Geostatistical seismic inversion and 3D modelling of metric flow units,porosity and permeability in Brazilian presalt reservoir

Flow units(FU)rock typing is a common technique for characterizing reservoir flow behavior,producing reliable porosity and permeability estimation even in complex geological settings.However,the lateral extrapolation of FU away from the well into the whole reservoir grid is commonly a difficult task and using the seismic data as constraints is rarely a subject of study.This paper proposes a workflow to generate numerous possible 3D volumes of flow units,porosity and permeability below the seismic resolution limit,respecting the available seismic data at larger scales.The methodology is used in the Mero Field,a Brazilian presalt carbonate reservoir located in the Santos Basin,who presents a complex and heterogenic geological setting with different sedimentological processes and diagenetic history.We generated metric flow units using the conventional core analysis and transposed to the well log data.Then,given a Markov chain Monte Carlo algorithm,the seismic data and the well log statistics,we simulated acoustic impedance,decametric flow units(DFU),metric flow units(MFU),porosity and permeability volumes in the metric scale.The aim is to estimate a minimum amount of MFU able to calculate realistic scenarios porosity and permeability scenarios,without losing the seismic lateral control.In other words,every porosity and permeability volume simulated produces a synthetic seismic that match the real seismic of the area,even in the metric scale.The achieved 3D results represent a high-resolution fluid flow reservoir modelling considering the lateral control of the seismic during the process and can be directly incorporated in the dynamic characterization workflow.

Cellular interplay to 3D in vitro microphysiological disease model:cell patterning microbiota-gut-brain axis

The microbiota-gut-brain axis(MGBA)has emerged as a key prospect in the bidirectional communication between two major organ systems:the brain and the gut.Homeostasis between the two organ systems allows the body to function without disease,whereas dysbiosis has long-standing evidence of etiopathological conditions.The most common communication paths are the microbial release of metabolites,soluble neurotransmitters,and immune cells.However,each pathway is intertwined with a complex one.With the emergence of in vitro models and the popularity of three-dimensional(3D)cultures and Transwells,engineering has become easier for the scientific understanding of neurodegenerative diseases.This paper briefly retraces the possible communication pathways between the gut microbiome and the brain.It further elaborates on three major diseases:autism spectrum disorder,Parkinson’s disease,and Alzheimer’s disease,which are prevalent in children and the elderly.These diseases also decrease patients’quality of life.Hence,understanding them more deeply with respect to current advances in in vitro modeling is crucial for understanding the diseases.Remodeling of MGBA in the laboratory uses many molecular technologies and biomaterial advances.Spheroids and organoids provide a more realistic picture of the cell and tissue structure than monolayers.Combining them with the Transwell system offers the advantage of compartmentalizing the two systems(apical and basal)while allowing physical and chemical cues between them.Cutting-edge technologies,such as bioprinting and microfluidic chips,might be the future of in vitro modeling,as they provide dynamicity.

A methodology for damage evaluation of underground tunnels subjected to static loading using numerical modeling

We have proposed a methodology to assess the robustness of underground tunnels against potential failure.This involves developing vulnerability functions for various qualities of rock mass and static loading intensities.To account for these variations,we utilized a Monte Carlo Simulation(MCS)technique coupled with the finite difference code FLAC^(3D),to conduct two thousand seven hundred numerical simulations of a horseshoe tunnel located within a rock mass with different geological strength index system(GSIs)and subjected to different states of static loading.To quantify the severity of damage within the rock mass,we selected one stress-based(brittle shear ratio(BSR))and one strain-based failure criterion(plastic damage index(PDI)).Based on these criteria,we then developed fragility curves.Additionally,we used mathematical approximation techniques to produce vulnerability functions that relate the probabilities of various damage states to loading intensities for different quality classes of blocky rock mass.The results indicated that the fragility curves we obtained could accurately depict the evolution of the inner and outer shell damage around the tunnel.Therefore,we have provided engineers with a tool that can predict levels of damages associated with different failure mechanisms based on variations in rock mass quality and in situ stress state.Our method is a numerically developed,multi-variate approach that can aid engineers in making informed decisions about the robustness of underground tunnels.

Numerical three-dimensional modeling of earthen dam piping failure

A physically-based numerical three-dimensional earthen dam piping failure model is developed for homogeneous and zoned soil dams.This model is an erosion model,coupled with force/moment equilibrium analyses.Orifice flow and two-dimensional(2D)shallow water equations(SWE)are solved to simulate dam break flows at different breaching stages.Erosion rates of different soils with different construction compaction efforts are calculated using corresponding erosion formulae.The dam's real shape,soil properties,and surrounding area are programmed.Large outer 2D-SWE grids are used to control upstream and downstream hydraulic conditions and control the boundary conditions of orifice flow,and inner 2D-SWE flow is used to scour soil and perform force/moment equilibrium analyses.This model is validated using the European Commission IMPACT(Investigation of Extreme Flood Processes and Uncertainty)Test#5 in Norway,Teton Dam failure in Idaho,USA,and Quail Creek Dike failure in Utah,USA.All calculated peak outflows are within 10%errors of observed values.Simulation results show that,for a V-shaped dam like Teton Dam,a piping breach location at the abutment tends to result in a smaller peak breach outflow than the piping breach location at the dam's center;and if Teton Dam had broken from its center for internal erosion,a peak outflow of 117851 m'/s,which is 81%larger than the peak outflow of 65120 m3/s released from its right abutment,would have been released from Teton Dam.A lower piping inlet elevation tends to cause a faster/earlier piping breach than a higher piping inlet elevation.

Mesh representation matters:investigating the influence of different mesh features on perceptual and spatial fidelity of deep 3D morphable models

Background Deep 3D morphable models(deep 3DMMs)play an essential role in computer vision.They are used in facial synthesis,compression,reconstruction and animation,avatar creation,virtual try-on,facial recognition systems and medical imaging.These applications require high spatial and perceptual quality of synthesised meshes.Despite their significance,these models have not been compared with different mesh representations and evaluated jointly with point-wise distance and perceptual metrics.Methods We compare the influence of different mesh representation features to various deep 3DMMs on spatial and perceptual fidelity of the reconstructed meshes.This paper proves the hypothesis that building deep 3DMMs from meshes represented with global representations leads to lower spatial reconstruction error measured with L_(1) and L_(2) norm metrics and underperforms on perceptual metrics.In contrast,using differential mesh representations which describe differential surface properties yields lower perceptual FMPD and DAME and higher spatial fidelity error.The influence of mesh feature normalisation and standardisation is also compared and analysed from perceptual and spatial fidelity perspectives.Results The results presented in this paper provide guidance in selecting mesh representations to build deep 3DMMs accordingly to spatial and perceptual quality objectives and propose combinations of mesh representations and deep 3DMMs which improve either perceptual or spatial fidelity of existing methods.

3D bioprinting of in vitro porous hepatoma models:establishment,evaluation,and anticancer drug testing

Traditional tumor models do not tend to accurately simulate tumor growth in vitro or enable personalized treatment and are particularly unable to discover more beneficial targeted drugs.To address this,this study describes the use of threedimensional(3D)bioprinting technology to construct a 3D model with human hepatocarcinoma SMMC-7721 cells(3DP-7721)by combining gelatin methacrylate(GelMA)and poly(ethylene oxide)(PEO)as two immiscible aqueous phases to form a bioink and innovatively applying fluorescent carbon quantum dots for long-term tracking of cells.The GelMA(10%,mass fraction)and PEO(1.6%,mass fraction)hydrogel with 3:1 volume ratio offered distinct pore-forming characteristics,satisfactorymechanical properties,and biocompatibility for the creation of the 3DP-7721 model.Immunofluorescence analysis and quantitative real-time fluorescence polymerase chain reaction(PCR)were used to evaluate the biological properties of the model.Compared with the two-dimensional culture cell model(2D-7721)and the 3D mixed culture cell model(3DM-7721),3DP-7721 significantly improved the proliferation of cells and expression of tumor-related proteins and genes.Moreover,we evaluated the differences between the three culture models and the effectiveness of antitumor drugs in the three models and discovered that the efficacy of antitumor drugs varied because of significant differences in resistance proteins and genes between the three models.In addition,the comparison of tumor formation in the three models found that the cells cultured by the 3DP-7721 model had strong tumorigenicity in nude mice.Immunohistochemical evaluation of the levels of biochemical indicators related to the formation of solid tumors showed that the 3DP-7721 model group exhibited pathological characteristics of malignant tumors,the generated solid tumors were similar to actual tumors,and the deterioration was higher.This research therefore acts as a foundation for the application of 3DP-7721 models in drug development research.

Three-dimensional Modeling of Ore-forming Elements and Mineralization Prognosis for the Yechangping Mo Deposit,Henan Province,China

Three-dimensional geochemical modeling of ore-forming elements is crucial for predicting deep mineralization.This approach provides key information for the quantitative prediction of deep mineral localization,three-dimensional fine interpolation,analysis of spatial distribution patterns,and extraction of quantitative mineral-seeking markers.The Yechangping molybdenum(Mo)deposit is a significant and extensive porphyry-skarn deposit in the East Qinling-Dabie Mo polymetallic metallogenic belt at the southern margin of the North China Block.Abundant borehole data on oreforming elements underpin deep geochemical predictions.The methodology includes the following steps:(1)Threedimensional geological modeling of the deposit was established.(2)Correlation,cluster,and factor analyses post delineation of mineralization stages and determination of mineral generation sequence to identify(Cu,Pb,Zn,Ag)and(Mo,W,mfe)assemblages.(3)A three-dimensional geochemical block model was constructed for Mo,W,mfe,Cu,Zn,Pb,and Ag using the ordinary kriging method,and the variational function was developed.(4)Spatial distribution and enrichment characteristics analysis of ore-forming elements are performed to extract geological information,employing the variogram and w(Cu+Pb+Zn+Ag)/w(Mo+W)as predictive indicators.(5)Identifying the western,northwestern,and southwestern areas of the mine with limited mineralization potential,contrasted by the northeastern and southeastern areas favorable for mineral exploration.

3D Road Network Modeling and Road Structure Recognition in Internet of Vehicles

Internet of Vehicles (IoV) is a new system that enables individual vehicles to connect with nearby vehicles,people, transportation infrastructure, and networks, thereby realizing amore intelligent and efficient transportationsystem. The movement of vehicles and the three-dimensional (3D) nature of the road network cause the topologicalstructure of IoV to have the high space and time complexity.Network modeling and structure recognition for 3Droads can benefit the description of topological changes for IoV. This paper proposes a 3Dgeneral roadmodel basedon discrete points of roads obtained from GIS. First, the constraints imposed by 3D roads on moving vehicles areanalyzed. Then the effects of road curvature radius (Ra), longitudinal slope (Slo), and length (Len) on speed andacceleration are studied. Finally, a general 3D road network model based on road section features is established.This paper also presents intersection and road section recognition methods based on the structural features ofthe 3D road network model and the road features. Real GIS data from a specific region of Beijing is adopted tocreate the simulation scenario, and the simulation results validate the general 3D road network model and therecognitionmethod. Therefore, thiswork makes contributions to the field of intelligent transportation by providinga comprehensive approach tomodeling the 3Droad network and its topological changes in achieving efficient trafficflowand improved road safety.

Rainfall-triggered waste dump instability analysis based on surface 3D deformation in physical model test

Landslide is the second largest natural disaster after earthquake. It is of significance to study the evolution laws and failure mechanism of landslides based on its surface 3D deformation information. Based on the rainfall-triggered waste dump instability model test, we studied the failure mechanisms of the waste dump by integrating surface deformation and internal slope stress and proposed novel parameters for identifying landslide stability. We developed a noncontact measurement device, which can obtain millimeter-level 3D deformation data for surface scene in physical model test;Then we developed the similar materials and established a test model for a waste dump. Based on the failure characteristics of slope surface, internal stress of slope body and displacement contours during the whole process, we divided the slope instability process in model test into four stages: rainfall infiltration and surface erosion, shallow sliding, deep sliding, and overall instability. Based on the obtained surface deformation data, we calculated the volume change during slope instability process and compared it with the point displacement on slope surface. The results showed that the volume change can not only reflect the slow-ultra acceleration process of slope failure, but also fully reflect the above four stages and reduce the fluctuations caused by random factors. Finally, this paper proposed two stability identification parameters: the volume change rate above the slip surface and the relative velocity of volume change rate. According to the calculation of these two parameters in model test, they can be used for study the deformation and failure mechanism of slope stability.

Multi-scale Modeling and Finite Element Analyses of Thermal Conductivity of 3D C/SiC Composites Fabricating by Flexible-Oriented Woven Process

Thermal conductivity is one of the most significant criterion of three-dimensional carbon fiber-reinforced SiC matrix composites(3D C/SiC).Represent volume element(RVE)models of microscale,void/matrix and mesoscale proposed in this work are used to simulate the thermal conductivity behaviors of the 3D C/SiC composites.An entirely new process is introduced to weave the preform with three-dimensional orthogonal architecture.The 3D steady-state analysis step is created for assessing the thermal conductivity behaviors of the composites by applying periodic temperature boundary conditions.Three RVE models of cuboid,hexagonal and fiber random distribution are respectively developed to comparatively study the influence of fiber package pattern on the thermal conductivities at the microscale.Besides,the effect of void morphology on the thermal conductivity of the matrix is analyzed by the void/matrix models.The prediction results at the mesoscale correspond closely to the experimental values.The effect of the porosities and fiber volume fractions on the thermal conductivities is also taken into consideration.The multi-scale models mentioned in this paper can be used to predict the thermal conductivity behaviors of other composites with complex structures.

Research on BIM Model Reshaping Method Based on 3D Point Cloud Recognition

In view of the limitations of traditional measurement methods in the field of building information,such as complex operation,low timeliness and poor accuracy,a new way of combining three-dimensional scanning technology and BIM(Building Information Modeling)model was discussed.Focused on the efficient acquisition of building geometric information using the fast-developing 3D point cloud technology,an improved deep learning-based 3D point cloud recognition method was proposed.The method optimised the network structure based on RandLA-Net to adapt to the large-scale point cloud processing requirements,while the semantic and instance features of the point cloud were integrated to significantly improve the recognition accuracy and provide a precise basis for BIM model remodeling.In addition,a visual BIM model generation system was developed,which systematically transformed the point cloud recognition results into BIM component parameters,automatically constructed BIM models,and promoted the open sharing and secondary development of models.The research results not only effectively promote the automation process of converting 3D point cloud data to refined BIM models,but also provide important technical support for promoting building informatisation and accelerating the construction of smart cities,showing a wide range of application potential and practical value.

UAV-based transient electromagnetic 3D forward modeling and inversion and analysis of exploration capability

Unmanned aerial vehicle transient electromagnetic(UAV-TEM)is a novel airborne exploration method that offers advantages such as low cost,simple operation,high exploration efficiency and suitability for near-surface exploration in complex terrain areas.To improve the accuracy of data interpretation in this method,the authors conducted a systematic three-dimensional(3D)forward modeling and inversion of the UAV-TEM.This study utilized the finite element method based on unstructured tetrahedral elements and employed the second-order backward Euler method for time discretization.This allowed for accurate 3D modeling and accounted for the effects of complex terrain.Based on these,the influence characteristics of flight altitudes and the sizes,burial depths,and resistivities of anomalies are compared and analyzed to explore the UAV-TEM systems’exploration capability.Lastly,four typical geoelectrical models of landslides are designed,and the inversion method based on the Gauss-Newton optimization method is used to image the landslide models and analyze the imaging effect of the UAV-TEM method on landslide geohazards.Numerical results showed that UAV-TEM could have better exploration resolution and fine imaging of nearsurface structures,providing important technical support for monitoring,early warning,and preventing landslides and other geological hazards.

Review of Artificial Intelligence for Oil and Gas Exploration: Convolutional Neural Network Approaches and the U-Net 3D Model

Deep learning, especially through convolutional neural networks (CNN) such as the U-Net 3D model, has revolutionized fault identification from seismic data, representing a significant leap over traditional methods. Our review traces the evolution of CNN, emphasizing the adaptation and capabilities of the U-Net 3D model in automating seismic fault delineation with unprecedented accuracy. We find: 1) The transition from basic neural networks to sophisticated CNN has enabled remarkable advancements in image recognition, which are directly applicable to analyzing seismic data. The U-Net 3D model, with its innovative architecture, exemplifies this progress by providing a method for detailed and accurate fault detection with reduced manual interpretation bias. 2) The U-Net 3D model has demonstrated its superiority over traditional fault identification methods in several key areas: it has enhanced interpretation accuracy, increased operational efficiency, and reduced the subjectivity of manual methods. 3) Despite these achievements, challenges such as the need for effective data preprocessing, acquisition of high-quality annotated datasets, and achieving model generalization across different geological conditions remain. Future research should therefore focus on developing more complex network architectures and innovative training strategies to refine fault identification performance further. Our findings confirm the transformative potential of deep learning, particularly CNN like the U-Net 3D model, in geosciences, advocating for its broader integration to revolutionize geological exploration and seismic analysis.

Analytical Solutions for Testing of Baroclinic and Wind-Driven Three-Dimensional Hydrodynamic Models

It is always a challenge for a model developer to verify a three-dimensional hydrodynamic model, especially for the baroclinic term over variable topography, due to a lack of observational data sets or suitable analytical solutions. In this paper, exact solutions for the periodic forcing by surface heat flux and wind stress are given by solving the linearized equations of motion neglecting the rotation, advection and horizontal diffusion terms. The temperature at the bottom is set to a prescribed periodic value and a slip condition on flow is enforced at the bottom. The geometry of the quarter annulus, which has been extensively studied for two- and three-dimensional analytical solutions of unstratified water bodies, is used with a general power law variation of the bottom slope in the radial direction and is constant in the azimuthal direction. The analytical solutions are derived in a cylindrical coordinate system, which describes the three-dimensional fluid field in a Cartesian coordinate system. The results presented in this paper should provide a foundation for studying and verifying the baroclinic term over a varied topography in a three-dimensional numerical model.

Modelling and Sizing of a Floor Reinforced by Ballasted Columns Intended to Support a Tank

This work aims to study the modeling and sizing of a floor reinforced by ballasted columns. We are studying the system of reinforcement by ballasted columns because this technique is able to replace deep foundations that are technically difficult to realize and their cost is higher. The modelling and dimensioning of foundations on a ballasted column will be an important contribution to the state of the art of this method because it will highlight the mode of transfer of loads, and will expose the induced deformations by also allowing to verification criteria of bearing capacity and allowable settlement according to geometric information of the model. The columns on a substrate located at 9 m have a length of 9 m and a diameter of 40 cm and were obtained by incorporating ballast of granular class 0/31.5 of internal friction angle of 38˚ and a density weight of 21 kN/m3. The choice of this method is based on the geotechnical characteristics of the initial soil. Thus, identification and characterization tests were carried out to estimate the bearing capacity and the settlement giving respectively 125 kPa and 57 cm. These results show the ground does not have sufficient mechanical properties to withstand the loads transmitted by the tank. By adopting the reinforcement of the soil with ballasted columns, numerical calculations show that after applying a load equal to 265.1 KPa, 20 cm vertical settlement and 17 cm horizontal displacement were obtained. This is in the tolerable deformation range for our tank, namely, less than 20 cm. Analytically, in addition to reducing settlement, ballasted columns, Due to their high stiffness, they have effectively contributed to the increase of the permissible soil stress up to 257 kPa.

Contribution to the Full 3D Finite Element Modelling of a Hybrid Stepping Motor with and without Current in the Coils

The paper presents our contribution to the full 3D finite element modelling of a hybrid stepping motor using COMSOL Multiphysics software. This type of four-phase motor has a permanent magnet interposed between the two identical and coaxial half stators. The calculation of the field with or without current in the windings (respectively with or without permanent magnet) is done using a mixed formulation with strong coupling. In addition, the local high saturation of the ferromagnetic material and the radial and axial components of the magnetic flux are taken into account. The results obtained make it possible to clearly observe, as a function of the intensity of the bus current or the remanent induction, the saturation zones, the lines, the orientations and the magnetic flux densities. 3D finite element modelling provide more accurate numerical data on the magnetic field through multiphysics analysis. This analysis considers the actual operating conditions and leads to the design of an optimized machine structure, with or without current in the windings and/or permanent magnet.

Three Subjects and Seven Duties Model:Empowering Informatization Teaching Ability of Pre-Service Teachers

By constructing a model,this study seeks to provide suggestions for strengthening pre-service teachers’informatization teaching ability.It aims to answer the following research questions:(1)What do the pre-service teachers know about informatization instruction?What is their level of informatization teaching ability?(2)What factors influence pre-service teachers’ability to deliver informatization instruction?How to overcome the obstacles?The inquiry focuses on the theoretical exploration of informatization teaching ability,questionnaire,and interview analysis on the current condition and improvement of pre-service teachers’informatization teaching ability.The data from the questionnaire and interview of the pre-service teachers were evaluated from three dimensions:awareness and attitude towards informatization teaching,knowledge of informatization teaching,and the ability to apply informatization teaching skills innovatively and comprehensively.The 3S-7D(Three Subjects and Seven Duties)model consisting of three subjects and the seven duties that go with them is established.The three subjects include pre-service teachers,teacher educators,and higher education schools.The seven duties involve pre-service teachers demonstrating learning motivation,cross-discipline thinking,and information and communications technology mastery;teacher educators actively constructing informatization teaching practice and formative assessment;and higher education schools providing adequate hardware and software equipment while offering cooperative opportunities with primary and junior schools through institutionalization.

Electrostatic Attraction and Repulsion Explained and Modelled Mathematically Using Classical Physics—A Detailed Mechanism Based on Particle Wave Functions

The phenomenon of electrical attraction and repulsion between charged particles is well known, and described mathematically by Coulomb’s Law, yet until now there has been no explanation for why this occurs. There has been no mechanistic explanation that reveals what causes the charged particles to accelerate, either towards or away from each other. This paper gives a detailed explanation of the phenomena of electrical attraction and repulsion based on my previous work that determined the exact wave-function solutions for both the Electron and the Positron. It is revealed that the effects are caused by wave interactions between the wave functions that result in Electromagnetic reflections of parts of the particle’s wave functions, causing a change in their momenta.

A Building Information Modeling-Life Cycle Cost Analysis Integrated Model to Enhance Decisions Related to the Selection of Construction Methods at the Conceptual Design Stage of Buildings

Life Cycle Cost Analysis (LCCA) provides a systematic approach to assess the total cost associated with owning, operating, and maintaining assets throughout their entire life. BIM empowers architects and designers to perform real-time evaluations to explore various design options. However, when integrated with LCCA, BIM provides a comprehensive economic perspective that helps stakeholders understand the long-term financial implications of design decisions. This study presents a methodology for developing a model that seamlessly integrates BIM and LCCA during the conceptual design stage of buildings. This integration allows for a comprehensive evaluation and analysis of the design process, ensuring that the development aligns with the principles of low carbon emissions by employing modular construction, 3D concrete printing methods, and different building design alternatives. The model considers the initial construction costs in addition to all the long-term operational, maintenance, and salvage values. It combines various tools and data through different modules, including energy analysis, Life Cycle Assessment (LCA), and Life Cycle Cost Analysis (LCCA) to execute a comprehensive assessment of the financial implications of a specific design option throughout the lifecycle of building projects. The development of the said model and its implementation involves the creation of a new plug-in for the BIM tool (i.e., Autodesk Revit) to enhance its functionalities and capabilities in forecasting the life-cycle costs of buildings in addition to generating associated cash flows, creating scenarios, and sensitivity analyses in an automatic manner. This model empowers designers to evaluate and justify their initial investments while designing and selecting potential construction methods for buildings, and enabling stakeholders to make informed decisions by assessing different design alternatives based on long-term financial considerations during the early stages of design.

2-D Modeling and Calculations of Stratospheric Ozone and Influences of Convection, Diffusion, and Time

An engineering system approach of 2-D cylindrical model of transient mass balance calculations of ozone and other concerned chemicals along with fourteen photolysis, ozone-generating and ozone-depleting chemical reaction equations was developed, validated, and used for studying the ozone concentrations, distribution and peak of the layer, ozone depletion and total ozone abundance in the stratosphere. The calculated ozone concentrations and profile at both the Equator and a 60˚N location were found to follow closely with the measured data. The calculated average ozone concentration was within 1% of the measured average, and the deviation of ozone profiles was within 14%. The monthly evolution of stratospheric ozone concentrations and distribution above the Equator was studied with results discussed in details. The influences of slow air movement in both altitudinal and radial directions on ozone concentrations and profile in the stratosphere were explored and discussed. Parametric studies of the influences of gas diffusivities of ozone DO3 and active atomic oxygen DO on ozone concentrations and distributions were also studied and delineated. Having both influences through physical diffusion and chemical reactions, the diffusivity (and diffusion) of atomic oxygen DO was found to be more sensitive and important than that of ozone DO3 on ozone concentrations and distribution. The 2-D ozone model present in this paper for stratospheric ozone and its layer and depletion is shown to be robust, convenient, efficient, and executable for analyzing the complex ozone phenomena in the stratosphere. .