Mean-field theoryIn physics and probability theory, Mean-field theory (MFT) or Self-consistent field theory studies the behavior of high-dimensional random (stochastic) models by studying a simpler model that approximates the original by averaging over degrees of freedom (the number of values in the final calculation of a statistic that are free to vary). Such models consider many individual components that interact with each other. The main idea of MFT is to replace all interactions to any one body with an average or effective interaction, sometimes called a molecular field.
Infinitesimal strain theoryIn continuum mechanics, the infinitesimal strain theory is a mathematical approach to the description of the deformation of a solid body in which the displacements of the material particles are assumed to be much smaller (indeed, infinitesimally smaller) than any relevant dimension of the body; so that its geometry and the constitutive properties of the material (such as density and stiffness) at each point of space can be assumed to be unchanged by the deformation.
Diffusionless transformationDiffusionless transformations, also referred to as displacive transformations, are solid-state changes in the crystal structure that do not rely on the diffusion of atoms over long distances. Instead, they occur due to coordinated shifts in atomic positions, where atoms move by a distance less than the span between neighboring atoms while maintaining their relative arrangement. An illustrative instance of this is the martensitic transformation observed in steel.
Powder metallurgyPowder metallurgy (PM) is a term covering a wide range of ways in which materials or components are made from metal powders. PM processes can reduce or eliminate the need for subtractive processes in manufacturing, lowering material losses and reducing the cost of the final product. Powder metallurgy is also used to make unique materials impossible to get from melting or forming in other ways. A very important product of this type is tungsten carbide.
MicrostructureMicrostructure is the very small scale structure of a material, defined as the structure of a prepared surface of material as revealed by an optical microscope above 25× magnification. The microstructure of a material (such as metals, polymers, ceramics or composites) can strongly influence physical properties such as strength, toughness, ductility, hardness, corrosion resistance, high/low temperature behaviour or wear resistance. These properties in turn govern the application of these materials in industrial practice.
Poisson point processIn probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one another. The Poisson point process is often called simply the Poisson process, but it is also called a Poisson random measure, Poisson random point field or Poisson point field.
Poisson distributionIn probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. It is named after French mathematician Siméon Denis Poisson ('pwɑːsɒn; pwasɔ̃). The Poisson distribution can also be used for the number of events in other specified interval types such as distance, area, or volume.
Creep (deformation)In materials science, creep (sometimes called cold flow) is the tendency of a solid material to undergo slow deformation while subject to persistent mechanical stresses. It can occur as a result of long-term exposure to high levels of stress that are still below the yield strength of the material. Creep is more severe in materials that are subjected to heat for long periods and generally increase as they near their melting point. The rate of deformation is a function of the material's properties, exposure time, exposure temperature and the applied structural load.
Non-linear sigma modelIn quantum field theory, a nonlinear σ model describes a scalar field Σ which takes on values in a nonlinear manifold called the target manifold T. The non-linear σ-model was introduced by , who named it after a field corresponding to a spinless meson called σ in their model. This article deals primarily with the quantization of the non-linear sigma model; please refer to the base article on the sigma model for general definitions and classical (non-quantum) formulations and results.
Ising modelThe Ising model (ˈiːzɪŋ) (or Lenz-Ising model or Ising-Lenz model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent magnetic dipole moments of atomic "spins" that can be in one of two states (+1 or −1). The spins are arranged in a graph, usually a lattice (where the local structure repeats periodically in all directions), allowing each spin to interact with its neighbors.
