Homogeneous Case Research Articles

A Data-Driven Approach for Stylolite Detection

Summary Stylolite is a specific geopattern that can occur in both sedimentary rocks and deformed zones, which could change the porosity of the reservoir, modify the permeability, and even result in horizontal permeability barriers. Though there are many related studies to characterize this geopattern, most of them focus on experimental methods. In this work, we investigated a new approach for recovering geometrical information of the stylolite zone (including its size and location) based on neural network architectures including convolutional neural network (CNN), long short-term memory (LSTM), and transformer encoder, which could serve as a data-driven solution to the problem. To our knowledge, this paper is the first to exclusively use well testing data for deducing field geopatterns, whereas other studies have relied on additional data sources such as well logging data. To simplify the problem, we first conducted simulation by building 3D multilayer reservoir models with one stylolite zone. We considered both simplified cases with only a few homogeneous layers and cases with heterogeneous layers to generalize our work. For the heterogeneous case, we extracted the permeability from SPE10 Model 2, a commonly used public resource (SPE 10 Benchmark, Model 2 2008). Producing and observing wells in the model are at different locations and provide pressure and production rate data as inputs for the deep learning models, in the form of multivariant time series data. For homogeneous cases, after zero-padding and standardizing our inputs to tackle different-length data and features with different scales, we applied a CNN-LSTM model to our data set, leveraging the CNN’s ability to capture short-term local features and the LSTM’s capacity to extract long-term dependencies. This combination improves the extraction of important information from time series data related to stylolites. The two subnetworks are connected in parallel to combine the advantages of CNN in extracting local temporal features and the strengths of LSTM in capturing long-time dependency via self-loops. Our work also separately covers the two subnetworks of the CNN-LSTM model as baseline models. For heterogeneous cases, a CNN-based model U-Net and an attention-based model set function for time series (SeFT) were introduced to make the predictions. In a more realistic scenario featuring fluid pathways with irregular shapes within a heterogeneous reservoir, we employed a transformer encoder model to predict both the shape and location of the fluid pathways. On the homogeneous data set, our CNN-LSTM model achieved a satisfactory performance and could predict the locations and sizes of the stylolite zone and outperformed the two baseline models. On the more challenging heterogeneous data set, our baseline and CNN-LSTM models failed to deliver meaningful results. In contrast, SeFT and U-Net performed better in the sense that we could successfully predict the locations of the stylolite zones. In a more realistic scenario involving irregularly-shaped fluid pathways, our transformer encoder model achieved accurate predictions of their locations.

Topological pumping in an inhomogeneous Aubry-André model

The Aubry-André model is a fundamental theoretical model that exhibits interesting topological features. In this paper, we examine topologically protected boundary states in the inhomogeneous off-diagonal Aubry-André model. In contrast to the homogeneous case, the inhomogeneity triggers boundary states at phase boundaries that separate two distinct non-trivial topological domains. Remarkably, the topological character of the boundary states is predicted through topological pumping, where a boundary state is transferred from one boundary across the bulk region to the other by adiabatically tuning the pump parameter. Moreover, the role of the off-diagonal modulation strength (λ) on the transfer efficiency of the topological pumping is addressed. To support our results, we investigate the time evolution of a continuous-time quantum walk and show that its spread rate and λ are inversely related. Our work provides a new avenue to harness topological features of the Aubry-André model, where topological pumping can be used for robust quantum transport.

Hydrogen underground storage potential in sandstone formation: A thorough study utilizing surface complexation modelling

This research focuses on the geochemical aspects of hydrogen underground storage, with particular emphasis on surface complexation modelling and its impact on surface potential and surface charge. The primary objective is to develop the first comprehensive surface complexation model specifically tailored for sandstone rocks, emphasizing key minerals such as quartz, kaolinite, and calcite, which are suitable for hydrogen underground storage applications. This model is intended to serve as a benchmark for more research in this field, providing a solid foundation for investigating and improving predictions related to wettability alteration. Additionally, the model has been integrated with hydrogen solubility to accurately capture changes in surface charge. The study identified six brine compositions with various minerals to examine the effect of monovalent and divalent ions. The results showed an increase in solubility with an overall reduction in salinity, and a decrease in divalent ions. The homogeneous surface complexation model demonstrated a neutral surface potential, attributed to an increased mole fraction of positively charged >SiOH+and a decreased in negatively charged >SiO-. Similar trends were observed in kaolinite and calcite minerals. The influence of pH was also explored, revealing a significant impact on the homogeneous quartz case, where an increase in pH shifted the surface potential from neutral to more negative. The heterogeneous cases exhibited less negative behavior as the quartz content increased per case, mainly due the increasing presence of positively charged species such as >SiOH+ and >AlOH+, and the reduction of the negatively charged >AlO-. Increasing the salinity of the solution resulted in less negative surface potential, attributed to the abundance of positive divalent and monovalent ions boosted by increasing salinity, thus the formation of positive surface complexes.

Librations and obliquity of the largest moons of Uranus

Following the discovery of several ocean worlds in the solar system, and the selection of Uranus as the highest priority objective by the Planetary Science and Astrobiology Decadal Survey 2023-2032, the five largest moons of Uranus (Miranda, Ariel, Umbriel, Titania and Oberon) have been receiving renewed attention as they may also harbor a subsurface ocean. We assess how rotation measurements could help confirm the internal differentiation of the bodies and detect internal oceans if any. Because of the time-varying gravitational torque of Uranus on the flattened shape of its synchronous satellites, the latter librate with respect to their mean rotation and precess with a non zero obliquity. For a range of interior models with a rocky core surrounded by a hydrosphere, either solid or divided into an outer ice shell with a liquid ocean underneath, we compute their diurnal libration amplitude and obliquity. We find that if the Uranian satellites were two-layer solid bodies, libration measurement accuracies from around 0.25 m for Oberon to around 6 m for Miranda would rule out the possibility of homogeneous interiors. In combination with independent estimates of the mean moment of inertia (MOI), libration measurements could also be used to detect the presence of an ocean, the measurement precision required for this depending on the actual value of the libration amplitude. To compute the obliquity, we first build series for the orbital precession of all five satellites with a secular perturbations model. With the exception of Miranda, we show that due to the mutual gravitational interactions between the satellites, the obliquity of the large Uranian moons exhibits relatively large periodic variations around the mean value. We find that an obliquity measurement accuracy from around 1 m for Ariel to around 400 m for Oberon can rule out the homogeneous case. The presence of an internal global ocean could allow a resonant amplification of the obliquity, facilitating its detection. If no such resonance occurs, the obliquity would be almost indistinguishable from that expected for a solid body. The effect of tidal deformations on the rotation of the small to medium-sized Uranian moons is showed to be limited. Librations would be reduced by up to 10% and obliquity increased by up to 15% for Titania and Oberon, the effects being negligible for Miranda.

Almost global synchronization of Kuramoto oscillators with symmetry breaking terms

M.A. Lohe first proposed the high-dimensional Kuramoto model with symmetry-breaking terms (Quantum synchronization over quantum networks, Journal of Physics A: Mathematical and Theoretical, 43:465301, 2010), which is the real form of a quantum network synchronization model. For the homogeneous case, by analyzing the limit set and the spectrum of the linearized model, the almost global synchronization is derived from the topology of some kind of connecting graphs.

Role of artificial intelligence in staging and assessing of treatment response in MASH patients.

The risk of disease progression in MASH increases proportionally to the pathological stage of fibrosis. This latter is evaluated through a semi-quantitative process, which has limited sensitivity in reflecting changes in disease or response to treatment. This study aims to test the clinical impact of Artificial Intelligence (AI) in characterizing liver fibrosis in MASH patients. The study included 60 patients with clinical pathological diagnosis of MASH. Among these, 17 received a medical treatment and underwent a post-treatment biopsy. For each biopsy (n = 77) a Sirius Red digital slide (SR-WSI) was obtained. AI extracts >30 features from SR-WSI, including estimated collagen area (ECA) and entropy of collagen (EnC). AI highlighted that different histopathological stages are associated with progressive and significant increase of ECA (F2: 2.6% ± 0.4; F3: 5.7% ± 0.4; F4: 10.9% ± 0.8; p: 0.0001) and EnC (F2: 0.96 ± 0.05; F3: 1.24 ± 0.06; F4: 1.80 ± 0.11, p: 0.0001); disclosed the heterogeneity of fibrosis among pathological homogenous cases; revealed post treatment fibrosis modification in 76% of the cases (vs 56% detected by histopathology). AI characterizes the fibrosis process by its true, continuous, and non-categorical nature, thus allowing for better identification of the response to anti-MASH treatment.

COMPARATIVE STUDY OF RESIDUAL VARIANCE ESTIMATORS CONSTRUCTED WITHOUT OR WITH THE PRESENCE OF ATYPICAL VALUES: CASE OF THE PARTIALLY LINEAR MODEL

Error variance is a measure of the goodness of fit for a regression model. Ahoutou et al. [1] proposed estimators of the error variance under the assumption that the dimension of the nonlinear covariate is one. In this paper, assuming that the dimension of the nonlinear covariate is greater than or equal to 2, we propose estimators of error variance in homogeneous and heterogeneous cases. We propose estimators of the error variance that are constructed without taking atypical values into account and others that are constructed by taking all the data into account. Using simulations, we compare the performance of estimators designed without taking into account atypical values with estimators designed taking into account all the data.

Pd-imidate@SBA-15: a multifunctional heterogeneous catalyst for the aqueous room temperature hydrogenation of CO2 to formic acid.

The incorporation of hydrophilic and basic sites from phosphotriazaadamantane and saccharine in a water-soluble Pd complex and the subsequent confinement into mesoporous silica support increases the activity and stability of the palladium catalytic species for the room-temperature aqueous hydrogenation of either bicarbonate or CO2 into formic acid. The use of low Pd loadings (<0.1mmolPd·g-1) of the well-dispersed complex on SBA-15 mesoporous silica allows performing the reaction under room temperature, and aqueous conditions, exhibiting TON of ca. 40-100, for the CO2 or bicarbonate hydrogenation, respectively, which is one order of magnitude higher than the homogeneous case, allowing the easy isolation and recycling of the solid catalyst.

Inhomogeneity effects on earthquake fault events.

We present a detailed analysis of the dynamical behavior of an inhomogeneous Burridge-Knopoff model, a simplified mechanical model of an earthquake. Regardless of the size of seismic faults, a soil element rarely has a continuous appearance. Instead, their surfaces have complex structures. Thus, the model we suggest keeps the full Newtonian dynamics with inertial effects of the original model, while incorporating the inhomogeneities of seismic fault surfaces in stick-slip friction force that depends on the local structure of the contact surfaces as shown in recent experiments. The numerical results of the proposed model show that the cluster size and the moment distributions of earthquake events are in agreement with the Gutenberg-Richter law without introducing any relaxation mechanism. The exponent of the power-law size distribution we obtain falls within a realistic range of value without fine tuning any parameter. On the other hand, we show that the size distribution of both localized and delocalized events obeys a power law in contrast to the homogeneous case. Thus, no crossover behavior between small and large events occurs.

Inference of a Susceptible-Infectious stochastic model.

We considered a time-inhomogeneous diffusion process able to describe the dynamics of infected people in a susceptible-infectious (SI) epidemic model in which the transmission intensity function was time-dependent. Such a model was well suited to describe some classes of micro-parasitic infections in which individuals never acquired lasting immunity and over the course of the epidemic everyone eventually became infected. The stochastic process related to the deterministic model was transformable into a nonhomogeneous Wiener process so the probability distribution could be obtained. Here we focused on the inference for such a process, by providing an estimation procedure for the involved parameters. We pointed out that the time dependence in the infinitesimal moments of the diffusion process made classical inference methods inapplicable. The proposed procedure were based on the generalized method of moments in order to find a suitable estimate for the infinitesimal drift and variance of the transformed process. Several simulation studies are conduced to test the procedure, these include the time homogeneous case, for which a comparison with the results obtained by applying the maximum likelihood estimation was made, and cases in which the intensity function were time dependent with particular attention to periodic cases. Finally, we applied the estimation procedure to a real dataset.

Prandtl boundary layer expansion with strong boundary layers for inhomogeneous incompressible magnetohydrodynamics equations in Sobolev framework

We consider the validity of Prandtl boundary layer expansion of solutions to the initial boundary value problem for inhomogeneous incompressible magnetohydrodynamics equations in the half-plane when both viscosity and resistivity coefficients tend to zero, where the no-slip boundary condition is imposed on velocity while the perfectly conducting condition is given on magnetic field. Since there exist strong boundary layers, the essential difficulty in establishing the uniform L∞ estimates of the error functions comes from the unboundedness of vorticity of strong boundary layers. Under the assumptions that the viscosity and resistivity coefficients take the same order of a small parameter and the initial tangential component of magnetic field has a positive lower bound near the boundary, we prove the validity of Prandtl boundary layer ansatz in L∞ sense in Sobolev framework. Compared with the homogeneous incompressible case considered in [33], there exists a strong boundary layer of density. Consequently, some suitable functionals should be designed and the elaborated co-normal energy estimates will be involved in analysis due to the variation of density and the interaction between the density and velocity.

A novel numerical approach for the third order Emden–Fowler type equations

AbstractThis article aims to achieve robust numerical results by applying the Chebyshev reproducing kernel method without homogenizing the initial‐boundary conditions of the Emden–Fowler (E‐F) equation, thereby introducing a new perspective to the literature. A novel numerical approach is presented for solving the initial‐boundary value problem of third‐order E‐F equations using Chebyshev reproducing kernel theory. Unlike previous applications, which were confined to homogeneous initial‐boundary value problems or required homogenization, the proposed method is effective for both homogeneous and nonhomogeneous cases. To handle the initial‐boundary conditions of the E‐F equations, additional basis functions are introduced rather than imposing conditions on the reproducing kernel Hilbert space. The method's effectiveness is demonstrated through five examples, which validate the theoretical analysis. Overall, the results emphasize the method's efficiency.

Non-homogeneous model for studying femur bone implants with considering defects

ABSTRACT In this article, the natural frequencies of the femur in the presence and absence of defects have been calculated. For this purpose, two approaches to bone modeling have been considered: one for the homogeneous case and the other for the non-homogeneous case, which more closely reflects the reality of the femur bone. In the next step, in order to identify suitable materials for femur bone implants, two materials AZ31 and CP Ti have been selected, and the natural frequencies of the femur made with these two materials have been calculated and compared with the results of the natural femur. From the obtained results, it can be concluded that although these two materials are attractive for bone implants from other aspects, they are not approved from the point of view of vibrations, although material AZ31 is a little better. It is also observed that the selected defect in the femur has little effect on the natural frequencies.

Assessment of mineral compositions on geo-mechanical time dependent plastic creep deformation

Understanding rock mechanical time-dependent plastic deformation enables the researchers to accurately predict rock responses during loading and unloading. This research focuses on the geomechanical aspects of hydrogen storage, particularly rock resistance to creep deformation under varying stresses and pressures. Modelling creep deformation in underground storage mediums has been overlooked and requires further consideration, as it is a critical, cyclical, time-dependent phenomenon essential for hydrogen containment. The study's novelty is demonstrated in its focus on geomechanical properties of rock minerals, providing insights that aid in site-selection criteria for hydrogen storage A creep deformation model with varying mineral compositions is used to assess creep deformation strain. In homogenous cases, calcite showed the highest resistance to creep deformation after three loading cycles, primarily due to its high Young's Modulus. As for the heterogenous cases, the results indicated that the mixture of calcite and quartz was the most creep-resistant rock composition. In terms of rock types, basalt samples demonstrated the highest resistance to creep deformation, while siltstone exhibited the highest susceptibility to deformation. It was observed that as the number of cycles increase, the rock mechanical stability decreases, hence optimizing the number of cycles is a must to ensure hydrogen geo-containment.

Dynamics of a susceptible-infected-recovered model on complex networks with interregional migration.

We present a susceptible-infected-recovered model based on a dynamic flow network that describes the epidemic process on complex metapopulation networks. This model views population regions as interconnected nodes and describes the evolution of each region using a system of differential equations. The next-generation matrix method is used to derive the global basic reproduction number for three cases: a general network with homogeneous infection rates in all regions, a fully connected network, and a star network with heterogeneous infection and recovery rates. For the homogeneous case, we show that this global basic reproduction number is independent of the migration rates between regions. However, the rate of convergence of each region to an equilibrium state exhibits a much larger variance in random (Erdős-Rényi) networks compared to small-scale (Barabási-Albert) networks. For the general heterogeneous case, we report interesting results, namely that the global basic reproduction number decays exponentially with respect to the smallest nonzero Laplacian eigenvalue (algebraic connectivity). Furthermore, we demonstrate both analytically and numerically that as the network's algebraic connectivity increases, either by increasing the average node degree of each region or the global migration rate, the global basic reproduction number decreases and converges to the ratio of the average local infection rate to the average local recovery rate, meaning that the lower bound of the global basic reproduction rate does not equal the mean of local basic reproduction rates.

Fuzzy Langevin fractional delay differential equations under granular derivative

Analytical studies of the class of the fuzzy Langevin fractional delay differential equations (FLFDDEs) are frequently complex and challenging. It is necessary to construct an effective technique for the solution of FLFDDEs. This article presents an explicit analytical representation of the solution to the class of FLFDDEs with the general fractional orders under granular differentiability. The closed-form solution to the FLFDDEs is extracted for both the homogeneous and non-homogeneous cases using the Laplace transform technique and presented in terms of the delayed Mittag-Leffler type function with double infinite series. Moreover, the existence and uniqueness of the solutions of the FLFDDEs are investigated using the generalized contraction principle. An illustrative example is provided to support the proposed technique. To add to the originality of the presented work, the FLFDDEs with constant delay are solved by applying vibration theory and visualizing their graphs to support the theoretical results.

Tempered nonlocal integrodifferential equations with nonsmooth solution data

This work on the time discretization for the solution of the tempered nonlocal integro-differential equation with smooth and nonsmooth initial data are extended. We find the difficulty arising from theoretical analysis can be overcome by Laplace transform technique. A mount of proof skills have been provided based on Laplace transform technique for this kind of equations. The Laplace transform method is employed effectively to show that the proposed interpolating quadrature scheme is convergence for smooth and non-smooth initial data in both homogeneous and inhomogeneous cases.

Dynamics of Saltwater Intrusion in a Heterogeneous Coastal Environment: Experimental, DC Resistivity, and Numerical Modeling Approaches

Saltwater intrusion (SWI) is a critical concern affecting coastal groundwater sources due to natural and anthropogenic activities. The health of coastal aquifers is deteriorated by excessive SWI, mainly caused by the disturbance of the freshwater–saltwater equilibrium due to the escalating population, climate change, and the rising demand for freshwater resources for human activities. Therefore, gaining insight into the dynamics of SWI is crucial, particularly concerning the various factors that influence the intrusion mechanism. The present study focuses on the experimental simulation of saltwater in freshwater aquifers, considering boundary conditions and density-dependent effects. Two geological scenarios within coastal environments were investigated: First, a uniform, homogeneous case consisting of only sand, and second, a heterogeneous case in which layers of sand, clay, and sand mixed with pebbles are used. During the experiment, DC resistivity sounding data, as part of a widely recognized geophysical method, were collected and subsequently inverted to determine the depth of the freshwater–saltwater interface (FSWI). A finite element analysis was employed to generate numerical models based on experimental feedback. Further, for validation purposes, electrical resistivity tomography (ERT) data were collected from two distinct locations: near the seacoast and an aquaculture area. The ERT results show the presence of salinity intrusion in the study area, attributed mainly to groundwater overpumping and fish farming practices. The experimental findings indicate that the advancement of saltwater is affected by the geological properties of the media they traverse. The porosity (ϕ) and permeability (k) of the geological layer play a crucial role during the passage of saltwater flux into freshwater aquifers. The FSWI deviated along the clay boundary and hindered the easy passage of saltwater into surrounding layers. The alignment of experimental, numerical, and geophysical data suggests that this integrated approach could be valuable for studying SWI and can be applied in different geological settings, including tidal flats and alluvial plains.

Detectability of hemodynamic oscillations in cerebral cortex through functional near-infrared spectroscopy: a simulation study.

We explore the feasibility of using time-domain (TD) and continuous-wave (CW) functional near-infrared spectroscopy (fNIRS) to monitor brain hemodynamic oscillations during resting-state activity in humans, a phenomenon that is of increasing interest in the scientific and medical community and appears to be crucial to advancing the understanding of both healthy and pathological brain functioning. Our general object is to maximize fNIRS sensitivity to brain resting-state oscillations. More specifically, we aim to define comprehensive guidelines for optimizing main operational parameters in fNIRS measurements [average photon count rate, measurement length, sampling frequency, and source-detector distance (SSD)]. In addition, we compare TD and CW fNIRS performance for the detection and localization of oscillations. A series of synthetic TD and CW fNIRS signals were generated by exploiting the solution of the diffusion equation for two different geometries of the probed medium: a homogeneous medium and a bilayer medium. Known and periodical perturbations of the concentrations of oxy- and deoxy-hemoglobin were imposed in the medium, determining changes in its optical properties. The homogeneous slab model was used to determine the effect of multiple measurement parameters on fNIRS sensitivity to oscillatory phenomena, and the bilayer model was used to evaluate and compare the abilities of TD and CW fNIRS in detecting and isolating oscillations occurring at different depths. For TD fNIRS, two approaches to enhance depth-selectivity were evaluated: first, a time-windowing of the photon distribution of time-of-flight was performed, and then, the time-dependent mean partial pathlength (TMPP) method was used to retrieve the hemoglobin concentrations in the medium. In the homogeneous medium case, the sensitivity of TD and CW fNIRS to periodical perturbations of the optical properties increases proportionally with the average photon count rate, the measurement length, and the sampling frequency and approximatively with the square of the SSD. In the bilayer medium case, the time-windowing method can detect and correctly localize the presence of oscillatory components in the TD fNIRS signal, even in the presence of very low photon count rates. The TMPP method demonstrates how to correctly retrieve the periodical variation of hemoglobin at different depths from the TD fNIRS signal acquired at a single SSD. For CW fNIRS, measurements taken at typical SSDs used for short-separation channel regression show notable sensitivity to oscillations occurring in the deep layer, challenging the assumptions underlying this correction method when the focus is on analyzing oscillatory phenomena. We demonstrated that the TD fNIRS technique allows for the detection and depth-localization of periodical fluctuations of the hemoglobin concentrations within the probed medium using an acquisition at a single SSD, offering an alternative to multi-distance CW fNIRS setups. Moreover, we offered some valuable guidelines that can assist researchers in defining optimal experimental protocols for fNIRS studies.

Conical indentation over a transversely isotropic and layered elastic half-space

We propose a novel method for solving the static response of a conical indenter on a transversely isotropic and layered elastic half-space. The newly developed Fourier-Bessel series (FBS) system of vector functions, along with the unconditionally stable dual-variable and position method, is employed to derive the Green's function in the transversely isotropic and layered elastic half-space under a vertical ring load on the surface. To calculate the response at different field points on the surface, we apply discrete love numbers within the FBS vector system. The load densities in the discretized rings within the contact radius of the conical indenter are determined using the integral least-square method, along with a self-adaptive algorithm developed in this study. Finally, the relationship between the indentation depth (vertical displacement) and the applied load is obtained through force balance between the external load and the summed contact traction. The developed scheme is validated using existing exact solutions for the reduced homogeneous half-space case. Selected numerical results clearly demonstrate the effect of anisotropic material and layering on the indentation response. It is observed that, regardless of whether the structure is a stratified half-space or a layered structure with a rigid substrate, the material properties in the top layer have the most significant influence on the indentation behavior. In the case of a layered structure with an underlying elastic half-space, the material properties in the interlayer and bottom layer could also affect the indentation behaviors.