Why engineering laws have been irrational for more than 70 years, and rational laws to replace them

This article describes why conventional engineering laws have been irrational since sometime before 1951, and presents rational laws to replace them. Conventional engineering laws are irrational because they are based on the assumption that dimensions can rationally be assigned to numbers. In 1951, a text on dimension analysis notes that dimensions cannot rationally be assigned to numbers. Therefore conventional engineering laws are irrational. Rational laws determined by induction are presented in the text.

Vibration Analysis of Deep Groove Ball Bearing using Finite Element Analysis and Dimension Analysis

Condition monitoring of rotor dynamic is recognized as an advanced preventative maintenance technique for fault-free operation. Faulty bearings in rotating machines may cause severe problems and even untimely breakdowns. This work demonstrates the power of the finite element analysis (FEA) model and dimension analysis technique (DAT) to analyze the effect of the depth and slope angle of surface faults on the bearing contact characteristic. Experimentation is performed to investigate the vibration characteristics of ball bearings. The FEA, DAT, and experimentation show that vibration amplitude is a vital function of surface fault size. The current approach of FEA with DAT reflects their reliability and accuracy for the diagnosis of rotor systems. The present method was found effective in predicting vibration amplitude and defect frequency within acceptable error.

A Phase-Field Study of Microstructure Evolution in Tungsten Polycrystalline under He/D Irradiation

Analyses in the present study focus on understanding the evolution of the tungsten microstructure under He/D irradiation. A fractal dimension analysis was utilized to characterize the structural pattern of the microstructure irradiated by both low (10–80 eV) and high (8–30 keV) irradiation energy. All examined W microstructures show a direct correlation between the fractal dimension and irradiation energy. Analyses establish an empirical relation expressing a change in the microstructure as a function of the irradiation energy based on the changes in the fractal dimension of the microstructures. The proposed relation was implemented in the phase-field model formulation with an account of the interfacial energy induced by the crystallographic mismatch between grains under irradiation. The current phase-field model captures the evolution of the void under irradiation, including nucleation and the growth of voids, and sink efficiency for vacancy annihilation in the vicinity of grain boundaries.

Molecular Dynamics and Kinetics of Isothermal Cold Crystallization in the Chiral Smectogenic 3F7HPhH6 Glassformer

An investigation of the glass transition of the antiferroelectric smectic C*A phase and cold crystallization of (S)-4’-(1-methylheptylcarbonyl)biphenyl-4-yl 4-[7-(2,2,3,3,4,4,4-heptafluoro- butoxy)heptyl-1-oxy]benzoate (denoted as 3F7HPhH6) by differential scanning calorimetry, polarizing optical microscopy and broadband dielectric spectroscopy is presented. The fragility index mf = 72, classifying 3F7HPhH6 as a glassformer with intermediate fragility, was obtained from the temperature dependence of the α-process relaxation time, measured upon cooling. Duplication of the α-process was observed exclusively upon heating, before the onset of cold crystallization, and is connected with the pre-transitional effect. The presence of two crystal phases likely influences the kinetics of cold crystallization; the idea stems from a comparison with previous results for the 3F7HPhF6 and 3F7HPhH7 compounds. Additionally, the presence of the smectic C*α; sub-phase in a narrow temperature range was proved based on the differential scanning calorimetry and broadband dielectric spectroscopy results, as well as the fractal dimension analysis of the textures obtained by polarizing optical microscopy.

Application of Texture and Fractal Dimension Analysis to Evaluate Subgingival Cement Surfaces in Terms of Biocompatibility

Biocompatibility is defined as “the ability of a biomaterial, prosthesis, or medical device to perform with an appropriate host response in a specific application”. Biocompatibility is especially important for restorative dentists as they use materials that remain in close contact with living tissues for a long time. The research material involves six types of cement used frequently in the subgingival region: Ketac Fil Plus (3M ESPE, Germany), Riva Self Cure (SDI, Australia) (Glass Ionomer Cements), Breeze (Pentron Clinical, USA) (Resin-based Cement), Adhesor Carbofine (Pentron, Czech Republic), Harvard Polycarboxylat Cement (Harvard Dental, Great Britain) (Zinc polycarboxylate types of cement) and Agatos S (Chema-Elektromet, Poland) (Zinc Phosphate Cement). Texture and fractal dimension analysis was applied. An evaluation of cytotoxicity and cell adhesion was carried out. The fractal dimension of Breeze (Pentron Clinical, USA) differed in each of the tested types of cement. Adhesor Carbofine (Pentron, Czech Republic) cytotoxicity was rated 4 on a 0–4 scale. The Ketac Fil Plus (3M ESPE, Germany) and Riva Self Cure (SDI, Australia) cements showed the most favorable conditions for the adhesion of fibroblasts, despite statistically significant differences in the fractal dimension of their surfaces.

Printable and Machinable Dental Restorative Composites for CAD/CAM Application—Comparison of Mechanical Properties, Fractographic, Texture and Fractal Dimension Analysis

Thanks to the continuous development of light-curing resin composites it is now possible to print permanent single-tooth restorations. The purpose of this study was to compare resin composites for milling -Gandio Blocks(GR), Brilliant Crios(CR) and Enamic(EN) with resin composite for 3D printing—VarseoSmileCrown plus(VSC). Three-point bending was used to measure flexural strength (σf) and flexural modulus (Ef). The microhardness was measured using a Vickers method, while fractographic, microstructural, texture and fractal dimension (FD) analyses were performed using SEM, optical microscope and picture analysis methods. The values of σf ranged from 118.96 (±2.81) MPa for EN to 186.02 (±10.49) MPa for GR, and the values of Ef ranged from 4.37 (±0.8) GPa for VSC to 28.55 (±0.34) GPa for EN. HV01 ranged from 25.8 (±0.7) for VSC to 273.42 (±27.11) for EN. The filler content ranged from 19–24 vol. % for VSC to 70–80 vol. % for GR and EN. The observed fractures are typical for brittle materials. The correlation between FD of materials microstructure and Ef was observed. σf of the printed resin depends on layers orientation and is significantly lower than σf of GR and CR. Ef of the printed material is significantly lower than Ef of blocks for milling.