in our analysis, [1, 2, 3]. The liver, the largest internal organ in the human body, is connected to two large blood vessels, the hepatic artery and the portal vein. The hepatic artery carries oxygen-rich blood from the aorta, whereas the portal vein carries blood rich in digested nutrients from the entire gastrointestinal tract and also from the spleen and pancreas. These blood vessels subdivide into small capillaries known as liver sinusoids, which then lead to a lobule. A hepatic lobule is a small division of the liver defined at the histological scale. The lobules are arranged into an hexagonal lattice.
We have evaluated the dependence of effective conductivity λeff for the composite consisting of the basic cells arranged in a two-dimensional periodic system and built of the collagen capillaries filled with the water. Analytical and numerical results are going to be verified by measurement of temperature using magnetic resonance imaging (MRI) and through measurement of backscattered ultrasound waves.

Słowa kluczowe:
liver tissue, Pennes’ equation, heat transport, asymptotic homogenization, effective coefficients

Afiliacje autorów:
Gambin B. - IPPT PAN
Kruglenko E. - IPPT PAN
Wojnar R. - IPPT PAN
12.  Wojnar R., Gambin B., Thermal properties of biomaterials on the example of the liver, PCM-CMM 2015, 3rd Polish Congress of Mechanics and 21st Computer Methods in Mechanics, 2015-09-08/09-11, Gdańsk (PL), pp.267-268, 2015

Streszczenie:
Lionel Smith Beale, FRS, (1828–1906), a physician and microscopist in an evocative comparison wrote that the liver resembles a magnificent tree with its trunk and branches, with myriad of leaves, synthesizing and detoxifying. The liver in a human is about the size of football, equipped in a circulatory system and is made of about one million primary lobules which are almost identical, like the leaves of the tree. Therefore, the liver from mathematical point of view can be considered as a micro-periodic medium, and the mathematical methods of homogenisation developed for micro-periodic media can be applied to determine some overall properties of the tissue. Pennes’ equation of heat propagation in biological tissue is a quasi-nonlinear partial differential equation with coefficients depending on temperature T. It consists of three terms, one of which describes Fourier’s heat diffusion, with the diffusion coefficient depending on T. This term is a subject of this contribution.

Słowa kluczowe:
Pennes’ equation, micro-periodic structure, effective conductivity

Afiliacje autorów:
Wojnar R. - IPPT PAN
Gambin B. - IPPT PAN
13.  Wojnar R., Budowa kolagenu: geometria i fizyka, III National Conference of Nano and Micromechanics, 2012-07-04/07-06, Warszawa (PL), pp.169-170, 2012

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