Data Physics & Cyber-Physical Systems - Part IV: 3D Spatial PDE Continuum Model and Silicon-Hydrodynamic Mapping: Comprehensive Descriptive Overview of the Spatial Model
Year: 2026
Type: article
Abstract: Publication Description (Abstract & Repository Overview). As Part IV and the capstone volume of the Data Physics & Cyber-Physical Systems series, this publication defines the spatial data physics framework describing the mechanics of latency in high-density compute clusters. Transitioning from lumped-parameter differential-algebraic systems (DAE) to a 3D spatial continuum partial differential equation (PDE) framework enables precise mapping of the dynamic relationships between continuous physical fields on the silicon die T(x,y,z,t) and local hydrodynamics within liquid cooling cold plate (mCDU) microchannels. The model precisely couples local hydraulic resistance vectors, spatial temperature distributions, and non-linear transistor leakage currents I_leak(T_j), analytically explaining the genesis of localized silicon hotspots. The paper rigorously demonstrates how two-phase flow phenomena (alpha_void) and micrometric flow disturbances (maldistribution) elevate local thermal resistance R_th(x,y), forcing Power Management IC (PMIC) systems to trigger localized clock throttling (DVFS) as a hardware safeguard. We prove the direct impact of these localized thermal-hydraulic degradation events on extending the deterministic instruction execution time integral (t_exec), triggering the destructive Straggler Effect and forcing multi-thousand-node GPU clusters to wait idly at network synchronization barriers (e.g., NCCL Ring-AllReduce). The Topological Solution: Finally, this work establishes a mathematical foundation for the topological optimization of microchannel geometry, enabling the physical synchronization of hydraulic resistance vectors with asymmetric algorithmic computational load maps to guarantee the temporal consistency and determinism of multi-GPU operations. The original PDF files attached to the respective Zenodo records have deliberately not been modified or re-issued, preserving their cryptographic qualified timestamp and digital signature (Profil Zaufany). This guarantees full Legal Continuity, Data Integrity, and Unalterable Patent/Scientific Priority (Prior Art) based on the original file checksums. Title updates and standardization under the Data Physics & Cyber-Physical Systems (Parts I–IV) monographic umbrella have been applied exclusively to the digital metadata layer (DataCite/Zenodo metadata) to optimize academic citation indexing without compromising the evidentiary integrity of the source documents.
Author: Olszewski, Rajmund
Language: English
Subfield: Mechanical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7219729755
FWCI:
Cites:
Cited by:
Related to: