Mathematical Models in Engineering (MME) ISSN (Print) 2351-5279, ISSN (Online) 2424-4627 publishes mathematical results relevant to engineering science and technology. The journal features formal descriptions of mathematical models related to engineering problems and mathematical results applicable to engineering. Access content on the application of mathematical models in mechanical, electrical, and industrial engineering, as well as in computer science and informatics. Topics of interest include ordinary, partial, and fractional differential equations; artificial neural networks and graphs; and algorithms for numeric and algebraic transformations.
Established in 2015 and published 4 times a year (quarterly). All volumes are available at https://doi.org/10.21595/mme
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What is a Mathematical Model in Engineering as a Field of Research?
Mathematical Models in Engineering (MME) is a dynamic field of research that explores the application of mathematical principles to engineer solutions for complex real-world problems. In essence, it involves the development and analysis of mathematical representations that simulate, describe, or predict behaviors within engineering systems..
Types of Mathematical Modeling:
- Ordinary, Partial, and Fractional Differential Equations (ODEs/PDEs/FDEs): These are fundamental tools in mathematical modeling, describing how quantities change with respect to one or more variables. ODEs model systems with one independent variable, PDEs extend to multiple variables, FDEs comprise non-local formulations and memory effects.
- Artificial Neural Networks and Graphs: These are powerful methods in mathematical modeling for complex data analysis and pattern recognition. Artificial neural networks are used for tasks like classification, regression, and image recognition. Graphs, consisting of vertices and edges, model relationships between entities, and are applied in network analysis, optimization problems, and social network dynamics.
- Algorithms for Numeric and Algebraic Transformations: These are essential techniques in mathematical modeling and solving complex numerical and algebraic problems. Algorithms for numerics encompass a wide range of techniques for approximation, optimization, and simulation of dynamical systems. Algebraic transformations, on the other hand, focus on manipulating variables, expressions, and equations using rules of algebra, facilitating analysis and applications in research areas such as symbolic dynamics and cryptography.
How Can Mathematical Modeling Be Applied to Real-World Problems?
- Predictive Analysis: Mathematical models allow engineers to predict the behavior of a system under different conditions before implementation. This is critical for designing and optimizing systems without the need for costly physical prototypes.
- Optimization: Mathematical models are used to find the best possible solutions to engineering problems. This is crucial in resource allocation, process design, and system performance enhancement.
- Risk Assessment: Incorporating stochastic models helps in assessing and managing risks associated with uncertainty, crucial in fields like finance, environmental engineering, and system reliability analysis.
- Decision Support: Operations research models provide a structured approach to decision-making, aiding engineers in making informed choices and optimizing processes.
Why Do We Need Mathematical Models for Engineering Problems?
- Complexity Handling: Real-world engineering problems are often too complex to be fully understood through intuition alone. Mathematical models provide a systematic and rigorous framework for understanding, analyzing, and solving these complex issues.
- Resource Efficiency: Developing and testing physical prototypes can be time-consuming and expensive. Mathematical models enable engineers to simulate and optimize systems in a cost-effective manner before physical implementation.
- Informed Decision-Making: By quantifying relationships and dependencies, mathematical models provide a basis for informed decision-making, reducing the risk of errors and inefficiencies in engineering projects.
- Innovation and Advancement: Mathematical modeling fosters innovation by providing a platform for exploring new ideas, theories, and approaches to engineering challenges, leading to advancements in technology and science.
In summary, Mathematical Models in Engineering play a crucial role in understanding, predicting, and optimizing complex systems, offering a powerful toolkit for researchers and practitioners in various engineering disciplines.
