Study of Burgers–Huxley Equation Using Neural Network Method

Wen, Ying; Chaolu, Temuer

doi:10.3390/axioms12050429

Cited by 5 publications

(4 citation statements)

References 28 publications

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“…Moreover, computational modeling approaches, including ordinary differential equations (ODEs), partial differential equations (PDEs), agent-based models, and network modeling, can simulate and predict the behaviors of complex systems like organoids (Gonçalves and García-Aznar, 2023;Pleyer and Fleck, 2023;Wen and Chaolu, 2023). These models integrate known biological mechanisms and parameters to study emergent properties, test hypotheses, and explore the effects of perturbations on organoid development, functionality, and response to external factors (Montes-Olivas et al, 2019).…”

Section: Characterization Of Organoids As Complex (Bio)systemsmentioning

confidence: 99%

Organoids as complex (bio)systems

Fernandes

2023

Front. Cell Dev. Biol.

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Organoids are three-dimensional structures derived from stem cells that mimic the organization and function of specific organs, making them valuable tools for studying complex systems in biology. This paper explores the application of complex systems theory to understand and characterize organoids as exemplars of intricate biological systems. By identifying and analyzing common design principles observed across diverse natural, technological, and social complex systems, we can gain insights into the underlying mechanisms governing organoid behavior and function. This review outlines general design principles found in complex systems and demonstrates how these principles manifest within organoids. By acknowledging organoids as representations of complex systems, we can illuminate our understanding of their normal physiological behavior and gain valuable insights into the alterations that can lead to disease. Therefore, incorporating complex systems theory into the study of organoids may foster novel perspectives in biology and pave the way for new avenues of research and therapeutic interventions to improve human health and wellbeing.

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Section: Characterization Of Organoids As Complex (Bio)systemsmentioning

confidence: 99%

Organoids as complex (bio)systems

Fernandes

2023

Front. Cell Dev. Biol.

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“…The Burgers-Huxley equation is widely used in biology, physics, economics, etc., as it describes the propagation of an impulse, such as that of a muscle. In its general form it includes an accumulation term, a drag term, a diffusion term, and a generation or decay term, as follows [1,2]:…”

Section: Burgers-huxley Equationmentioning

confidence: 99%

“…The Burgers-Huxley equation is a partial differential equation [1,2], based on the Burgers equation, which involves accumulation, diffusion, drag, and species generation or sink phenomena. This or similar equations [3][4][5][6], together with its approximate solutions, are common in many areas of science and engineering, such as fluid mechanics [7,8], heat transmission [9][10][11][12][13][14], air pollutant emissions [15][16][17], chloride diffusion in concrete [18][19][20][21][22][23][24], nonlinear acoustics [25,26], optical fibres [27][28][29][30][31][32], and other areas.…”

Section: Introductionmentioning

confidence: 99%

Methodology for Solving Engineering Problems of Burgers–Huxley Coupled with Symmetric Boundary Conditions by Means of the Network Simulation Method

Sánchez-Pérez,

Marín-García,

Castro

et al. 2023

Symmetry

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The Burgers–Huxley equation is a partial differential equation which is based on the Burgers equation, involving diffusion, accumulation, drag, and species generation or sink phenomena. This equation is commonly used in fluid mechanics, air pollutant emissions, chloride diffusion in concrete, non-linear acoustics, and other areas. A general methodology is proposed in this work to solve the mentioned equation or coupled systems formed by it using the network simulation method. Additionally, the implementation of the most common possible boundary conditions in different engineering problems is indicated, including the Neumann condition that enables symmetry to be applied to the problem, reducing computation times. The method consists mainly of establishing an analogy between the variables of the differential equations and the electrical voltage at a central node. The methodology is also explained in detail, facilitating its implementation to similar engineering problems, since the equivalence, for example, between the different types of spatial and time derivatives and its correspondence with the electrical device is detailed. As an example, several cases of both the equation and a coupled system are solved by varying the boundary conditions on one side and applying symmetry on the other.

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“…Thus, the Burgers-Huxley equation is an ordinary differential equation that is widely used in physics, biology, economics, etc., and includes terms such as drag, accumulation, generation or decay, and diffusion. This equation has the following form [2,3,32]:…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Burgers–Huxley Equation Using the Nondimensionalisation Technique: Universal Solution for Dirichlet and Symmetry Boundary Conditions

Sánchez-Pérez,

Solano-Ramírez,

Castro

et al. 2023

Axioms

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The Burgers–Huxley equation is important because it involves the phenomena of accumulation, drag, diffusion, and the generation or decay of species, which are common in various problems in science and engineering, such as heat transmission, the diffusion of atmospheric contaminants, etc. On the other hand, the mathematical technique of nondimensionalisation has proven to be very useful in the appropriate grouping of the variables involved in a physical–chemical phenomenon and in obtaining universal solutions to different complex engineering problems. Therefore, a deep analysis using this technique of the Burgers–Huxley equation and its possible boundary conditions can facilitate a common understanding of these problems through the appropriate grouping of variables and propose common universal solutions. Thus, in this case, the technique is applied to obtain a universal solution for Dirichlet and symmetric boundary conditions. The validation of the methodology is carried out by comparing different cases, where the coefficients or the value of the boundary condition are varied, with the results obtained through a numerical simulation. Furthermore, one of the cases presented presents a boundary condition that changes at a certain time. Finally, after applying the technique, it is studied which phenomenon is predominant, concluding that from a certain value diffusion predominates, with the rest being practically negligible.

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Study of Burgers–Huxley Equation Using Neural Network Method

Cited by 5 publications

References 28 publications

Organoids as complex (bio)systems

Organoids as complex (bio)systems

Methodology for Solving Engineering Problems of Burgers–Huxley Coupled with Symmetric Boundary Conditions by Means of the Network Simulation Method

Analysis of the Burgers–Huxley Equation Using the Nondimensionalisation Technique: Universal Solution for Dirichlet and Symmetry Boundary Conditions

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