Physical world and mathematics

Phase rule

The phase rule, or Gibbs phase rule, is the thermodynamic relation F = C − P + 2, formulated by Josiah Willard Gibbs in the 1870s.

Phase shift

In quantum scattering theory, the phase shift δℓ(k) is the angle by which a scattered partial wave is rotated relative to the wave propagating with no potential.

Phase space

Phase space is the space of all possible instantaneous states of a physical system, where a single point specifies the complete state; for n degrees of freedom it is 2n-dimensional.

Phase space reconstruction is a nonlinear time series analysis method that rebuilds a dynamical system's attractor from a single scalar signal using time-delayed coordinates, justified by Takens' embedding theorem.

Phase stability (accelerator physics)

Phase stability, conceived independently by Vladimir Veksler in 1944 and Edwin McMillan in 1945, is the principle that keeps circular accelerator particles bound to a fixed RF phase.

Phase transition

A phase transition, also called a phase change, is a change in the nature or number of phases of a system as temperature, pressure, or an applied field varies.

Phase unwrapping

Phase unwrapping is the computational recovery of an unambiguous phase field from measurements known only modulo 2π radians, central to SAR interferometry, digital holography, and fringe projection.

Phase velocity and group velocity

Phase velocity and group velocity are two distinct speeds of a wave: the speed of a single crest and the speed of a wave packet's energy.

Phase-change material

A phase-change material (PCM), also called a phase transition material, stores and releases large amounts of latent heat while melting or freezing at a nearly constant temperature.

Phase-change metasurfaces

Phase-change material reconfigurable metasurfaces are flat optical devices incorporating switchable materials such as Ge₂Sb₂Te₅, letting one fixed structure deliver beam steering, holography, and reconfigurable lenses.

Phase-change solvent

A phase-change solvent is a liquid absorbent for CO2 capture that separates into CO2-rich and CO2-lean phases, so only the rich fraction is regenerated, lowering energy use.

Phase-contrast imaging

Phase-contrast imaging is a family of techniques that converts phase shifts of light, X-rays, or electrons into intensity contrast, revealing weakly absorbing structures; Frits Zernike invented the method in 1934.

Phase-contrast microscopy

Phase-contrast microscopy, also known as Zernike phase-contrast microscopy, is a light microscopy technique that makes transparent specimens such as living cells visible, invented by Dutch physicist Frits Zernike.

Phase-imaging ion-cyclotron-resonance mass spectrometry

Introduced in 2013 by Sergey Eliseev and Klaus Blaum, PI-ICR mass spectrometry is a Penning trap technique that measures atomic masses by projecting ion motion onto a sensitive detector.

Phase-sensitive amplification (spectroscopy)

Phase-sensitive amplification, also called lock-in amplification, is a signal-recovery technique that measures weak signals by detecting the component matching a known reference frequency, standard in spectroscopy for roughly a century.

Phase-sensitive optical time-domain reflectometry

Phase-sensitive optical time-domain reflectometry, or φ-OTDR, is a fiber-optic sensing technique that detects vibrations and acoustic waves, and is the principle behind most distributed acoustic sensing.

Phase-shifting holography

Phase-shifting holography is a digital holography technique, proposed by Ichirou Yamaguchi and Tong Zhang in 1997, that recovers the complex object wave from interferograms with known phase shifts.

Phase-shifting interferometry

Phase-shifting interferometry (PSI) is a technique for measuring an optical wavefront by recording several interferograms at known phase offsets and combining them into a phase map.

Phase-space formulation of quantum mechanics

The phase-space formulation of quantum mechanics represents quantum states and observables as functions on phase space, centered on the Wigner function introduced by Eugene Wigner in 1932.

Phase-space spiral

The phase-space spiral, also called the Gaia snail, is a spiral pattern in the velocities of stars near the Sun, discovered in Gaia data in 2018.

Phase-transfer catalysis

Phase-transfer catalysis (PTC) is a method in organic chemistry in which a quaternary ammonium or phosphonium salt carries ionic reactants between immiscible phases, applied in over 700 industrial processes.

Phase-type distribution

A phase-type distribution is the distribution of the time until absorption in a finite continuous-time Markov chain with transient phases, systematized by Marcel F. Neuts and applied in queueing, reliability, and insurance.

Phased Array Radar (NSSL)

Phased Array Radar at NOAA's National Severe Storms Laboratory in Norman, Oklahoma, tests electronically steered antennas that scan storms once a minute, faster than NEXRAD.

PhaseNet

PhaseNet is a deep-neural-network method that picks the arrival times of P and S waves from three-component seismic waveforms, introduced by Weiqiang Zhu and Gregory C. Beroza in 2018.

Phases of ice

The phases of ice are the distinct crystalline and amorphous forms water takes; 20 were known by 2021, with ordinary ice Ih the only one on Earth.

Phason

A phason is an additional elastic degree of freedom of quasicrystals, distinct from ordinary vibrational phonon modes, arising from the higher-dimensional description and detectable in diffraction as broadened Bragg peaks and diffuse scattering.

Phasor

A phasor, or phase vector, is a complex number representing the amplitude and phase of a sinusoidal signal of fixed frequency, used in AC circuit analysis.

Phasor fluorescence lifetime imaging

Phasor fluorescence lifetime imaging (phasor FLIM) is a fit-free analysis method for fluorescence lifetime imaging microscopy, introduced in a 2008 Biophysical Journal paper by Michelle Digman, Valeria Caiolfa, Moreno Zamai, and Enrico Gratton.

Phenacene

Phenacene is a polycyclic aromatic hydrocarbon whose benzene rings fuse in a zigzag, phenanthrene-like pattern, including phenanthrene, chrysene, and picene; more stable than linear acenes, phenacenes serve as organic semiconductors in transistors.