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Файл:Мікро- та наносенсори / L2.9.pdf
Principles of Electronic Nanobiosensors
Unit 2: Settling Time
Lecture 2.9: First Passage and Narrow Escape Time II
By Muhammad A. Alam
Professor of Electrical and Computer Engineering Purdue University
alam@purdue.edu
1
Outline
•‘Blind’ molecule escaping from a cell
•First passage time (FPT)
•First passage time (FPT): examples
•Narrow escape time (NET)
•Conclusion
2
MFPT and NET
r
Concentric spheres |
One disk and one sphere |
3
Example: NET in 2D
c2 x22 ( )+ c2 y22 ( ) =1
cosh µ sinh µ
a = c×cosh (µ) b = c×sinh (µ)
τ |
−1 |
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µD |
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πD |
con−cyl |
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2πD |
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NET |
~ CD,ss = |
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~ |
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CD.ss |
= |
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ln (r a) |
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π |
ln (r a) |
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V |
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NET is twice as long as MFPT |
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4 |
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