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Assessing large‐scale pressurization at the regional scale—a possible outcome of large subsurface storage applications such as wastewater injection and geological carbon sequestration—presents significant computational challenges. These challenges are particularly pronounced when accounting for complex geologic structures with multiple reservoir and caprock layers, fault zones, and wells. This study introduces a computationally efficient model that integrates single‐phase semi‐analytical solutions with a boundary element (BE) approach. The model simulates pressure propagation in multilayered 3D systems, including vertical faults, caprock, basement, and confining units. We apply this new model to a representative scenario involving CO2 injection near a partially sealing fault with verification against an independent two‐phase flow model. Results demonstrate that our model accurately captures far‐field pressure responses and that, outside the CO2 plume zone, pressure predictions from single‐phase and two‐phase models are nearly identical. This supports the use of single‐phase models like ours for efficient estimation of far‐field pressure changes. Additionally, we demonstrate its effectiveness at a large scale, incorporating multiple wells and faults. With its ability to represent multiple wells, fault zones, and geological heterogeneity, our model is well suited for assessments of basin‐scale pressurization. Its computational efficiency also makes it a promising tool for integration with optimization frameworks aimed at designing and managing injection strategies in faulted storage systems.

For a better engineering design, the paper is concerned primarily with the study of analytical solutions for output voltage ripple coefficient and the required minimum capacitance of BOOST converter using the relative inductance as an independent variable. Taking diode current as a current source, the analytical equation of output capacitor voltage is derived based on KCL. The output voltage ripple and its coefficient are calculated in three working modes. Furthermore, based on the analytical solution for OVRC, the analytical solution for the required minimum capacitance is presented. Both simulation and experiment are carried out, and results are obtained to verify the research. The achievements of this are able to be used in BOOST converter optimal design.

This study presents analytical and numerical‐analytical decomposition methods for determining complex one‐parameter generalized inverse Moore–Penrose matrices. The analytical approach is based on the third Moore–Penrose condition, offering three solution options. The first option employs complex decompositions of the given matrix and its Moore–Penrose inverse. The second option combines the first and third Moore–Penrose conditions, while the third option integrates the second and third conditions. For the first and third options, if any derived iterative procedure converges, the Moore–Penrose inverse matrix can be constructed using the corresponding matrix blocks. In contrast, the second option provides simplified relations, enabling the direct computation of the Moore–Penrose inverse matrix. Numerical‐analytical methods build on the second analytical solution, utilizing differential Pukhov transformations as the primary mathematical tool. A model example featuring a rectangular complex matrix is analyzed. A numerical‐analytical solution is derived using three matrix discretes, from which corresponding matrix blocks are reconstructed. The Moore–Penrose inverse matrix is then obtained through its complex decomposition.

A local thermal non-equilibrium analysis of heat and fluid flow in a channel fully filled with aluminum foam is performed for three cases: (a) pore density of 5 PPI (pore per inch), (b) pore density of 40 PPI, and (c) two different layers of 5 and 40 PPI. The dimensionless forms of fully developed heat and fluid flow equations for the fluid phase and heat conduction equation for the solid phase are solved analytically. The effects of interfacial heat transfer coefficient and thermal dispersion conductivity are considered. Analytical expressions for temperature profile of solid and fluid phases, and also the channel Nusselt number (NuH) are obtained. The obtained results are discussed in terms of the channel-based Reynolds number (ReH) changing from 10 to 2000, and thickness ratio between the channel height and sublayers. The Nusselt number of the channel with 40 PPI is always greater than that of the 5 PPI channel. It is also greater than the channel with two-layer aluminum foams until a specific Reynolds number then the Nusselt number of the channel with two-layer aluminum foams becomes greater than the uniform channels due to the higher velocity in the outer region and considerable increase in thermal dispersion.

The wetting pattern which occurs under surface drip irrigation is an important component for the optimum design of the system and for irrigation programming. The aim of this investigation was to devise a model which enables estimation of the 2D cross-sectional area of the wetting pattern which occurs under a surface dripper by an analytical method. The main parameters of the wetting pattern are the wetting diameter on the soil surface, the maximum wetted depth and maximum wetted width in the soil profile, and the depth of this maximum wetted width from the soil surface. In the laboratory experiments, water applications were carried out on two soil textures (clay loam and clay) with homogeneous soil profiles at two discharge rates over 125 min and 170 min periods. The sizes of the parameters of the wetting pattern were measured as consecutive series over 5-min intervals during the water application period. The general/main shape which represents the wetting patterns which occur under diferent irrigation conditions was defined and mathematically modelled. When the results were evaluated statistically, a correlation of 0.9128 was found between the momentary rates of change of the maximum depth of the wetting pattern predicted by the model and those measured in the experiment. The correlation between the momentary variations of accelerations of the same parameter was 0.9205. In addition, the size of the wetting pattern showed an increment in reducing velocities during the water application period. The results indicate that the model devised in this investigation can be used in the prediction of the cross-sectional area of the wetting pattern which occurs under a surface dripper.

This research paper targets the fractional Hirota’s analytical solutions–Satsuma (HS) equations. The conformable fractional derivative is employed to convert the fractional system into a system with an integer–order. The extended simplest equation (ESE) and modified Kudryashov (MKud) methods are used to construct novel solutions of the considered model. The solutions’ accuracy is investigated by handling the computational solutions with the Adomian decomposition method. The solutions are explained in some different sketches to demonstrate more novel properties of the considered model.

We study the impact of a spatially homogeneous yet non-stationary dielectric permittivity on the dynamical and spectral properties of light. Our choice of potential is motivated by the interest in   -symmetric systems as an extension of quantum mechanics. Because we consider a homogeneous and non-stationary medium,   symmetry reduces to time-reversal symmetry in the presence of balanced gain and loss. We construct the instantaneous amplitude and angular frequency of waves within the framework of Maxwell's equations and demonstrate the modulation of light amplification and attenuation associated with the well-defined temporal domains of gain and loss, respectively. Moreover, we predict the splitting of extrema of the angular frequency modulation and demonstrate the associated shrinkage of the modulation period. Our theory can be extended for investigating similar time-dependent effects with matter and acoustic waves in   -symmetric structures.

The corner of stone of this paper is the numerical treatment of the Robot arm control problem and its integral representation. The semi-analytic and numerical solutions are introduced using two impressive techniques. The first is the Chebyshev collocation method and the second is the differential transform method. The comparison from the error point of view between the exact solution and the numerical solution obtained by two techniques used are considered. Also, the integral representation of the Robot arm control system of equations are constructed and gives the same result obtained for the differential form. The advantage of the integral form is the non-locality and globality. The results and comparison between our techniques with other classic techniques which solve the same problem are introduced in the form of tables and figures with the help of Mathematica program to investigate and explain the efficiency and applicability of differential transform and Chebyshev collocation methods.

The objective of this study was to evaluate the applicability of a flow model with different numbers of spatial dimensions in a hydraulic features solution, with parameters such a free surface profile, water depth variations, and averaged velocity evolution in a dam-break under dry and wet bed conditions with different tailwater depths. Two similar three-dimensional (3D) hydrodynamic models (Flow-3D and MIKE 3 FM) were studied in a dam-break simulation by performing a comparison with published experimental data and the one-dimensional (1D) analytical solution. The results indicate that the Flow-3D model better captures the free surface profile of wavefronts for dry and wet beds than other methods. The MIKE 3 FM model also replicated the free surface profiles well, but it underestimated them during the initial stage under wet-bed conditions. However, it provided a better approach to the measurements over time. Measured and simulated water depth variations and velocity variations demonstrate that both of the 3D models predict the dam-break flow with a reasonable estimation and a root mean square error (RMSE) lower than 0.04, while the MIKE 3 FM had a small memory footprint and the computational time of this model was 24 times faster than that of the Flow-3D. Therefore, the MIKE 3 FM model is recommended for computations involving real-life dam-break problems in large domains, leaving the Flow-3D model for fine calculations in which knowledge of the 3D flow structure is required. The 1D analytical solution was only effective for the dam-break wave propagations along the initially dry bed, and its applicability was fairly limited.

A bi-directional static load test (BDSLT) is one of the most effective methods for accurately estimating pile bearing capacity, in which the test pile is divided into two portions by activating the single-loading device welded along the pile shaft. BDSLT, thus, eliminates the safety concerns and space limitations imposed by the reaction system, as compared to conventional static load tests (kentledge). Based on this study’s project requirements, two loading devices (supercells) were welded along the pile shaft to provide sufficient bearing capacity under the BDSLT, and an equivalent method was applied to interpret the measured load–settlement response. Since the sacrificial loading device welded along the pile shaft cannot be re-used, BDSLTs lead to increased construction costs; however, their capacity for rapid set-up in a limited space and reliable application for long piles are benefits that easily justify their use. Therefore, researchers must understand how BDSLTs perform, especially regarding double-loading devices. As informed by site investigation, this paper validates the conventional analytical solutions regarding test piles in preliminary designs, including Alpha and Beta and semi-empirical methods. In terms of a soil stiffness reduction model, modified closed-form analytical solutions based on Randolph’s analytical method were applied to predict the load–settlement response.