In this paper, we model a heterogeneous dielectric medium exhibiting fractal geometry or disordered random structures by applying non-integer dimensions to determine its capacitance between two parallel plates. The depends on the fractional of slab, which may be obtained from theoretical dimension box-counting method. findings are verified CST Studio Suite (Electromagnetic field simulation soft...

We show how, by a constructive process we can generate arbitrarily large instances of the Traveling Salesman Problem (TSP) using standard fractals such as those of Peano, Koch or Sierpinski. We show that optimal solutions for these TSPs can be known a priori and thus they provide us with new non-trivial TSP instances ooering the possibility of testing heuristics well beyond the scope of testbed...

There has been an ever growing demand for antenna designs that possesses compact size, low profile and multiband features. Recently the possibility of developing antenna designs that exploit in some way the properties of fractals to achieve these goals, at least in part, has attracted a lot of attention. Fractal antennas have useful applications in cellular telephone and microwave communication...

Small-angle scattering (SAS) technique is applied to study the nano and microstructural properties of spatial patterns generated from chaos game representation (CGR). Using a simplified version of Debye formula, we calculate and analyze in momentum space, the monodisperse scattering structure factor from a system of randomly oriented and non-interacting 2D Sierpinski gaskets (SG). We show that ...

Percolation on a one-dimensional lattice and fractals such as the Sierpinski gasket is typically considered to be trivial because they percolate only at full bond density. By dressing up such lattices with small-world bonds, a novel percolation transition with explosive cluster growth can emerge at a nontrivial critical point. There, the usual order parameter, describing the probability of any ...

We study , the average conductance of the backbone, defined by two points separated by Euclidean distance r, of mass M(B) on two-dimensional percolation clusters at the percolation threshold. We find that with increasing M(B) and for fixed r, asymptotically decreases to a constant, in contrast with the behavior of homogeneous systems and nonrandom fractals (such a...

We outline a Hodge-deRham theory of K-forms ( for k=0,1,2) on two fractals: the Sierpinski Carpet(SC) and a new fractal that we call the Magic Carpet(MC), obtained by a construction similar to that of SC modified by sewing up the edges whenever a square is removed. Our method is to approximate the fractals by a sequence of graphs, use a standard Hodge-deRham theory on each graph, and then pass ...

Trophic interactions are highly complex and modern sequencing techniques reveal enormous biodiversity across multiple scales in marine microbial communities. Within the chemically and physically relatively homogeneous pelagic environment, this calls for an explanation beyond spatial and temporal heterogeneity. Based on observations of simple parasite-host and predator-prey interactions occurrin...