Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Poisson-Nernst-Planck equations with steric effects - non-convexity and multiple stationary solutions (1703.07164v2)

Published 21 Mar 2017 in math.AP, math-ph, math.MP, and physics.bio-ph

Abstract: We study the existence and stability of stationary solutions of Poisson-Nernst- Planck equations with steric effects (PNP-steric equations) with two counter-charged species. These equations describe steady current through open ionic channels quite well. The current levels in open ionic channels are known to switch between open' orclosed' states in a spontaneous stochastic process called gating, suggesting that their governing equations should give rise to multiple stationary solutions that enable such multi-stable behavior. We show that within a range of parameters, steric effects give rise to multiple stationary solutions that are smooth. These solutions, however, are all unstable under PNP-steric dynamics. Following these findings, we introduce a novel PNP-Cahn-Hilliard model, and show that it admits multiple stationary solutions that are smooth and stable. The various branches of stationary solutions and their stability are mapped utilizing bifurcation analysis and numerical continuation methods.

Summary

We haven't generated a summary for this paper yet.