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pro vyhledávání: '"Van Siclen, Clinton DeW."'
Autor:
Van Siclen, Clinton DeW.
Algebraic expressions are found for the effective conductivities of some infinite tessellations composed of conducting square, triangular, or hexagonal tiles. A tessellation is further characterized by the number N of different colors (different tile
Externí odkaz:
http://arxiv.org/abs/2402.10909
Autor:
Van Siclen, Clinton DeW.
The Menger sponge is a three-dimensional cube that comprises a self-similar, fractal domain and a non-fractal domain, both of which are continuous. Thus it is a useful heuristic model for natural and engineered fractal systems. For this purpose the e
Externí odkaz:
http://arxiv.org/abs/2304.07635
Autor:
Van Siclen, Clinton DeW.
Fluid infiltration of a permeable brick in contact with a pressurized reservoir of fluid is considered. A stochastic model, informed by Darcy's law and the incompressibility of the fluid, shows how the heterogeneity of the permeability field affects
Externí odkaz:
http://arxiv.org/abs/2201.08487
Autor:
Van Siclen, Clinton DeW.
The empirical Archie's law, relating the measured electrical resistivity of an electrolyte-saturated rock to its connected porosity, is derived by consideration of the fractal character of the pore space. The derivation thus imposes some conditions o
Externí odkaz:
http://arxiv.org/abs/2103.14099
Autor:
Van Siclen, Clinton DeW.
An algebraic formula for the effective conductivity of a d-dimensional, two-component chessboard (checkerboard) is proposed. The derivation relies on the self-duality of the square bond lattice, the principle of universality, and the analytical capab
Externí odkaz:
http://arxiv.org/abs/2006.16313
Autor:
Van Siclen, Clinton DeW.
A probabilistic method is derived for solution of ohmic circuit problems. It is compared to the standard approach, which is construction and solution of a set of coupled, linear equations manifesting Kirchhoff's laws. An example is made of an electri
Externí odkaz:
http://arxiv.org/abs/1906.10245
Autor:
Van Siclen, Clinton DeW.
The classic Sierpinski triangle comprised of conducting bonds is multifractal. Thus the critical exponents and dimensions related to the conductivity are obtained asymptotically--that is, in the limit that the correlation length {\xi} of the recursiv
Externí odkaz:
http://arxiv.org/abs/1710.06346
Autor:
Van Siclen, Clinton DeW.
Iterative construction of a Sierpinski carpet or sponge is shown to be a critical phenomenon analogous to uncorrelated percolation. Critical exponents are derived or calculated (by random walks over the carpet or sponge at infinite iteration) that ar
Externí odkaz:
http://arxiv.org/abs/1706.03410
Autor:
Van Siclen, Clinton DeW.
Connections are found between the two-component percolation problem and the conductor/insulator percolation problem. These produce relations between critical exponents, and suggest formulae connecting the conductivity exponents in different dimension
Externí odkaz:
http://arxiv.org/abs/1609.01229
Autor:
Van Siclen, Clinton DeW.
Subsurface radioactivity may be due to transport of radionuclides from a contaminated surface into the solid volume, as occurs for radioactive fallout deposited on soil, or from fast neutron activation of a solid volume, as occurs in concrete blocks
Externí odkaz:
http://arxiv.org/abs/1112.3597