Discrete network approximation for highly-packed composites with irregular geometry in three dimensions

Lecture Notes in Computational Science and Engineering

Volumn 44, Issue , 2005, Pages 21-57

  Berlyand, Leonid ^a   Gorb, Yuliya ^a   Novikov, Alexei ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Discrete network; Effective conductivity; Error estimate; Variational bounds

Indexed keywords

ERRORS; ESTIMATION;

DISCRETE NETWORKS; EFFECTIVE CONDUCTIVITY; ERROR ESTIMATES; IRREGULAR GEOMETRIES; MATHEMATICAL JUSTIFICATION; PRIORI ERROR ESTIMATE; THREE DIMENSIONS; VARIATIONAL BOUNDS;

COMPLEX NETWORKS;

EID: 33749036883     PISSN: 14397358     EISSN: None     Source Type: Book Series    
DOI: 10.1007/3-540-26444-2_2     Document Type: Article

References (15)

1. Aizenman, M., Kesten, H., Newman, C.M.: Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation. Comm. Math. Phys., 111, 505-532 (1987)
2. Aurenhammer, F., Klein, R.: Voronoi Diagrams. In: Sack J. and Urrutia G. (ed) Handbook of Computational Geometry. Chapter V, 201-290. Elsevier Science Publishing (2000)
3. Berlyand, L., Borcea, L., Panchenko, A.: Network approximation for effective viscosity of concentrated suspensions with complex geometries. SIAM J. Math. Anal. (2003)
4. Bakhvalov, N.S., Panasenko, G.P.: Homogenization: Averaging Processes in Periodic Media. Kluwer, Dordrecht/Boston/London (1989)
5. Bensoussan, A., Lions, J.L., Papanicolaou, G. Asymptotic Analysis for Periodic Structure. North-Holland, Amsterdam (1978)
6. Berlyand, L., Kolpakov, A.: Network Approximation in the Limit of Small Interparticle Distance of the Effective Properties of a High Contrast Random Dispersed Composite. Arch. Rat. Math. Anal., 159:3, 179-227 (2001)
7. Berlyand, L., Novikov, A.: Error of the Network Approximation for Densely Packed Composites with Irregular Geometry. SIAM J. Math. Anal., 34:2, 385-408 (2002)
8. Borcea, L., Papanicolaou, G.: Network approximation for transport properties of high contrast conductivity. Inverse Problems, 15:4, 501-539 (1998)
9. Conway, J.H., Sloane, N. J. A.: The kissing number problem, and Bounds on kissing numbers, § 1.2 and Ch. 13. In: Sphere Packings, Lattices and Groups. 2nd ed. Springer-Verlag, New York. 21-24 (1993)
10. Ekeland, I., Temam, R. Convex Analysis and Variational problems. North Holland: Amsterdam (1976)
11. Jikov, V.V., Kozlov, S.M., Oleinik, O.A.: Homogenization of Differential Operators and Integral Functionals. Springer-Verlag, Berlin Heidelberg (1994)
12. Keller, J.B.: Conductivity of a medium containing a dense array of perfectly conducting spheres or cylinders or nonconducting cylinders. J. Appl. Phys., 34:4, 991-993 (1963)
13. Sanchez-Palencia, E.: Non-homogeneous Media and Vibration Theory. In: Lecture Notes in Physics, 127. Springer-Verlag, Berlin (1980)
14. Shewchuk, J.R.: What Is a Good Linear Finite Element? Interpolation, Conditioning, Anisotropy, and Quality Measures. Unpublished preprint, (2002) available at http://www-2.cs.cmu.edu/~jrs/jrspapers.html#quality
15. Steinhaus, H.: Mathematical Snapshots. 3rd ed. Dover, New York. 202-203, (1999)