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The curves form a hysteresis loop. Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past. Plots of a single component of the moment often form a loop or hysteresis curve, where there are ...
The response of the magnetic moment to a magnetic field boosts the response of the coil wrapped around it. Low coercivity reduces that energy loss associated with hysteresis. Magnetic hysteresis material (soft nickel-iron rods) has been used in damping the angular motion of satellites in low Earth orbit since the dawn of the space age. [5]
Hysteresivity derives from “hysteresis”, meaning “lag”. It is the tendency to react slowly to an outside force, or to not return completely to its original state. Whereas the area within a hysteresis loop represents energy dissipated to heat and is an extensive quantity with units of energy, the hysteresivity represents the fraction of the elastic energy that is lost to heat, and is an ...
In structural engineering, the Bouc–Wen model of hysteresis is a hysteretic model typically employed to describe non-linear hysteretic systems. It was introduced by Robert Bouc [ 1 ] [ 2 ] and extended by Yi-Kwei Wen, [ 3 ] who demonstrated its versatility by producing a variety of hysteretic patterns.
A nonlinear dynamical system exhibits chaotic hysteresis if it simultaneously exhibits chaotic dynamics (chaos theory) and hysteresis.As the latter involves the persistence of a state, such as magnetization, after the causal or exogenous force or factor is removed, it involves multiple equilibria for given sets of control conditions.
The red area is a hysteresis loop and shows the amount of energy lost (as heat) in a loading and unloading cycle. It is equal to ∮ σ d ε {\textstyle \oint \sigma \,d\varepsilon } , where σ {\displaystyle \sigma } is stress and ε {\displaystyle \varepsilon } is strain.
The Einstein field equations (EFE) may be written in the form: [5] [1] + = EFE on the wall of the Rijksmuseum Boerhaave in Leiden, Netherlands. where is the Einstein tensor, is the metric tensor, is the stress–energy tensor, is the cosmological constant and is the Einstein gravitational constant.
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