FIG. 4: Smooth construction of a cluster (lower panel) from a dimer (upper panel). The parts determined by z ∈ [ − z$_{1}$, z$_{1}$ ] are “glued” together with the ends of the dimer. The arrows show where the junctions will be placed in the cluster. In Figure 6 we plot P$_{k,}$$_{1}$/ (1 / 2 − χ$_{k}$ ) versus (1 / 2 − χ$_{k}$ ), which shows that the number of dipole-active eigenmodes increases with the number of particles in the cluster. According to (27) and (28), Figure 6 shows in fact the dielectric decrement versus its corresponding relaxation frequency for each dipole-active eigenmode of the given clusters. For clusters of two or three particles, there is one important active eigenmode close to 1 / 2, while for clusters of four particles there are two active eigenmodes. It can be conjectured that for a general linear cluster made of m particles, there are m − 1 eigenvalues close to 1 / 2, of which the largest one is always dipole-active and has the largest 20 GLYPH<s45>GLYPH<s50>GLYPH<s122> GLYPH<s49> GLYPH<s45>GLYPH<s122> GLYPH<s109> GLYPH<s97>GLYPH<s120> GLYPH<s32> GLYPH<s103> GLYPH<s52> GLYPH<s40>GLYPH<s122>GLYPH<s41> GLYPH<s45>GLYPH<s51>GLYPH<s122> GLYPH<s49> GLYPH<s45>GLYPH<s50>GLYPH<s122> GLYPH<s45>GLYPH<s122> GLYPH<s50>GLYPH<s122> GLYPH<s49> GLYPH<s43> GLYPH<s122> GLYPH<s109> GLYPH<s97>GLYPH<s120> GLYPH<s50>GLYPH<s122> GLYPH<s49> GLYPH<s122> GLYPH<s49> GLYPH<s32> GLYPH<s32> GLYPH<s45> GLYPH<s122> GLYPH<s49> GLYPH<s122> GLYPH<s49> GLYPH<s122> GLYPH<s109> GLYPH<s97>GLYPH<s120> GLYPH<s45> GLYPH<s122> GLYPH<s109> GLYPH<s97>GLYPH<s120> GLYPH<s48> GLYPH<s48> GLYPH<s103> GLYPH<s40>GLYPH<s122>GLYPH<s41>