TY - JOUR
T1 - Mapping physical problems on fractals onto boundary value problems within continuum framework
AU - Balankin, Alexander S.
N1 - Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2018/1/30
Y1 - 2018/1/30
N2 - In this Letter, we emphasize that methods of fractal homogenization should take into account a loop structure of the fractal, as well as its connectivity and geodesic metric. The fractal attributes can be quantified by a set of dimension numbers. Accordingly, physical problems on fractals can be mapped onto the boundary values problems in the fractional-dimensional space with metric induced by the fractal topology. The solutions of these problems represent analytical envelopes of non-analytical functions defined on the fractal. Some examples are briefly discussed. The interplay between effects of fractal connectivity, loop structure, and mass distributions on electromagnetic fields in fractal media is highlighted. The effects of fractal connectivity, geodesic metric, and loop structure are outlined.
AB - In this Letter, we emphasize that methods of fractal homogenization should take into account a loop structure of the fractal, as well as its connectivity and geodesic metric. The fractal attributes can be quantified by a set of dimension numbers. Accordingly, physical problems on fractals can be mapped onto the boundary values problems in the fractional-dimensional space with metric induced by the fractal topology. The solutions of these problems represent analytical envelopes of non-analytical functions defined on the fractal. Some examples are briefly discussed. The interplay between effects of fractal connectivity, loop structure, and mass distributions on electromagnetic fields in fractal media is highlighted. The effects of fractal connectivity, geodesic metric, and loop structure are outlined.
KW - Electromagnetic fields
KW - Fractal materials
KW - Fractal metric
KW - Fractional-dimensional space
KW - Physics on fractals
UR - http://www.scopus.com/inward/record.url?scp=85033789673&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2017.11.005
DO - 10.1016/j.physleta.2017.11.005
M3 - Artículo
AN - SCOPUS:85033789673
SN - 0375-9601
VL - 382
SP - 141
EP - 146
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 4
ER -