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Category: Continental Slope

Posts with moderate math

Source of the source: Pressure in the axisymmetric momentum equation

Posted on April 16, 2021April 16, 2021 By MathFish
Continental Slope, Numerics

Consider the equation for conservation of momentum in an inviscid flow, first in differential form: $$\displaystyle \frac{\partial}{\partial t} (\rho\vec{u}) = -\nabla\cdot(\rho\vec{u}\vec{u}) – \nabla P $$ and then integrated over an arbitrary control volume $\Omega$, using the divergence theorem on the momentum term and the gradient theorem on the pressure term: $$\displaystyle \frac{d}{dt} \int_\Omega \rho\vec{u}\,dx = … Read More “Source of the source: Pressure in the axisymmetric momentum equation” »

Power to the Penny-Pinchers

Posted on January 29, 2021January 29, 2021 By MathFish
Continental Slope

Being almost obsessively parsimonious, I once joked that if everyone’s spending habits were like mine the economy would collapse. Mathematician that I am, I wondered if that was actually true and whether it could be predicted mathematically. Now you can enjoy the result. For simplicity, consider an economy with two kinds of people who differ … Read More “Power to the Penny-Pinchers” »

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