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Geodesy and Geodynamics 2024年第3期15卷 264-275页

作者： Mykhailo Fys Mariana Yurkiv Andrii Brydun Andrii Sohor Department of Cartography and Geospatial modelling Lviv Polytechnic National UniversityLviv 79013Ukraine

This paper utilizes the mathematical concept of approximation within an ellipsoid from a single viewpoint to present the spatial mass distribution function of the Earth's interior and its internal *** primary focus lies in constructing the volume distribution of masses in the planet's interior, with the expansion coefficients being linear combinations of the Stokes constants. Several possible approaches are suggested for determining accurately these coefficients employing three-dimensional(biorthogonal)polynomials. By expressing the mass distribution function of the Earth's interior and its internal potential as a series, an algorithm is introduced for the calculation of gravitational energy. It allows us to estimate fluctuations in gravitational energy. The implementation of this algorithm offers the means of establishing the extent to which the Earth deviates from a state of hydrostatic equilibrium as a celestial *** to the aforementioned method, calculations have been conducted to validate its effectiveness and reliability. This example is given as an illustration of a given method for studying the internal structure of planets.

关键词： Mass distribution function Potential Stokes constants Biorthogonal polynomials

Seabed structures and foundations related to deep-sea resource development:A review based on design and research

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Deep Underground Science and Engineering 2024年第2期3卷 131-148页

作者： Shengjie Rui Haojie Zhang Hang Xu Xing Zha Mengtao Xu Kanmin Shen Key Laboratory of Offshore Geotechnics and Material of Zhejiang Province College of Civil Engineering and ArchitectureZhejiang UniversityHangzhouChina advanced modelling Offshore EnergyNorwegian Geotechnical InstituteOsloNorway Geotechnical Technology Center(Overseas Engineering Center) PowerChina Huadong Engineering Corporation LimitedHangzhouChina

The deep‐sea ground contains a huge amount of energy and mineral resources,for example,oil,gas,and *** infrastructures such as floating structures,seabed structures,and foundations have been developed to exploit these *** seabed structures and foundations can be mainly classified into three types:subsea production structures,offshore pipelines,and *** study reviewed the development,installation,and operation of these infrastructures,including their structures,design,installation,marine environment loads,and *** this basis,the research gaps and further research directions were explored through this literature ***,different floating structures were briefly analyzed and reviewed to introduce the design requirements of the seabed structures and ***,the subsea production structures,including subsea manifolds and their foundations,were reviewed and ***,the basic characteristics and design methods of deep‐sea pipelines,including subsea pipelines and risers,were analyzed and ***,the installation and bearing capacity of deep‐sea subsea anchors and seabed trench influence on the anchor were *** the review,it was found that marine environment conditions are the key inputs for any offshore structure *** fabrication,installation,and operation of infrastructures should carefully consider the marine loads and geological *** structures have their own mechanical *** fatigue and stability of pipelines mainly depend on the soil‐structure *** selection should consider soil types and possible trench *** focuses and research gaps can provide a helpful guide on further research,installation,and operation of deep‐sea structures and foundations.

关键词： anchors floating structures pipelines risers subsea foundations

Multiscale spatiotemporal meteorological drought prediction:A deep learning approach

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Advances in Climate Change Research 2024年第2期15卷 211-221页

作者： Jia-Li ZHANG Xiao-Meng HUANG Yu-Ze SUN Department of Earth System Science Ministry of Education Key Laboratory for Earth System ModellingInstitute for Global Change StudiesTsinghua UniversityBeijing 100084China

Reliable monitoring and thorough spatiotemporal prediction of meteorological drought are crucial for early warning and decision-making regarding drought-related *** utilisation of multiscale methods is effective for a comprehensive evaluation of drought occurrence and progression,given the complex nature of meteorological ***,the nonlinear spatiotemporal features of meteorological droughts,influenced by various climatological,physical and environmental factors,pose significant challenges to integrated prediction that considers multiple indicators and time *** address these constraints,we introduce an innovative deep learning framework based on the shifted window transformer,designed for executing spatiotemporal prediction of meteorological drought across multiple *** formulate four prediction indicators using the standardized precipitation index and the standard precipitation evaporation index as core methods for drought definition using the ERA5 reanalysis *** indicators span time scales of approximately 30 d and one ***-term indicators capture more anomalous variations,whereas long-term indicators attain comparatively higher accuracy in predicting future *** focus on the East Asian region,notable for its diverse climate conditions and intricate terrains,to validate the model's efficacy in addressing the complexities of nonlinear spatiotemporal *** model's performance is evaluated from diverse spatiotemporal viewpoints,and practical application values are analysed by representative drought *** results substantiate the effectiveness of our proposed model in providing accurate multiscale predictions and capturing the spatiotemporal evolution characteristics of *** of the four drought indicators accurately delineates specific facets of the meteorological drought ***,three representative drought events,namely flash drought,sustained drought and severe drought,

关键词： Meteorological drought Spatiotemporal prediction Multiscale Swim transformer Deep learning

Metagenomics reveals the microbial community and functional metabolism variation in the partial nitritation-anammox process:From collapse to recovery

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Journal of Environmental Sciences 2024年第1期135卷 210-221页

作者： Hong Wang Hui Gong Xiaohu Dai Min Yang State Key Laboratory of Pollution Control and Resource Reuse College of Environmental Science and EngineeringTongji UniversityShanghai 200092China BIOMATH Department of Data Analysis and Mathematical ModellingGhent UniversityGhent 9000Belgium

Mainstream partial nitritation-anammox(PNA)process easily suffers from performance instability and even reactor collapse in ***,it is of great significance to unveil the characteristic of performance recovery,understand the intrinsic mechanism and then propose operational *** this study,we combined long-term reactor operation,batch tests,and metagenomics to reveal the succession of microbial community and functional metabolism variation from system collapse to *** aeration control(0.10-0.25mg O_(2)/L)was critical for performance *** was also found that Candidatus Brocadia became the dominant flora and its abundance increased from 3.5%to 11.0%.Significant enhancements in carbon metabolism and phospholipid biosynthesis were observed during system recovery,and the genes abundance related to signal transduction was dramatically *** up-regulation of sdh and suc genes showed the processes of succinate dehydrogenation and succinyl-CoA synthesis might stimulate the production of amino acids and the synthesis of proteins,thereby possibly improving the activity and abundance of AnAOB,which was conducive to the performance ***,the increase in abundance of hzs and hdh genes suggested the enhancement of the anammox *** in the abundance of key genes involved in nitrogen metabolism indicated that nitrogen removal pathway was more diverse after system *** achievement of performance recovery was driven by anammox,nitrification and denitrification coupled with dissimilatory nitrate reduction to *** results provide deeper insights into the recovery mechanism of PNA system and also provide a potential regulation strategy for the stable operation of the mainstream PNA process.

关键词： Partial nitritation-anammox Metagenomics Microbial community Functional metabolism Recovery

Conserved vectors and symmetry solutions of the Landau–Ginzburg–Higgs equation of theoretical physics

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Communications in Theoretical Physics 2024年第4期76卷 51-65页

作者： Chaudry Masood Khalique Mduduzi Yolane Thabo Lephoko Material Science Innovation and Modelling Research Focus AreaDepartment of Mathematical SciencesNorth-West UniversityMafikeng CampusPrivate Bag X 2046Mmabatho 2735South Africa

This paper is devoted to the investigation of the Landau–Ginzburg–Higgs equation(LGHe),which serves as a mathematical model to understand phenomena such as superconductivity and cyclotron *** LGHe finds applications in various scientific fields,including fluid dynamics,plasma physics,biological systems,and *** study adopts Lie symmetry analysis as the primary framework for *** analysis involves the identification of Lie point symmetries that are admitted by the differential *** leveraging these Lie point symmetries,symmetry reductions are performed,leading to the discovery of group invariant *** obtain explicit solutions,several mathematical methods are applied,including Kudryashov's method,the extended Jacobi elliptic function expansion method,the power series method,and the simplest equation *** methods yield solutions characterized by exponential,hyperbolic,and elliptic *** obtained solutions are visually represented through 3D,2D,and density plots,which effectively illustrate the nature of the *** plots depict various patterns,such as kink-shaped,singular kink-shaped,bell-shaped,and periodic ***,the paper employs the multiplier method and the conservation theorem introduced by Ibragimov to derive conserved *** conserved vectors play a crucial role in the study of physical quantities,such as the conservation of energy and momentum,and contribute to the understanding of the underlying physics of the system.

关键词： Landau-Ginzburg-Higgs equation Lie symmetry analysis group invariant solutions conserved vectors multiplier method Ibragimov's method

Improving the accuracy of precipitation estimates in a typical inland arid area of China using a dynamic Bayesian model averaging approach

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Journal of Arid Land 2024年第3期16卷 331-354页

作者： XU Wenjie DING Jianli BAO Qingling WANG Jinjie XU Kun College of Geography and Remote Sensing Sciences Xinjiang UniversityUrumqi 830017China Key Laboratory of Smart City and Environment modelling of Higher Education Institute Xinjiang UniversityUrumqi 830017China

Xinjiang Uygur Autonomous Region is a typical inland arid area in China with a sparse and uneven distribution of meteorological stations,limited access to precipitation data,and significant water *** and integrating precipitation datasets from different sources to accurately characterize precipitation patterns has become a challenge to provide more accurate and alternative precipitation information for the region,which can even improve the performance of hydrological *** study evaluated the applicability of widely used five satellite-based precipitation products(Climate Hazards Group InfraRed Precipitation with Station(CHIRPS),China Meteorological Forcing Dataset(CMFD),Climate Prediction Center morphing method(CMORPH),Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks-Climate Data Record(PERSIANN-CDR),and Tropical Rainfall Measuring Mission Multi-satellite Precipitation Analysis(TMPA))and a reanalysis precipitation dataset(ECMWF Reanalysis v5-Land Dataset(ERA5-Land))in Xinjiang using ground-based observational precipitation data from a limited number of meteorological *** on this assessment,we proposed a framework that integrated different precipitation datasets with varying spatial resolutions using a dynamic Bayesian model averaging(DBMA)approach,the expectation-maximization method,and the ordinary Kriging interpolation *** daily precipitation data merged using the DBMA approach exhibited distinct spatiotemporal variability,with an outstanding performance,as indicated by low root mean square error(RMSE=1.40 mm/d)and high Person's correlation coefficient(CC=0.67).Compared with the traditional simple model averaging(SMA)and individual product data,although the DBMA-fused precipitation data were slightly lower than the best precipitation product(CMFD),the overall performance of DBMA was more *** error analysis between DBMA-fused precipitation dataset and the more advanced Inte

关键词： precipitation estimates satellite-based and reanalysis precipitation dynamic Bayesian model averaging streamflow simulation Ebinur Lake Basin Xinjiang

Applications of cnoidal and snoidal wave solutions via optimal system of subalgebras for a generalized extended (2+1)-D quantum Zakharov-Kuznetsov equation with power-law nonlinearity in oceanography and ocean engineering

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Journal of Ocean Engineering and Science 2024年第2期9卷 126-153页

作者： Oke Davies Adeyemo International Institute for Symmetry Analysis and Mathematical modelling Department of Mathematical SciencesNorth-West UniversityMafikeng CampusPrivate Bag X 2046Mmabatho 2735Republic of South Africa

The nonlinear evolution equations have a wide range of applications,more precisely in physics,biology,chemistry and engineering *** domain serves as a point of interest to a large extent in the world’s mathematical ***,this paper purveys an analytical study of a generalized extended(2+1)-dimensional quantum Zakharov-Kuznetsov equation with power-law nonlinearity in oceanography and ocean *** Lie group theory of differential equations is utilized to compute an optimal system of one dimension for the Lie algebra of the *** further reduce the equation using the subalgebras ***,more general solutions of the underlying equation are secured for some special cases of n with the use of extended Jacobi function expansion ***,we secure new bounded and unbounded solutions of interest for the equation in various solitonic structures including bright,dark,periodic(cnoidal and snoidal),compact-type as well as singular *** applications of cnoidal and snoidal waves of the model in oceanography and ocean engineering for the first time,are outlined with suitable *** can be of interest to oceanographers and ocean engineers for future ***,to visualize the dynamics of the results found,we present the graphic display of each of the ***,we construct conservation laws of the understudy equation via the application of Noether’s theorem.

关键词： A generalized extended(2+1)-dimensional quantum Zakharov-Kuznetsov equation Lie point symmetries Optimal system of subalgebras Cnoidal and snoidal waves Extended Jacobi function expansion technique Conservation laws

Approximations to Isentropic Planar Magneto-Hydrodynamics Equations by Relaxed Euler-Type Systems

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Chinese Annals of Mathematics,Series B 2024年第3期45卷 413-440页

作者： Yachun LI Zhaoyang SHANG Chenmu WANG Liang ZHAO School of Mathematical Sciences CMA-ShanghaiMOE-LSC and SHL-MACShanghai Jiao Tong UniversityShanghai 200240China School of Finance Shanghai Lixin University of Accounting and FinanceShanghai 201209China School of Mathematical Sciences Shanghai Jiao Tong UniversityShanghai 200240China School of Mathematical Sciences Harbin Engineering UniversityHarbin 150001China Mathematical modelling&Data Analytics Center Oxford Suzhou Centre for Advanced ResearchSuzhou 215123JiangsuChina

In this paper, the authors consider an approximation to the isentropic planar Magneto-hydrodynamics(MHD for short) equations by a kind of relaxed Euler-type system. The approximation is based on the generalization of the Maxwell law for nonNewtonian fluids together with the Maxwell correction for the Ampe`re law, hence the approximate system becomes a first-order quasilinear symmetrizable hyperbolic systems with partial dissipation. They establish the global-in-time smooth solutions to the approximate Euler-type equations in a small neighbourhood of constant equilibrium states and obtain the global-in-time convergence towards the isentropic planar MHD equations. In addition, they also establish the global-in-time error estimates of the limit based on stream function techniques and energy estimates for error variables.

关键词： Planar MHD equations Relaxation limits Global convergence Stream function

Towards data-efficient mechanical design of bicontinuous composites usinggenerative AI

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Theoretical & Applied Mechanics Letters 2024年第1期14卷 57-64页

作者： Milad Masrouri Zhao Qin Department of Civil and Environmental Engineering Syracuse UniversitySyracuseNY 13244USA Laboratory for Multiscale Material modelling Syracuse UniversitySyracuseNY 13244USA The BioInspired Institute Syracuse UniversitySyracuseNY 13244USA

The distribution of material phases is crucial to determine the composite’s mechanical *** the full structure-mechanics relationship of highly ordered material distributions can be studied with finite number of cases,this relationship is difficult to be revealed for complex irregular distributions,preventing design of such material structures to meet certain mechanical *** noticeable developments of artificial intelligence(AI)algorithms in material design enables to detect the hidden structure-mechanics correlations which is essential for designing composite of complex *** is intriguing how these tools can assist composite ***,we focus on the rapid generation of bicontinuous composite structures together with the stress distribution in *** find that generative AI,enabled through fine-tuned Low Rank Adaptation models,can be trained with a few inputs to generate both synthetic composite structures and the corresponding von Mises stress *** results show that this technique is convenient in generating massive composites designs with useful mechanical information that dictate stiffness,fracture and robustness of the material with one model,and such has to be done by several different experimental or simulation *** research offers valuable insights for the improvement of composite design with the goal of expanding the design space and automatic screening of composite designs for improved mechanical functions.

关键词： Generative artificial intelligence Stable diffusion Composite design Phase field model Molecular dynamics simulation

A combined Liouville integrable hierarchy associated with a fourth-order matrix spectral problem

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Communications in Theoretical Physics 2024年第07期76卷 3-10页

作者： Wen-Xiu Ma Department of Mathematics Zhejiang Normal University Department of Mathematics King Abdulaziz University Department of Mathematics and Statistics University of South Florida Tampa Material Science Innovation and modelling Department of Mathematical Sciences North-West University Mafikeng Campus

This paper aims to propose a fourth-order matrix spectral problem involving four potentials and generate an associated Liouville integrable hierarchy via the zero curvature formulation. A bi-Hamiltonian formulation is furnished by applying the trace identity and a recursion operator is explicitly worked out, which exhibits the Liouville integrability of each model in the resulting hierarchy. Two specific examples, consisting of novel generalized combined nonlinear Schr?dinger equations and modified Korteweg–de Vries equations, are given.

关键词： Hamiltonian structure integrable hierarchy Lax pair matrix spectral problem zero curvature equation