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Image of Vibration Testing and System Dynamics
ISSN: 2475-4811 (print)
ISSN: 2475-482X (online)
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn

Multi-Scale Modeling of Proteins and Cells: A Protocol for Modeling of Complex Systems

Journal of Vibration Testing and System Dynamics 9(1) (2025) 21--46 | DOI:10.5890/JVTSD.2025.03.002

Sheldon (Xiaodong) Wang

McCoy School of Engineering, Midwestern State University, A Member of the Texas Tech University System

Wichita Falls, TX 76308, USA

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Abstract

One of the major challenges in today's science and engineering fields is how to handle complex systems. Reductionist principles have helped scientists and engineers to develop uncanny an understanding of the universe ranging from mechanical to electro-magnetic properties and phenomena. Ever since that famous quote from Albert Einstein, ``God does not play dice," people often wonder what happened to obvious uncertainties in life and in nature. What would have happened if the Asteroid missed the Yucatan Peninsula in Mexico and the Earth 65 million years ago? The research in chaotic nonlinear systems seems to point us in a direction that even the deterministic nonlinear system can produce unpredictable results. Is it possible that when a large number of factors or entities interact nonlinearly with each other, they eventually yield a completely different system which is quantifiable with an entirely different set of phenomenological rules? Of course, the intermediate stage is characterized by a so-called positive Lyapunov exponent, fractals, and bifurcations. It is not difficult to imagine that a large or infinitely large positive Lyapunov exponent tends to produce a stochastic or random system. Overall, the accurate description of physical, chemical, and biological phenomena over a wide range of spatial and temporal scales is extremely difficult if not feasible. Nevertheless, although the intricate nature of turbulence poses seemingly insurmountable challenges to scientists and engineers with its spatial and temporal chaotic behaviors, many useful strategies have been discovered and implemented in various engineering applications. In the same spirit, in this study, various hierarchical modeling techniques have been explored in multi-scale and multi-physics modeling of proteins and cells. In addition, singular value decomposition, the key concept of importance to many reduced order modeling strategies, is reiterated with respect to four fundamental subspaces, namely, left null space, column space, null space, and row space for a rectangular matrix representative of any linear space tangent to a curved space or differentiable manifold. Using the singular value decomposition, it is possible to identify the hidden spatial and temporal correlations and patterns between variables and material properties. Hopefully, a computational protocol with phenomenological rules derived from experimental and computational approaches can be established for the modeling of complex systems.

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