In 1653, the French philosopher and scientist Blaise Pascal published "Treatise on the Equilibrium of Liquids," which discussed the principles of static fluids. A static fluid is a fluid that is not in motion. When a fluid is not flowing, we say that the fluid is in static equilibrium. If the fluid is water, we say it is in hydrostatic equilibrium. For a fluid in static equilibrium, the net force on any part of the fluid must be zero; otherwise, the fluid will start to flow. Pascal...

Total internal reflection fluorescence microscopy or TIRF is an advanced microscopic technique used to visualize fluorophores in samples close to a solid surface with a higher refractive index, such as a glass coverslip. TIRF only allows fluorophores in proximity to the solid surface to be excited. When light from a medium with a lower refractive index (such as air) hits the glass coverslip at a critical angle, the light undergoes total internal reflection stead of passing through the glass.

When a body is in motion, it encounters resistance because the body interacts with its surroundings. This resistance is known as friction, a common yet complex force whose behavior is still not completely understood. Friction opposes relative motion between systems in contact, but also allows us to move. Friction arises in part due to the roughness of surfaces in contact. For one object to move along a surface, it must rise to where the peaks of the surface can skip along the bottom of the...

The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...