Computational electromagnetics and the rational design of new dielectric heterostructures

Progress in Materials Science

Volumn 48, Issue 5, 2003, Pages 373-456

  Brosseau, C ^a   Beroual, A ^b  

^a UNIVERSITÉ DE BRETAGNE OCCIDENTALE   (France)

^b ECOLE CENTRALE DE LYON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; DIELECTRIC DEVICES; GREEN'S FUNCTION; HETEROJUNCTIONS; INTEGRAL EQUATIONS; MORPHOLOGY; SENSORS; THEOREM PROVING;

RATIONAL DESIGN;

MAGNETOELECTRIC EFFECTS;

EID: 0037263029     PISSN: 00796425     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0079-6425(02)00013-0     Document Type: Review

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81. Yee K.S. IEEE Trans. Antennas Prop. AP-14:1966;303. There have been a number of modifications to the traditional FDTD method, for solving Maxwell equations in the time domain, which avoids the limitations of Yee's 1966 pioneering paper. One of them is implementation of the surface impedance boundary conditions to remove the body of high conductivity from the computational space and replace it with a relationship between the tangential electric and magnetic fields on the surface of the body. Since the discretization size of the space in the FDTD lattice is proportional to the wavelength of the wave propagating in the medium, removal of the medium where the wavelength becomes very small, significant simplifies the problem and decreases the requirements of the computational resource, see, for example Maloney J.G., Smith G.S. IEEE Trans. Antennas Prop. 40:1992;38 Beggs J.H., Luebbers R.J., Yee K.S., Kunz K.S. IEEE Trans. Antennas Prop. 40:1992;49. The main deficiency of the FDTD method is that only structural grids are allowed in calculation models. Consequently, it is difficult to model curved surfaces efficiently.
82. Yee K.S. IEEE Trans. Antennas Prop. AP-14:1966;303. There have been a number of modifications to the traditional FDTD method, for solving Maxwell equations in the time domain, which avoids the limitations of Yee's 1966 pioneering paper. One of them is implementation of the surface impedance boundary conditions to remove the body of high conductivity from the computational space and replace it with a relationship between the tangential electric and magnetic fields on the surface of the body. Since the discretization size of the space in the FDTD lattice is proportional to the wavelength of the wave propagating in the medium, removal of the medium where the wavelength becomes very small, significant simplifies the problem and decreases the requirements of the computational resource, see, for example Maloney J.G., Smith G.S. IEEE Trans. Antennas Prop. 40:1992;38 Beggs J.H., Luebbers R.J., Yee K.S., Kunz K.S. IEEE Trans. Antennas Prop. 40:1992;49. The main deficiency of the FDTD method is that only structural grids are allowed in calculation models. Consequently, it is difficult to model curved surfaces efficiently.
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182. Carmona F., Barreau F., Delhaes P., Conet R. J. Phys. Lett. 41:1980;L531. See also Carmona F., Delhaes P., Barreau F., Ordiera D., Canet R., Lafeychine L. Rev. Chim. Min. 18:1981;498 Lagarkov A.N., Sarychev A.K. Phys. Rev. B. 53:1998;6319 Lagarkov N., Matytsin S.M., Rozanov K.N., Sarychev A.K. Physica A. 241:1997;58. Observe that the r l dependence of the percolation threshold concentration in fiber filled composites was also discussed by several independent groups, raising a legitimate doubt on the general validity of the square law dependence for intermediate values of r l. Thus, there is some uncertainty over this issue. See Boissonade J., Barreau F., Carmona F. J. Phys. A. 16:1983;2777 Celzard A., McRae E., Deleuze C., Dufort M., Furdin G., Marêché J.F. Phys. Rev. B. 53:1998;6209 Garboczi E.J., Snyder K.A., Douglas J.F., Thorpe M.F. Phys. Rev. E. 52:1995;819. From the theoretical standpoint, we also also refer the interested reader to Balberg I., Anderson C.H., Alexander S., Wagner N. Phys. Rev. B. 30:1984;3933 Balberg I., Binenbaum N., Wagner N. Phys. Rev. Lett. 52:1984;1465 Balberg I. Philos. Mag. B. 56:1987;991 Browning L., Lodge J., Price R.R., Schelleng J., Schoen P.E., Zabetakis Z. J. Appl. Phys. 84:1998;6109 Garboczi E.J., Snyder K.A., Douglas J.F., Thorpe M.F. Phys. Rev. E. 52:1995;819.
183. Carmona F., Barreau F., Delhaes P., Conet R. J. Phys. Lett. 41:1980;L531. See also Carmona F., Delhaes P., Barreau F., Ordiera D., Canet R., Lafeychine L. Rev. Chim. Min. 18:1981;498 Lagarkov A.N., Sarychev A.K. Phys. Rev. B. 53:1998;6319 Lagarkov N., Matytsin S.M., Rozanov K.N., Sarychev A.K. Physica A. 241:1997;58. Observe that the r l dependence of the percolation threshold concentration in fiber filled composites was also discussed by several independent groups, raising a legitimate doubt on the general validity of the square law dependence for intermediate values of r l. Thus, there is some uncertainty over this issue. See Boissonade J., Barreau F., Carmona F. J. Phys. A. 16:1983;2777 Celzard A., McRae E., Deleuze C., Dufort M., Furdin G., Marêché J.F. Phys. Rev. B. 53:1998;6209 Garboczi E.J., Snyder K.A., Douglas J.F., Thorpe M.F. Phys. Rev. E. 52:1995;819. From the theoretical standpoint, we also also refer the interested reader to Balberg I., Anderson C.H., Alexander S., Wagner N. Phys. Rev. B. 30:1984;3933 Balberg I., Binenbaum N., Wagner N. Phys. Rev. Lett. 52:1984;1465 Balberg I. Philos. Mag. B. 56:1987;991 Browning L., Lodge J., Price R.R., Schelleng J., Schoen P.E., Zabetakis Z. J. Appl. Phys. 84:1998;6109 Garboczi E.J., Snyder K.A., Douglas J.F., Thorpe M.F. Phys. Rev. E. 52:1995;819.
184. Carmona F., Barreau F., Delhaes P., Conet R. J. Phys. Lett. 41:1980;L531. See also Carmona F., Delhaes P., Barreau F., Ordiera D., Canet R., Lafeychine L. Rev. Chim. Min. 18:1981;498 Lagarkov A.N., Sarychev A.K. Phys. Rev. B. 53:1998;6319 Lagarkov N., Matytsin S.M., Rozanov K.N., Sarychev A.K. Physica A. 241:1997;58. Observe that the r l dependence of the percolation threshold concentration in fiber filled composites was also discussed by several independent groups, raising a legitimate doubt on the general validity of the square law dependence for intermediate values of r l. Thus, there is some uncertainty over this issue. See Boissonade J., Barreau F., Carmona F. J. Phys. A. 16:1983;2777 Celzard A., McRae E., Deleuze C., Dufort M., Furdin G., Marêché J.F. Phys. Rev. B. 53:1998;6209 Garboczi E.J., Snyder K.A., Douglas J.F., Thorpe M.F. Phys. Rev. E. 52:1995;819. From the theoretical standpoint, we also also refer the interested reader to Balberg I., Anderson C.H., Alexander S., Wagner N. Phys. Rev. B. 30:1984;3933 Balberg I., Binenbaum N., Wagner N. Phys. Rev. Lett. 52:1984;1465 Balberg I. Philos. Mag. B. 56:1987;991 Browning L., Lodge J., Price R.R., Schelleng J., Schoen P.E., Zabetakis Z. J. Appl. Phys. 84:1998;6109 Garboczi E.J., Snyder K.A., Douglas J.F., Thorpe M.F. Phys. Rev. E. 52:1995;819.
185. Carmona F., Barreau F., Delhaes P., Conet R. J. Phys. Lett. 41:1980;L531.
186. Carmona F., Barreau F., Delhaes P., Conet R. J. Phys. Lett. 41:1980;L531. See also Carmona F., Delhaes P., Barreau F., Ordiera D., Canet R., Lafeychine L. Rev. Chim. Min. 18:1981;498 Lagarkov A.N., Sarychev A.K. Phys. Rev. B. 53:1998;6319 Lagarkov N., Matytsin S.M., Rozanov K.N., Sarychev A.K. Physica A. 241:1997;58. Observe that the r l dependence of the percolation threshold concentration in fiber filled composites was also discussed by several independent groups, raising a legitimate doubt on the general validity of the square law dependence for intermediate values of r l. Thus, there is some uncertainty over this issue. See Boissonade J., Barreau F., Carmona F. J. Phys. A. 16:1983;2777 Celzard A., McRae E., Deleuze C., Dufort M., Furdin G., Marêché J.F. Phys. Rev. B. 53:1998;6209 Garboczi E.J., Snyder K.A., Douglas J.F., Thorpe M.F. Phys. Rev. E. 52:1995;819. From the theoretical standpoint, we also also refer the interested reader to Balberg I., Anderson C.H., Alexander S., Wagner N. Phys. Rev. B. 30:1984;3933 Balberg I., Binenbaum N., Wagner N. Phys. Rev. Lett. 52:1984;1465 Balberg I. Philos. Mag. B. 56:1987;991 Browning L., Lodge J., Price R.R., Schelleng J., Schoen P.E., Zabetakis Z. J. Appl. Phys. 84:1998;6109 Garboczi E.J., Snyder K.A., Douglas J.F., Thorpe M.F. Phys. Rev. E. 52:1995;819.
187. Carmona F., Barreau F., Delhaes P., Conet R. J. Phys. Lett. 41:1980;L531. See also Carmona F., Delhaes P., Barreau F., Ordiera D., Canet R., Lafeychine L. Rev. Chim. Min. 18:1981;498 Lagarkov A.N., Sarychev A.K. Phys. Rev. B. 53:1998;6319 Lagarkov N., Matytsin S.M., Rozanov K.N., Sarychev A.K. Physica A. 241:1997;58. Observe that the r l dependence of the percolation threshold concentration in fiber filled composites was also discussed by several independent groups, raising a legitimate doubt on the general validity of the square law dependence for intermediate values of r l. Thus, there is some uncertainty over this issue. See Boissonade J., Barreau F., Carmona F. J. Phys. A. 16:1983;2777 Celzard A., McRae E., Deleuze C., Dufort M., Furdin G., Marêché J.F. Phys. Rev. B. 53:1998;6209 Garboczi E.J., Snyder K.A., Douglas J.F., Thorpe M.F. Phys. Rev. E. 52:1995;819. From the theoretical standpoint, we also also refer the interested reader to Balberg I., Anderson C.H., Alexander S., Wagner N. Phys. Rev. B. 30:1984;3933 Balberg I., Binenbaum N., Wagner N. Phys. Rev. Lett. 52:1984;1465 Balberg I. Philos. Mag. B. 56:1987;991 Browning L., Lodge J., Price R.R., Schelleng J., Schoen P.E., Zabetakis Z. J. Appl. Phys. 84:1998;6109 Garboczi E.J., Snyder K.A., Douglas J.F., Thorpe M.F. Phys. Rev. E. 52:1995;819.
188. Carmona F., Barreau F., Delhaes P., Conet R. J. Phys. Lett. 41:1980;L531. See also Carmona F., Delhaes P., Barreau F., Ordiera D., Canet R., Lafeychine L. Rev. Chim. Min. 18:1981;498 Lagarkov A.N., Sarychev A.K. Phys. Rev. B. 53:1998;6319 Lagarkov N., Matytsin S.M., Rozanov K.N., Sarychev A.K. Physica A. 241:1997;58. Observe that the r l dependence of the percolation threshold concentration in fiber filled composites was also discussed by several independent groups, raising a legitimate doubt on the general validity of the square law dependence for intermediate values of r l. Thus, there is some uncertainty over this issue. See Boissonade J., Barreau F., Carmona F. J. Phys. A. 16:1983;2777 Celzard A., McRae E., Deleuze C., Dufort M., Furdin G., Marêché J.F. Phys. Rev. B. 53:1998;6209 Garboczi E.J., Snyder K.A., Douglas J.F., Thorpe M.F. Phys. Rev. E. 52:1995;819. From the theoretical standpoint, we also also refer the interested reader to Balberg I., Anderson C.H., Alexander S., Wagner N. Phys. Rev. B. 30:1984;3933 Balberg I., Binenbaum N., Wagner N. Phys. Rev. Lett. 52:1984;1465 Balberg I. Philos. Mag. B. 56:1987;991 Browning L., Lodge J., Price R.R., Schelleng J., Schoen P.E., Zabetakis Z. J. Appl. Phys. 84:1998;6109 Garboczi E.J., Snyder K.A., Douglas J.F., Thorpe M.F. Phys. Rev. E. 52:1995;819.
189. Carmona F., Barreau F., Delhaes P., Conet R. J. Phys. Lett. 41:1980;L531. See also Carmona F., Delhaes P., Barreau F., Ordiera D., Canet R., Lafeychine L. Rev. Chim. Min. 18:1981;498 Lagarkov A.N., Sarychev A.K. Phys. Rev. B. 53:1998;6319 Lagarkov N., Matytsin S.M., Rozanov K.N., Sarychev A.K. Physica A. 241:1997;58. Observe that the r l dependence of the percolation threshold concentration in fiber filled composites was also discussed by several independent groups, raising a legitimate doubt on the general validity of the square law dependence for intermediate values of r l. Thus, there is some uncertainty over this issue. See Boissonade J., Barreau F., Carmona F. J. Phys. A. 16:1983;2777 Celzard A., McRae E., Deleuze C., Dufort M., Furdin G., Marêché J.F. Phys. Rev. B. 53:1998;6209 Garboczi E.J., Snyder K.A., Douglas J.F., Thorpe M.F. Phys. Rev. E. 52:1995;819. From the theoretical standpoint, we also also refer the interested reader to Balberg I., Anderson C.H., Alexander S., Wagner N. Phys. Rev. B. 30:1984;3933 Balberg I., Binenbaum N., Wagner N. Phys. Rev. Lett. 52:1984;1465 Balberg I. Philos. Mag. B. 56:1987;991 Browning L., Lodge J., Price R.R., Schelleng J., Schoen P.E., Zabetakis Z. J. Appl. Phys. 84:1998;6109 Garboczi E.J., Snyder K.A., Douglas J.F., Thorpe M.F. Phys. Rev. E. 52:1995;819.
190. Carmona F., Barreau F., Delhaes P., Conet R. J. Phys. Lett. 41:1980;L531. See also Carmona F., Delhaes P., Barreau F., Ordiera D., Canet R., Lafeychine L. Rev. Chim. Min. 18:1981;498 Lagarkov A.N., Sarychev A.K. Phys. Rev. B. 53:1998;6319 Lagarkov N., Matytsin S.M., Rozanov K.N., Sarychev A.K. Physica A. 241:1997;58. Observe that the r l dependence of the percolation threshold concentration in fiber filled composites was also discussed by several independent groups, raising a legitimate doubt on the general validity of the square law dependence for intermediate values of r l. Thus, there is some uncertainty over this issue. See Boissonade J., Barreau F., Carmona F. J. Phys. A. 16:1983;2777 Celzard A., McRae E., Deleuze C., Dufort M., Furdin G., Marêché J.F. Phys. Rev. B. 53:1998;6209 Garboczi E.J., Snyder K.A., Douglas J.F., Thorpe M.F. Phys. Rev. E. 52:1995;819. From the theoretical standpoint, we also also refer the interested reader to Balberg I., Anderson C.H., Alexander S., Wagner N. Phys. Rev. B. 30:1984;3933 Balberg I., Binenbaum N., Wagner N. Phys. Rev. Lett. 52:1984;1465 Balberg I. Philos. Mag. B. 56:1987;991 Browning L., Lodge J., Price R.R., Schelleng J., Schoen P.E., Zabetakis Z. J. Appl. Phys. 84:1998;6109 Garboczi E.J., Snyder K.A., Douglas J.F., Thorpe M.F. Phys. Rev. E. 52:1995;819.
191. Lagarkov A.N., Matytsin S.M., Rozanov K.N., Sarychev A.K. J. Appl. Phys. 84:1998;3806.
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200. Many electromagnetic field problems can be expressed as a Freedholm integral equation of the first kind or the second kind. In integral formulations volume or surface charges or currents are usually the unknowns. These equations are solved by means of Harrington's methods of moments, i.e. Harrington R.F. Field computation by moment methods. 1982;Krieger Publishing Co, Melbourne, Florida. See also Harrington R.F. IEE Proc. 55:1967;136 Wang J.J.H. Generalized moment method in electromagnetics. 1991;Wiley, New York. It should be noted that one of the disadvantages of the Harrington's methods of moments is the possibility of unstable solutions. Moreover, the most ill-conditioned is the Freedholm integral equation of the first kind. See also the proceedings of recent Compumags, CEFCs, and ISEMs.
201. Many electromagnetic field problems can be expressed as a Freedholm integral equation of the first kind or the second kind. In integral formulations volume or surface charges or currents are usually the unknowns. These equations are solved by means of Harrington's methods of moments, i.e. Harrington R.F. Field computation by moment methods. 1982;Krieger Publishing Co, Melbourne, Florida. See also Harrington R.F. IEE Proc. 55:1967;136 Wang J.J.H. Generalized moment method in electromagnetics. 1991;Wiley, New York. It should be noted that one of the disadvantages of the Harrington's methods of moments is the possibility of unstable solutions. Moreover, the most ill-conditioned is the Freedholm integral equation of the first kind. See also the proceedings of recent Compumags, CEFCs, and ISEMs.
202. Many electromagnetic field problems can be expressed as a Freedholm integral equation of the first kind or the second kind. In integral formulations volume or surface charges or currents are usually the unknowns. These equations are solved by means of Harrington's methods of moments, i.e. Harrington R.F. Field computation by moment methods. 1982;Krieger Publishing Co, Melbourne, Florida. See also Harrington R.F. IEE Proc. 55:1967;136 Wang J.J.H. Generalized moment method in electromagnetics. 1991;Wiley, New York. It should be noted that one of the disadvantages of the Harrington's methods of moments is the possibility of unstable solutions. Moreover, the most ill-conditioned is the Freedholm integral equation of the first kind. See also the proceedings of recent Compumags, CEFCs, and ISEMs.
203. Mur G., De Hoop A.T. IEEE Trans. Magn. 21:1985;2188.
204. Zienkiewicz O.C., Taylor R.L. The finite element method. 1994;McGraw-Hill, New York. The finite element method (FEM) has considerable flexibility because arbitrary shape can be modeled. The FEM takes much more time and memory than the FDTD because it is required to solve linear equations in each time step. Consequently, the FEM is mainly used in the frequency domain and eigenmode analysis. For a general presentation of the finite element modeling of non-destructive material evaluation, we refer the interested reader to Mackerle J. Model. Simul. Mater. Sci. Eng. 7:1999;107.
205. Zienkiewicz O.C., Taylor R.L. The finite element method. 1994;McGraw-Hill, New York. The finite element method (FEM) has considerable flexibility because arbitrary shape can be modeled. The FEM takes much more time and memory than the FDTD because it is required to solve linear equations in each time step. Consequently, the FEM is mainly used in the frequency domain and eigenmode analysis. For a general presentation of the finite element modeling of non-destructive material evaluation, we refer the interested reader to Mackerle J. Model. Simul. Mater. Sci. Eng. 7:1999;107.
206. There is a vast literature on the FEM in the context of engineering. It is also worth noting that FEM softwares with flexible mesh generators, robust equation solvers and versatile post-processors have become available in recent years. For a general introduction, the reader is refered to Strang G, Fix GJ. An analysis of the finite element method. Englewoods Cliffs: Prentice-Hall; 1973. Other important books are: Bathe KJ, Wilson EL. Numerical methods in finite element analysis. Englewoods Cliffs: Prentice-Hall; 1976, Jin J. The finite element in electromagnetics, New York: Wiley; 1993), Sylvester PP, Ferrari RL. Finite elements for electrical engineers. 2nd ed. New York: Cambridge University Press; 1991, Johnson C. Numerical solution of partial differential equations by the finite element method, Cambridge: Cambridge University Press; 1987, and Hughes TJR. The finite element method. Englewood Cliffs, New Jersey: Prentice-Hall; 1987.
207. There is a vast literature on the FEM in the context of engineering. It is also worth noting that FEM softwares with flexible mesh generators, robust equation solvers and versatile post-processors have become available in recent years. For a general introduction, the reader is refered to Strang G, Fix GJ. An analysis of the finite element method. Englewoods Cliffs: Prentice-Hall; 1973. Other important books are: Bathe KJ, Wilson EL. Numerical methods in finite element analysis. Englewoods Cliffs: Prentice-Hall; 1976, Jin J. The finite element in electromagnetics, New York: Wiley; 1993), Sylvester PP, Ferrari RL. Finite elements for electrical engineers. 2nd ed. New York: Cambridge University Press; 1991, Johnson C. Numerical solution of partial differential equations by the finite element method, Cambridge: Cambridge University Press; 1987, and Hughes TJR. The finite element method. Englewood Cliffs, New Jersey: Prentice-Hall; 1987.
208. There is a vast literature on the FEM in the context of engineering. It is also worth noting that FEM softwares with flexible mesh generators, robust equation solvers and versatile post-processors have become available in recent years. For a general introduction, the reader is refered to Strang G, Fix GJ. An analysis of the finite element method. Englewoods Cliffs: Prentice-Hall; 1973. Other important books are: Bathe KJ, Wilson EL. Numerical methods in finite element analysis. Englewoods Cliffs: Prentice-Hall; 1976, Jin J. The finite element in electromagnetics, New York: Wiley; 1993), Sylvester PP, Ferrari RL. Finite elements for electrical engineers. 2nd ed. New York: Cambridge University Press; 1991, Johnson C. Numerical solution of partial differential equations by the finite element method, Cambridge: Cambridge University Press; 1987, and Hughes TJR. The finite element method. Englewood Cliffs, New Jersey: Prentice-Hall; 1987.
209. There is a vast literature on the FEM in the context of engineering. It is also worth noting that FEM softwares with flexible mesh generators, robust equation solvers and versatile post-processors have become available in recent years. For a general introduction, the reader is refered to Strang G, Fix GJ. An analysis of the finite element method. Englewoods Cliffs: Prentice-Hall; 1973. Other important books are: Bathe KJ, Wilson EL. Numerical methods in finite element analysis. Englewoods Cliffs: Prentice-Hall; 1976, Jin J. The finite element in electromagnetics, New York: Wiley; 1993), Sylvester PP, Ferrari RL. Finite elements for electrical engineers. 2nd ed. New York: Cambridge University Press; 1991, Johnson C. Numerical solution of partial differential equations by the finite element method, Cambridge: Cambridge University Press; 1987, and Hughes TJR. The finite element method. Englewood Cliffs, New Jersey: Prentice-Hall; 1987.
210. There is a vast literature on the FEM in the context of engineering. It is also worth noting that FEM softwares with flexible mesh generators, robust equation solvers and versatile post-processors have become available in recent years. For a general introduction, the reader is refered to Strang G, Fix GJ. An analysis of the finite element method. Englewoods Cliffs: Prentice-Hall; 1973. Other important books are: Bathe KJ, Wilson EL. Numerical methods in finite element analysis. Englewoods Cliffs: Prentice-Hall; 1976, Jin J. The finite element in electromagnetics, New York: Wiley; 1993), Sylvester PP, Ferrari RL. Finite elements for electrical engineers. 2nd ed. New York: Cambridge University Press; 1991, Johnson C. Numerical solution of partial differential equations by the finite element method, Cambridge: Cambridge University Press; 1987, and Hughes TJR. The finite element method. Englewood Cliffs, New Jersey: Prentice-Hall; 1987.
211. There is a vast literature on the FEM in the context of engineering. It is also worth noting that FEM softwares with flexible mesh generators, robust equation solvers and versatile post-processors have become available in recent years. For a general introduction, the reader is refered to Strang G, Fix GJ. An analysis of the finite element method. Englewoods Cliffs: Prentice-Hall; 1973. Other important books are: Bathe KJ, Wilson EL. Numerical methods in finite element analysis. Englewoods Cliffs: Prentice-Hall; 1976, Jin J. The finite element in electromagnetics, New York: Wiley; 1993), Sylvester PP, Ferrari RL. Finite elements for electrical engineers. 2nd ed. New York: Cambridge University Press; 1991, Johnson C. Numerical solution of partial differential equations by the finite element method, Cambridge: Cambridge University Press; 1987, and Hughes TJR. The finite element method. Englewood Cliffs, New Jersey: Prentice-Hall; 1987.
212. Stölzle S., Enders A., Nimtz G. J. Phys. I France. 2:1991;401. See also Coverdale R.T., Garboczi E.J., Jennings H.M. Comput. Mater. Sci. 3:1995;465 Coverdale R.T., Christensen B.J., Mason T.O., Jennings H.M., Garboczi E.J. J. Mater. Sci. 29:1994;4984.
213. Stölzle S., Enders A., Nimtz G. J. Phys. I France. 2:1991;401. See also Coverdale R.T., Garboczi E.J., Jennings H.M. Comput. Mater. Sci. 3:1995;465 Coverdale R.T., Christensen B.J., Mason T.O., Jennings H.M., Garboczi E.J. J. Mater. Sci. 29:1994;4984.
214. Stölzle S., Enders A., Nimtz G. J. Phys. I France. 2:1991;401. See also Coverdale R.T., Garboczi E.J., Jennings H.M. Comput. Mater. Sci. 3:1995;465 Coverdale R.T., Christensen B.J., Mason T.O., Jennings H.M., Garboczi E.J. J. Mater. Sci. 29:1994;4984.
215. Weiland T. Part. Accel. 15:1984;245. ibidem 17, 227, 1987. This paper deals with the MAFIA (Maxwell's equations Finite Integration Algorithm) code, which has been developed for the computation of eigenvalue equations by the Householder transformation.
216. Weiland T. Part. Accel. 15:1984;245. ibidem 17, 227, 1987. This paper deals with the MAFIA (Maxwell's equations Finite Integration Algorithm) code, which has been developed for the computation of eigenvalue equations by the Householder transformation.
217. Bossavit A. Computational electromagnetism, variational formulations, edge elements, complementarity. 1998;Academic Press, New York. See also Bossavit A. Electromagnétisme en vue de la modélisation. 1993;Springer Verlag, New York, Finlaysson B.A. The method of weighted residuals and variational principles. 1972;Academic, New York. Briefly stated, the variational principle leads to an approximate solution of a partial differential equation (PDE) by extremizing a functional. The solution thus found is guaranteed to be an approximation of the unique solution of the PDE in question.
218. Bossavit A. Computational electromagnetism, variational formulations, edge elements, complementarity. 1998;Academic Press, New York. See also Bossavit A. Electromagnétisme en vue de la modélisation. 1993;Springer Verlag, New York, Finlaysson B.A. The method of weighted residuals and variational principles. 1972;Academic, New York. Briefly stated, the variational principle leads to an approximate solution of a partial differential equation (PDE) by extremizing a functional. The solution thus found is guaranteed to be an approximation of the unique solution of the PDE in question.
219. Bossavit A. Computational electromagnetism, variational formulations, edge elements, complementarity. 1998;Academic Press, New York. See also Bossavit A. Electromagnétisme en vue de la modélisation. 1993;Springer Verlag, New York, Finlaysson B.A. The method of weighted residuals and variational principles. 1972;Academic, New York. Briefly stated, the variational principle leads to an approximate solution of a partial differential equation (PDE) by extremizing a functional. The solution thus found is guaranteed to be an approximation of the unique solution of the PDE in question.
220. Brebbia J.C. The boundary element method of engineers. 1980;Pentech, London.
221. Tuncer E. PhD thesis, Chalmers University of Technology, Gothenburg, Sweden; 2001. See also Tuncer E., Gubanski S.M., Nettelblad B. J. Appl. Phys. 89:2001;8092.
222. Tuncer E. PhD thesis, Chalmers University of Technology, Gothenburg, Sweden; 2001. See also Tuncer E., Gubanski S.M., Nettelblad B. J. Appl. Phys. 89:2001;8092.
223. Batchelor G.K. Ann. Rev. Fluid Mech. 6:1974;227. See also Schulgasser K.A. Int. Commun. Heat Mass Transfer. 19:1992;639. Insofar as the inclusions have a well-defined magnetic permeability, the problem of calculating the effective magnetic permeability is identical to that of calculating the effective permittivity. However, there is an important added aspect to the magnetic problem, i.e. the eddy current effect. Under an applied magnetic field, eddy currents are set in the inclusions which generate an induced magnetic field opposed to the applied field, and which suffer resistive losses. Thus, the eddy current effect is both diamagnetic and lossy.
224. Batchelor G.K. Ann. Rev. Fluid Mech. 6:1974;227. See also Schulgasser K.A. Int. Commun. Heat Mass Transfer. 19:1992;639. Insofar as the inclusions have a well-defined magnetic permeability, the problem of calculating the effective magnetic permeability is identical to that of calculating the effective permittivity. However, there is an important added aspect to the magnetic problem, i.e. the eddy current effect. Under an applied magnetic field, eddy currents are set in the inclusions which generate an induced magnetic field opposed to the applied field, and which suffer resistive losses. Thus, the eddy current effect is both diamagnetic and lossy.
225. There are many commercial software packages available with various libraries that can be used to implement the numerical method previously described, for example, FLUX 2D and 3D (Cedrat), PHI3D, Vector Fields, Ansoft, etc.
226. Gillespie J.B., Jennings S.G., Lindberg J.D. Appl. Opt. 17:1978;989. See also Bohren C.F. J. Atmos. Sci. 43:1986;68.
227. Gillespie J.B., Jennings S.G., Lindberg J.D. Appl. Opt. 17:1978;989. See also Bohren C.F. J. Atmos. Sci. 43:1986;68.
228. Calame J.P., Birman A., Carmel Y., Gershon D., Levush B., Sorokin A.A., Semenov V.E., Dadon D., Martin L.P., Rosen M. J. Appl. Phys. 80:1996;3992.
229. Steeman P.A.M., Maurer F.H.J. Colloid Polym. Sci. 270:1992;1069. Three-phase confocal spheroid-background mixtures were also treated by Jones S.B., Friedman S.P. Water Resour. Res. 36:2000;2821. The authors would like to thank Shmulik Friedman for providing a copy of his above mentioned article.
230. Steeman P.A.M., Maurer F.H.J. Colloid Polym. Sci. 270:1992;1069. Three-phase confocal spheroid-background mixtures were also treated by Jones S.B., Friedman S.P. Water Resour. Res. 36:2000;2821. The authors would like to thank Shmulik Friedman for providing a copy of his above mentioned article.
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232. We fully agree with Kroemer [Kroemer H. Rev Mod Phys 2001;73:783] when he says that "I do not think we can realistically predict which new devices and applications may emerge, but I believe we can create an environment encouraging progress, by not asking immediately what any new science might be good for (and cutting off the funds if no answer full of fanciful promises is forthcoming".
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245. Ponte Castaneda P. Philos. Trans. R. Soc. London Ser. A. 340:1992;531 Ponte Castaneda P., Kailsam M. Philos. Trans. R. Soc. London Ser. A. 453:1997;793 Ponte Castaneda P., Suquet P. Adv. Appl. Mech. 34:1998;171 Ponte Castaneda P. J. Mech. Phys. Solids. 39:1991;45. ibidem 1996;44:827, ibidem 1997;45:317 Ponte Castaneda P., Willis J.R. Philos. Trans. R. Soc. London, Ser. A. 455:1999;1799. The interested reader may also consult Pellegrini Y.P. Phys. Rev. B. 64:2001;134211. for a self-consistent effective medium theory for random dielectric composites of arbitrary nonlinear constitutive law Sipe J.E., Boyd R.W. Phys. Rev. A. 46:1992;1614. for a theory of the enhancement of the nonlinear optical susceptibility of nano-composite materials.
246. Ponte Castaneda P. Philos. Trans. R. Soc. London Ser. A. 340:1992;531 Ponte Castaneda P., Kailsam M. Philos. Trans. R. Soc. London Ser. A. 453:1997;793 Ponte Castaneda P., Suquet P. Adv. Appl. Mech. 34:1998;171 Ponte Castaneda P. J. Mech. Phys. Solids. 39:1991;45. ibidem 1996;44:827, ibidem 1997;45:317 Ponte Castaneda P., Willis J.R. Philos. Trans. R. Soc. London, Ser. A. 455:1999;1799. The interested reader may also consult Pellegrini Y.P. Phys. Rev. B. 64:2001;134211. for a self-consistent effective medium theory for random dielectric composites of arbitrary nonlinear constitutive law Sipe J.E., Boyd R.W. Phys. Rev. A. 46:1992;1614. for a theory of the enhancement of the nonlinear optical susceptibility of nano-composite materials.
247. Ponte Castaneda P. Philos. Trans. R. Soc. London Ser. A. 340:1992;531 Ponte Castaneda P., Kailsam M. Philos. Trans. R. Soc. London Ser. A. 453:1997;793 Ponte Castaneda P., Suquet P. Adv. Appl. Mech. 34:1998;171 Ponte Castaneda P. J. Mech. Phys. Solids. 39:1991;45. ibidem 1996;44:827, ibidem 1997;45:317 Ponte Castaneda P., Willis J.R. Philos. Trans. R. Soc. London, Ser. A. 455:1999;1799. The interested reader may also consult Pellegrini Y.P. Phys. Rev. B. 64:2001;134211. for a self-consistent effective medium theory for random dielectric composites of arbitrary nonlinear constitutive law Sipe J.E., Boyd R.W. Phys. Rev. A. 46:1992;1614. for a theory of the enhancement of the nonlinear optical susceptibility of nano-composite materials.
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250. Ponte Castaneda P. Philos. Trans. R. Soc. London Ser. A. 340:1992;531 Ponte Castaneda P., Kailsam M. Philos. Trans. R. Soc. London Ser. A. 453:1997;793 Ponte Castaneda P., Suquet P. Adv. Appl. Mech. 34:1998;171 Ponte Castaneda P. J. Mech. Phys. Solids. 39:1991;45. ibidem 1996;44:827, ibidem 1997;45:317 Ponte Castaneda P., Willis J.R. Philos. Trans. R. Soc. London, Ser. A. 455:1999;1799. The interested reader may also consult Pellegrini Y.P. Phys. Rev. B. 64:2001;134211. for a self-consistent effective medium theory for random dielectric composites of arbitrary nonlinear constitutive law Sipe J.E., Boyd R.W. Phys. Rev. A. 46:1992;1614. for a theory of the enhancement of the nonlinear optical susceptibility of nano-composite materials.
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252. John S. Phys. Rev. Lett. 58:1987;2486. There exist many analogies between photonic crystals and the more familiar electronic structure of crystalline solids. In both cases, the reciprocical lattice can be described by Brillouin zones that reflect the symmetry of the real-space crystal.
253. There is much work in this area. See, for example, Joannopoulos JD, Meade RD, Winn JN. Photonic crystals, Princeton, NJ: Princeton University Press; 1995. The periodic dielectric structure affects the dispersion relations and spatial distribution of the electromagnetic wave traveling through the photonic crystal. For large enough dielectric contrast, there exist wavelength regions (irrespective of the polarization or propagation direction) where no solutions of Maxwell's equations in the periodic structure can be found, creating photonic band gaps. For a bibliography of papers on optical and acoustic photonic band gaps, the interested reader should refer to the URL, http://www.home.earthlink.net/̃jpdowling/pbgbib.html.
254. In the mid 1980s, Drexler introduced the term "nanotechnology" to describe atomically precise molecular manufacturing systems and their products. Within the past two decades, a variety of terms sharing the prefix "nano-" (from the Greek root nanos, or dwarf), such as nanoparticle, nanomaterial, nanophase, nanomachine and nanostructured, have emerged to describe certain materials, technologies, and even businesses. See Drexler KE. Proc Natl Acad Sci USA 1981;78:5275, Drexler KE. Engines of creation: the coming era of nanotechnology. New York: Anchor Press; 1986, and Drexler KE. Nanosystems: molecular machinery, manufacturing, and computation. New York: Wiley; 1992. The excitement in the field of nanotechnology has led to a sea-change in our perception of what nanodevices can do, for example, Roco MC, Williams RS, Alivisatos P, editors. Nanotechnology research directions. Dordrecht, The Netherlands: Kluwer; 2000. Most current information in this rapidly progressing area can be found on the web pages, for example, http://www.foresight.com and http://www.zyvex.com.
255. In the mid 1980s, Drexler introduced the term "nanotechnology" to describe atomically precise molecular manufacturing systems and their products. Within the past two decades, a variety of terms sharing the prefix "nano-" (from the Greek root nanos, or dwarf), such as nanoparticle, nanomaterial, nanophase, nanomachine and nanostructured, have emerged to describe certain materials, technologies, and even businesses. See Drexler KE. Proc Natl Acad Sci USA 1981;78:5275, Drexler KE. Engines of creation: the coming era of nanotechnology. New York: Anchor Press; 1986, and Drexler KE. Nanosystems: molecular machinery, manufacturing, and computation. New York: Wiley; 1992. The excitement in the field of nanotechnology has led to a sea-change in our perception of what nanodevices can do, for example, Roco MC, Williams RS, Alivisatos P, editors. Nanotechnology research directions. Dordrecht, The Netherlands: Kluwer; 2000. Most current information in this rapidly progressing area can be found on the web pages, for example, http://www.foresight.com and http://www.zyvex.com.
256. In the mid 1980s, Drexler introduced the term "nanotechnology" to describe atomically precise molecular manufacturing systems and their products. Within the past two decades, a variety of terms sharing the prefix "nano-" (from the Greek root nanos, or dwarf), such as nanoparticle, nanomaterial, nanophase, nanomachine and nanostructured, have emerged to describe certain materials, technologies, and even businesses. See Drexler KE. Proc Natl Acad Sci USA 1981;78:5275, Drexler KE. Engines of creation: the coming era of nanotechnology. New York: Anchor Press; 1986, and Drexler KE. Nanosystems: molecular machinery, manufacturing, and computation. New York: Wiley; 1992. The excitement in the field of nanotechnology has led to a sea-change in our perception of what nanodevices can do, for example, Roco MC, Williams RS, Alivisatos P, editors. Nanotechnology research directions. Dordrecht, The Netherlands: Kluwer; 2000. Most current information in this rapidly progressing area can be found on the web pages, for example, http://www.foresight.com and http://www.zyvex.com.
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