Publication Date

12-2020

Comments

Technical Report: UTEP-CS-20-122

Abstract

In many application areas such as pavement engineering, the phenomena are complex, and as a result, we do not have first-principle models describing the corresponding dependencies. Luckily, in many such areas, there is a lot of empirical data and, based on this data, many useful empirical dependencies have been found. The problem is that since many of these dependencies do not have a theoretical explanation, practitioners are often hesitant to use them: there have been many cases when an empirical formula stops being valid when circumstances change. To make the corresponding empirical formulas more reliable, it is therefore desirable to look for theoretical foundations of these formulas. In this paper, we show that many of such dependencies can be naturally explained by using symmetries and invariances. We illustrate this approach on the example of pavement engineering, but the approach is very general, and can be applied to other systems as well.

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Mathematics Commons

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