Year: 2026
Type: preprint
Abstract: Transport in certain systems fails when diffusion cannot replenish or remove material from a boundary rapidly enough, causing the boundary concentration to reach a critical minimum or maximum. Motivated by experiments in electrochemical systems that demonstrate this diffusion-limited failure of charge transport, we determine dynamic current protocols that maximize charge transfer subject to a prescribed concentration constraint. The optimal protocol has a "bang-ride" structure: the maximum feasible current is used until the boundary concentration reaches its critical value, after which the current is progressively reduced to maintain that value. For semi-infinite domains, we derive the optimal currents analytically and obtain system-independent upper bounds on their improvement over constant-current operation. We also extend the framework to finite and multilayer domains and show that the same formulation applies to both charging and discharging.
Source: arXiv (Cornell University)
Authors: Mannattil, Manu, Mahadevan, L.
Institution: Harvard University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7206214685