Mathematical Modelling, Analysis, and Optimization for Engineering and Mechanics, 2nd Edition

Dear Colleagues,

Mathematical modeling, analysis, and further optimization aimed at understanding nonlinear phenomena are fundamentally present in nature and form the basis of science, engineering, and consequently, mechanics. Mathematical modelling and optimization form the foundation of our understanding of all engineering applications and are thus present in the solutions/states of the dynamical modelling of mechanics. From spontaneous symmetry breaking in particle physics and the formation of coherent states in ubiquitous flows to the analysis of pattern and stress formation in physico-chemical processes, mathematical techniques and modelling play a pivotal role in the discovery of the solutions and states preferred by nature.

Through the theoretical application and numerical implementation of pioneering theoretical techniques such as Poincaré sections, weakly nonlinear analysis and perturbation methods, Floquet analysis and bifurcation theory within Euclidean or curvilinear space fixed-point/solutions and their stability can be identified, while transient solutions can be tracked. This offers the possibility to explicitly optimize mechanical states that both have engineering applications and present significant theoretical and simulative advances.

Mathematical modelling enables us to continuously pioneer new emerging technologies for the benefit of society, while encouraging fresh insights into technology, engineering, and science; explaining and organizing complex behaviors; and establishing the basis for new pathways of exploitation by future generations.

As a follow-up to the first edition, this Special Issue aims to publish original research papers and reviews on the latest advancements in modeling, analysis, and optimization for engineering and mechanics.

Dr. Sotos C. Generalis
Dr. Philip Trevelyan
Guest Editors

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