Thomas precession is the kinematic rotation arising when the successive instantaneous rest frames of an accelerated particle are connected by noncollinear Lorentz boosts. Its contribution is needed in deriving the leading atomic spin-orbit coupling: for an electron in central potential energy $U(r)$, the corrected term is $H_{\mathrm{so}}=[2m_e^2{c}^{2}r{]}^{-1}(dU/dr)\mathbf{L}\cdot \mathbf{S}$. A rest-field argument alone gives twice this coefficient.^[ref]

Special relativity connects measurable clock rates, length contraction, light propagation, and four-momentum through the Lorentz transformation. Tests probe particular predictions rather than measuring a coordinate transformation in isolation. Examples include cosmic-ray muon time-dilation experiments, muon storage-ring time-dilation experiments, the Michelson-Morley experiment, the Fizeau experiment, and particle-collision energy and momentum balances.

The first postulate is Einstein's principle of relativity: nongravitational laws have the same form in every inertial frame. The second states that light in vacuum propagates at the same finite speed of light $c$ in every inertial frame, independently of the source's motion. Together with the usual spacetime symmetries and calibrated coordinates, these postulates yield the Lorentz transformation. The relativity principle alone also admits the Galilean transformation with its infinite invariant-speed limit.

Filtration separates suspended solid particles from a fluid using a porous barrier. Dissolved ions can pass with the fluid; the separation does not establish the filtrate's composition. Solubility product measurement by titration requires removal of undissolved calcium hydroxide before acid-base titration.

An ideal solution is a chemical solution whose component chemical potentials depend on composition throughHere $n_i$ is an amount of substance, $x_i$ its mole fraction, $R$ the molar gas constant, and ${\mu }_i^{\ast }$ the pure-component liquid reference at the same temperature $T$ and pressure $P$. This model applies to every component across the composition range; it is stronger than an approximation valid only near a pure solvent.^[ref]

With this pure-liquid standard state convention, the thermodynamic activity satisfies ${\mu }_i={\mu }_i^{\ast }+RT\ln a_i$, so an ideal solution has $a_i=x_i$, or activity coefficient ${\gamma }_i=a_i/x_i=1$.^[ref] This statement concerns the liquid. Assuming that a coexisting vapor is an ideal gas mixture is an additional approximation. Its mole fractions $y_i$ generally differ from the liquid mole fractions $x_i$.

For an original two-component example, stipulate $T=300\mathrm{K}$ and pure-component vapor pressures $p_A^{\ast }=80\mathrm{kPa}$ and $p_B^{\ast }=20\mathrm{kPa}$. A and B are invented distinguishable components; these numbers are chosen model inputs, not material data. Combine an ideal solution with an ideal gas vapor, neglect the pure-liquid reference's pressure correction, and exclude other gases. At liquid mole fractions $x_A=0.4$ and $x_B=0.6$, Raoult's law and addition of partial pressures giveThus the coexisting vapor contains about $72.73\%$ A by amount of substance, although the liquid contains only $40\%$. The total pressure is neither pure-component vapor pressure, and $x_A$ cannot be substituted for $y_A$. This enrichment is the basis of distillation.

The usefulness of the ideal solution is that one composition law connects chemical potentials, vapor-liquid equilibrium, entropy of mixing and Gibbs free energy of mixing. Its liquid components can interact strongly: the defining condition is their composition dependence, rather than the absence of all interactions as in an ideal gas model.

A chemical solution with a polymer as a solute. The polymer conformation and interactions depend on the solvent and concentration.

A semiconductor solid solution whose composition changes its band gap.

Test coverage measures which selected program elements a test run exercises. Statement coverage counts executed statements; branch coverage counts executed control-flow alternatives. Exercising both sides of a conditional can reveal gaps missed by statement coverage, but even full branch coverage need not exercise all paths or meaningful value combinations. Coverage records execution, not whether assertions checked the right behaviour. A suite that calls every function and verifies nothing can have impressive coverage while failing to detect wrong results.

Soft matter physics studies the physical behaviour of soft matter, including its response to mechanical and thermal perturbations.

A flexible silicone polymer that can form an elastomer when lightly crosslinked. The network's recoverable deformation provides an example of rubber elasticity.

A power spectral density distributes the mean square of a signal over frequency. Its integral over the specified frequency domain gives that mean square. State whether the convention is one-sided or two-sided and whether frequency is measured in hertz or as angular frequency. For a zero-mean stationary signal, the mean square is its variance; spectral density of a stationary process gives the discrete-time convention.

A signal-to-noise ratio compares a chosen measure of a signal with the corresponding noise measure. For a constant measured electric potential difference $V$ and a root mean square noise voltage $v_n$, an amplitude ratio is $|V|/v_n$; the corresponding power ratio under equal electrical resistance is its square. State the convention and measurement signal bandwidth, since changing either changes the numerical ratio.

An oocyte is a female germ biological cell developing toward an ovum.

A quantum well confines a particle in one spatial direction while allowing motion along the layer. In a semiconductor heterostructure, band offsets can create that confinement. The following finite square well model makes the resulting discrete transverse energy levels explicit.

A double heterostructure sandwiches one semiconductor between two layers of another, for example gallium arsenide between aluminium gallium arsenide layers. Suitable band offsets confine injected charge carriers centrally.^[ref]

A heterojunction joins different semiconductors; its two sides need not have opposite semiconductor doping.^[ref]