Wyniki wyszukiwania - Biblioteka Nauki

1

High Conductivity Limits for Reaction-Diffusion Equations

100%

Zamani S.

Probability and Mathematical Statistics

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1999

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tom Vol. 19, Fasc. 1

63--75

EN

A reaction-diffusion equation an [0, 1] with the heat conductivity κ > 0, a polynomial drift term, and an additive random perturbation is considered. It is shown that if κ tends to infinity, then the corresponding solutions of the equation converge to a process satisfying an ordinary Itô equation.

2

Differential quadrature methodfor some diffusion-reaction problems

75%

Szukiewicz M. K.

Chemical and Process Engineering

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2020

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tom Vol. 41, nr 1

3--11

EN

In the paper, differential quadrature method (DQM) is used to find numerical solutions of reaction-diffusion equations with different boundary conditions. The DQM-method changes the reaction-diffusion equation (ordinary differential equation) into a system of algebraic equations. The obtainedsystem is solved using built-in procedures of Maple®(Computer Algebra System-type program).Calculations were performed with Maple®program. The test problems include reaction-diffusionequation applied in heterogeneous catalysis. The method can be employed even in relatively hard tasks(e.g. ill-conditioned, free boundary problems).

3

A study on efficiency of 3D partial differential diffusive model of presynaptic processes

63%

Bielecki A. , Gierdziewicz M. , Kalita P.

Biocybernetics and Biomedical Engineering

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2020

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tom Vol. 40, no. 1

100--110

EN

The verification of efficiency of the diffusive-type model of neurotransmitter transport dynamics inside the presynaptic bouton, including the spatial aspect of the transport, is the main objective of the simulations described in this paper. Finite element and finite difference methods were applied to solve the model numerically. The bouton was represented by a 3D tetrahedral mesh. Some biological parameters have been taken from scientific literature whereas some other remain unknown. Therefore the simulations were performed for various values of the unknown parameters. Such an approach allowed us to assess the proper order of magnitude of those parameters by comparison of the dynamics of the process implied by the model with the observed post-synaptic potentials. The effect of synaptic depression has been captured in the simulations. The presented approach allowed us to verify to what extent the presynaptic transport can be explained by the diffusive mechanism. Furthermore, the sensitivity of the model to release rate and the synthesis rate is considered. Moreover, the algebraic models of the diminishment of released neurotransmitter amounts were proposed and tested, showing a good accuracy. Various geometrical aspects of the dynamics were studied. In particular, the influence of the geometry of the synthesis region was examined. In the paper, the aspects of numerical simulations are studied as well. Namely, the quality of the generated mesh was discussed. The results of the simulations were compared with the results of measurements and observations and will be later contrasted with more complex models.

4

Logistic equations in tumour growth modelling

63%

Foryś U. , Marciniak-Czochra A.

International Journal of Applied Mathematics and Computer Science

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2003

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tom 13

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nr 3

317-325

EN

The aim of this paper is to present some approaches to tumour growth modelling using the logistic equation. As the first approach the well-known ordinary differential equation is used to model the EAT in mice. For the same kind of tumour, a logistic equation with time delay is also used. As the second approach, a logistic equation with diffusion is proposed. In this case a delay argument in the reaction term is also considered. Some mathematical properties of the presented models are studied in the paper. The results are illustrated using computer simulations.

5

Stability analysis and comparison of the models for carcinogenesis mutations in the case of two stages of mutations

63%

Foryś U.

Journal of Applied Analysis

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2005

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tom Vol. 11, nr 2

283-302

EN

The present paper is focused on the analysis of three very simple models of carcinogenesis mutations that are based on reaction-diffusion systems and Lotka-Volterra food chains. We consider the case with two stages of mutations and study the systems of three reaction-diffusion equations with zero-flux boundary conditions. We focus on the Turing instability and show that this type of instability is not possible for these models. We also propose some modifications of the considered equations. Results are illustrated by computer simulations.

6

Logistic Equations in Tumour Growth Modelling

51%

Foryś U. , Marciniak-Czochra A.

International Journal of Applied Mathematics and Computer Science

|

2003

|

tom Vol. 13, no 3

317-325

EN

The aim of this paper is to present some approaches to tumour growth modelling using the logistic equation. As the first approach the well-known ordinary differential equation is used to model the EAT in mice. For the same kind of tumour, a logistic equation with time delay is also used. As the second approach, a logistic equation with diffusion is proposed. In this case a delay argument in the reaction term is also considered. Some mathematical properties of the presented models are studied in the paper. The results are illustrated using computer simulations.