Physical world and mathematics

Direct C–H arylation via photoredox catalysis

Direct C–H arylation via photoredox catalysis is a family of reactions in which a visible-light photocatalyst generates aryl radicals that install aryl groups onto carbon–hydrogen bonds without prefunctionalization.

Direct collapse black hole seed

A direct collapse black hole seed is a hypothetical massive black hole, 10,000 to a million solar masses, formed when pristine gas in the early Universe collapses directly.

Direct CP violation

Direct CP violation is CP violation arising in the decay amplitudes of a particle rather than in particle-antiparticle mixing, first seen in neutral kaon decays by the NA31 experiment at CERN.

Direct current

Direct current (DC) is the flow of electric charge in a single, constant direction, unlike alternating current; it powers computers, LEDs, solar cells, and electric vehicles.

Direct deep-sea carbon dioxide injection

Direct deep-sea carbon dioxide injection is a proposed sequestration method that releases captured liquid CO2 into deep ocean, where it would stay isolated from the atmosphere for centuries.

Direct detection of dark matter

Direct detection of dark matter is the experimental search for dark matter particles elastically scattering off atomic nuclei or electrons in terrestrial detectors, typically placed deep underground.

Direct detection of the thorium-229 nuclear clock transition

The direct detection of the thorium-229 nuclear clock transition was the first unambiguous observation of the thorium-229 isomer, reported by researchers at LMU Munich in Nature in May 2016.

Direct electron detector

A direct electron detector is an imaging sensor for transmission electron microscopy in which electrons strike the semiconductor itself, improving efficiency and enabling high-frame-rate movie acquisition.

Direct imaging (astronomy)

Direct imaging of exoplanets is an observational astronomy technique that records light from planets resolved from their host star, first achieving success with 2M1207b in 2004.

Direct integral

A direct integral assembles a family of Hilbert spaces, von Neumann algebras, or operators indexed by a measure space, generalizing the direct sum of Hilbert spaces.

Direct measurement of the quantum wavefunction

Direct measurement of the quantum wavefunction is a technique demonstrated at the National Research Council of Canada in 2011 using a weak measurement followed by a strong one.

Direct methods (crystallography)

Direct methods are crystallographic techniques that estimate missing diffraction phases from intensities alone, developed by Karle and Hauptman, who won the 1985 Nobel Prize in Chemistry.

Direct nuclear reaction

A direct nuclear reaction is a nuclear reaction in which a projectile interacts with a few surface nucleons in one fast step, without forming a compound nucleus.

Direct numerical simulation

Direct numerical simulation (DNS) is a computational fluid dynamics method that resolves all scales of turbulent flow with no turbulence model, serving mainly as a research tool.

Direct ocean capture

Direct ocean capture (DOC) is a marine carbon removal technology that extracts dissolved CO₂ from seawater using electrochemical processes, letting the treated water absorb more atmospheric CO₂.

Direct product

The direct product is a construction in algebra that combines structures of the same kind, such as groups or rings, into a single structure with coordinatewise operations.

Direct proof

A direct proof establishes a statement by assuming its hypotheses and deriving the conclusion through an explicit chain of deductions, proving the proposition in its originally stated form rather than a transformed equivalent.

Direct reaction mechanisms

A direct reaction mechanism is a nuclear reaction in which the projectile interacts with the target nucleus in a single, fast step without forming a compound nucleus.

Direct sampling (Monte Carlo)

Direct sampling is a Monte Carlo technique that generates independent, unweighted draws exactly from a target probability distribution by transforming uniform random numbers, without rejecting candidates.

Direct search (optimization)

Direct search is a derivative-free optimization method that improves an objective function by sampling trial points and using function values alone, with no gradients or models.

Direct simulation Monte Carlo

Direct simulation Monte Carlo (DSMC) is a stochastic, particle-based numerical method for solving the Boltzmann equation in rarefied gas flows, developed by Graeme Bird and first implemented in 1962.

Direct solver

A direct solver is a numerical linear algebra method that solves linear systems by factorizing the matrix, giving the solution in a fixed number of steps.

Direct stochastic optical reconstruction microscopy

Direct stochastic optical reconstruction microscopy (dSTORM) is a single-molecule localization microscopy technique achieving about 20 nm resolution using standard fluorescent dyes instead of engineered photoactivatable proteins.

Direct sum

The direct sum is an algebraic construction combining modules, vector spaces, or abelian groups into one larger object, whose elements are tuples with only finitely many nonzero entries.

Direct Z-scheme heterojunction

A direct Z-scheme heterojunction is a mediator-free composite photocatalyst of two semiconductors with staggered band alignment, where low-energy carriers recombine while high-energy electrons and holes drive reactions.

Direct-drive inertial confinement fusion

Direct-drive inertial confinement fusion is a fusion approach in which laser energy strikes the fuel capsule directly instead of a hohlraum, offering higher implosion efficiency.

Directed acyclic graph

A directed acyclic graph (DAG), also called an acyclic digraph, is a directed graph containing no directed cycles, so it admits a topological ordering of its vertices.

Directed C–H borylation

Directed C–H borylation is a family of reactions converting a specific carbon–hydrogen bond into a carbon–boron bond, with the site chosen by a directing group rather than sterics alone.

Directed C–H cyanation

Directed C–H cyanation is a transition-metal-catalyzed reaction in which a directing group on an arene positions the catalyst to convert a chosen carbon–hydrogen bond into a nitrile.