FIG. 5: (Color online) Effective permittivity for clusters (shown in the inset) of one, two, three, and four cells connected by tight and smooth junctions. The field is either parallel (solid lines with symbols) or perpendicular (solid lines only) to the cluster axis. The effective permittivity either increases strongly with the number of cells for parallel geometry, or does not change for a perpendicular geometry. weight. In fact one can show that for two cells connected by smooth and tight junction characterized by parameter h , (1 / 2 − χ$_{2}$ ) ∝ h 2 when h → 0, or more precisely (1 / 2 − χ$_{2}$ ) is proportional with the solid angle encompassed by the missing part of a cell when it is connected with other cell in the dimer. The proof is based on the theorem of the solid angle [12]. The generalization to a finite cluster is also straightforward to (1 / 2 − χ$_{2}$ ) ∝ h $^{2}$/m (in that case the solid angle encompassed by the middle junction is proportional to h $^{2}$/m . The weight of the second eigenmode is P$_{2}$$_{,}$$_{1}$ = 〈 x · N$_{1}$ | u$_{2}$ 〉〈 v$_{2}$ | n · N$_{1}$ 〉 /V$_{1}$ . If we consider that the surface of the cluster is determined by the function g ( z ) then, up to a constant factor, 〈 v$_{2}$ | n · N$_{1}$ 〉 ≈ g (0) 2 = h 2 for two cells connected by smooth and tight junctions. The proof considers that the second eigenfunction of M † is an antisymmetric combination of constant distributions on each part of the dimer. This assertion is confirmed in Figure 7. Moreover, 〈 x · N$_{1}$ | u$_{2}$ 〉 /V$_{1}$ is weakly dependent on h . Therefore, for a parallel setting of the field stimulus, P$_{2}$$_{,}$$_{1}$/ (1 / 2 − χ$_{2}$ ), which is the measure of the dielectric decrement of low-frequency relaxation, 21 GLYPH<s49>GLYPH<s48> GLYPH<s49> GLYPH<s49>GLYPH<s48> GLYPH<s50> GLYPH<s49>GLYPH<s48> GLYPH<s51> GLYPH<s49>GLYPH<s48> GLYPH<s52> GLYPH<s49>GLYPH<s48> GLYPH<s53> GLYPH<s49>GLYPH<s48> GLYPH<s54> GLYPH<s49>GLYPH<s48> GLYPH<s55> GLYPH<s49>GLYPH<s48> GLYPH<s56> GLYPH<s49>GLYPH<s48> GLYPH<s57> GLYPH<s49>GLYPH<s48> GLYPH<s49>GLYPH<s48> GLYPH<s48> GLYPH<s53> GLYPH<s48> GLYPH<s48> GLYPH<s49> GLYPH<s48> GLYPH<s48> GLYPH<s48> GLYPH<s49> GLYPH<s53> GLYPH<s48> GLYPH<s48> GLYPH<s50> GLYPH<s48> GLYPH<s48> GLYPH<s48> GLYPH<s50> GLYPH<s53> GLYPH<s48> GLYPH<s48> GLYPH<s112> GLYPH<s97> GLYPH<s114> GLYPH<s44> GLYPH<s112> GLYPH<s101> GLYPH<s114>GLYPH<s112> GLYPH<s102>GLYPH<s40>GLYPH<s72>GLYPH<s122>GLYPH<s41> GLYPH<s32>GLYPH<s49> GLYPH<s32>GLYPH<s99>GLYPH<s101> GLYPH<s108> GLYPH<s108> GLYPH<s32>GLYPH<s50> GLYPH<s32>GLYPH<s99>GLYPH<s101> GLYPH<s108> GLYPH<s108> GLYPH<s115> GLYPH<s32>GLYPH<s51> GLYPH<s32>GLYPH<s99>GLYPH<s101> GLYPH<s108> GLYPH<s108> GLYPH<s115> GLYPH<s32>GLYPH<s52> GLYPH<s32>GLYPH<s99>GLYPH<s101> GLYPH<s108> GLYPH<s108> GLYPH<s115> GLYPH<s112>GLYPH<s101>GLYPH<s114>GLYPH<s112>