Physical world and mathematics

Fractional Josephson effect

The fractional Josephson effect is a variant of the ac Josephson effect where the supercurrent is 4π-periodic, oscillating at half the conventional frequency under voltage.

The fractional Laplacian is a nonlocal pseudo-differential operator, written (-Δ)^(α/2) for 0 < α < 2, that generalizes the Laplacian to fractional powers and appears in models of anomalous diffusion and stable Lévy processes.

Fractional quantum anomalous Hall effect

The fractional quantum anomalous Hall effect is a fractional quantum Hall effect that appears at zero magnetic field in fractional Chern insulators, first observed in twisted MoTe₂ bilayers in 2023.

Fractional quantum anomalous Hall effect in moiré TMDs

The fractional quantum anomalous Hall effect is fractionally quantized Hall conductance at zero magnetic field in a moiré material, first demonstrated in twisted bilayer MoTe2 in 2023.

Fractional quantum Hall effect

The fractional quantum Hall effect (FQHE) quantizes Hall conductance at fractional values in a two-dimensional electron gas under a strong magnetic field, arising from strong electron-electron correlations.

Fractional quantum Hall effect in bilayer graphene

The fractional quantum Hall effect in bilayer graphene produces quantized Hall plateaus at fractional filling factors in two stacked graphene sheets in a strong magnetic field.

Fractional statistics

Fractional statistics is the quantum-mechanical behavior of identical particles in two dimensions whose exchange phase lies strictly between bosons (0) and fermions (π), yielding anyons.

Fractional-order model

A fractional-order model is a mathematical model whose derivatives or integrals appear at non-integer order, describing systems whose response depends on their entire past history.

Fractionalization

Fractionalization is the phenomenon in quantum many-body systems where excitations carry fractions of the constituents' quantum numbers, such as e/3 charges in the fractional quantum Hall effect.

Fractionating column

A fractionating column, also called a distillation column, is a packed or trayed tube between flask and condenser that separates liquids with close boiling points by repeated vaporization-condensation cycles.

Fracton

A fracton is a quasiparticle excitation of a quantum many-body system that cannot move freely, giving rise to fracton phases that defy standard topological order.

Fracton topological order

Fracton topological order is a three-dimensional topological order in which pointlike fracton excitations are immobile or move only along restricted lines, planes, or fractals, promising for quantum memory.

Fracture

Fracture is the separation of a solid body into pieces under stress. Fracture mechanics predicts the strength of cracked structures from the stress field at the crack tip.

Fracture (geology)

A fracture, also called a rock fracture, is a break in a rock formed under stress; fractures form interconnected networks that often dominate fluid flow in rock.

Fracture mechanics

Fracture mechanics is the field of engineering science that predicts the behavior of cracks in solids using parameters such as the stress intensity factor, and underpins aircraft damage tolerance analysis.

Fracture toughness

Fracture toughness is a material property measuring resistance to crack extension, the critical stress intensity factor Kc at which a pre-existing sharp crack begins to grow rapidly.

Fracture zone

A fracture zone is a long, linear belt of ocean floor extending beyond an active transform fault, where the two sides move together and faulting ceases, leaving a scar.

Fragile topology

Fragile topology is a band topology in crystals whose topological obstruction vanishes when suitable trivial bands are added, identified by Po, Watanabe, and Vishwanath in 2018.

Fragility (glass physics)

In glass physics, fragility is a measure of how steeply a liquid's viscosity increases on cooling toward the glass transition, introduced by C. Austen Angell in 1985.

Fragment molecular orbital method

The fragment molecular orbital (FMO) method is an approximate ab initio quantum chemistry technique for large molecules such as protein-ligand complexes, introduced by Kazuo Kitaura and colleagues in 1999.

Fragmentation functions

A fragmentation function gives the probability density that an outgoing high-energy quark or gluon produces an observed hadron carrying a fraction of the parton's momentum.

Frailty model

A frailty model is a survival analysis model extending proportional hazards models with a multiplicative random effect representing unobserved heterogeneity, such as clustering or shared risk factors.

Frame bundle

In differential geometry, the frame bundle of a vector bundle is the bundle whose fiber over each point is the set of all bases of that fiber.

Frame of reference

A frame of reference, also called a reference frame, is an object with rules for measuring locations and time, used by an observer to describe motion relative to that object.

Frame-dragging

Frame-dragging, the Lense-Thirring effect, is a general-relativistic effect in which a rotating mass drags spacetime around with its rotation, first derived by Lense and Thirring in 1918 and measured by Gravity Probe B.