Research Article
Mathematical Modeling of Dynamic Feedback Loops in Carbon Cycle Using Differential Equations
Francis Omondi Owino*
,
Beatrice Adhiambo Odero Obiero,
Vincent Bulinda
Issue:
Volume 11, Issue 3, September 2026
Pages:
53-69
Received:
20 July 2026
Accepted:
7 August 2026
Published:
24 September 2026
DOI:
10.11648/j.mma.20261103.11
Downloads:
Views:
Abstract: Carbon dioxide is very important during photosynthesis. However, it increases as a result of deforestation, burning of fossil fuels, cement manufacturing factories and other agricultural practices and this causes global warming. Carbon cycle as a process involves interactions among major reservoirs controlled by complex feed back relationships that are not easy to understand without a well organized mathematical framework. Some of the existing carbon cycle models are too complex while others are too simple and fail to include nonlinear feedback loops between reservoirs. This study built a model that captures the dynamic feedback interactions between the most relevant carbon reservoirs and investigate their effects on carbon partitioning and stability of the system through centuries. Carbon exchanges (sequestration, respiration, decomposition and interaction with the atmosphere) were simulated using a mathematical modeling approach based on systems of differential equations. Equilibrium and stability characteristics of the model were analyzed and the behavior of the model was examined numerically under various environmental conditions. These results demonstrated that feedback interactions are important for the regulation of carbon and in determining long-term equilibrium states. The model demonstrated that a disturbance in one of the reservoirs affects the entire system, changing the overall carbon dynamics. Conditions were identified under which the system stays in balance or changes to new states. The stability analysis showed conditions for maintaining a balance or changing to new state of the system. The study concluded that differential equation modeling provides a clear framework for understanding dynamic feedback loops in the carbon cycle. It is recommended that the model be extended to incorporate additional environmental variables and be used as a basis for further quantitative studies in climate and environmental modeling.
Abstract: Carbon dioxide is very important during photosynthesis. However, it increases as a result of deforestation, burning of fossil fuels, cement manufacturing factories and other agricultural practices and this causes global warming. Carbon cycle as a process involves interactions among major reservoirs controlled by complex feed back relationships that...
Show More
Research Article
Optimization of Multigonal Corner Combined Footings:
A Mathematical Model for Minimum Dimensions Under Varying Load and Soil Conditions Using Python and Maple
Nigusie Tsehay Demeke,
Getasew Kindie Mihiretu,
Girma Moges Teshager,
Girmay Mengesha Azanaw*
Issue:
Volume 11, Issue 3, September 2026
Pages:
70-89
Received:
14 July 2026
Accepted:
27 September 2026
Published:
21 October 2026
DOI:
10.11648/j.mma.20261103.12
Downloads:
Views:
Abstract: Foundations are important in structural engineering, as they transfer loads to the ground. It is challenging to design combined footings on uneven ground due to load eccentricity, soil heterogeneity, and material efficiency. Traditional methods, based on oversimplified assumptions of soil pressure, fail. This paper introduces a new model for optimal multigonal corner combined footing design, with minimum size but with the capacity to adapt to varying loads and soil strengths. The model offers flexible footing slopes (90° to 0°) to place the load and geometric centers, offering uniform stress distribution and preventing eccentric loading. Optimized in Python for numerical accuracy and Maple for symbolic calculation, the model is computed using numerical analysis. The result is better regions of footing, with lower b1 and b2 in end columns, and greater n and m, which enhance stress distribution and lessen load eccentricity. The model is recommended for the design of corner combined footings with four continuous lines of property. Practical recommendations and future research for smaller dimensions and column spacing effects on footing design finalize the paper.
Abstract: Foundations are important in structural engineering, as they transfer loads to the ground. It is challenging to design combined footings on uneven ground due to load eccentricity, soil heterogeneity, and material efficiency. Traditional methods, based on oversimplified assumptions of soil pressure, fail. This paper introduces a new model for optima...
Show More
