Maximum principle and numerical method for the multi-term time-space Riesz-Caputo fractional differential equations

The maximum principle for the space and time–space fractional partial differential equations is still an open problem. In this paper, we consider a multi-term time–space Riesz–Caputo fractional differential equations over an open bounded domain. A maximum principle for the equation is proved. The uniqueness and continuous dependence of the solution are derived. Using a fractional predictor–corrector method combining the L1 and L2 discrete schemes, we present a numerical method for the specified equation. Two examples are given to illustrate the obtained results

Compact difference scheme for distributed-order time-fractional diffusion-wave equation on bounded domains

In this paper, we derive and analyse a compact difference scheme for a distributed-order time-fractional diffusion-wave equation. This equation is approximated by a multi-term fractional diffusion-wave equation, which is then solved by a compact difference scheme. The unique solvability of the difference solution is discussed. Using the discrete energy method, we prove the compact difference scheme is unconditionally stable and convergent. Finally, numerical results are presented to support our theoretical analysis

Factors That Control the Reservoir Quality of the Carboniferous–Permian Tight Sandstones in the Shilounan Block, Ordos Basin

The Carboniferous–Permian, coal-bearing, sedimentary succession on the eastern edge of the Ordos Basin in the Shilounan Block contains large accumulations of hydrocarbon resources. During the exploration of coalbed methane and tight sandstone gas in the study area, multiple drilling wells in the tight sandstone reservoirs have yielded favorable gas logging results. The Benxi, Taiyuan, Shanxi, Shihezi, and Shiqianfeng formations contain multiple sets of sandstone reservoirs, and the reservoir quality and the controlling factors of its tight sandstones were affected by sedimentation, diagenetic alteration, and pore structure. This study comprehensively examines the sedimentary environment, distribution of sand bodies, and physical characteristics of tight sandstone reservoirs through drilling, coring, logging, and experimental testing. The results indicate that the Carboniferous–Permian tight sandstones are mainly composed of lithic sandstone and lithic quartz sandstone. The reservoir quality is relatively poor, with an average permeability of 0.705 mD and porosity of 6.20%. The development of reservoirs in the study area is primarily influenced by diagenesis and sedimentation. Compaction and cementation, which are destructive diagenetic processes, significantly reduced the porosity of the sandstone reservoirs in the study area. Compaction primarily causes a reduction in porosity and accounts for over 70% of the overall decrease in porosity. Dissolution, as a constructive diagenetic process, has a limited effect on porosity and is the primary reason for the relatively tight nature of these reservoirs. The macroscopic and microscopic characteristics of tight sandstone reservoirs were used to establish the evaluation and classification criteria, after which the sandstone reservoirs in the study area were divided into three types. The poor quality type II and type III reservoirs are predominant, while high quality type I reservoirs are primarily limited to the Shihezi Formation

Numerical analysis for the time distributed-order and Riesz space fractional diffusions on bounded domains

Subdiffusion equations with distributed-order fractional derivatives describe some important physical phenomena. In this paper, we consider the time distributed-order and Riesz space fractional diffusions on bounded domains with Dirichlet boundary conditions. Here, the time derivative is defined as the distributed-order fractional derivative in the Caputo sense, and the space derivative is defined as the Riesz fractional derivative. First, we discretize the integral term in the time distributed-order and Riesz space fractional diffusions using numerical approximation. Then the given equation can be written as a multi-term time–space fractional diffusion. Secondly, we propose an implicit difference method for the multi-term time–space fractional diffusion. Thirdly, using mathematical induction, we prove the implicit difference method is unconditionally stable and convergent. Also, the solvability for our method is discussed. Finally, two numerical examples are given to show that the numerical results are in good agreement with our theoretical analysis

Organic Matter of the Wufeng–Longmaxi Formation Shales Using Scanning Electron Microscopy

Fine-grained organic matter (OM) particles are commonly widely dispersed in shale deposits. However, carrying out investigations of pores hosted by OM particles and the nature of grain interactions in OM particles and associated detrital grains using optical microscopy is difficult at best. Scanning electron microscopy (SEM) is much better suited for characterizing the microstructure of dispersed OM particles and has found wide application in the study of unconventional oil and gas systems. Scanning electron microscopy was used to define the types of OM contained in marine shale deposits of the Wufeng and Longmaxi Formations spanning the Ordovician–Silurian transition in South China. Of particular interest was the development of OM-hosted pores and the identification of the factors that controlled their formation. The dominant OM type contained in the studied deposits is pyrobitumen, with subordinate graptolitic OM and sparse OM of unknown origin. Pyrobitumen is present in four forms, including pore fillings among authigenic quartz grains, within framboidal pyrite, and between authigenic clay grains and massive material. Diagenetic alteration has given rise to OM pores of differing morphology, size, and time of formation. Common small, equisized circular or oval OM pores are most developed and appear to have formed in association with the generation of hydrocarbons. Shale deposits containing abundant pyrobitumen filling interparticle pores among authigenic quartz crystals display robust reservoir and fracturing capacity. A sedimentary environment appears to have been the main factor affecting the type of OM and the nature of its association with detrital and authigenic minerals. Results of this study demonstrate that a sedimentary environment is a primary requisite for the formation of highly prospective/high-yielding hydrocarbon shale reservoir deposits

Unsteady Mixed Convection Heat Transfer of Fractional Viscoelastic Nanofluids over an Inclined Plate

This study aims to investigate the unsteady mixed convection boundary layer heat transfer of fractional viscoelastic nanofluids over an inclined plate. The Scott Blair model and fractional Fourier's law are introduced in the constitutive relations. The boundary layer equations are solved by a finite difference method. The results show that the convection flow and heat transfer are weakened by the velocity and temperature fractional derivative parameters \alpha and \beta, respectively. The effects of the involved parameters (nanoparticle volume fraction, magnetic parameter, and inclined angle) on the velocity and temperature fields are analyzed in detail.</p

Spaceborne SAR Image Geometric Rectification Method without Ground Control Points Using Orbit Parameters Modulation

When using the Range-Doppler model for SAR image geometric correction, the error of satellite orbit, imaging parameter and DEM elevation will affect the geometric correction accuracy. A new geometric rectification method has been presented for spaceborne SAR image. First, polynomial was used for parameterizing SAR orbit. Then orbit parameters were corrected by control points that acquired by matching of simulated SAR image and real SAR image. Finally, the precise geometric rectification using corrected parameters was accomplished. The presented method can be applied for SAR image geometric rectification where the ground control points are difficult to be acquired. It has higher precision compared to the geometric rectification based on image simulation and polynomial correction. The Radarsat-2 image was used in experiments, and the ground control points measured by GPS validated the proposed approach

Application and Evaluation of Deep Neural Networks for Airborne Hyperspectral Remote Sensing Mineral Mapping: A Case Study of the Baiyanghe Uranium Deposit in Northwestern Xinjiang, China

Deep learning is a popular topic in machine learning and artificial intelligence research and has achieved remarkable results in various fields. In geological remote sensing, mineral mapping is an appealing application of hyperspectral remote sensing for geological surveyors. Whether deep learning can improve the mineral identification ability in hyperspectral remote sensing images, especially for the discrimination of spectrally similar and intimately mixed minerals, needs to be evaluated. In this study, shortwave airborne spectrographic imager (SASI) hyperspectral images of the Baiyanghe uranium deposit in Northwestern Xinjiang, China, were used as experimental data. Three deep neural network (DNN) models were designed: a fully connected neural network (FCNN), a one-dimensional convolutional neural network (1D CNN), and a one-dimensional and two-dimensional convolutional neural network (1D and 2D CNN). A sample dataset containing five minerals was constructed for model training and validation, which was divided into training, validation and test sets at a ratio of 6:2:2. The final test accuracies of the FCNN, 1D CNN, and 1D and 2D CNN were 91.24%, 93.67% and 94.77%, respectively. The three DNNs were used for mineral identification and mapping of SASI hyperspectral images of the Baiyanghe uranium mining area. The mapping results were compared with the mapping results of the support vector machine (SVM) and the mixture-tuned matched filtering (MTMF) method. Combined with the ground spectral data obtained by the spectrometer, spectral verification and interpretation were carried out on sections that the two kinds of methods identified differently. The verification results show that the mapping results of the 1D and 2D CNN were more accurate than those of the other methods. More importantly, for minerals with similar spectral characteristics, such as short-wavelength white mica and medium-wavelength white mica, the 1D and 2D CNN model had a more accurate discrimination effect than the other DNN models, indicating that the introduction of spatial information can improve the mineral identification ability in hyperspectral remote sensing images. In general, CNNs have good application prospects in geological mapping of hyperspectral remote sensing images and are worthy of further development in future work

Application and Evaluation of Deep Neural Networks for Airborne Hyperspectral Remote Sensing Mineral Mapping: A Case Study of the Baiyanghe Uranium Deposit in Northwestern Xinjiang, China

Deep learning is a popular topic in machine learning and artificial intelligence research and has achieved remarkable results in various fields. In geological remote sensing, mineral mapping is an appealing application of hyperspectral remote sensing for geological surveyors. Whether deep learning can improve the mineral identification ability in hyperspectral remote sensing images, especially for the discrimination of spectrally similar and intimately mixed minerals, needs to be evaluated. In this study, shortwave airborne spectrographic imager (SASI) hyperspectral images of the Baiyanghe uranium deposit in Northwestern Xinjiang, China, were used as experimental data. Three deep neural network (DNN) models were designed: a fully connected neural network (FCNN), a one-dimensional convolutional neural network (1D CNN), and a one-dimensional and two-dimensional convolutional neural network (1D and 2D CNN). A sample dataset containing five minerals was constructed for model training and validation, which was divided into training, validation and test sets at a ratio of 6:2:2. The final test accuracies of the FCNN, 1D CNN, and 1D and 2D CNN were 91.24%, 93.67% and 94.77%, respectively. The three DNNs were used for mineral identification and mapping of SASI hyperspectral images of the Baiyanghe uranium mining area. The mapping results were compared with the mapping results of the support vector machine (SVM) and the mixture-tuned matched filtering (MTMF) method. Combined with the ground spectral data obtained by the spectrometer, spectral verification and interpretation were carried out on sections that the two kinds of methods identified differently. The verification results show that the mapping results of the 1D and 2D CNN were more accurate than those of the other methods. More importantly, for minerals with similar spectral characteristics, such as short-wavelength white mica and medium-wavelength white mica, the 1D and 2D CNN model had a more accurate discrimination effect than the other DNN models, indicating that the introduction of spatial information can improve the mineral identification ability in hyperspectral remote sensing images. In general, CNNs have good application prospects in geological mapping of hyperspectral remote sensing images and are worthy of further development in future work

Phylogenetic position of Odorrana macrotympana (Yang, 2008) (Anura, Ranidae) and extension of its geographical distribution

Based on a 16S rRNA gene fragment, a molecular phylogeny for the genus Odorrana Fei, Ye & Huang, 1990 was reconstructed, the validity of the poorly-known ranid species O. macrotympana (Yang, 2008) was confirmed and its phylogenetic position was evaluated. In addition, we report the first country record of O. macrotympana from Myanmar, based on our new records from Htamanthi Wildlife Sanctuary, Sagaing Division and present a supplementary description of this species. This report also constitutes the first record of O. macrotympana from outside of China