Fig. 1 Representative volume renderings of 3D DLA structures SP1 ( a ), SP2 ( b ), SP3 ( c ), and SP4 ( d ) with nominal fractal dimensions given in Table 1 More about this image found in Representative volume renderings of 3D DLA structures SP1 ( a ), SP2 ( b ),...

Fig. 2 Three-dimensional printed multifractal structures SP1 ( a ), SP2 ( b ), SP3 ( c ), and SP4 ( d ) with nominal dimension given in Table 1 More about this image found in Three-dimensional printed multifractal structures SP1 ( a ), SP2 ( b ), SP3...

Fig. 3 Bayesian posterior probability densities of fractal dimensions ( D f ) for each fractal specimen. Mean values are given in Table 1 . SP6 (3D cube) is omitted because the fractal dimension of a perfect cube is exactly 3. More about this image found in Bayesian posterior probability densities of fractal dimensions ( D ...

Fig. 4 Plots of box size ( ϵ ) against the logarithm of the number of covering boxes ( N ϵ ) along with the prediction and confidence intervals, illustrating low uncertainty in the power-law assumption More about this image found in Plots of box size ( ϵ ) against the logarithm of the number of covering...

Fig. 5 Snapshots of the temperature distributions in C for three fractal structures and solid cube: ( a ) D f  = 2.52, ( b ) D f  = 2.58, ( c ) D f  = 2.66, and ( d ) D f  = 3.00 More about this image found in Snapshots of the temperature distributions in C for three fractal struct...

Fig. 6 DRAM pairwise correlation for the D f = 2.55 specimen with a fit relating D and α derived from the second law of thermodynamics. The fit with C = 0.1115 and k = 4.931 has an R 2 of 0.96. This plot is representative of the fits ... More about this image found in DRAM pairwise correlation for the D f = 2.55 specimen wi...

Fig. 7 Representative fractal diffusion model fit of temperature for a structure with a fractal dimension D f = 2.66 More about this image found in Representative fractal diffusion model fit of temperature for a structure w...

Fig. 8 Bayesian posterior densities for all fractal dimensions (top row). The chains (middle row) and pairwise correlation (bottom row) are shown for the D f = 2.52 specimen as a representative example of all chains and pairwise correlations. A normalized spatial grid was used f... More about this image found in Bayesian posterior densities for all fractal dimensions (top row). The chai...

Fig. 1 Schematic of the concentration decay problem considered in this work: ( a ), ( b ), and ( c ) present schematics of Cartesian, cylindrical and spherical problems, respectively. Both homogeneous and two-layer geometries are shown: ( a ) slab, ( b ) cylinder, and ( c ) sphere. More about this image found in Schematic of the concentration decay problem considered in this work: ( a )...

Fig. 2 Comparison of present diffusion-reaction work with past work in the pure diffusion limit [ 15 ]: Decay characteristics for a homogeneous Cartesian problem for multiple values of ( a ) β ¯ approaching zero and ( b ) Sh approaching infinity More about this image found in Comparison of present diffusion-reaction work with past work in the pure di...

Fig. 3 Comparison of present diffusion-reaction work with past work [ 15 ] in the pure diffusion limit: λ / ( 3 S h 3 + Sh ) as a function of β ¯ for multiple values of Sh for a homogeneous Cartesian problem More about this image found in Comparison of present diffusion-reaction work with past work [ 15 ] in the ...

Fig. 4 Comparison with past work on drug-delivery from an encapsulated sphere [ 7 ]: Comparison of decay characteristics between the surrogate model S ( τ ) and previously reported data for ( a ) Sh = 0.1 and ( b ) Sh = 2.0 . Other problem parameters are β ¯ ... More about this image found in Comparison with past work on drug-delivery from an encapsulated sphere [ 7 ...