Stacked ensemble machine learning for porosity and absolute permeability prediction of carbonate rock plugs.

This study employs a stacked ensemble machine learning approach to predict carbonate rocks' porosity and absolute permeability with various pore-throat distributions and heterogeneity. Our dataset consists of 2D slices from 3D micro-CT images of four carbonate core samples. The stacking ensemble learning approach integrates predictions from several machine learning-based models into a single meta-learner model to accelerate the prediction and improve the model's generalizability. We used the randomized search algorithm to attain optimal hyperparameters for each model by scanning over a vast hyperparameter space. To extract features from the 2D image slices, we applied the watershed-scikit-image technique. We showed that the stacked model algorithm effectively predicts the rock's porosity and absolute permeability.

Turing patterns and long-time behavior in a three-species food-chain model.

We consider a spatially explicit three-species food chain model, describing generalist top predator-specialist middle predator-prey dynamics. We investigate the long-time dynamics of the model and show the existence of a finite dimensional global attractor in the product space, L(2)(Ω). We perform linear stability analysis and show that the model exhibits the phenomenon of Turing instability, as well as diffusion induced chaos. Various Turing patterns such as stripe patterns, mesh patterns, spot patterns, labyrinth patterns and weaving patterns are obtained, via numerical simulations in 1d as well as in 2d. The Turing and non-Turing space, in terms of model parameters, is also explored. Finally, we use methods from nonlinear time series analysis to reconstruct a low dimensional chaotic attractor of the model, and estimate its fractal dimension. This provides a lower bound, for the fractal dimension of the attractor, of the spatially explicit model.

Hydromagnetic thin film flow: linear stability.

This paper deals with the long wave instability of an electroconductor fluid film, flowing down an inclined plane at small to moderate Reynolds numbers, under the action of electromagnetic fields. A coherent second order long wave model and two simplified versions of it, referred to as first and second reduced models (FRM and SRM), are proposed to describe the nonlinear behavior of the flow. The modeling procedure consists of a combination of the lubrication theory and the weighted residual approach using an appropriate projection basis. A suitable choice of weighting functions allows a significant reduction of the dimension of the problem. The full model is naturally unique, i.e., independent of the particular form of the trial functions. The linear stability of the problem is investigated, and the influence of electromagnetic field on the flow stability is analyzed. Two cases are considered: the applied magnetic field is either normal or parallel to the fluid flow direction, while the electric field is transversal. The numerical solution of the Orr-Sommerfeld (OS) eigenvalue problem and those of the depth averaging model are used to assess the accuracy of the reduced models. It is found that the current models have the advantage of the Benney-like model, which is known to asymptote the exact solution near criticality. Moreover, far from the instability threshold, the current reduced models continue to follow the OS solution up to moderate Reynolds numbers, while the averaging model diverges rapidly. The model SRM gives better results than FRM beyond sufficiently high Reynolds numbers.

Rotating solitary wave at the wall of a cylindrical container.

This paper deals with the theoretical modeling of a rotating solitary surface wave that was observed during water drainage from a cylindrical reservoir, when shallow water conditions were reached. It represents an improvement of our previous study, where the radial flow perturbation was neglected. This assumption led to the classical planar Korteweg-de Vries equation for the wall wave profile, which did not account for the rotational character of the base flow. The present formulation is based on a less restricting condition and consequently corrects the last shortcoming. Now the influence of the background flow appears in the wave characteristics. The theory provides a better physical depiction of the unique experiment by predicting fairly well the wave profile at least in the first half of its lifetime and estimating the speed of the observed wave with good accuracy.