Wyniki wyszukiwania - BazTech

1

Analiza naprężeń w słupie OWS-7 obudowy wykopu firmy Kopras w zależności od położenia rozpory oraz od rozkładu parcia gruntu działającego na obudowę

Buczkowski Wiesław, Kopras Marek, Fleming Wojciech

Przegląd Budowlany

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2025

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R. 96, nr 3

77--84

PL

Artykuł prezentuje kompleksową analizę naprężeń w słupach systemowej obudowy słupowej, stosowanych do zabezpieczania głębokich wykopów. W badaniu uwzględniono wpływ różnych schematów rozkładu parcia gruntu, takich jak równomierny, hydrostatyczny oraz modele zaproponowane przez Terzaghiego, Klennera, Lehmanna i Siemińską-Lewandowską. Dodatkowo przeanalizowano znaczenie wysokości położenia rozpory rolkowej względem słupa i jej wpływ na generowane naprężenia. Badania, przeprowadzone przy zastosowaniu metody różnic skończonych przy wykorzystaniu funkcjonału energii sprężystej pozwoliły na precyzyjną ocenę rozkładu momentów zginających w zależności od przyjętych założeń obciążeniowych. Wyniki wskazują, że schemat Terzaghiego generuje największe momenty zginające, przewyższając wartości wynikające z innych modeli, takich jak hydrostatyczny czy równomierny. Szczegółowa metodyka wraz z analizą wyników została zamieszczona w artykule. Artykuł podkreśla praktyczne znaczenie optymalnego doboru schematów obciążeń i konfiguracji konstrukcji w kontekście zwiększenia bezpieczeństwa oraz efektywności kosztowej obudów systemowych. Wyniki badania stanowią istotny krok w kierunku dalszej optymalizacji konstrukcji zabezpieczających wykopy i ich adaptacji do zmiennych warunków gruntowych.

EN

The article presents a comprehensive analysis of stresses in posts of a system shoring structure used for securing deep excavations. The study considers the impact of various soil pressure distribution schemes, such as uniform, hydrostatic, and models proposed by Terzaghi, Klenner, Lehmann, and Siemińska-Lewandowska. Additionally, the significance of the vertical position of the roller brace relative to the post and its effect on the generated stresses is analyzed. The research, conducted using the finite difference method and applying the elastic energy functional, enabled a precise evaluation of bending moment distribution based on the adopted load assumptions. The results indicate that Terzaghi’s scheme generates the highest bending moments, surpassing the values derived from other models, such as hydrostatic or uniform. Detailed methodology and analysis of the results are included in the article. The article emphasizes the practical importance of optimizing load distribution schemes and structural configurations to enhance safety and cost-efficiency in system shoring structures. The findings represent a significant step toward further optimization of excavation shoring designs and their adaptation to varying soil conditions.

2

Numerical analysis and experimental studies three-layer slabs of the Hoff

Sadowska-Buraczewska Barbara, Głodkowska Wiesława

Materiały Budowlane

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2025

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nr 7

1--9

EN

The paper concerns three-layer slabs of the Hoff in terms of their use as independent slab floor elements. Three variants of the panels were analyzed, differing in the material from which the cladding and the core of the board were made. The result of the analysis was to determine the relationship between the load of the three-layer slab and its vertical displacements (deflections). The practical possibility of using the variational finite difference approach (MRS) and the finite element method (FEM) for the calculation of plate three-layer elements of the Hoff and homogeneous, isotropic plates has been demonstrated. For three variants of the plate, computer simulations were carried out using these methods and experimental verification of one of the variants was carried out. The article presents only a fragment of extensive experimental and analytical research.

PL

W artykule zaprezentowano płyty trójwarstwowe Hoffa w aspekcie zastosowania ich jako samodzielnych płytowych elementów stropowych. Przeanalizowano trzy warianty płyt z różnymi okładzinami i rdzeniem. Wynikiem analiz było określenie zależności pomiędzy wielkością obciążenia płyty trójwarstwowej a jej przemieszczeniami pionowymi (ugięciami). Wykazano praktyczną możliwość stosowania metody wariacyjnego ujęcia różnic skończonych (MRS) i metody elementów skończonych (MES) do obliczania płytowych elementów trójwarstwowych Hoffa oraz izotropowych płyt jednorodnych. Przeprowadzono symulacje komputerowe tymi metodami trzech wariantów płyty oraz dokonano weryfikacji doświadczalnej jednego z wariantów. W artykule przedstawiono tylko fragment szerokich badań doświadczalnych i analitycznych.

3

The waveform comparison of three fractional viscous acoustic wave equations

Wang Dan, Wang Zhiliang, Zhang Xinmin, Huang Rong, Song Ziang, Song Guojie

Acta Geophysica

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2025

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Vol. 73, no. 1

311--320

EN

The forward simulation of the viscous acoustic wave equation is essential for understanding wave propagation and seismic inversion. The viscous acoustic seismic wave equations are diverse, even if we limit the study scope to the fractional viscous wave equations. In present study, we consider three Riesz fractional viscous wave equations: the Fractional Viscous Acoustic Wave (FVAW) equation, Dispersion-Dominated Wave (DDW) equation, and Attenuation-Dominated Wave (ADW) equation. The Acoustic Wave (AW) equation, as a special fractional wave equation, is used to compare with the three fractional viscous acoustic equations. The Asymptotic Local Finite Difference (ALFD) method is adopted to solve the fractional derivative term; while, the Lax-Wendroff Correction (LWC) scheme is used to solve the integer derivative term. The analysis results indicate that the numerical scheme of the ADW equation exhibits the most rigorous stability condition, and that of the DDW equation is the most flexible. When the product of complex wavenumber k and spatial step size h equal to π, the maximum phase velocity errors of the FVAW equation, DDW equation, ADW equation, and AW equation are 27.78%, 28.02%, 2.25%, and 3.04%, respectively. Numerical experiments demonstrate that the FVAW equation not only governs the arrival time but also influences the amplitude. The DDW equation governs the arrival time but not amplitude; while, the ADW equation controls the amplitude but not arrival time. As the quality factor Q decreases, the viscous features of these three wave equations become pronounced. The change of amplitude is more noticeable than that of arrival time, suggesting that arrival time is more robust than amplitude. Based on these findings, we suggest incorporating the step for selecting the governing equations when dealing with practical Full-Waveform Inversion, which is helpful to improve the accuracy and reliability of the inversion results. Our results not only emphasize the importance of understanding the behavior of viscous wave equations, but also provide waveform evidence for selecting seismic governing equations in Full-Waveform Inversion.

4

Numerical simulation of oxygen distribution in soft tissue exposed to an external heat impulse

Zadoń Maria, Jasiński Marek

Journal of Applied Mathematics and Computational Mechanics

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2024

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Vol. 23, nr 4

133--144

EN

The purpose of this study is to analyse the effect of elevated temperature on oxygen distribution in biological tissue. The effect of temperature and thermal tissue damage on the values of thermophysical parameters was considered. Changes in the perfusion coefficient affect blood velocity in the capillary, thereby influencing the distribution of partial oxygen pressure. In the tissue area, the effect of myoglobin was taken into account. Furthermore, the effect of mitochondrial clustering on oxygen distribution was also analysed. The finite difference method and the shooting method were used in the numerical implementation stage.

5

Optimization of Rectangular Tank Cross-Section Using Trust Region Gradient Method

Grabowski Tomasz, Szymczak-Graczyk Anna, Rutkowski Janusz

Inżynieria Mineralna

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2024

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Vol. 1, no. 2

art. no. 99

EN

In various industries, rectangular tanks are commonly used for storing liquids and other materials. The design and optimization of these tanks are crucial for ensuring structural integrity and material efficiency. Traditional designs often utilize constant wall thickness, which does not align optimally with the stress distribution, leading to potential overuse of materials and increased costs. Recent studies have shown that tanks with variable wall thickness, such as trapezoidal cross-sections, can better match stress distributions, particularly under hydrostatic loads, resulting in more efficient use of materials. This research aims to build upon previous studies by introducing an advanced optimization algorithm based on the Trust Region Gradient Method to further refine the cross-sectional design of rectangular tanks. The primary objective is to minimize the material usage while maintaining structural safety and performance under various load conditions, including hydrostatic pressure and thermal effects. The proposed algorithm iteratively adjusts the tank's wall thickness, seeking an optimal configuration that reduces bending moments and material costs. Initial static calculations is verified using the finite difference method, emphasizing energy minimization conditions for elastic strain in bent plates on elastic foundations. This approach is compared with traditional discretization methods to validate accuracy. The trust region method is then applied to optimize the design, with a focus on achieving a balance between structural integrity and economic feasibility. Preliminary results indicate that the trust region gradient method can significantly enhance the design process, leading to substantial material savings and improved structural performance. The algorithm's effectiveness is demonstrated through case studies comparing tanks with constant and variable wall thickness. This research contributes to sustainable construction practices by promoting designs that use materials more efficiently and meet safety standards.

6

Influence of Geometric Parameters on Internal Forces in the Walls of Rectangular Tanks

Szymczak-Graczyk Anna, Grabowski Tomasz, Ksit Barbara

Inżynieria Mineralna

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2024

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Vol. 1, no. 2

art. no. 27

EN

Rectangular tanks are commonly used in various industries for storing materials and products. The design of reinforced concrete liquid tanks, which must be preceded by a static analysis, is a complex issue requiring specialized knowledge and engineering experience. All types of actions, design situations, and resulting load combinations must be considered, including deformations caused by temperature gradients and the interaction of the bottom plate with the ground. Most tanks are designed and constructed with constant wall thickness, regardless of their rectangular or circular cross-section. However, tanks with variable wall thickness (e.g., trapezoidal cross-section) are rarely designed, despite their optimal fit to stress distribution. For hydrostatically loaded tanks, the load on walls increases with depth, causing the highest bending moments at the wall-bottom connection, while the value at the top, free edge is zero. Thus, structural and economic considerations favour walls with thickness increasing with depth. This article presents the results of a verification of static calculations of a monolithic rectangular tank with trapezoidal cross-section walls, comparing it with three other commonly designed tanks with different thickness and wall designs. Static calculations were performed using the finite difference method in terms of energy, employing the condition for the minimum energy of elastic strain stored in a bent plate resting on the elastic base. Traditional calculation methods were used by discretizing the object and creating systems of equations. Analysis of the results shows that constructing walls of linearly variable thickness results in a redistribution of bending moments compared to tanks with uniform wall thickness. This significantly impacts the required reinforcement area. Tanks with linearly variable wall thickness are more economical in terms of material use, aligning with the principles of sustainable construction.

7

Modeling of photochemical and photothermal effects in soft tissue subjected to laser irradiation

Jasiński Marek, Zadoń Maria

Computer Assisted Methods in Engineering and Science

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2024

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Vol. 31, no. 1

29--50

EN

The purpose of this study is to analyze the phenomena that occur in biological tissueduring photodynamic therapy (PDT). Under the influence of the laser, triplet oxygen istransformed into singlet oxygen, which is cytotoxic to cancer tissue. The impact of thelaser on the tissue may also be accompanied by changes in the thermophysical parameters,e.g., perfusion, which can affect the supply of oxygen to the tissue and, consequently,the outcome of the therapy. The proposed model uses the optical diffusion equation,the Pennes bioheat transfer equation, and reactions equations for PDT. The connectionbetween bioheat transfer and PDT models is taken into account through the respectiverelationships between perfusion rate, capillary blood velocity, and the maximum oxygensupply rate. Furthermore, a method is proposed to model abnormal vascular patterns inthe tumor subdomain. The boundary element method and the finite difference methodwere used in the numerical implementation stage.

8

A blow up of solutions for a system of Klein-Gordon equations with variable exponent : theoretical and numerical results

Gözen Sedanur Mazi, Yılmaz Nebi, Pişkin Erhan, Okutmustur Baver

Mathematica Applicanda

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2023

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Vol. 51, no. 2

143--164

EN

In this paper, we consider a system of Klein-Gordon equations with variable exponents. The first part of the manuscript is devoted to the proof of the blow up of solutions with negative initial energy under suitable conditions on variable exponents and initial data. The theoretical part is supported by numerical experiments based on P1-finite element method in space and the BDF and the Generalized-alpha methods in time illustrated in the second part. The numerical and analytical results of the blow up solutions agree with each other.

PL

Praca poświęcona jest układowi równań Kleina-Gordona ze zmiennymi wykładnikami. W pierwszej części pokazano, że rozwiązania o ujemnej energii początkowej uciekają do nieskończoności przy odpowiednich warunkach na wykładniki oraz dane początkowe. Część teoretyczną uzupełniają obliczenia numeryczne oparte na metodzie elementu skończonego dla zmiennych przestrzennych oraz metodzie różniczkowania wstecz (Backward Differentiation Formula, BDF). Wyniki numeryczne i analityczne dotyczące wybuchowego charakteru rozwiązań wzajemnie potwierdzają się.

9

Projektowanie obudowy tunelu z wykorzystaniem metody kontroli konwergencji

Blajer Mateusz

Materiały Budowlane

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2023

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nr 5

10--13

PL

W artykule przedstawiono wykorzystanie metody kontroli konwergencji do weryfikacji obudowy tunelu drążonego w warunkach fliszu karpackiego. Bazuje ona na obliczeniach numerycznych MES lub MRS i stanowi rozwinięcie metod analitycznych i seminumerycznych, które wykorzystywano w początkach jej stosowania. Dzięki użyciu modeli MES lub MRS możliwe jest odwzorowanie tak skomplikowanego ośrodka, jakim jest flisz karpacki i jego (w większości przypadków) asymetrycznego oddziaływania. Obecnie jedynie przestrzenne modele MES i MRS przewyższają opisywaną metodę pod względem możliwości obliczeniowych.

EN

The paper presents the use of the convergence confinement method for designing and verifying the tunnel lining in the conditions of the Carpathian flysch. It is based on numerical calculations using FEM or FDM and it is a development of the analytical and semi-analytical methods that were used at the beginning of its application. By using FEM or FDM models, it is possible to reproduce such a complex medium as the Carpathian flysch and its (mostly asymmetric) actions. Currently, only spatial FEM and FDM models exceed the described method in terms of computational capabilities.

10

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.

11

Numerical solution of a malignant invasion model using some finite difference methods

Appadu Appanah Rao, de Waal Gysbert Nicolaas

Demonstratio Mathematica

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2023

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Vol. 56, nr 1

art. no. 20220244

EN

In this article, one standard and four nonstandard finite difference methods are used to solve a cross-diffusion malignant invasion model. The model consists of a system of nonlinear coupled partial differential equations (PDEs) subject to specified initial and boundary conditions, and no exact solution is known for this problem. It is difficult to obtain theoretically the stability region of the classical finite difference scheme to solve the set of nonlinear coupled PDEs, this is one of the challenges of this class of method in this work. Three nonstandard methods abbreviated as NSFD1, NSFD2, and NSFD3 are considered from the study of Chapwanya et al., and these methods have been constructed by the use of a more general function replacing the denominator of the discrete derivative and nonlocal approximations of nonlocal terms. It is shown that NSFD1, which preserves positivity when used to solve classical reaction-diffusion equations, does not inherit this property when used for the cross-diffusion system of PDEs. NSFD2 and NSFD3 are obtained by appropriate modifications of NSFD1. NSFD2 is positivity-preserving when the functional relationship [ψ(h)]2=2ϕ(k) holds, while NSFD3 is unconditionally dynamically consistent with respect to positivity. First, we show that NSFD2 and NSFD3 are not consistent methods. Second, we tried to modify NSFD2 in order to make it consistent but we were not successful. Third, we extend NSFD3 so that it becomes consistent and still preserves positivity. We denote the extended version of NSFD3 as NSFD5. Finally, we compute the numerical rate of convergence in time for NSFD5 and show that it is close to the theoretical value. NSFD5 is consistent under certain conditions on the step sizes and is unconditionally positivity-preserving.

12

Application of genetic algorithm for double-lap adhesive joint design

Kurennov Sergei, Barakhov Konstantin, Polyakov Olexander, Taranenko Igor

Archive of Mechanical Engineering

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2023

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LXX, nr 1

27--42

EN

The problem of optimal design of symmetrical double-lap adhesive joint is considered. It is assumed that the main plate has constant thickness, while the thickness of the doublers can vary along the joint length. The optimization problem consists in finding optimal length of the joint and an optimal cross-section of the doublers, which provide minimum structural mass at given strength constraints. The classical Goland-Reissner model was used to describe the joint stress state. A corresponding system of differential equations with variable coefficients was solved using the finite difference method. Genetic optimization algorithm was used for numerical solution of the optimization problem. In this case, Fourier series were used to describe doubler thickness variation along the joint length. This solution ensures smoothness of the desired function. Two model problems were solved. It is shown that the length and optimal shape of the doubler depend on the design load.

13

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.

14

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.

15

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.

16

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.

17

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.

18

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

|

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.

19

Finite difference method for the fractional order pseudo telegraph integro-differential equation

Modanli Mahmut, Ozbag Fatih, Akgül Ali

Journal of Applied Mathematics and Computational Mechanics

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2022

|

Vol. 21, nr 1

41--54

EN

The main goal of this paper is to investigate the numerical solution of the fractional order pseudo telegraph integro-differential equation. We establish the first order finite difference scheme. Then for the stability analysis of the constructed difference scheme, we give theoretical statements and prove them. We also support our theoretical statements by performing numerical experiments for some fractions of order α.

20

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

|

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.