In this study, the authors use existing mathematical models to how high school athletes pace 800 m, 1600 m, and 3200 m distance track events compared to elite athletes.

Here, seeking to develop an understanding of the properties that determine the viability of piezoelectric flexible materials for applications in electro-mechanical sensors, the authors investigated the effects of the inclusion BaTiO₃ nanoparticles in electrospun Polyvinyledene Fluoride. They found the voltage generated had a piecewise linear dependence on the applied force at a few temperatures.

This study examines the higher harmonics in an oscillating string by analyzing the sound produced by a guitar with a spectrum analyzer. The authors mathematically hypothesized that the higher harmonics in the series of the directly excited 2^nd harmonic contain the alternate frequencies of the fundamental series, the higher harmonics of the directly excited 3^rd harmonic series contain every third frequency of fundamental series, and so on. To test the hypotheses, they enforced artificial nodes to excite the 2^nd, 3^rd, and 4^th harmonics directly, and analyzed the resulting spectrum to verify the mathematical hypothesis. The data analysis corroborates both hypotheses.

Here, recognizing the need to improve the efficiency of the conversion of solar energy to electrical energy, the authors used MATLAB to mathematically simulate a multi-layered thin film with an without an antireflective coating. They found that the use of alternating ZnO-SiO₂ multilayers enhanced the transmission of light into the solar cell, increasing its efficiency and reducing the reflectivity of the Si-Air interface.

Here, beginning from an interest in fractals, infinitely complex shapes. The authors investigated the fractal object that results from crumpling a sheet of paper. They determined its fractal dimension using continuous Chi-squared analysis, thereby testing and validating their model against the more conventional least squares analysis.

Here, the authors sought to identify a method to optimize the lift generated by an airfoil based solely on its shape. By beginning with a Bernoullian model to predict an optimized wing shape, the authors then tested their model against other possible shapes by constructing them from Styrofoam and testing them in a small wind tunnel. Contrary to their hypothesis, they found their expected optimal airfoil shape did not result in the greatest lift generation. They attributed this to a variety of confounding variables and concluded that their results pointed to a correlation between airfoil shape and lift generation.

These authors mathematically deduce a model that explains the interesting (and unintuitive) physical phenomenon that occurs when water falls.

Bubbles! In this study, the authors investigate the effects that different materials, temperature, and distance have on the formation of water bubbles on the surface of copper and steel. They calculated mathematical relations based on the outcomes to better understand whether interstitial hydrogen present in the d-block metals form hydrogen bonds with the water bubbles to account for the structural and mechanical stability.

Machine learning algorithms are becoming increasingly popular for data crunching across a vast area of scientific disciplines. Here, the authors compare two machine learning algorithms with respect to accuracy and user-friendliness and find that random forest algorithms outperform logistic regression when applied to the same dataset.

Middle school math forms the basis for advanced mathematical courses leading up to the university level. Large language models (LLMs) have the potential to power next-generation educational technologies, acting as digital tutors to students. The main objective of this study was to determine whether LLMs like ChatGPT, Bard, and Llama 2 can serve as reliable middle school math tutoring assistants on three tutoring tasks: hint generation, comprehensive solution, and exercise creation.