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Physical world and mathematics

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Nonclassical light

Nonclassical light is light whose quantum state cannot be described as a mixture of classical electromagnetic waves, including squeezed states, antibunched light, and single photons.

Noncommutative geometry

Noncommutative geometry, developed principally by Alain Connes, extends geometry, topology, and calculus to spaces described by noncommuting algebras, with the spectral triple as its central object.

Noncommutative geometry in string theory

Noncommutative geometry in string theory is the appearance of noncommuting spacetime coordinates in open-string gauge theories on D-branes in a background B-field, established by Seiberg and Witten in 1999.

Noncommutative integration

Noncommutative integration is a branch of operator algebra theory extending measure and integration theory to von Neumann algebras, reducing to classical integration when the algebra is abelian.

Noncommutative Moyal spacetime

Noncommutative Moyal spacetime, also called canonical noncommutative spacetime or the Moyal plane, is a spacetime model whose coordinates obey constant commutation relations, handled by the Moyal star product.

Nonconservative force

A nonconservative force is a force whose work between two points depends on the path taken, like friction, so no potential energy can be defined for it.

Noncovalent catalysis

Noncovalent catalysis is a mode of catalysis in which catalysts, typically small organic molecules, aromatic scaffolds, or enzymes, stabilize transition states through weak noncovalent interactions rather than covalent or coordination bonds.

Noncovalent interaction analysis (NCI)

Noncovalent interaction analysis (NCI) is a computational method introduced in 2010 that visualizes weak interactions, such as hydrogen bonds and steric repulsion, directly from electron density.

Noncovalent interactions

Noncovalent interactions are weak attractive or repulsive forces between molecules that do not share electrons, including hydrogen bonds and dispersion forces, typically 1 to 10 kcal/mol.

Nondeterministic finite automaton

A nondeterministic finite automaton (NFA) is a finite-state machine whose transitions can lead to several next states at once; it recognizes exactly the regular languages, like a deterministic automaton.

Nondeterministic Turing machine

A nondeterministic Turing machine is a mathematical model of computation that can choose among several possible transitions at each step, and it underlies the complexity class NP.

Nonequilibrium candidate Monte Carlo

Nonequilibrium candidate Monte Carlo is a Markov chain Monte Carlo method, introduced in 2011, that drives molecular systems out of equilibrium and accepts moves based on work performed.

Nongjian Tao

Nongjian Tao (N. J. Tao), 1963–2020, was a Chinese-born physicist and electrical engineer at Arizona State University who invented the STM break junction for measuring single-molecule conductance.

Nonholonomic system

A nonholonomic system is a mechanical system subject to velocity constraints that cannot be integrated into position constraints; rolling spheres and wheeled vehicles are standard examples.

Nonlinear acoustics

Nonlinear acoustics is the branch of acoustics studying sound waves so intense that the wave's own pressure changes the medium, causing waveform distortion, shocks, and harmonic generation.

Nonlinear anomalous Hall effect

The nonlinear anomalous Hall effect is a second-order transport effect in which transverse current grows as the square of the applied field, without magnetism or broken time-reversal symmetry.

Nonlinear autoregressive distributed lag model

The nonlinear autoregressive distributed lag (NARDL) model is a single-equation error correction model, introduced in 2014, that estimates separate effects of positive and negative changes in each explanatory variable.

Nonlinear Hall effect

The nonlinear Hall effect is a transverse voltage arising without a magnetic field in materials whose inversion symmetry is broken, predicted in 2015 and observed in bilayer WTe2 in 2018.

Nonlinear Hall effect in Weyl semimetals

The nonlinear Hall effect in Weyl semimetals is a transverse voltage at zero magnetic field that scales quadratically with current, driven by the Berry curvature dipole.

Nonlinear metasurface harmonic generation

Nonlinear metasurface harmonic generation is the conversion of light to harmonics of its frequency by metasurfaces, whose nanoresonators are far smaller than the nonlinear coherence length, relaxing phase matching and enabling wavefront-shaped harmonic light.

Nonlinear metasurfaces

Nonlinear metasurfaces are ultrathin, planar arrays of engineered nanostructures that convert light to new frequencies via harmonic generation while controlling the wavefront, without the phase-matching limits of bulk crystals.

Nonlinear mixed-effects model

A nonlinear mixed-effects model (NLME model) is a statistical model for repeated-measures data in which some parameters vary between individuals, and the standard tool of pharmacometrics.

Nonlinear optics

Nonlinear optics is the branch of optics studying effects that appear when a material's response to light is no longer proportional to the light's electric field.

Nonlinear phononics

Nonlinear phononics is a technique for controlling the structure and functional properties of solids, in which intense mid-infrared or terahertz light pulses drive phonons to large amplitudes, inducing targeted crystal deformations.

Nonlinear programming

Nonlinear programming, also known as nonlinear optimization, is the branch of mathematical optimization dealing with problems whose objective function, constraints, or both are nonlinear, generalizing linear programming.

Nonlinear regression

Nonlinear regression is a form of regression analysis in which the expected response is modeled by a function nonlinear in the unknown parameters, estimated by iterative least squares algorithms such as Levenberg-Marquardt.

Nonlinear Schrödinger equation

The nonlinear Schrödinger equation (NLS) is a partial differential equation combining dispersion and nonlinear self-interaction, with focusing and defocusing regimes, and applications in optics, water waves, and Bose–Einstein condensation.

Nonlinear sigma model

The nonlinear sigma model is a field theory whose field maps spacetime into a curved target manifold, governed by the target metric; it is named for the σ particle of Gell-Mann and Lévy's 1960 model.

Nonlinear system

A nonlinear system is a system whose equations describe behavior where output is not proportional to input; when the equations evolve in time it is called a dynamical system.

Nonlinearity (journal)

Nonlinearity is a peer-reviewed scientific journal covering nonlinear mathematics and nonlinear science, founded in 1988 by the Institute of Physics and the London Mathematical Society and published by IOP Publishing.