tetthetsfeltet

Tetthetsfeltet, commonly translated as the density field, is a scalar field that assigns to every point in space (and time, when needed) a density value. It is fundamental in many areas of physics and applied science, where density can refer to mass density, material composition, or other conserved quantities that vary spatially.

In mathematics and physics, the density field is denoted ρ(x, t), with units such as kg/m^3 for mass density. In fluid dynamics, its evolution is governed by the continuity equation ∂ρ/∂t + ∇·(ρv) = 0, where v is the velocity field. In cosmology, the density field describes how matter is distributed in the universe; one often uses the density contrast δ(x, t) = [ρ(x, t) − ρ̄(t)]/ρ̄(t), where ρ̄ is the mean density. The statistical properties of δ, including the power spectrum P(k) and the two-point correlation function, characterize large-scale structure.

Construction and analysis typically involve either measurements or simulations. Observational data from galaxy surveys, seismic imaging, or medical tomography can be processed to reconstruct a continuous density field via smoothing kernels or interpolation onto a grid. In simulations, the field arises naturally from discretized matter or material distributions and is analyzed with Fourier methods, wavelets, or filtering to study scales and patterns.

Applications span cosmology, materials science, geophysics, and medical imaging. Limitations include sensitivity to the chosen smoothing scale, reference frame, and measurement resolution, which affect how features in the density field are interpreted.