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1

Comparison of heat transfer phenomena for two different cryopreservation methods : slow freezing and vitrification

Skorupa Anna, Piasecka-Belkhayat Alicja

Journal of Applied Mathematics and Computational Mechanics

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2023

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Vol. 22, nr 1

57--69

EN

The purpose of the research is to prepare a mathematical and numerical model for the phenomenon of heat transfer during cryopreservation. In the paper, two popular methods, slow freezing and vitrification, are compared. Furthermore, the basic model of thermal processes is supplemented by the phenomenon of phase transitions. To determine the temperature distribution during cryopreservation processes, one uses the heat transfer equation proposed by Pennes. An integral part of the energy equation is the substitute thermal capacity (STC) performed according to the concept named one domain method (fixed domain method), The numerical model is developed using the finite difference method (FDM) connected with directed interval arithmetic. The final part of the article contains the results of numerical simulations.

2

Simulation of infeasible instruments in a sound synthesizer - implementation and control

Pluta Marek

Vibrations in Physical Systems

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2022

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Vol. 33, nr 2

art. no. 2022206

EN

Sound synthesis using mathematical modelling of musical instruments is a method particularly well suited for live performance using a physical controller. Depending on model complexity, it may be able to reproduce various subtle phenomena related to excitation and real time control of an instrument, providing an intuitive tool for a musician. A variant of physical modelling synthesis, referred to as the simulation of infeasible instruments, uses a model of an object that does not have a physical counterpart. Such model has some properties of a real object, which makes it still intuitive for a musician. However, other features, such as geometry, or material properties, are intentionally altered in such manner, that it could not function in reality. These infeasible features introduce new properties to the sound it produces. The study presents a few such models with a discussion regarding their implementation and control issues in a real-time sound synthesizer.

3

Wpływ konstrukcji budowlanej na propagację fal elektromagnetycznych

Choroszucho Agnieszka, Tymiński Jakub, Orzechowski Damian, Kondrusik Alan, Duchnowski Szymon Piotr

Napędy i Sterowanie

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2022

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R. 24, nr 12

22--27

PL

Praca przedstawia wpływ konstrukcji budowlanej na rozkład pola elektromagnetycznego wewnątrz części budynku. W analizowanym obszarze zamontowano źródło pola o częstotliwości związanej z komunikacją bezprzewodową (2,4 GHz). Artykuł zawiera dyskusję dotyczącą zjawisk fizycznych związanych z propagacją fali elektromagnetycznej w złożonych konstrukcjach zawierających beton, zbrojenie i cegły. Zastosowano numeryczną metodę różnic skończonych w dziedzinie czasu (FDTD). Analizowany obszar modelowano według typowych budowlanych technologii. Dokładna analiza wyników może przyczynić się do rozwiązania problemu związanego z zanikami sygnału i problemem związanym z komunikacją bezprzewodową.

4

Numerical solution of MHD channel flow in a porous medium with uniform suction and injection in the presence of an inclined magnetic field

Chutia Muhim

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 2

5--13

EN

In this paper, the steady fully developed MHD flow of a viscous incompressible electrically conducting fluid through a channel filled with a porous medium and bounded by two infinite walls is investigated numerically for the cases (i) Poiseuille flow and (ii) Couette-Poiseuille flow; with uniform suction and injection at the walls in the presence of an inclined magnetic field. The Brinkman equation is used for the flow in the porous channel and solved numerically using the finite difference method. Numerical results are obtained for velocity. The effects of various dimensionless parameters such as Hartmann number (M), suction/injection parameter (S), permeability parameter (α) and angle of inclination (θ) on the flow are discussed and presented graphically.

5

Numerical analysis of thermal damage and oxygen distribution in laser irradiated tissue

Jasiński Marek

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 2

51--62

EN

A numerical analysis of the thermal damage process that proceeds in biological tissue during laser irradiation is presented. Heat transfer in the tissue is assumed to be transient and two-dimensional. The internal heat source resulting from the laser irradiation based on the solution of optical diffusion equation is taken into account. Changes in tissue oxygen distribution resulting from temperature changes are analyzed using the Krogh cylinder model with Michaelis-Menten kinetics. A Hill model was used to describe the oxyhemoglobin dissociation curve. At the stage of numerical realization, the boundary element method and the finite difference method have been applied.

6

Numerical analysis of biological tissue heating using the dual-phase lag equation with temperature – dependent parameters

Majchrzak Ewa, Stryczyński Mikołaj

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 3

85--98

EN

The dual-phase lag equation is formulated for the case when the thermophysical parameters occurring in this equation are temperature-dependent. The axial-symmetrical domain of biological tissue heated by an external heat source is considered. The problem is solved using the implicit scheme of the finite difference method. At the stage of numerical computations, the analytical relationships taken from the literature describing changes in parameters are taken into account.

7

Mathematical modeling of the phenomena that occur in a biological tissue containing photosensitizer

Jasiński Marek, Zadoń Maria

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 4

40--51

EN

The aim of the study is to analyze photothermal and photochemical phenomena that occur during photodynamic therapy (PDT). In this type of therapy, under the influence of the laser, reactions take place related to the transformation of triplet oxygen form into its singlet form which is cytotoxic to the tissue. The increases in temperature resulting from the laser-tissue interaction during PDT are not big; however, they can lead to changes in tissue perfusion, which can affect oxygen delivery to the tissue. The proposed model uses optical diffusion equation, Pennes bioheat transfer equation, and reactions equations for PDT. The main findings of the analysis show the impact of temperature on the value of the perfusion coefficient and triplet oxygen distributions at the end of the treatment procedure.

8

An extended finite difference method for singular perturbation problems on a non-uniform mesh

Swarnakar D., Kumar V. Ganesh, Soujanya G. B. S. L.

International Journal of Applied Mechanics and Engineering

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2022

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Vol. 27, no. 1

203--214

EN

An extended second order finite difference method on a variable mesh is proposed for the solution of a singularly perturbed boundary value problem. A discrete equation is achieved on the non uniform mesh by extending the first and second order derivatives to the higher order finite differences. This equation is solved efficiently using a tridiagonal solver. The proposed method is analysed for convergence, and second order convergence is derived. Model examples are solved by the proposed scheme and compared with available methods in the literature to uphold the method.

9

Analysis of traffic load effects in railway backfilled arch bridges

Kamiński Tomasz, Machelski Czesław

Archives of Civil Engineering

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2022

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Vol. 68, nr 2

243--260

EN

The problem of the arch barrel deformation in railway backfilled arch bridges caused by their typical service loads is analysed. The main attention is paid to vertical or radial displacements of characteristic points of the arch barrel. In the study results of deflection measurements carried out on single and multi-span backfilled arch bridges made of bricks or plain concrete during passages of various typical railway vehicles are used. On the basis of such results empirical influence functions of displacements are being created. In the next step, the results are utilised to estimate bending effects within the arch. The paper includes different procedures based on measurements of displacements in various points and directions. Using empirical influence functions arbitrary virtual load cases may be also considered. In this manner the proposed methodology shows a potential to be an effective tool of comprehensive calibration of numerical models of backfilled arch bridges on the basic of field tests carried out under any live loads.

PL

Artykuł skupia się na zagadnieniu przemieszczeń sklepień mostów murowanych wywołanych ich typowymi obciążeniami użytkowymi. Szczególna uwaga zwrócona jest na pomiar przemieszczeń pionowych i radialnych w charakterystycznych punktach sklepienia. W przedstawionych przykładach rozpatrzono zachowanie jedno- i wieloprzęsłowych mostów łukowych opartych na sklepieniach murowanych i betonowych pod obciążeniem przejeżdżającymi pojazdami kolejowymi różnego rodzaju. Na podstawie otrzymanych wyników pomiarów terenowych prowadzonych na powyższych obiektach stworzono doświadczalne funkcje wpływu przemieszczeń. W kolejnym kroku uzyskane wyniki wykorzystywane są do wyznaczenia momentów zginających w sklepieniu. W artykule przedstawiono odmienne procedury postępowania bazujące na pomiarach przemieszczeń w różnych kierunkach i w różnie rozmieszczonych punktach. Szczególną zaletą przedstawionego całościowego podejścia jest możliwość wykonania pożądanych pomiarów podczas standardowej eksploatacji mostu bez jakiegokolwiek zakłócania ruchu taboru, co w wielu sytuacjach czyni przeprowadzenie tego typu badań w ogóle możliwymi. Przyjęte schematy postępowania są szczególnie skuteczne w przypadku obiektów kolejowych charakteryzujących się regularnością i łatwości w identyfikacji ich schematów obciążeń reprezentowanych zwłaszcza przez lokomotywy. Niemniej jednak przedstawione podejście może być wykorzystane również w analizie mostów drogowych. Podane procedury mogą opierać się też na innych efektach statycznych (przemieszczeniach i odkształceniach w dowolnych kierunkach) mierzonych w dowolnych punktach konstrukcji. Zaproponowaną metodykę można wykorzystywać, co również zobrazowano w artykule, jako efektywne narzędzie do wszechstronnej kalibracji modeli numerycznych mostów sklepionych obejmującej np. weryfikację ich parametrów materiałowych, niewidocznej geometrii czy, w przypadku modeli dwuwymiarowych, ich szerokości efektywnej.

10

A new numerical scheme for solving the two dimensional fractional diffusion equation

Altan Koç Dilara, Gülsu Mustafa

Journal of Applied Mathematics and Computational Mechanics

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2021

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Vol. 20, nr 2

5--16

EN

In this study, the locally one dimensional (LOD) method is used to solve the two dimensional time fractional diffusion equation. The fractional derivative is the Caputo fractional derivative of order α. The rate of convergence of the finite difference method is presented. It is seen that this method is in agreement with the obtained numerical solutions with acceptable central processing unit time (CPU time). Error estimates, numerical and exact results are tabulated. The graphics of errors are given.

11

The implicit numerical method for the one-dimensional anomalous subdiffusion equation with a nonlinear source term

Błasik Marek

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2021

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Vol. 69, nr 6

art. no. e138240

EN

In the paper, the numerical method of solving the one-dimensional subdiffusion equation with the source term is presented. In the approach used, the key role is played by transforming of the partial differential equation into an equivalent integro-differential equation. As a result of the discretization of the integro-differential equation obtained an implicit numerical scheme which is the generalized Crank-Nicolson method. The implicit numerical schemes based on the finite difference method, such as the Carnk-Nicolson method or the Laasonen method, as a rule are unconditionally stable, which is their undoubted advantage. The discretization of the integro-differential equation is performed in two stages. First, the left-sided Riemann-Liouville integrals are approximated in such a way that the integrands are linear functions between successive grid nodes with respect to the time variable. This allows us to find the discrete values of the integral kernel of the left-sided Riemann-Liouville integral and assign them to the appropriate nodes. In the second step, second order derivative with respect to the spatial variable is approximated by the difference quotient. The obtained numerical scheme is verified on three examples for which closed analytical solutions are known.

12

Investigation of fault zone induced site effect in the İzmit basin, Turkey

Firtana-Elcomert Karolin, Kocaoğlu Argun

Acta Geophysica

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2021

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Vol. 69, no. 6

2069--2083

EN

The seismic hazard in the İzmit basin, located in Marmara region of western Turkey, is high due to the northern branch of the North Anatolian Fault (NAF) and the potential ground motion amplification that may be caused by local site conditions, sedimentary basin effect as well as fault zone (FZ) induced site effect resulting from the generation of guided waves. In this study, we elaborate the relevance of the FZ-induced site effect in the İzmit basin along a 16.5-km-long N-S profile across the basin and perpendicular to the NAF by time and frequency domain analysis of waveforms obtained from two-dimensional (2D) simulations of viscoelastic wave propagation for a double-couple source at 14 km depth using a reference (basin-only) model and three basin-with-fault models: shallow (6 km), intermediate (12 km) and deep (19 km) FZ models. Our results show that the FZ-induced site effect within and near the northern branch of NAF in the İzmit basin can be very prominent with amplification of about 5–10 in the frequency range of 0.05–4 Hz and about 20 at frequencies above 2 Hz, respectively. We obtain the most dramatic results for the deep FZ model causing shear- and surface-wave amplification of about 15 at frequencies higher than 2.5 Hz for the distances between 6 and 13 km.

13

The finite difference method on adaptive mesh for singularly perturbed nonlinear 1D reaction diffusion boundary value problems

Duru Hakkı, Güneş Baransel

Journal of Applied Mathematics and Computational Mechanics

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2020

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Vol. 19, nr 4

45--56

EN

In this paper, we study singularly perturbed nonlinear reaction-diffusion equations. The asymptotic behavior of the solution is examined. The difference scheme which is accomplished by the method of integral identities with using of interpolation quadrature rules with weight functions and remainder term integral form is established on adaptive mesh. Uniform convergence and stability of the difference method are discussed in the discrete maximum norm. The discrete scheme shows that orders of convergent rates are close to 2. An algorithm is presented, and some problems are solved to validate the theoretical results.

14

Numerical simulation of channel flow over a skewed equilateral cavity

Kamel Abanoub G., Haraz Eman H., Hanna Sarwat N.

Journal of Applied Mathematics and Computational Mechanics

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2020

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Vol. 19, nr 3

29--43

EN

In this paper, an incompressible, two-dimensional (2D), time-dependent, Newtonian, laminar, and internal channel fluid flow over a skewed equilateral cavity is simulated using the finite difference method (FDM) and alternating direction implicit (ADI) technique. Navier-Stokes equations are solved numerically in stream function-vorticity formulation. The goal of tackling this problem depends on its academic significance by studying the difference between lid-driven and shear-driven cavity flows in terms of the formation of Moffatt eddies at the sharp corner, also to obtain the length and intensity ratios of these counter-rotating vortices. The value of velocity components along the centerlines of the skewed cavity was revealed at low and intermediate Reynolds numbers (Re), typically (Re = 200 and 2000) at two different skew angles of mainly 30° and 45°. Likewise, the blocked-off regions’ method is used to deal with the geometry of the skewed cavity especially the sharp corners. Furthermore, as Re increases, the main vortex approaches the skewed cavity center and the counter-rotating vortices get bigger in size and intensity, and their number increases.

15

Numerical analysis of the temperature impact to the oxygen distribution in the biological tissue

Jasiński Marek

Journal of Applied Mathematics and Computational Mechanics

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2020

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Vol. 19, nr 3

17--28

EN

The aim of the study was to analyze changes in tissue oxygen distribution resulting from temperature changes by the use of the Krogh cylinder model with Michaelis-Menten kinetics. A Hill model was also used to describe the oxyhemoglobin dissociation curve. In particular, variable values of parameters of dissociation curve and blood velocity in capillary were considered. Mathematical description was based on two separate equations for radial and axial directions. An additional task related to determination of the temperature, tissue thermal damage and perfusion was also solved. At the stage of numerical realization, the finite difference method was used.

16

Modeling of heat transfer and fluid flow in a rectangular channel with an obstacle

Stryczyński Mikołaj, Majchrzak Ewa

Journal of Applied Mathematics and Computational Mechanics

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2020

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Vol. 19, nr 2

121--132

EN

Heat transfer and fluid flow in the rectangular channel with an obstacle are considered. The problem is described by the Fourier-Kirchhoff equation, Navier-Stokes equations and continuity equation supplemented by appropriate boundary and initial conditions. To solve this system of equations the finite difference method with a staggered grid is used. The results of computations obtained using authorial computer program are compared with ANSYS Fluent simulation. Computations are carried out for obstacles of various sizes and positions, and on this basis the conclusions are formulated.

17

Effects of the porous boundary and inclined magnetic field on MHD flow in a rectangular duct

Chutia Muhim

Journal of Applied Mathematics and Computational Mechanics

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2020

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Vol. 19, nr 4

33--44

EN

In this work, a steady two dimensional MHD flow of a viscous incompressible fluid through a rectangular duct under the action of an inclined magnetic field with a porous boundary has been investigated. The coupled partial differential equations are transformed into a system of algebraic equations using the finite difference method and are then solved simultaneously using the Gauss Seidal iteration method by programming in Matlab software. Numerical solutions for velocity, induced magnetic field and current density lines are obtained and analyzed for different values of dimensionless parameters namely suction/injection parameter (S), Hartmann number (M) and inclination angle (θ) and are presented graphically.

18

Numerical analysis of the transient and non-isothermal channel flow of a third-grade fluid with convective cooling

Chinyoka Tiri, Makinde Oluwole Daniel

Engineering Transactions

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2020

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Vol. 68, iss. 4

335--351

EN

We investigate the unsteady, non-isothermal, pressure driven channel flow of a third grade liquid subject to exothermic reactions. We assume temperature dependent fluid viscosity and also that the flow is subjected to convective cooling at the channel walls. The exothermic reactions are modelled via Arrhenius kinetics and the convective heat exchange with the ambient at the channel walls follows Newton’s law of cooling. The time-dependent, coupled, and nonlinear partial differential equations governing the flow and heat transfer problem are solved numerically using efficient, semi-implicit finite difference algorithms. The sensitivity of the fluid flow and heat transfer system to the various embedded parameters is explored.

19

Combination of artificial neural networks and numerical modeling for predicting deformation modulus of rock masses

Tayarani Narges Saadat, Jamali Saeed, Zadeh Mehdi Motevalli

Archives of Mining Sciences

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2020

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Vol. 65, no. 2

337--346

EN

The deformation modulus of the rock mass as a very important parameter in rock mechanic projects generally is determined by the plate load in-situ tests. While this test is very expensive and time-consuming, so in this study a new method is developed to combin artificial neural networks and numerical modeling for predicting deformation modulus of rock masses. For this aim, firstly, the plate load test was simulated using a Finite Difference numerical model that was verified with actual results of the plate load test in Pirtaghi dam galleries in Iran. Secondly, an artificial neural network is trained with a set of data resulted from numerical simulations to estimate the deformation modulus of the rock mass. The results showed that an ANN with five neurons in the input layer, three hidden layers with 4, 3 and 2 neurons, and one neuron in the output layer had the best accuracy for predicting the deformation modulus of the rock mass.

20

Identification of boundary heat flux assuring the destruction of target region of biological tissue application of the generalized dual-phase lag model and gradient method

Turchan Łukasz, Majchrzak Ewa

Computer Assisted Methods in Engineering and Science

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2019

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Vol. 26, no. 1

21--34

EN

In this paper, an axially symmetrical biological tissue domain subjected to an external heat source is analyzed. The thermal processes occurring in the domain considered are described using the generalized dual-phase lag model supplemented by the Neumann boundary conditions and the appropriate initial conditions. The problem of tissue heating is solved using the implicit scheme of the finite difference method. The obtained solution allows one to determine the local and temporary values of the Arrhenius integral. Next, the inverse problem related to the identification of the boundary heat flux assuring the postulated destruction of the tissue target region is considered. The problem is solved using the gradient method. In the final part of the paper, the results of computations and the conclusions are presented.