coercitiv

Coercitiv is an adjective used in several disciplines to describe concepts related to coercion or to coercivity. In English the corresponding terms are coercive and coercivity; in other languages, including Romanian and French, a form such as coercitiv or coercitif appears in technical writing. The root is Latin coercere, to restrain or compel.

In magnetism, coercivity (coercitiv) is the resistance of a ferromagnetic material to demagnetization. It is defined by the coercive field Hc, the external magnetic field required to bring the material's magnetization to zero after saturation. Materials with high coercivity—hard magnets—retain magnetic order and are used in permanent magnets and data-storage devices. Low-coercivity materials—soft magnets—are easily demagnetized and often used in transformer cores. Coercivity is influenced by composition, microstructure, temperature, and mechanical treatment; it is typically measured in amperes per meter (A/m) or oersted (Oe).

In mathematics, a function f is called coercive if f(x) grows without bound as the norm of x tends to infinity. This property helps guarantee the existence of minimizers for optimization problems on unbounded domains. For example, f(x) = ||x||^2 is coercive on Euclidean space. Coercivity is a common hypothesis in the calculus of variations and in convex analysis, often together with lower semicontinuity.

In social or law contexts, coercive describes actions that enforce compliance by threat or use of force, such as coercive measures or coercive control. This use is distinct from mathematical or physical notions of coercivity.