The authors use the Lanczos algorithm to computationally solve the Schrodinger equation for 2D potentials with a Python program

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Solving the Schrödinger equation computationally using the Lanczos algorithm

The authors use the Lanczos algorithm to computationally solve the Schrodinger equation for 2D potentials with a Python program

Read More...An Analysis of the Density and Patterns of the Solutions of Diophantine Equations of the Third Power

In this study, the authors sought to find out how many mathematical solutions there were to the Indian mathematician Ramanujan's formula, which is *a ^{3}* +

Modeling Hartree-Fock approximations of the Schrödinger Equation for multielectron atoms from Helium to Xenon using STO-nG basis sets

The energy of an atom is extremely useful in nuclear physics and reaction mechanism pathway determination but is challenging to compute. This work aimed to synthesize regression models for Pople Gaussian expansions of Slater-type Orbitals (STO-nG) atomic energy vs. atomic number scatter plots to allow for easy approximation of atomic energies without using computational chemistry methods. The data indicated that of the regressions, sinusoidal regressions most aptly modeled the scatter plots.

Read More...Heat conduction: Mathematical modeling and experimental data

In this experiment, the authors modify the heat equation to account for imperfect insulation during heat transfer and compare it to experimental data to determine which is more accurate.

Read More...What is the optimal fuel for space flight? Efficiency, cost, and environmental impact

Here, the authors sought to investigate the efficiency, cost, and environmental impact of several possible propellants that are or could be used for space flight. By deriving three novel equations, they identified harm, energy, and cost scores for each fuel, suggesting that considering each factor will be essential to the ongoing growth of the space industry.

Read More...Optimizing airfoil shape for small, low speed, unmanned gliders: A homemade investigation

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.

Read More...Fractals: Exploring Mandelbrot Coordinates and qualitative characteristics of the corresponding Julia Set

Here based on an interest in fractals, the authors used a Julia Set Generator to consider a specific point on the Mandelbrot set with an associated coordinate. In this manner, they found that the complexity of the Mandelbrot and Julia Sets are governed by relatively simple rules, revealing that the intricate patterns of fractals can be defined by defined by simple rules and patterns.

Read More...Indoor near-field target detection characteristics under radio and radar joint operation at 2.4 GHz ISM band

In our modern age, the burgeoning use of radios and radars has resulted in competition for electromagnetic spectrum resources. With recent research highlighting solutions to radio and radar mutual interference, there is a desperate need for a cost-effective configuration that permits a radar-radio joint system. In this study, the authors have set out to determine the feasibility of using single-tone continuous-wave radars in a radar-joint system. With this system, they aim to facilitate cost-effective near-field target detection by way of the popularized 2.4-GHz industrial, scientific, and medical (ISM) band.

Read More...Linearity of piezoelectric response of electrospun polymer-based (PVDF) fibers with barium titanate nanoparticles

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 BaTiO_{3} nanoparticles in electrospun Polyvinyledene Fluoride. They found the voltage generated had a piecewise linear dependence on the applied force at a few temperatures.

Behavioral Longevity: The Impact of Smoking, Alcohol Consumption, and Obesity on Life Expectancy

In this article, the authors look into what is already known about the factor affecting longevity and determine the importance of behavioral factors including alcohol consumption, smoking, and obesity on longevity. The authors quantify data from over 150 countries and, interestingly, find that the impact each factor has on longevity is at least in part dependent on the country's economic development status. Overall, they conclude that an average person’s life expectancy can increase by more than 3 years if smoking and alcohol consumption is reduced by a half and weight is decreased by 10%.

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