Related papers: Old but Not Obsolete: Dimensional Analysis in Nond…
The Buckingham's $\pi$, theorem has been recently introduced in the context of Non destructive Testing \& Evaluation (NdT\&E) , giving a theoretical basis for developing simple but effective methods for multi-parameter estimation via…
In the absence of governing equations, dimensional analysis is a robust technique for extracting insights and finding symmetries in physical systems. Given measurement variables and parameters, the Buckingham Pi theorem provides a procedure…
Dimensional analysis is one of the most fundamental tools for understanding physical systems. However, the construction of dimensionless variables, as guided by the Buckingham-$\pi$ theorem, is not uniquely determined. Here, we introduce…
On the verge of the centenary of dimensional analysis (DA), we present a generalisation of the theory and a methodology for the discovery of empirical laws from observational data. It is well known that DA: a) reduces the number of free…
Dimensional analysis, and in particular the Buckingham $\Pi$ theorem is widely used in fluid mechanics. In this article we obtain an expression for the impact parameter from Buckingham's theorem and we compare our result with Rutherford's…
Dimensional analysis is fundamental to the formulation and validation of physical laws, ensuring that equations are dimensionally homogeneous and scientifically meaningful. In this work, we use Lean 4 to formalize the mathematics of…
We consider the design of dimensional analysis experiments when there is more than a single response. We first give a brief overview of dimensional analysis experiments and the dimensional analysis (DA) procedure. The validity of the DA…
Lurking variables represent hidden information, and preclude a full understanding of phenomena of interest. Detection is usually based on serendipity -- visual detection of unexplained, systematic variation. However, these approaches are…
A group of dimensionless numbers, termed DLV (Density-Length-Velocity) system, is put forward to represent the scaled behavior of structures under impact loads. It is obtained by means of the Buckingham Pi theorem with an alternative basis.…
The contribution introduces the principles, methods, and applications of non-destructive testing in the context of particle accelerators and related technologies is presented. Both surface inspection methods (visual testing, penetrant…
The aim of this work is to classify the aerospace structure defects detected by eddy current non-destructive testing. The proposed method is based on the assumption that the defect is bound to the reaction of the probe coil impedance during…
Many advanced driver assistance schemes or autonomous vehicle controllers are based on a motion model of the vehicle behavior, i.e., a function predicting how the vehicle will react to a given control input. Data-driven models, based on…
The inductance/impedance due to thin metallic structures in non-destructive testing (NDT) is difficult to evaluate. In particular, in Finite Element Method (FEM) eddy current simulation, an extremely fine mesh is required to accurately…
Disentangled representation learning plays a pivotal role in making representations controllable, interpretable and transferable. Despite its significance in the domain, the quest for reliable and consistent quantitative disentanglement…
Computing the electric eddy currents in non-linear materials, such as superconductors, is \E{not straightforward}. The design of superconducting magnets and power applications needs electromagnetic computer modeling, being in many cases a…
The goal of this paper is to contribute to the field of nondestructive testing by eddy currents. We provide a mathematical analysis and a numerical framework for simulating the imaging of arbitrarily shaped small volume conductive…
Building on recent work in statistical science, the paper presents a theory for modelling natural phenomena that unifies physical and statistical paradigms based on the underlying principle that a model must be nondimensionalizable. After…
Dynamical energy analysis was recently introduced as a new method for determining the distribution of mechanical and acoustic wave energy in complex built up structures. The technique interpolates between standard statistical energy…
Dimensionless numbers and scaling laws provide elegant insights into the characteristic properties of physical systems. Classical dimensional analysis and similitude theory fail to identify a set of unique dimensionless numbers for a…
Electrical Impedance Tomography (EIT) is a powerful imaging technique with diverse applications, e.g., medical diagnosis, industrial monitoring, and environmental studies. The EIT inverse problem is about inferring the internal conductivity…