نظرية التخلل
| فهم الشبكات |
|---|
|
|
| النظرية • التاريخ |
|
Graph • Complex network • Contagion |
| أنواع الشبكات |
|
Information • Telecommunication |
| Graphs |
|
Vertex • Edge • Component |
| المقاييس والخوارزميات |
|
Centrality • Degree • Betweenness |
| النماذج |
|
Random • Erdős–Rényi |
| تصفح |
|
Topics • Software • Network scientists
Graph theory • Network theory |
نظرية التخلل Percolation theory (أونظرية التطعيم) في الرياضيات سلوك العقد المتصلة في خط بياني عشوائي. تضم تطبيقات هذه النظرية بشكل أساسي مجال علوم المواد الهندسية وبالإضافة إلى مجالات أخرى تتعلق بالترشيح.
وترتبط هذه النظرية بالنظرية الكسيرية Fractal.
مقدمة
انظر أيضاً
- Continuum percolation theory
- Critical exponent
- Directed percolation
- Erdős–Rényi model
- Fractal
- Giant component
- Graph theory
- Interdependent networks
- Invasion percolation
- Network theory
- Percolation threshold
- Percolation critical exponents
- Scale-free network
- Shortest path
References
للاستزادة
- Aizenman, Michael; Barsky, David (1987), "Sharpness of the phase transition in percolation models", Communications in Mathematical Physics 108 (3): 489–526, doi:, Bibcode: 1987CMaPh.108..489A
- Bollobás, Béla; Riordan, Oliver (2006), Percolation, Cambridge University Press, ISBN 978-0521872324, http://www.cambridge.org/catalogue/catalogue.asp?isbn=0521872324
- Broadbent, Simon; Hammersley, John (1957), "Percolation processes I. Crystals and mazes", Proceedings of the Cambridge Philosophical Society 53 (3): 629–641, doi:, Bibcode: 1957PCPS...53..629B
- Bunde A. and Havlin S. (1996), Fractals and Disordered Systems, Springer, http://havlin.biu.ac.il/Shlomo%20Havlin%20books_fds.php
- Cohen R. and Havlin S. (2010), Complex Networks: Structure, Robustness and Function, Cambridge University Press, http://havlin.biu.ac.il/Shlomo%20Havlin%20books_com_net.php
- Grimmett, Geoffrey (1999), Percolation, Springer, http://www.statslab.cam.ac.uk/~grg/papers/perc/perc.html
- Grimmett, Geoffrey; Marstrand, John (1990), "The supercritical phase of percolation is well behaved", Proceedings of the Royal Society A 430 (1879): 439–457, doi:, Bibcode: 1990RSPSA.430..439G
- Hara, Takashi; Slade, Gordon (1990), "Mean-field critical behaviour for percolation in high dimensions", Communications in Mathematical Physics 128 (2): 333–391, doi:, Bibcode: 1990CMaPh.128..333H
- Kesten, Harry (1982), Percolation theory for mathematicians, Birkhauser
- Menshikov, Mikhail (1986), "Coincidence of critical points in percolation problems", Soviet Mathematics - Doklady 33: 856–859
- Smirnov, Stanislav (2001), "Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits", Comptes Rendus de l'Académie des Sciences 333 (3): 239–244, doi:, Bibcode: 2001CRASM.333..239S
- Stauffer, Dietrich; Aharony, Anthony (1994), Introduction to Percolation Theory (2nd ed.), CRC Press, ISBN 978-0-7484-0253-3
وصلات خارجية
- program to visualize percolation on networks in real time
- Interactive Percolation
- Kesten, Harry (May 2006), "What Is ... Percolation?" (PDF), Notices of the American Mathematical Society 53 (5): 572–573, ISSN 1088-9477, http://www.ams.org/notices/200605/what-is-kesten.pdf
- Austin, David (July 2008), Percolation: Slipping through the Cracks, American Mathematical Society, http://www.ams.org/featurecolumn/archive/percolation.html
- Introduction to Percolation Theory: short course by Shlomo Havlin
