Hostname: page-component-7dd5485656-jtdwj Total loading time: 0 Render date: 2025-10-31T00:12:32.262Z Has data issue: false hasContentIssue false
  • English
  • Français

Infinite simple 3D cubic lattice of identical resistors (two missing bonds)

Published online by Cambridge University Press:  13 February 2008

R. S. Hijjawi ,
J. H. Asad ,
A. J. Sakaji ,
M. Al-sabayleh  and
J. M. Khalifeh
R. S. Hijjawi
Affiliation:
Dep. of Physics – Mutah University, Karak, Jordan
J. H. Asad*
Affiliation:
Tabuk University, Teachers College, Department of Sciences (Physics), PO Box 1144, Saudi Arabia
A. J. Sakaji
Affiliation:
Dep. of Basic Sciences, Ajman University, Ajman, UAE
M. Al-sabayleh
Affiliation:
Dep. of Physics – Mutah University, Karak, Jordan
J. M. Khalifeh
Affiliation:
Department of Physics, University of Jordan, Amman-11942, Jordan
*
jhasad1@yahoo.com
Get access

Abstract

An infinite regular three-dimensional network is composed of identical resistors each of resistance R joining adjacent nodes. What is the equivalent resistance between the lattice site $\mathaccent"017E{r}_i $ and the lattice $\mathaccent"017E{r}_j $  site, when two bonds are removed from the perfect network? Three cases are considered here, and some numerical values are calculated. Finally, the asymptotic behavior of the equivalent resistance is studied for large distances between the two sites.

Keywords

Information

Type
Research Article
Information
The European Physical Journal - Applied Physics , Volume 41 , Issue 2 , February 2008 , pp. 111 - 114
Copyright
© EDP Sciences, 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Cserti, J., Am. J. Phys. 68, 896 (2000) CrossRef
J.H. Asad, Ph.D. thesis, University of Jordan (unpublished, 2004)
P.G. Doyle, J.L. Snell, Random Walks and Electric Networks (The Carus Mathematical Monograph, Series 22, The Mathematical Association of America, USA, (1984), p. 83
L. Lovasz, Random Walks on Graphs: A Survey, in Combinatorics, Paul Erdös is Eighty, Vol. 2, edited by D. Mikl'os, V.T. S'os, T. Sz'onyi (Budepest: J'anos Bolyai Mathematical Society, 1996), pp. 353–398 (at http://research.microsoft.com/~Lovasz/ as a survey paper)
B. Van der Pol, H. Bremmer, Operation Calculus Based on the Two-Sided Laplace Integral (Cambridge University Press, England, 1955)
S. Redner A Guide to First-Passage Processes (Cambridge: Cambridge University Press, 2001)
Cserti, J., David, G., Piroth, A., Am. J. Phys. 70, 153 (2002) CrossRef
Asad, J.H., Hijjawi, R.S., Sakaji, A., Khalifeh, J.M., Int. J. Theor. Phys. 43, 2223 (2004) CrossRef
Asad, J.H., Hijjawi, R.S., Sakaji, A., Khalifeh, J.M., Eur. J. Phys. B 2, 365 (2006) CrossRef
Venezian, G., Am. J. Phys. 62, 1000 (1994) CrossRef
Atkinson, D., Van Steenwijk, F.J., Am. J. Phys. 67, 486 (1999) CrossRef
J. Monwhea, Am. J. Phys. 68 37 (2000)
Asad, J.H., Hijjawi, R.S., Sakaji, A., Khalifeh, J.M., Int. J. Theor. Phys. 44, 471 (2005) CrossRef
Osterberg, P.M, Inan, A.S., Am. J. Phys. 72, 972 (2004) CrossRef
Wu, F.Y., J. Phys. A: Math. Gen. 37, 6653 (2004) CrossRef
Joyce, G.S., J. Math. Phys. 12, 1390 (1971) CrossRef
Katsura, S., Horiguchi, T., J. Math. Phys. 12, 230 (1971) CrossRef
Morita, T., Horigucih, T., Math. Phys. 12, 986 (1971) CrossRef
Horiguchi, T., J. Phys. Soc. Jpn 30, 1261 (1971) CrossRef
Glasser, M.L., J. Math. Phys. 13, 1145 (1972) CrossRef
Mano, K., J. Math. Phys. 16, 1726 (1975) CrossRef
Inoue, M., J. Math. Phys. 16, 809 (1975) CrossRef
Morita, T., Horiguchi, T., J. Phys. C: Solid State Physics 8, L232 (1975)
Glasser, M.L., Boersma, J., J. Phys. A: Math. Gen. 33, 5017 (2000) CrossRef
Sakaji, A., Hijjawi, R.S., Shawagfeh, N., Khalifeh, J.M., J. Theor. Phys. 41, 973 (2002) CrossRef
Hijjawi, R.S., Khalifeh, J.M., J. Theor. Phys. 41, 1769 (2002) CrossRef
R.S. Hijjawi, J.M. Khalifeh, J. Math. Phys. 43 (2002)
E.N. Economou. Green's Functions in Quantum Physics (Springer-Verlag, Berlin, 1983)
Glasser, M.L., Boersma, J., J. Phys. A: Math. Gen. 33, 5017 (2000) CrossRef
Duffin, R.J., Shelly, E.P., Duke Math. J. 25, 209 (1958) CrossRef