Hybrid ramified Sierpinski carpet: percolation transition, critical exponents, and force field

Abstract

This methodological note introduces the concept of and calculates percolation transition characteristics for a Sierpinski carpet with hybrid (énite-inénite) ramifying. Recurrence formulas for calculating the force éelds of Sierpinski prefractals of arbitrary generation are obtained. The possibility of using the obtained results in the model of oscillatory interacting different-scale inner boundaries of a heterogeneous material is discussed. . 182, å 5] ¬°£ §² ³¦²±ª¯³¬°¤°³ ¤ª¢²ª¥¯°« ²¡©£¦´£ §¯¯°³´¾À

A Method for Analyzing Physical Processes at the Vortex Front in High-Temperature Superconductors

“…To explain the mechanism of current flow through current clusters and the flow of vortices along normal zones, it is more appropriate to apply the block model of Meissner domains rather than the cluster model of weak links 41) . To take into consideration the transformation of the topology of Meissner domains and the multiple scale phenomena, as well as to calculate the characteristics of the percolation transition and the critical exponents, it is much more convenient to apply the Sierpinski carpet with infinite ramification − a modified two-dimensional analog of the Cantor set [42][43][44] .…”

Computer simulation mesostructure of cluster systems

“…This also helps to explain the existence of "magical" doses at which properties reach their extreme values [4].…”

“…A percolation model proposed in [4] allows interpreting the result of the long-range effect as a result of the critical behavior of an amorphous layer. It is assumed in the model that the defect layer located at a depth of the most probable projective run of ions is a quasi-plane non-continuous amorphous aggregate of different sizes.…”

“…Depending on the physical nature of a percolation cluster, this can cause an abnormal diffusion, hardening effects, destruction of a material and emergence of spontaneous magnetization in ferromagnetic materials or appearance of the Mott transitions in doped semiconductors, a change in heat or moisture capacities, etc. [1][2][3][4][5][6][7].…”

Percolation Model of Composites: Fraction Clusters and Internal Boundaries

“…Th is aggravates the anisotropy, leads to a self-affine mu lt ifractal pattern of cracks and internal borders. A simp le analogy to the plane and in the volume can be modified using affine maps such as other fractal Sierp inski carpet (square), Menger sponge, and their complements, respectively, as well as other suitable form of fractals [4,17].…”