Where does breakdown collide?

The sudden onset of large electric current through a material that normally insulates, once the applied electric field passes a critical value and charge carriers multiply or tunnel across the gap. Zener's 1934 A theory of the electrical breakdown of solid dielectrics described how a strong enough field can lift electrons across the forbidden energy gap of an insulator so that it abruptly conducts, and McKay's 1954 Avalanche breakdown in silicon traced the competing mechanism in which one fast carrier knocks loose others in a self-amplifying cascade. The referent is a physical failure of insulation at a threshold field, scaled in volts per unit thickness, and it has nothing to do with a society losing its ordering controls or a statistical estimator losing its resistance to bad data.[1][2]

Unit

A field-driven onset of conduction, scaled as a breakdown voltage or field strength in volts per metre

Recovery means

Reversible below a current limit, but a sustained avalanche can permanently damage the material

Measured by

Found as the voltage or field at which current rises sharply in a controlled test on the material or junction

In the study of collective action, the loosening or collapse of the everyday social ties and controls that normally keep people integrated and orderly, which some theories treat as the condition that releases protest, riot, or movement activity. Kornhauser's 1959 The politics of mass society argued that when the groups standing between the individual and the state weaken and people become socially unattached, they grow available for mass mobilisation, and Useem's 1998 review Breakdown theories of collective action gathered this family of accounts and set it against rival theories that credit stable organisation and resources instead. The referent is a change in the fabric of social order, gauged by indicators of disintegration and unrest, and it is not a physical failure of insulation or a numerical limit on an estimator.[3][4]

Unit

A degree of loosening in the social ties and controls across a population or community

Recovery means

Not applicable

Measured by

Studied through indicators of social disintegration alongside rates of protest, unrest, or disorder

The largest fraction of a sample that can be replaced by arbitrary, even extreme, values before an estimator can be forced to give a useless answer, so a high value means the method tolerates many bad points. Hampel's 1971 A general qualitative definition of robustness introduced this limiting fraction as a way to rank how robust an estimator is, and Donoho and Huber's 1983 The notion of breakdown point gave the exact finite-sample version now in common use, under which the median withstands up to half the data being corrupted while the mean withstands none. The referent is a numerical tipping fraction for a statistical estimator, a pure proportion between zero and one half, and it shares nothing with insulation failing under a field or a society losing its ordering ties.[5][6]

Unit

A proportion between 0 and 0.5: the share of contaminated data an estimator withstands

Recovery means

Not applicable

Measured by

Derived analytically or by simulation as the fraction of outliers that drives the estimate to a useless value