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The propagation of radiation through a medium is affected by absorption, emission, and scattering processes. The equation of radiative transfer describes these interactions mathematically. Equations of radiative transfer have application in a wide variety of subjects including optics, astrophysics, atmospheric science, and remote sensing.
The Elliott formula describes analytically, or with few adjustable parameters such as the dephasing constant, the light absorption or emission spectra of solids. It was originally derived by Roger James Elliott to describe linear absorption based on properties of a single electron–hole pair. [ 1 ]
The absorption coefficient for spectral flux (a beam of radiation with a single wavelength, [W/m 2 /μm]) differs from the absorption coefficient for spectral intensity [W/sr/m 2 /μm] used in Schwarzschild's equation. Integration of an absorption coefficient over a path from s 1 and s 2 affords the optical thickness (τ) of that path, a ...
In deterministic methods the transport equation (or an approximation of it, such as diffusion theory) is solved as a differential equation. In stochastic methods such as Monte Carlo discrete particle histories are tracked and averaged in a random walk directed by measured interaction probabilities. Deterministic methods usually involve multi ...
In nuclear physics, the Bateman equation is a mathematical model describing abundances and activities in a decay chain as a function of time, based on the decay rates and initial abundances. The model was formulated by Ernest Rutherford in 1905 [ 1 ] and the analytical solution was provided by Harry Bateman in 1910.
Beer's law states that a beam of visible light passing through a chemical solution of fixed geometry experiences absorption proportional to the solute concentration. Other applications appear in physical optics , where it quantifies astronomical extinction and the absorption of photons , neutrons , or rarefied gases .
Defining equation (physical chemistry) List of electromagnetism equations; List of equations in classical mechanics; List of equations in quantum mechanics; List of equations in wave theory; List of photonics equations; List of relativistic equations; Relativistic wave equations
Modeling photon propagation with Monte Carlo methods is a flexible yet rigorous approach to simulate photon transport. In the method, local rules of photon transport are expressed as probability distributions which describe the step size of photon movement between sites of photon-matter interaction and the angles of deflection in a photon's trajectory when a scattering event occurs.