Physical world and mathematics

Modal analysis

Modal analysis is the process of extracting a vibrating system's mode shapes, natural frequencies, damping ratios, and modal masses from measured transfer functions, used to diagnose vibration problems.

Modal dispersion

Modal dispersion, or intermodal dispersion, is the spreading of an optical pulse in time as it travels through multimode fiber, usually limiting bit rate and link length.

Modal logic

Modal logic is a family of formal logics extending classical logic with operators for necessity and possibility, plus logics of obligation, time, and belief, originating with C.I. Lewis in 1912.

Modal logic D

Modal logic D, also written KD, adds to K the axiom that what is necessary is possible, making it the modal basis of Standard Deontic Logic.

Modal logic of agency

The modal logic of agency formalizes what agents do, can do, and are responsible for, chiefly through Belnap and Perloff's "seeing to it that" (stit) operator.

Modal realism

Modal realism is the metaphysical thesis that possible worlds are concrete entities like our own world, associated above all with David Lewis's 1986 book On the Plurality of Worlds.

Modal voice

Modal voice, also called the modal register or normal voice, is the vocal register used in everyday speech, produced by vocal folds vibrating as thick, full-mass structures between vocal fry and falsetto.

Modal μ-calculus

The modal μ-calculus is a temporal logic of programs extending modal logic with least and greatest fixed-point operators, used to model check recursive correctness properties.

Mode (statistics)

The mode in statistics is the value that occurs most often in a data set, one of the three classical measures of central tendency alongside the mean and the median.

Mode 2

Mode 2 is a science and technology studies concept describing knowledge produced in a context of application by transient teams, contrasted with traditional Mode 1 science.

Mode effect

A mode effect is a systematic difference in survey results arising from how data are collected, covering selection effects on who responds and measurement effects on how.

Mode field diameter

Mode field diameter (MFD) measures the transverse extent of light in a single-mode optical fiber, typically larger than the core, and is defined by the Petermann II integral.

Mode shape

A mode shape is the deformation pattern a structure adopts when vibrating freely at a natural frequency, mathematically the eigenvector of the structure's eigenvalue problem.

Mode-coupling theory

Mode-coupling theory (MCT) is a first-principles theoretical framework describing the slow dynamics of dense liquids, predicting a transition to a nonergodic glassy state from a liquid's static structure alone.

Mode-locked fiber laser

A mode-locked fiber laser is a fiber laser whose cavity modes are locked in phase, emitting ultrashort femtosecond or picosecond pulses at a fixed repetition rate.

Mode-locked laser diode

A mode-locked laser diode is a semiconductor laser that emits ultrashort optical pulses, typically 0.5 to 5 picoseconds, at repetition rates used in telecoms and optical data transmission.

Mode-locking

Mode-locking is a family of laser techniques that fixes the relative phases of a laser's longitudinal modes, turning continuous light into a train of ultrashort, high-peak-power pulses.

Model

A scientific model is a purposeful, simplified representation of a system, phenomenon, or process, built to explain data, connect theories to situations, and support decisions.

Model category

A model category is a category with three classes of morphisms, weak equivalences, fibrations, and cofibrations, introduced by Daniel Quillen in 1967 as an axiomatic framework for homotopy theory.

Model checking

Model checking is a formal verification technique that automatically checks whether a finite model of a system satisfies a temporal logic property, producing counterexamples on failure.

Model companion

A model companion of a first-order theory T is a model complete theory whose models each embed in models of T and vice versa, introduced by Abraham Robinson.

Model for Prediction Across Scales

The Model for Prediction Across Scales (MPAS) is a modeling framework developed by NCAR and Los Alamos National Laboratory, using variable-resolution Voronoi meshes for weather and climate simulation.

Model of computation

A model of computation is a formal mathematical description of what a computing device can do, the most famous being the Turing machine, introduced by Alan Turing in 1936.

Model theory

Model theory, also called the theory of models, is the branch of mathematical logic studying how formal languages are interpreted, especially first-order languages and their structures.

Model-based clustering

Model-based clustering is a statistical method that groups data by fitting a finite mixture model, usually of multivariate normal distributions, fitted with the EM algorithm and choosing the number of clusters by BIC.

Modeling Instruction

Modeling Instruction is an inquiry-based science pedagogy developed at Arizona State University in the 1980s by David Hestenes and Malcolm Wells, organizing courses around student-built models.

Moderate deviations

Moderate deviations are asymptotic results in probability theory describing tail probabilities at intermediate scales, between the central limit theorem and large deviations, where Gaussian approximations still hold.

Moderated mediation

Moderated mediation, also known as moderated mediation analysis, is a statistical method testing whether the indirect effect of a variable through a mediator varies with a moderator, coined by James and Brett in 1984.

Moderation analysis

Moderation analysis is a regression-based statistical method for testing whether the relationship between an independent and dependent variable changes as a function of a third variable, the moderator.