Hysteresis describes systems where the current state is shaped by both past and present influences. Notable for its path dependence and non-linearity, the concept is particularly relevant in disciplines such as material science, engineering, and economics.
Definition
Hysteresis: Phenomenon where the current state of a system depends on both its current input and past states.
Types and Qualitative Differences
- Mechanical: Found in materials like rubber bands, characterized by elastic energy loss.
- Magnetic: Seen in ferromagnetic materials such as iron, involves magnetic field alignment.
- Electrical: Present in systems like capacitors, related to charge storage.
- Thermal: Observed in phase transitions, such as the melting of ice.
- Biological: Manifests in physiological processes like neuron firing.
Mathematical Models
- First-Order Systems: Described by the ordinary differential equation \( \frac{dy}{dt} = f(y, u, t) \).
- Higher-Order Systems: Captured by systems of ordinary or partial differential equations.
Key Parameters
- Threshold: Value at which the system changes state.
- Memory: Reflects how past states influence the current state.
- Rate-Dependence: Indicates the speed at which a system returns to equilibrium.
- Time-Dependence: Hysteresis is often a time-dependent phenomenon.
Distinctive Features
- Path Dependence: Response is tied to the history of inputs.
- Non-Linearity: The system does not adhere to the principle of superposition.
- Asymmetry: Responses to increasing and decreasing inputs differ.
- Energy Dissipation: Energy is usually lost in a hysteresis loop, crucial for understanding efficiency in various applications.
- Scale Invariance: In some systems, hysteresis manifests across multiple scales.
Etymology
Derived from the Greek word “hysteresis,” meaning “deficiency” or “lagging behind.”
Applications
- Electric Motors: Design critically relies on understanding magnetic hysteresis and energy dissipation.
- Seismology: Earthquake understanding enhanced by mechanical hysteresis and scale invariance.
- Medicine: Hysteresis concepts relevant to drug dosing and metabolic rate calculations.
Relevant Academic Fields
- Physics: Material properties, energy dissipation, and quantum mechanics.
- Engineering: Control systems, energy efficiency, and materials science.
- Economics: Labor market and consumer behavior models often include hysteresis effects.
Related Concepts
- Feedback Loops: Can induce hysteresis phenomena.
- Rate-Independent: A subset where the effect of rate-dependence is negligible.
Common Misunderstandings
Not Inertia: Unlike inertia, hysteresis involves memory of past states.
