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2021
The expression of the equations describing the physical phenomena requires the respect of some formal rules and the knowledge of some basic principles that guarantee correctness and logical coherence. In particular, the structure of an equation that connects physical quantities must respect the principle of dimensional homogeneity.
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The expression of the equations describing the physical phenomena requires the respect of some formal rules and the knowledge of some basic principles that guarantee correctness and logical coherence. In particular, the structure of an equation that connects physical quantities must respect the principle of dimensional homogeneity.
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IBM Journal of Research and Development, 1960
The dimensions of physical quantities q are interpreted as vectors q i (γ i1 , γ i2 , …,γ in )≡γ i1 b 1 +γ i2 b 2 +…+γ in b n , where the basic elements b j generating the vector space represent the basic quantities of the dimensional system and the coefficients γ j are defined by an equation.
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The dimensions of physical quantities q are interpreted as vectors q i (γ i1 , γ i2 , …,γ in )≡γ i1 b 1 +γ i2 b 2 +…+γ in b n , where the basic elements b j generating the vector space represent the basic quantities of the dimensional system and the coefficients γ j are defined by an equation.
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Dimensional Invariance and Dimensional Analysis
2015The notion of invariance is a fundamental one in mathematics and the sciences. This chapter is a brief introduction to two of its subtopics, dimensional invariance and dimensional analysis, which are relevant to the subject of this book. Specifically, dimensional invariance is closely related to, but technically different from, meaningfulness.
Jean-Claude Falmagne, Christopher Doble
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On an Application of Dimensional Analysis
American Journal of Physics, 1951Based upon dimensional reasoning and utilizing the known invariants of physical tensors, it is shown that the complete forms (except for multiplying constants) of certain differential and integral equations of applied mechanics can be obtained. The procedure equates physical and tensor invariants in a basic postulated form of equation.
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Dimensional Analysis and Dimensional Reasoning
2012This chapter explores some of the ways physical dimensions, such as length, mass and time, impact on the work of scientists and engineers. Two main themes are considered: dimensional analysis, which involves deriving algebraic expressions to relate quantities based on their dimensions; and dimensional rea-soning, a more general and often more subtle ...
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Dimensional analysis and dimensional similarity
2013A physical quantity is a physical property or quality that can be quantified by measurement. A physical quantity is defined by the product of a numerical value and a unit of measurement. In this section we present a structured approach in order to obtain the dimensionless numbers of any dimensional relation. The approach is based on matrix computations,
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Dimensional analysis in Pascal
ACM SIGPLAN Notices, 1984Mukul Babu Agrawal, Vijay Kumar Garg
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Universal strategies to multi-dimensional noble-metal-based catalysts for electrocatalysis
Coordination Chemistry Reviews, 2021Fei Gao, Yangping Zhang, Zhengying Wu
exaly
Dimensional Analysis and Scaling
2006Tim A. Osswald, Juan P. Hernández-Ortiz
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Vapour-phase deposition of two-dimensional layered chalcogenides
Nature Reviews Materials, 2023Tianyi Zhang, Jiangtao Wang, Peng Wu
exaly