← Mathematical compendium

Published equation contexts

WLWL

Why this formula appears here

where P\mathcal{P} is a candidate placement of dies on the carrier, WL is total interconnect wirelength, Tmax⁡T_{\max} is peak steady-state junction temperature anywhere in the assembly, and σmax⁡\sigma_{\max} is peak mechanical stress at any bonded interface. This is a schematic statement of the shape these tools optimize, not a reproduction of any one paper’s exact formula, but it makes the practitioner point concrete: whichever of α\alpha , β\beta , and γ\gamma a design team weights most heavily determines where dies actually land, and a floorplan tuned only for WL is optimizing a real but incomplete objective.

Read the full article-specific guide →

Read the representative guide

WW

Symbol W

W is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Read this term in its guide →
LL

Symbol L

L is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Read this term in its guide →

How to interpret it

Read this expression with the definitions, units, and assumptions supplied by the article.

Research cited beside this formula

Learn the mathematics behind it

Published contexts (2)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

WLWL

Equation 3 · AI Hardware & Semiconductors

Chiplets and Advanced Packaging in Practice: Floorplanning, UCIe, and Thermal Co-Design

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

where P\mathcal{P} is a candidate placement of dies on the carrier, WL is total interconnect wirelength, Tmax⁡T_{\max} is peak steady-state junction temperature anywhere in the assembly, and σmax⁡\sigma_{\max} is peak mechanical stress at any bonded interface. This is a schematic statement of the shape these tools optimize, not a reproduction of any one paper’s exact formula, but it makes the practitioner point concrete: whichever of α\alpha , β\beta , and γ\gamma a design team weights most heavily determines where dies actually land, and a floorplan tuned only for WL is optimizing a real but incomplete objective.

Equation guide → · Article →
WLWL

Equation 9 · AI Hardware & Semiconductors

Chiplets and Advanced Packaging in Practice: Floorplanning, UCIe, and Thermal Co-Design

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

where P\mathcal{P} is a candidate placement of dies on the carrier, WL is total interconnect wirelength, Tmax⁡T_{\max} is peak steady-state junction temperature anywhere in the assembly, and σmax⁡\sigma_{\max} is peak mechanical stress at any bonded interface. This is a schematic statement of the shape these tools optimize, not a reproduction of any one paper’s exact formula, but it makes the practitioner point concrete: whichever of α\alpha , β\beta , and γ\gamma a design team weights most heavily determines where dies actually land, and a floorplan tuned only for WL is optimizing a real but incomplete objective.

Equation guide → · Article →