Perturbed Infinite 3D Simple Cubic Network of Identical Capacitors

• Authors: J. Asad , A. Diab , M. Owaidat , J. Khalifeh
• Languages of publication: EN

Abstracts

EN

The effective capacitance between the origin and any other lattice site, in an infinite 3D simple cubic network consisting of identical capacitors, is evaluated in terms of the lattice Green function of the network. The perfect case is reviewed shortly, while the perturbed case (a capacitor is removed) is studied in two cases. Numerical values of the effective capacitance are presented and the asymptotic behavior is studied for the both cases.

Keywords

EN

61.50.Ah; 84.37.+q; 05.50.+q; 04.60.Nc; 63.90.+t; 84.30.Bv; 02.90.+p

Discipline

• 61.50.Ah: Theory of crystal structure, crystal symmetry; calculations and modeling
• 63.90.+t: Other topics in lattice dynamics (restricted to new topics in section 63)
• 84.37.+q: Measurements in electric variables (including voltage, current, resistance, capacitance, inductance, impedance, and admittance, etc.)
• 04.60.Nc: Lattice and discrete methods
• 84.30.Bv: Circuit theory
• 05.50.+q: Lattice theory and statistics (Ising, Potts, etc.)(see also 64.60.Cn Order-disorder transformations, and 75.10.Hk Classical spin models)
• 02.90.+p: Other topics in mathematical methods in physics (restricted to new topics in section 02)

• Journal: Acta Physica Polonica A
• Year: 2014
• Volume: 126
• Issue: 3
• Pages: 777-782

Dates

published

2014-08

received

2014-03-31

(unknown)

2014-07-24

Contributors

author

J. Asad

• Department of Physics, College of Arts and Sciences, Palestine Technical University, P.O. Box 7, Tulkarm, Palestine

author

A. Diab

• Department of General Studies, Yanbu Industrial College, P.O. Box 30436, Yanbu Industrial City, Saudi Arabia

author

M. Owaidat

• Department of Physics, Al-Hussein Bin Talal University, Ma'an 71111, Jordan

author

J. Khalifeh

• Department of Physics, The University of Jordan, Amman 11942, Jordan

References

• [1] G.L. Montent, Phys. Rev. B 7, 650 (1975), doi: 10.1103/PhysRevB.7.650
• [2] G.F. Koster, D.C. Slater, Phys. Rev. 96, 1208 (1954), doi: 10.1103/PhysRev.96.1208
• [3] V. Bryksin, P. Kleinert, Z. Phys. B, Condens. Matter 90, 167 (1993), doi: 10.1007/BF02198150
• [4] P.H. Dederichs, K. Shroeder, R. Zeller, Point Defect in Metals II, Springer-Verlag, Berlin 1980, doi: 10.1007/BFb0043423
• [5] B. Hughes, J. Math. Phys. 23, 1688 (1982), doi: 10.1063/1.525554
• [6] G.F. Koster, J.C. Slater, Phys. Rev. 94, 1498 (1954), doi: 10.1103/PhysRev.94.1498
• [7] N.W. Dalton, D.W. Wood, Proc. Phys. Soc. (London) 90, 4591 (1967), doi: 10.1088/0370-1328/90/2/316
• [8] M. Lax, Phys. Rev. 97, 629 (1955), doi: 10.1103/PhysRev.85.621
• [9] E. Montroll, G. Weiss, J. Math. Phys. 6, 168 (1965), doi: 10.1063/1.1704269
• [10] E.W. Montroll, R.B. Potts, Phys. Rev. 100, 525 (1955), doi: 10.1103/PhysRev.100.525
• [11] G.N. Watson, Quart. J. Math (Oxford) 10, 266 (1939), doi: 10.1093/qmath/os-10.1.266
• [12] E.N. Economou, Green's Functions in Quantum Physics, 2nd ed., Springer-Verlag, Berlin 1983, doi: 10.1002/zamm.19800600318
• [13] R. Brout, Phys. Rev. 118, 1009 (1960), doi: 10.1103/PhysRev.118.1009
• [14] G.S. Joyce, J. Math. Phys. 12, 1390 (1971), doi: 10.1088/0305-4470/34/18/311
• [15] S. Katsura, T. Horiguchi, J. Math. Phys. 12, 230 (1971), doi: 10.1063/1.1665581
• [16] T. Morita, T. Horiguci, Math. Phys. 12, 986 (1971), doi: 10.1063/1.1665692
• [17] T. Horiguchi, J. Phys. Soc. Jpn. 30, 1261 (1971), doi: 10.1143/JPSJ.30.1261
• [18] M.L. Glasser, J. Math. Phys. 13, 1145 (1972), doi: 10.1063/1.1666113
• [19] K. Mano, J. Math. Phys. 16, 1726 (1975), doi: 10.1063/1.522770
• [20] M. Inoue, J. Math. Phys. 16, 809 (1975), doi: 10.1063/1.522609
• [21] T. Morita, T. Horiguchi, J. Phys. C, Solid State Phys. 8, L232 (1975), doi: 10.1088/0022-3719/8/11/002
• [22] M.L. Glasser, J. Boersma, J. Phys. A, Math. Gen. 33, 5017 (2000), doi: 10.1088/0305-4470/33/28/306
• [23] J. Cserti, Am. J. Phys. 68, 896 (2000), doi: 10.1119/1.1285881
• [24] J. Cserti, D. Gyula, P. Attila, Am. J. Phys. 70, 153 (2002), doi: 10.1119/1.1419104
• [25] M. Jeng, Am. J. Phys. 68, 37 (2000), doi: 10.1119/1.19370
• [26] R.E. Aitchison, Am. J. Phys. 32, 566 (1964), doi: 10.1119/1.1970777
• [27] G. Venezian, 10.1119/1.17696 HUKHUKAm. J. Phys. 62, 1000 (1994)
• [28] D. Atkinson, F.J. van Steenwijk, Am. J. Phys. 67, 486 (1999), doi: 10.1119/1.19311
• [29] J.H. Asad, R.S. Hijjawi, A. Sakaji, J.M. Khaleh, Int. J. Theor. Phys. 43, 2223 (2004), doi: 10.1023/B:IJTP.0000049021.94530.6e
• [30] J.H. Asad, R.S. Hijjawi, A. Sakaji, J.M. Khaleh, Int. J. Theor. Phys. 44, 471 (2004), doi: 10.1007/s10773-005-3977-6
• [31] J.H. Asad, A.J. Sakaji, R.S. Hijjawi, J.M. Khalifeh, Eur. Phys. J. B 52, 365 (2006), doi: 10.1140/epjb/e2006-00311-x
• [32] R.S. Hijjawi, J.H. Asad, A.J. Sakaji, M. Al-Sabayleh, J.M. Khalifeh, EPJ Appl. Phys. 41, 111 (2008), doi: 10.1051/epjap:2008015
• [33] J. Cserti, G. Szechenyi, G. David, J. Phys. A, Math. Gen. 44, 215201 (2011), doi: 10.1088/1751-8113/44/21/215201
• [34] F.Y. Wu, J. Phys. A, Math. Gen. 37, 6653-6673 (2004), doi: 10.1088/0305-4470/37/26/004
• [35] J.W. Essam, F.Y. Wu, J. Phys. A, Math. Theor. 42, 025205 (2009), doi: 10.1088/1751-8113/42/2/025205
• [36] N.Sh. Izmailian, M.-C. Huang, Phys. Rev. E 82, 011125 (2010), doi: 10.1103/PhysRevE.82.011125
• [37] J.H. Asad, A.A. Diab, R.S. Hijjawi, J.M. Khalifeh, Eur. Phys. J. Plus 128, 1 (2013), doi: 10.1140/epjp/i2013-13002-8
• [38] J.H. Asad, J. Stat. Phys. 150, 1177 (2013), doi: 10.1007/s10955-013-0716-x
• [39] M.Q. Owaidat, R.S. Hijjawi, J.M. Khalifeh, Mod. Phys. Lett. B 19, 2057 (2010), doi: 10.1142/S0217984910024468
• [40] M.Q. Owaidat, R.S. Hijjawi, J.M. Khalifeh, J. Phys. A, Math. Theor. 43, 375204 (2010), doi: 10.1088/1751-8113/43/37/375204
• [41] M.Q. Owaidat, R.S. Hijjawi, J.M. Khalifeh, Int. J. Theor. Phys. 51, 3152 (2012), doi: 10.1007/s10773-012-1196-5
• [42] J.H. Asad, R.S. Hijjawi, A.J. Sakaji, J.M. Khalifeh, Int. J. Mod. Phys. B 19, 3713 (2005), doi: 10.1142/S0217979205032401
• [43] R.S. Hijjawi, J.H. Asad, A.J. Sakaji, J.M. Khalifeh, Int. J. Mod. Phys. B 21, 199 (2007), doi: 10.1142/S0217979207035972
• [44] J.H. Asad, A.J. Sakaji, R.S. Hijjawi, J.M. Khalifeh, Eur. Phys. J. Appl. Phys. 40, 257 (2007)
• [46] J.H. Asad, R.S. Hijjawi, A.J. Sakaji, J.M. Khalifeh, Eur. Phys. J. Appl. Phys. 32, 149 (2005), doi: 10.1051/epjap:2007160
• [47] R.J. Duffin, E.P. Shelly, Duke Math. J. 25, 209 (1958), doi: 10.1215/S0012-7094-58-02521-3
• [48] J.H. Asad, Mod. Phys. Lett. B. 27, 15 (2013), doi: 10.1142/S0217984913501121

Identifiers

DOI

10.12693/APhysPolA.126.777