DefinitionDefinition: AI-adaptedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Scalar added-mass staggered recurrence

Definition

For positive scalars $m_{s}$ and $m_{f}$ , call $m_{s}$ the structure mass and $m_{f}$ the fluid added mass in the scalar toy added-mass recurrence. Given a scalar initial velocity increment $δ v_{0}$ , define successive increments by

$m_{s} δ v_{n + 1} = - m_{f} δ v_{n} (n \geq 0) .$

This is a stipulated one-mode sequential update used only to expose its amplification factor. It is not derived from, and makes no stability claim about, a general fluid-structure discretization.

Used by

A toy sequential coupling can amplify velocity error Example

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

Martina Maria Joosten, Aspects of interface modelling in fluid-structure interaction problems, PhD thesis, Swansea University (2011) (standard reference, not scraped)