Pulse Core Lexicon
Tension Propagation
Definition
Mathematical Expression
From the book · Chapter 4 · The Architecture of Dimensional Layers
āT/āt = Dā¹(x,t) Ć ā²T + Sā¹(x,t) - Aāø(x,t) Ć T [šĀ·šā»Ā¹Ā·šā»Ā³]
Dimensional analysis:
Where (from the book): T [šĀ·šā»Ā¹Ā·šā»Ā²], Dā¹(x,t) [šĀ²Ā·šā»Ā¹], ā²T [šĀ·šā»Ā³Ā·šā»Ā²], Sā¹(x,t) [šĀ·šā»Ā¹Ā·šā»Ā³], Aāø(x,t) [šā»Ā¹], x [š], t [š]
Read dimensionally: (T/t) = Dā¹(x,t) Ć ā²T + Sā¹(x,t) - Aāø(x,t) Ć T
([šĀ·šā»Ā¹Ā·šā»Ā²] Ć· [š]) = [šĀ·šā»Ā¹Ā·šā»Ā³]
[šĀ²Ā·šā»Ā¹] Ć [šĀ·šā»Ā³Ā·šā»Ā²] + [šĀ·šā»Ā¹Ā·šā»Ā³] - [šā»Ā¹] Ć [šĀ·šā»Ā¹Ā·šā»Ā²] = [šĀ·šā»Ā¹Ā·šā»Ā³] + [šĀ·šā»Ā¹Ā·šā»Ā³] - [šā»Ā¹] Ć [šĀ·šā»Ā¹Ā·šā»Ā²] = [šĀ·šā»Ā¹Ā·šā»Ā³] - [šā»Ā¹] Ć [šĀ·šā»Ā¹Ā·šā»Ā²] = [šĀ·šā»Ā¹Ā·šā»Ā³] - [šĀ·šā»Ā¹Ā·šā»Ā³] = [šĀ·šā»Ā¹Ā·šā»Ā³]
[šĀ·šā»Ā¹Ā·šā»Ā³] = [šĀ·šā»Ā¹Ā·šā»Ā³] ā Valid PulseCore Verified ā
Stress spreads, builds, and drains to maintain stability.
Where:
- T is unified tension field [šĀ·šā»Ā¹Ā·šā»Ā²]
- Dā¹(x,t) is effective diffusion coefficient [šĀ²Ā·šā»Ā¹]
- ā²T is Laplacian of tension field [šĀ·šā»Ā³Ā·šā»Ā²]
- Sā¹(x,t) is source terms from Recursive State Evolution [šĀ·šā»Ā¹Ā·šā»Ā³]
- Aāø(x,t) is absorption coefficient [šā»Ā¹]
- x is spatial position [š]
- t is time [š]
Technical Details
Category Concept
Chapter Chapter 4
Importance