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A Stochastic Model of Icosahedral Capsid Growth

“…In the case of fullerenes, the correction is due to the Boltzmann factors that reflect the energy differences between the following basic processes: Creation of a new pentagon in a (6,6) cavity, or the creation of a new hexagon in a (5,6) or in a (6,6) cavity, under the assumption that the energy barrier against creation of two or three pentagons sticking together is so large that the corresponding Boltzmann factor is close to 0. These factors could be evaluated by requiring that the successive probabilities of finding pentagons among ail polygons in clusters of a given size (after the n-\h agglomeration step) and the corresponding yields form a geometric progression [10,11].…”

“…; , is very close to the value observed in the final structure, which is P5 -12/32 = 3/8 = 0.385. The simplest stochastic model of growth successfully applied to fullerene formation [10,11], is based on the assumption that the dominant agglomeration processes consist of forming new polygons in the cavities between two polygons on tbe border of the existing cluster, by adjoining a C2 or a C3 molecule to a cavity found in a cluster already formed. One of such processes is shown in figure I below.…”

A Z3-graded generalization of supermatrices

“…The generators defined in this way have the following properties: their cubes vanish, as also does a product of any four generators 8 .…”

“…Recently, there have been many attempts to generalize Z 2 -graded constructions to the Z 3 -graded case [6][7][8][9][10] . Many such attempts, though, were aimed at the description of exotic statistics.…”

Monopoles in non-Abelian Einstein–Born–Infeld theory

“…Vortex, monopole and other soliton-like solutions to theories containing a DBI action have been studied for Abelian and non-Abelian gauge symmetry [19]- [23], in this last case both using the symmetrised and the normal trace operation to define a scalar DBI action. A distinctive feature was discovered for DBI vortices and monopoles: there exists a critical value β c of the Born-Infeld β-parameter below which regular solutions cease to exist [20]- [22].…”