Numerical Methods for Solving Space Fractional Partial Differential Equations Using Hadamard Finite-Part Integral Approach

From Springer Nature via Jisc Publications RouterHistory: received 2018-09-29, rev-recd 2018-11-09, accepted 2018-11-10, registration 2019-06-11, epub 2019-07-26, online 2019-07-26, ppub 2019-12Publication status: PublishedAbstract: We introduce a novel numerical method for solving two-sided space fractional partial differential equations in two-dimensional case. The approximation of the space fractional Riemann–Liouville derivative is based on the approximation of the Hadamard finite-part integral which has the convergence order O(h3-α), where h is the space step size and α∈(1, 2) is the order of Riemann–Liouville fractional derivative. Based on this scheme, we introduce a shifted finite difference method for solving space fractional partial differential equations. We obtained the error estimates with the convergence orders O(τ+h3-α+hβ), where τ is the time step size and β>0 is a parameter which measures the smoothness of the fractional derivatives of the solution of the equation. Unlike the numerical methods for solving space fractional partial differential equations constructed using the standard shifted Grünwald–Letnikov formula or higher order Lubich’s methods which require the solution of the equation to satisfy the homogeneous Dirichlet boundary condition to get the first-order convergence, the numerical method for solving the space fractional partial differential equation constructed using the Hadamard finite-part integral approach does not require the solution of the equation to satisfy the Dirichlet homogeneous boundary condition. Numerical results show that the experimentally determined convergence order obtained using the Hadamard finite-part integral approach for solving the space fractional partial differential equation with non-homogeneous Dirichlet boundary conditions is indeed higher than the convergence order obtained using the numerical methods constructed with the standard shifted Grünwald–Letnikov formula or Lubich’s higher order approximation schemes

Fracturing and thermal extraction optimization methods in enhanced geothermal systems

Fracture networks, fluid flow and heat extraction within fractures constitute pivotal aspects of enhanced geothermal system advancement. Conventional hydraulic fracturing in dry hot rock reservoirs typically requires high breakdown pressure and only produces a single major fracture morphology. Thus, it is imperative to explore better fracturing methods and consider more reasonable coupling mechanisms to improve the prediction efficiency. Cyclic fracturing using liquid nitrogen instead of water can generate more complex fracture networks and improve the fracturing performance. The simulation of fluid flow and heat transfer processes in the fracture network is crucial for an enhanced geothermal system, which requires a more comprehensive coupled thermo-hydro-mechanical-chemical model for matching, especially the characterization of coupling mechanism between the chemical and mechanical field. Based on the results of field engineering, laboratory experiments and numerical simulation, the optimum engineering scheme can be obtained by a multi-objective optimization and decision-making method. Furthermore, combining it with the deep-learning-based proxy model to achieve dynamic optimization with time is a meaningful future research direction.Document Type: PerspectiveCited as: Yang, R., Wang, Y., Song, G., Shi, Y. Fracturing and thermal extraction optimization methods in enhanced geothermal systems. Advances in Geo-Energy Research, 2023, 9(2): 136-140. https://doi.org/10.46690/ager.2023.08.0

Higher Order Time Stepping Methods for Subdiffusion Problems Based on Weighted and Shifted Grünwald–Letnikov Formulae with Nonsmooth Data

Two higher order time stepping methods for solving subdiffusion problems are studied in this paper. The Caputo time fractional derivatives are approximated by using the weighted and shifted Gr\"unwald-Letnikov formulae introduced in Tian et al. [Math. Comp. 84 (2015), pp. 2703-2727]. After correcting a few starting steps, the proposed time stepping methods have the optimal convergence orders $O(k^2)$ and $O(k^3)$, respectively for any fixed time $t$ for both smooth and nonsmooth data. The error estimates are proved by directly bounding the approximation errors of the kernel functions. Moreover, we also present briefly the applicabilities of our time stepping schemes to various other fractional evolution equations. Finally, some numerical examples are given to show that the numerical results are consistent with the proven theoretical results

Feasibility analysis of storing solar energy in heterogeneous deep aquifer by hot water circulation: Insights from coupled hydro-thermo modeling

Storing solar energy in the subsurface as heat is a promising way for energy storage and conversion, which has a great potential to address the temporal and spatial mismatch between energy demand and supply. Thermal energy storage in deep aquifers can convert intermittent solar energy into stable high temperature geothermal energy. In this study, a new solar energy storage and conversion system is proposed where solar energy is firstly converted into heat using parabolic troughs and then stored in deep aquifers by high temperature hot water circulation. The geostatistical modelling and hydro-thermo coupling simulations are adopted to investigate the feasibility and efficiency of solar energy storage in deep aquifers. Specifically, how rock permeability heterogeneity (in terms of autocorrelation length and global permeability heterogeneity) impacts the temporal and spatial evolution of temperature distribution and storage efficiency is examined. The simulation results indicate that increased horizontal autocorrelation length and global heterogeneity may accelerate thermal breakthrough, deteriorating storage efficiency. High permeability heterogeneity may also lead to high injection pressure. Deep aquifers with small horizontal autocorrelation lengths and low global heterogeneity tend to have higher storage efficiency. These findings may improve our understanding of solar energy storage mechanism in deep aquifers and guide field applications.Document Type: Original articleCited as: Wang, Y., Zhong, K., Gao, Y., Sun, Z., Dong, R., Wang, X. Feasibility analysis of storing solar energy in heterogeneous deep aquifer by hot water circulation: Insights from coupled hydro-thermo modeling. Advances in Geo-Energy Research, 2023, 10(3): 159-173. https://doi.org/10.46690/ager.2023.12.0

Phytoestrogen -zearalanol ameliorates memory impairment and neuronal DNA oxidation in ovariectomized mice

OBJECTIVE: The aim of this study was to evaluate the effect of a novel phytoestrogen, α-Zearalanol, on Alzheimer's disease-related memory impairment and neuronal oxidation in ovariectomized mice. METHODS: Female C57/BL6 mice were ovariectomized or received sham operations and treatment with equivalent doses of 17β-estradiol or α-Zearalanol for 8 weeks. Their spatial learning and memory were analyzed using the Morris water maze test. The antioxidant enzyme activities and reactive oxygen species generation, neuronal DNA oxidation, and MutT homolog 1 expression in the hippocampus were measured. RESULTS: Treatment with 17β-estradiol or α-Zearalanol significantly improved spatial learning and memory performance in ovariectomized mice. In addition, 17β-estradiol and α-Zearalanol attenuated the decrease in antioxidant enzyme activities and increased reactive oxygen species production in ovariectomized mice. The findings indicated a significant elevation in hippocampi neuronal DNA oxidation and reduction in MutT homolog 1 expression in estrogen-deficient mice, but supplementation with 17β-estradiol or α-Zearalanol efficaciously ameliorated this situation. CONCLUSION: These results demonstrate that α-Zearalanol is potentially beneficial for improving memory impairments and neuronal oxidation damage in a manner similar to that of 17β-estradiol. Therefore, the compound may be a potential therapeutic agent that can ameliorate neurodegenerative disorders related to estrogen deficiency

Multi-Modal 3D Object Detection in Autonomous Driving: a Survey

In the past few years, we have witnessed rapid development of autonomous driving. However, achieving full autonomy remains a daunting task due to the complex and dynamic driving environment. As a result, self-driving cars are equipped with a suite of sensors to conduct robust and accurate environment perception. As the number and type of sensors keep increasing, combining them for better perception is becoming a natural trend. So far, there has been no indepth review that focuses on multi-sensor fusion based perception. To bridge this gap and motivate future research, this survey devotes to review recent fusion-based 3D detection deep learning models that leverage multiple sensor data sources, especially cameras and LiDARs. In this survey, we first introduce the background of popular sensors for autonomous cars, including their common data representations as well as object detection networks developed for each type of sensor data. Next, we discuss some popular datasets for multi-modal 3D object detection, with a special focus on the sensor data included in each dataset. Then we present in-depth reviews of recent multi-modal 3D detection networks by considering the following three aspects of the fusion: fusion location, fusion data representation, and fusion granularity. After a detailed review, we discuss open challenges and point out possible solutions. We hope that our detailed review can help researchers to embark investigations in the area of multi-modal 3D object detection

Numerical methods for solving space fractional partial differential equations by using Hadamard finite-part integral approach

We introduce a novel numerical method for solving two-sided space fractional partial differential equation in two dimensional case. The approximation of the space fractional Riemann-Liouville derivative is based on the approximation of the Hadamard finite-part integral which has the convergence order $O(h^{3- \alpha})$, where $h$ is the space step size and $\alpha\in (1, 2)$ is the order of Riemann-Liouville fractional derivative. Based on this scheme, we introduce a shifted finite difference method for solving space fractional partial differential equation. We obtained the error estimates with the convergence orders $O(\tau +h^{3-\alpha}+ h^{\beta})$, where $\tau$ is the time step size and $\beta >0$ is a parameter which measures the smoothness of the fractional derivatives of the solution of the equation. Unlike the numerical methods for solving space fractional partial differential equation constructed by using the standard shifted Gr\"unwald-Letnikov formula or higher order Lubich'e methods which require the solution of the equation satisfies the homogeneous Dirichlet boundary condition in order to get the first order convergence, the numerical method for solving space fractional partial differential equation constructed by using Hadamard finite-part integral approach does not require the solution of the equation satisfies the Dirichlet homogeneous boundary condition. Numerical results show that the experimentally determined convergence order obtained by using the Hadamard finite-part integral approach for solving space fractional partial differential equation with non-homogeneous Dirichlet boundary conditions is indeed higher than the convergence order obtained by using the numerical methods constructed with the standard shifted Gr\"unwald-Letnikov formula or Lubich's higer order approximation schemes

Decision Rules Acquisition for Inconsistent Disjunctive Set-Valued Ordered Decision Information Systems

Set-valued information system is an important formal framework for the development of decision support systems. We focus on the decision rules acquisition for the inconsistent disjunctive set-valued ordered decision information system in this paper. In order to derive optimal decision rules for an inconsistent disjunctive set-valued ordered decision information system, we define the concept of reduct of an object. By constructing the dominance discernibility function for an object, we compute reducts of the object via utilizing Boolean reasoning techniques, and then the corresponding optimal decision rules are induced. Finally, we discuss the certain reduct of the inconsistent disjunctive set-valued ordered decision information system, which can be used to simplify all certain decision rules as much as possible

EdgeCalib: Multi-Frame Weighted Edge Features for Automatic Targetless LiDAR-Camera Calibration

In multimodal perception systems, achieving precise extrinsic calibration between LiDAR and camera is of critical importance. Previous calibration methods often required specific targets or manual adjustments, making them both labor-intensive and costly. Online calibration methods based on features have been proposed, but these methods encounter challenges such as imprecise feature extraction, unreliable cross-modality associations, and high scene-specific requirements. To address this, we introduce an edge-based approach for automatic online calibration of LiDAR and cameras in real-world scenarios. The edge features, which are prevalent in various environments, are aligned in both images and point clouds to determine the extrinsic parameters. Specifically, stable and robust image edge features are extracted using a SAM-based method and the edge features extracted from the point cloud are weighted through a multi-frame weighting strategy for feature filtering. Finally, accurate extrinsic parameters are optimized based on edge correspondence constraints. We conducted evaluations on both the KITTI dataset and our dataset. The results show a state-of-the-art rotation accuracy of 0.086{\deg} and a translation accuracy of 0.977 cm, outperforming existing edge-based calibration methods in both precision and robustness