Preisach model of hysteresis¶
A rate-independent hysteresis model that represents path-dependent output as a weighted superposition of two-threshold relay operators retaining state between threshold crossings.
Core Idea¶
The classical scalar Preisach model represents rate-independent hysteresis as a weighted parallel superposition of two-threshold relay operators. Each relay switches at an upper threshold and a lower threshold, retaining its prior state between them. Present output therefore depends on the input's path, not only its current value.
Ordered threshold pairs occupy the Preisach plane, and a density weights their contributions. A continuous model integrates relay states; a discrete implementation uses a weighted grid. The construction is phenomenological: a fitted density need not correspond to literal independent material domains.
Cross-Domain Echoes¶
See how this entry connects to another domain.
Scope of Application¶
The operator supports path-dependent systems with suitable relay-like memory:
- Magnetic materials — Model field–magnetization loops and reversal histories.
- Smart-material actuators — Predict displacement or polarization under cycling.
- Control compensation — Track internal relay state during command reversals.
- Porous media — Represent retention or transport paths under changing inputs.
- Mechanical systems — Approximate repeatable scalar hysteresis within a calibrated regime.
Classical use assumes approximate rate independence. Vector direction, frequency effects, drift, stochastic switching, or changing temperature can require modified models.
Clarity¶
State which threshold is upper or lower, the switching inequalities, relay output levels, initial state, integration domain, density normalization, input history, and output scale. Symbol conventions vary, so letters alone cannot establish orientation.
Distinguish the model from a memoryless curve, one relay, a Prandtl–Ishlinskii operator, a dynamic Preisach variant, or a claimed physical domain population. Major-loop fit alone does not validate minor-loop memory.
Manages Complexity¶
The model compresses distributed path memory into a relay-state boundary over threshold space. Updating threshold crossings is simpler than retaining the complete input history, and weighted superposition can reproduce nested loops. The price is a potentially large identification problem and a density whose physical meaning may remain limited.
Abstract Reasoning¶
Define input, output, rate range, and initial state. Choose a consistent threshold convention and relay rule. Identify weights from histories that excite the relevant plane, then update states and sum outputs. Validate major loops, minor loops, reversals, and unseen paths separately. Add dynamic or vector structure only when residual behavior demonstrates failure of the classical boundary.
Knowledge Transfer¶
The model transfers across domains when a scalar input drives repeatable, approximately rate-independent hysteresis decomposable into weighted relay memory. A visually similar loop is insufficient if its dynamics or state structure differ. No immediate DAG parent is asserted because the catalog lacks a verified hysteresis-operator genus; memory, threshold, and superposition are participating structures rather than strict parents.
Threshold values and density units must be reidentified in the receiving domain. Only the operator architecture transfers unchanged; calibration, admissibility constraints, physical interpretation, error tolerance, and evidence for rate independence remain local to the modeled system.
History remains part of state.
Relationships to Other Abstractions¶
Current abstraction Preisach model of hysteresis Domain-specific
Parents (1) — more general patterns this builds on
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Preisach model of hysteresis is a kind of Formal Model Domain-specific
It is a mathematical operator model of hysteresis.
Hierarchy path (1) — routes to 1 parentless root
- Preisach model of hysteresis → Formal Model → Representation → Abstraction
Neighborhood in Abstraction Space¶
Preisach model of hysteresis sits in a sparse region of the domain-specific corpus (97th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Unclustered & Miscellaneous (2551 abstractions)
Nearest neighbors
- Deterministic Finite Automaton — 0.77
- In-Place Adjacent-Block Rotation — 0.77
- Flux Qubit — 0.76
- DEVS — 0.76
- Verlet Integration — 0.76
Computed from structural-signature embeddings · 2026-10-08