Infinite Body Centered Cubic Network of Identical Resistors

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

Abstracts

EN

We express the equivalent resistance between the origin (0,0,0) and any other lattice site (n_1,n_2,n_3) in an infinite body centered cubic network consisting of identical resistors each of resistance R rationally in terms of known values b_{0} and π. The equivalent resistance is then calculated. For large separations two asymptotic formulae for the resistance are presented and some numerical results with analysis are given.

Keywords

EN

61.50.Ah; 61.50.+f; 61.66.f; 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)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2014
• Volume: 125
• Issue: 1
• Pages: 60-64

Dates

published

2014-01

received

2013-05-15

Contributors

author

Jihad Asad

• Dep. of Physics, Faculty of Arts and Sciences, P.O. Box 7, Palestine Techn. Univ., Kadoorie, Tulkarm, Palestine

author

A. Diab

• General Studies Department, 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

R. Hijjawi

• Department of Physics, Mutah University, Karak, Jordan

author

J. Khalifeh

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

References

• [1] R. Brout, doi: 10.1103/PhysRev.118.1009, Phys. Rev. 118, 1009 (1960)
• [2] N.W. Dalton, D.W. Wood, doi: 10.1088/0370-1328/90/2/316, Proc. Phys. Soc. (London) 90, 4591 (1967)
• [3] M. Tax, doi: 10.1103/PhysRev.97.629, Phys. Rev. 97, 629 (1955)
• [4] P.H. Dederichs, K. Schroeder, R. Zeller, Point Defect in Metals II, Springer, Berlin 1980
• [5] B.D. Hughes, doi: 10.1016/0378-4371(86)90058-0, Physica A 134, 443 (1986)
• [6] E.W. Montroll, doi: 10.1137/0104014 , J. Soc. Industr. Appl. Math. 4, 241 (1956)
• [7] G.F. Koster, D.C. Slater, doi: 10.1103/PhysRev.96.1208, Phys. Rev. 96, 1208 (1954)
• [8] Q. Li, C. Soukoulis, E.N. Economou, G.S. Grest, doi: 10.1103/PhysRevB.40.2825, Phys. Rev. B 40, 2825 (1989)
• [9] E.N. Economou, Green's Functions in Quantum Physics, 2nd ed., Springer-Verlag, Berlin 1983, p. 3, p. 71
• [10] T. Morita, T. Horiguchi, doi: 10.1063/1.1665692, J. Math. Phys. 12, 981 (1971)
• [11] T. Morita, T. Horiguchi, doi: 10.1063/1.1665693 , J. Math. Phys. 12, 986 (1971)
• [12] T. Morita, doi: 10.1063/1.1665800, J. Math. Phys. 12, 1744 (1971)
• [13] G.S. Joyce, doi: 10.1063/1.1665748, J. Math. Phys. 23, 1390 (1971)
• [14] G.S. Joyce, doi: 10.1088/0022-3719/4/12/008, J. Phys. C: Solid State Phys. 23, 1510 (1971)
• [15] T. Horiguchi, doi: 10.1143/JPSJ.30.1261, J. Phys. Soc. Jpn. 30, 1261 (1971)
• [16] S. Katsura, T. Horiguchi, doi: 10.1063/1.1665581, J. Math. Phys. 12, 230 (1971)
• [17] M.L. Glasser, doi: 10.1063/1.1666113, J. Math. Phys. 13, 1145 (1972)
• [18] M. Inoue, doi: 10.1063/1.522609, J. Math. Phys. 16, 809 (1975)
• [19] K. Mano, doi: 10.1063/1.522770, J. Math. Phys. 16, 1726 (1975)
• [20] T. Morita, doi: 10.1088/0305-4470/8/4/008, J. Phys. A, Math. Gen. 8, 478 (1975)
• [21] T. Morita, T. Horiguchi, doi: 10.1088/0022-3719/8/11/002, J. Phys. C, Solid State Phys. 8, L232 (1975)
• [22] M.L. Glasser, I.J. Zucker, doi: 10.1073/pnas.74.5.1800, Proc. Natl. Acad. Sci. USA 74, 1800 (1977)
• [23] M.L. Glasser, J. Boersma, doi: 10.1088/0305-4470/33/28/306, J. Phys. A, Math. Gen. 33, 5017 (2000)
• [24] R.S. Hijjawi, J.H. Asad, A.J. Sakaji, J.M. Khalifeh, doi: 10.1023/B:IJTP.0000049028.18912.b1, Int. J. Theor. Phys. 43, 2299 (2004)
• [25] J.H. Asad, doi: 10.1142/S021798490701244X, Mod. Phys. Lett. B 21, 139 (2007)
• [26] F.J. Bartis, doi: 10.1119/1.1974081, Am. J. Phys. 35, 354 (1967)
• [27] G. Venezian, doi: 10.1119/1.17696, Am. J. Phys. 62, 1000 (1994)
• [28] D. Atkinson, F.J. Van Steenwijk, doi: 10.1119/1.19311, Am. J. Phys. 67, 486 (1999)
• [29] M. Jeng, doi: 10.1119/1.19370, Am. J. Phys. 68, 37 (2000)
• [30] J. Cserti, doi: 10.1119/1.1285881, Am. J. Phys. 68, 896 (2000)
• [31] J. Cserti, G. David, A. Piroth, doi: 10.1119/1.1419104, Am. J. Phys. 70, 153 (2002)
• [32] J. Cserti, G. Szechenyi, G. David, doi: 10.1088/1751-8113/44/21/215201, J. Phys. A, Math. Theor. 44, 215201 (2011)
• [33] J.H. Asad, A. Sakaji, R.S. Hijjawi, J.M. Khalifeh, doi: 10.1023/B:IJTP.0000049021.94530.6e, Int. J. Theor. Phys. 43, 2223 (2004)
• [34] J.H. Asad, A. Sakaji, R.S. Hijjawi, J.M. Khalifeh, doi: 10.1140/epjb/e2006-00311-x, Eur. Phys. J. B 52, 365 (2006)
• [35] J.H. Asad, R.S. Hijjawi, A.J. Sakaji, J.M. Khalifeh, doi: 10.1007/s10773-005-3977-6, Int. J. Theor. Phys. 44, 471 (2005)
• [36] R.S. Hijjawi, J.H. Asad, A.J. Sakaji, M. Al-Sabayleh, J.M. Khalifeh, doi: 10.1051/epjap:2008015, Eur. Phys. J. Appl. Phys. 41, 111 (2008)
• [37] J.H. Asad, A.A. Diab, R.S. Hijjawi, J.M. Khalifeh, doi: 10.1140/epjp/i2013-13002-8, Europ. Phys. J. Plus 128, 1 (2013)
• [38] J.H. Asad, doi: 10.1007/s10955-013-0716-x, J. Stat. Phys. 150, 1177 (2013)
• [39] G. Horwitz, H.B. Callen, doi: 10.1103/PhysRev.124.1757, Phys. Rev. 124, 1757 (1961)
• [40] B.V. Thompson, D.A. Lavis, doi: 10.1088/0370-1328/91/3/318, Proc. Phys. Soc. (Lond.) 91, 645 (1967)
• [41] R. Tahir-Kheli, D. ter Haar, doi: 10.1103/PhysRev.127.88, Phys. Rev. 127, 88 (1962)
• [42] H.B. Callen, doi: 10.1103/PhysRev.130.890, Phys. Rev. 130, 890 (1963)
• [43] E.W. Montroll, doi: 10.1007/BF02780990, Nuovo Cimento Suppl. 6, 265 (1949)
• [44] T.H. Berlin, M. Kac, doi: 10.1103/PhysRev.86.821, Phys. Rev. 86, 821 (1952)
• [45] M. Lax, doi: 10.1103/PhysRev.97.629, Phys. Rev. 97, 629 (1955)
• [46] W.F. Van Peijpe, doi: 10.1016/S0031-8914(38)80158-0, Physica 5, 465 (1938)
• [47] G.N. Watson, doi: 10.1093/qmath/os-10.1.266, Quart. J. Math. (Oxford) 10, 266 (1939)

Identifiers

DOI

10.12693/APhysPolA.125.60