scholarly journals Coupled Systems of Linear Differential-Algebraic and Kinetic Equations with Application to the Mathematical Modelling of Muscle Tissue

2020 ◽  
pp. 357-395
Author(s):  
Steffen Plunder ◽  
Bernd Simeon
Keyword(s):  
Mathematical Modelling ◽  
Muscle Tissue ◽  
Kinetic Equations ◽  
Coupled Systems ◽  
Linear Differential

scholarly journals Mathematical Modelling of Deforestation Due to Population Density and Industrialization

Jurnal Varian ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 9-16
Author(s):  
Didiharyono D. ◽  
Irwan Kasse
Keyword(s):  
Numerical Simulation ◽  
Population Density ◽  
Mathematical Modelling ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Stability Criteria ◽  
Hurwitz Stability ◽  
Stable Conditions ◽  
Linear Differential ◽  
The Stability

The focus of the study in this paper is to model deforestation due to population density and industrialization. To begin with, it is formulated into a mathematical modelling which is a system of non-linear differential equations. Then, analyze the stability of the system based on the Routh-Hurwitz stability criteria. Furthermore, a numerical simulation is performed to determine the shift of a system. The results of the analysis to shown that there are seven non-negative equilibrium points, which in general consist equilibrium point of disturbance-free and equilibrium points of disturbances. Equilibrium point TE7(x, y, z) analyzed to shown asymptotically stable conditions based on the Routh-Hurwitz stability criteria. The numerical simulation results show that if the stability conditions of a system have been met, the system movement always occurs around the equilibrium point.

scholarly journals Mathematical Modelling of Isothermal Decomposition ofAustenite in Steel

Metals ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 1292
Author(s):  
Božo Smoljan ◽  
Dario Iljkić ◽  
Sunčana Smokvina Hanza ◽  
Krunoslav Hajdek
Keyword(s):  
Computer Simulation ◽  
Mathematical Modelling ◽  
Kinetic Equations ◽  
Isothermal Heat Treatment ◽  
Isothermal Decomposition ◽  
Treatment Results ◽  
Optimization And Control ◽  
Complex Engineering ◽  
Indispensable Tool ◽  
And Control

The main goal of this paper is mathematical modelling and computer simulation of isothermal decomposition of austenite in steel. Mathematical modelling and computer simulation of isothermal decomposition of austenite nowadays is becoming an indispensable tool for the prediction of isothermal heat treatment results of steel. Besides that, the prediction of isothermal decomposition of austenite can be applied for understanding, optimization and control of microstructure composition and mechanical properties of steel. Isothermal decomposition of austenite is physically one of the most complex engineering processes. In this paper, methods for setting the kinetic expressions for prediction of isothermal decomposition of austenite into ferrite, pearlite or bainite were proposed. After that, based on the chemical composition of hypoeutectoid steels, the quantification of the parameters involved in kinetic expressions was performed. The established kinetic equations were applied in the prediction of microstructure composition of hypoeutectoid steels.

scholarly journals Optimisation of Synthetic Medium Composition for Levorin Biosynthesis by Streptomyces levoris 99/23 and Investigation of its Accumulation Dynamics Using Mathematical Modelling Methods

2010 ◽  
Vol 59 (3) ◽  
pp. 179-183
Author(s):  
VESELIN S. STANCHEV ◽  
LUBKA Y. KOZHUHAROVA ◽  
BORIANA Y. ZHEKOVA ◽  
VELIZAR K. GOCHEV
Keyword(s):  
Mathematical Modelling ◽  
Culture Medium ◽  
Synthetic Medium ◽  
Equation System ◽  
Medium Composition ◽  
Antibiotic Biosynthesis ◽  
Medium Components ◽  
Linear Differential ◽  
Modelling Methods ◽  
Streptomyces Levoris

The composition of a synthetic culture medium for levorin biosynthesis by Streptomyces levoris 99/23 was optimised using mathematical modelling methods. The optimal concentrations of the medium components were established by means of an optimum composition design at three factor variation levels. An adequate regression model was obtained. Levorin biosynthesis by Streptomyces levoris 99/23 in the optimised synthetic medium was over 38% higher than in the initial medium. The antibiotic biosynthesis dynamics in the optimised culture medium was studied by means of a non-linear differential equation system. The resultant model was valid.

How to Deal with Several Reservoirs

1991 ◽  
Author(s):  
James C. G. Walker
Keyword(s):  
Steady State ◽  
Euler Method ◽  
Coupled Systems ◽  
Algebraic Equations ◽  
Coupled Equations ◽  
Linear Algebraic Equations ◽  
Linear Differential ◽  
Surface Reservoir

The previous chapter showed how the reverse Euler method can be used to solve numerically an ordinary first-order linear differential equation. Most problems in geochemical dynamics involve systems of coupled equations describing related properties of the environment in a number of different reservoirs. In this chapter I shall show how such coupled systems may be treated. I consider first a steady-state situation that yields a system of coupled linear algebraic equations. Such a system can readily be solved by a method called Gaussian elimination and back substitution. I shall present a subroutine, GAUSS, that implements this method. The more interesting problems tend to be neither steady state nor linear, and the reverse Euler method can be applied to coupled systems of ordinary differential equations. As it happens, the application requires solving a system of linear algebraic equations, and so subroutine GAUSS can be put to work at once to solve a linear system that evolves in time. The solution of nonlinear systems will be taken up in the next chapter. Most simulations of environmental change involve several interacting reservoirs. In this chapter I shall explain how to apply the numerical scheme described in the previous chapter to a system of coupled equations. Figure 3-1, adapted from Broecker and Peng (1982, p. 382), is an example of a coupled system. The figure presents a simple description of the general circulation of the ocean, showing the exchange of water in Sverdrups (1 Sverdrup = 106 m3/sec) among five oceanic reservoirs and also the addition of river water to the surface reservoirs and the removal of an equal volume of water by evaporation. The problem is to calculate the steady-state concentration of dissolved phosphate in the five oceanic reservoirs, assuming that 95 percent of all the phosphate carried into each surface reservoir is consumed by plankton and carried downward in particulate form into the underlying deep reservoir. The remaining 5 percent of the incoming phosphate is carried out of the surface reservoir still in solution.

scholarly journals Mathematical modelling of light-induced electric reaction of Cucurbita pepo L. leaves

2014 ◽  
Vol 57 (2) ◽  
pp. 271-278 ◽  
Author(s):  
Jan Stolarek ◽  
Waldemar Karcz ◽  
Mariusz Pietruszka
Keyword(s):  
Differential Equation ◽  
Mathematical Modelling ◽  
Visible Light ◽  
Linear Differential Equation ◽  
Cucurbita Pepo ◽  
Plant Cells ◽  
Green Plant ◽  
Nitellopsis Obtusa ◽  
Linear Differential ◽  
Uv C

The bioelectRIc reactions of 14-16 day old plants of pumpkin (<em>Cucurbita pepo</em> L.) and internodal cells of <em>Nitellopsis obtusa</em> to the action of visible and ultraviolet light (UV-C) were studied. The possibility of analyzing the bioelectric reaction of pumpkin plants induced by visible light by means of mathematical modelling using a linear differential equation of the second order was considered. The solution of this equation (positive and negative functions) can, in a sufficient way, reflect the participation of H<sup>+</sup> and CI<sup>-</sup> ions in the generation of the photoelectric response in green plant cells.

scholarly journals On the problem of uncoupling systems of linear differential equations

1989 ◽  
Vol 30 (4) ◽  
pp. 483-501 ◽  
Author(s):  
James M. Hill ◽  
Alex McNabb
Keyword(s):  
Differential Equations ◽  
Solution Structure ◽  
Boundary Value ◽  
Problem Area ◽  
Coupled Systems ◽  
Linear Differential Equations ◽  
Kernel Matrix ◽  
Reaction Diffusion Systems ◽  
Dependent Variables ◽  
Linear Differential

AbstractIn modelling phenomena involving diffusion and chemical reactions, coupled systems of linear differential equations are often obtained, which can involve several dependent variables. For two dependent variables, coupled reaction-diffusion systems can be uncoupled, and in principle the original boundary value problem can be reduced to two separate boundary value problems for the classical heat equation. Here we address various aspects of the fundamental unsolved problem of the determination of corresponding uncoupling transformations for systems involving several dependent variables. We present, in an elementary manner, the current state of knowledge relating to this complex problem area. Several new results are obtained here. For example, in reviewing known results two dependent variables we observe that those systems for which uncoupling transformations have been found are essentially those which can be reduced to a coupled system involving a single spatial operator L. In addition, for several dependent variables, the general solution structure for the kernel matrix, involved in the uncoupling transformation, is presented together with some explicit results for values of components of the kernel matrix along characteristics, which are deduced from elementary considerations.

scholarly journals Chebyshev–Taylor Parameterization of Stable/Unstable Manifolds for Periodic Orbits: Implementation and Applications

2017 ◽  
Vol 27 (14) ◽  
pp. 1730050 ◽  
Author(s):  
J. D. Mireles James ◽  
Maxime Murray
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Invariant Manifolds ◽  
Posteriori Error ◽  
Coupled Systems ◽  
Parameterization Method ◽  
Taylor Coefficients ◽  
Unstable Manifolds ◽  
Linear Differential ◽  
Posteriori Error Analysis

This paper develops a Chebyshev–Taylor spectral method for studying stable/unstable manifolds attached to periodic solutions of differential equations. The work exploits the parameterization method — a general functional analytic framework for studying invariant manifolds. Useful features of the parameterization method include the fact that it can follow folds in the embedding, recovers the dynamics on the manifold through a simple conjugacy, and admits a natural notion of a posteriori error analysis. Our approach begins by deriving a recursive system of linear differential equations describing the Taylor coefficients of the invariant manifold. We represent periodic solutions of these equations as solutions of coupled systems of boundary value problems. We discuss the implementation and performance of the method for the Lorenz system, and for the planar circular restricted three- and four-body problems. We also illustrate the use of the method as a tool for computing cycle-to-cycle connecting orbits.

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