A new analytic model of fractal imbibition in porous media is derived. The topological Hausdorff dimension is used as a fractal parameter inthe proposed model. The fractal formulation is based on the model introduced by Li and Zhao to predict the production rate by spontaneousimbibition. Cantor Tartans and Menger sponge fractals are used to simulate fractal porous media with different ramifications. Results ofillustrative examples are presented in the form of a set of curves, which reveal the features of enhanced oil recovery of the model underconsideration. The results are compared with the experimental behaviour found on core samples of previous publications.

In this paper, we study the creep phenomena for self-similar models of viscoelastic materials and derive a generalization of the Kelvin–Voigt model in the framework of fractal continuum calculus. Creep compliance for the Kelvin–Voigt model is extended to fractal manifolds through local fractal-continuum differential operators. Generalized fractal creep compliance is obtained, taking into account the intrinsic time $\tau$ and the fractal dimension of time-scale $\beta$. The model obtained is validated with experimental data obtained for resin samples with the fractal structure of a Sierpinski carpet and experimental data on rock salt. Comparisons of the model predictions with the experimental data are presented as the curves of slow continuous deformations.

In this work, the fractal continuum Maxwell law for the creep phenomenon is introduced. By mapping standard integer space-time into fractal continuum space-time using the well-known Balankin’s approach to variable-order fractal calculus, the fractal version of Maxwell model is developed. This methodology employs local fractional differential operators on discontinuous properties of fractal sets embedded in the integer space-time so that they behave as analytic envelopes of non-analytic functions in the fractal continuum space-time. Then, creep strain $\epsilon \left(t\right)$, creep modulus $J\left(t\right)$, and relaxation compliance $G\left(t\right)$ in materials with fractal linear viscoelasticity can be described by their generalized forms, ${\epsilon }^{\beta }\left(t\right),J^{\beta }\left(t\right) \mathrm{and} G^{\beta }\left(t\right)$, where $\beta =dimS/dimH$ represents the time fractal dimension, and it implies the variable-order of fractality of the self-similar domain under study, which are $dimS$ and $dimH$ for their spectral and Hausdorff dimensions, respectively. The creep behavior depends on beta, which is characterized by its geometry and fractal topology: as beta approaches one, the fractal creep behavior approaches its standard behavior. To illustrate some physical implications of the suggested fractal Maxwell creep model, graphs that showcase the specific details and outcomes of our results are included in this study.

The time scaling exponent for the analytical expression of capillary rise $\ell \sim t^{\delta }$ for several theoretical fractal curves is derived. It is established that the actual distance of fluid travel in self-avoiding fractals at the first stage of imbibition is in the Washburn regime, whereas at the second stage it is associated with the Hausdorff dimension $d_{\mathcal{H}}$. Mapping is converted from the Euclidean metric into the geodesic metric for linear fractals $\mathcal{F}$ governed by the geodesic dimension $d_g=d_{\mathcal{H}}/d_{\ell }$, where $d_{\ell }$ is the chemical dimension of $\mathcal{F}$. The imbibition measured by the chemical distance ${\ell }_g$ is introduced. Approximate spatiotemporal maps of capillary rise activity are obtained. The standard differential equations proposed for the von Koch fractals are solved. Illustrative examples to discuss some physical implications are presented.

Se presenta un análisis de la tendencia de la movilidad durante un fenómeno natural como fue el caso de la pandemia provocada por el virus SARS-CoV-2 en la Ciudad de México. Se analiza la preferencia que tiene la población para desplazarse de un lugar a otro teniendo como variables el uso del automóvil, el transporte público y la caminata, recolectando información del 13 de enero de 2020 al 28 de marzo de 2022. A partir de los datos disponibles se obtienen resultados de curvas polinómicas de diverso orden, encontrándose que la de grado 15 es la que presenta un mejor ajuste con respecto a los datos, presentando un coeficiente de determinación R2=0.84 para el modo de transporte público, obteniendo así, una aproximación en la predicción del comportamiento humano en la movilidad bajo fenómenos naturales.