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We often run into unstable conditions while solving the heat and wave equations. This report details the proof of the stability criterion for 1D heat and wave equations which then dictates the choice for spatial and temporal intervals.
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Creating Python virtual environments is essential for isolating project-specific dependencies from your system’s global Python installation. This helps prevent version conflicts and ensures that your work does not interfere with other projects or system-level packages.
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The Discrete Element Method (DEM) models granular materials by simulating particle interactions. This study compares the Cundall-Strack and Hertz-Mindlin contact models, highlighting differences in energy, stiffness, force distribution, and dynamics.
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I often revisit the Navier-Stokes equation and find myself grappling with the same questions about its structure, underlying assumptions, and the linear algebra concepts I’ve forgotten over time. This summary report provides a clear explanation of the equation’s structure while also serving as a refresher on essential linear algebra and vector calculus concepts.
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An exciting technique in data analysis, chi-squared minimization by convolution allows researchers to accurately identify the positions and sizes of particles in 2D. By comparing observed data with theoretical models and minimizing the difference, this approach offers a precise method for particle tracking and analysis.