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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

Radiative Blood-Based Hybrid Copper-Graphene Nanoliquid Flows along a Source-Heated Leaning Cylinder

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Computer Modeling in Engineering & Sciences 2024年第4期139卷 1017-1037页

作者： Siti Nur Ainsyah Ghani Noor Fadiya Mohd Noor Institute of mathematical Sciences Faculty of ScienceUniversiti MalayaKuala Lumpur50603Malaysia center for data analytics Consultancy&Services(UM-CDACS) Faculty of ScienceUniversiti MalayaKuala Lumpur50603Malaysia

Variant graphene,graphene oxides(GO),and graphene nanoplatelets(GNP)dispersed in blood-based copper(Cu)nanoliquids over a leaning permeable cylinder are the focus of this *** forms of graphene are highly beneficial in the biological and medical fields for cancer therapy,anti-infection measures,and drug *** non-Newtonian Sutterby(blood-based)hybrid nanoliquid flows are generalized within the context of the Tiwari-Das model to simulate the effects of radiation and heating *** governing partial differential equations are reformulated into a nonlinear set of ordinary differential equations using similar transformational *** equations are then transformed into boundary value problems through a shooting technique,followed by the implementation of the bvp4c tool in *** influences of various parameters on the model’s nondimensional velocity and temperature profiles,reduced skin friction,and reduced Nusselt number are presented for detailed *** results indicated that Cu-GNP/blood and Cu-GO/blood hybrid nanofluids exhibit the lowest and highest velocity distributions,respectively,for increased nanoparticles volume fraction,curvature parameter,Sutterby fluid parameter,Hartmann number,and wall permeability ***,opposite trends are observed for the temperature distribution for all considered parameters,except the mixed convection *** in the reduced skin friction magnitude and the reduced Nusselt number with higher values of graphene/GO/GNP nanoparticle volume fraction are also ***,GNP is identified as the superior heat conductor,with an average increase of approximately 5%and a peak of 7.8%in the reduced Nusselt number compared to graphene and GO nanoparticles in the Cu/blood nanofluids.

关键词： Hybrid nanofluid sutterby fluid tiwari-das model thermal radiation graphene graphene oxides graphene nanoplatelets

Approximations of Euler-Maxwell systems by drift-diffusion equations through zero-relaxation limits near the non-constant equilibrium

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Science China Mathematics 2024年

作者： Rui Jin Yachun Li Liang Zhao School of mathematical Sciences Shanghai Jiao Tong University CMA-Shanghai MOE-LSC and SHL-MAC Shanghai Jiao Tong University mathematical modelling & data analytics center Oxford Suzhou Centre for Advanced Research Department of Mathematics National University of Singapore

Due to extreme difficulties in numerical simulations of Euler-Maxwell equations, which are caused by the highly complicated structures of the equations, this paper concerns the simplification of the Euler-Maxwell system through the zero-relaxation limit towards drift-diffusion equations with non-constant doping *** carry out the global-in-time convergence analysis by establishing uniform estimates of solutions near nonconstant equilibrium regarding the relaxation parameter and passing to the limit by using classical compactness arguments. Furthermore, we generalize the stream function method to the non-constant equilibrium case, and together with the anti-symmetric structure of the error system and an induction argument, we establish globalin-time error estimates between smooth solutions to the Euler-Maxwell system and those to the drift-diffusion system, which are bounded by some power of the relaxation parameter.

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A note on semidefinite programming relaxations for polynomial optimization over a single sphere

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Science China Mathematics 2016年第8期59卷 1543-1560页

作者： HU Jiang JIANG Bo LIU Xin WEN ZaiWen Beijing International center for mathematical Research Peking University Research center for Management Science and data analytics School of Information Management and EngineeringShanghai University of Finance and Economics LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems Science Chinese Academy of Sciences

We study two instances of polynomial optimization problem over a single sphere. The first problem is to compute the best rank-1 tensor approximation. We show the equivalence between two recent semidefinite relaxations methods. The other one arises from Bose-Einstein condensates(BEC), whose objective function is a summation of a probably nonconvex quadratic function and a quartic term. These two polynomial optimization problems are closely connected since the BEC problem can be viewed as a structured fourth-order best rank-1 tensor approximation. We show that the BEC problem is NP-hard and propose a semidefinite relaxation with both deterministic and randomized rounding procedures. Explicit approximation ratios for these rounding procedures are presented. The performance of these semidefinite relaxations are illustrated on a few preliminary numerical experiments.

关键词： polynomial optimization over a single sphere semidefinite programming best rank-1 tensor ap-proximation Bose-Einstein condensates

Massive data clustering by multi-scale psychological observations

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National Science Review 2022年第2期9卷 43-51页

作者： Shusen Yang Liwen Zhang Chen Xu Hanqiao Yu Jianqing Fan Zongben Xu National Engineering Laboratory of Big data analytics Xi'an Jiaotong University Department of Mathematics and Statistics University of Ottawa center for Statistics and Machine Learning Princeton University Industrial Artificial Intelligent center Pazhou Laboratory

Clustering is the discovery of latent group structure in data and is a fundamental problem in artificial intelligence,and a vital procedure in data-driven scientific research over all ***,existing methods have various limitations,especially we ak cognitive interpretability and poor computational scalability,when it comes to clustering massive datasets that are increasingly available in all ***,by simulating the multi-scale cognitive observation process of humans,we design a scalable algorithm to detect clusters hierarchically hidden in massive *** observation scale changes,following the Weber-Fechner law to capture the gradually emerging meaningful grouping *** validated our approach in real datasets with up to a billion records and 2000 dimensions,including taxi trajectories,single-cell gene expressions,face images,computer logs and *** approach outperformed popular methods in usability,efficiency,effectiveness and robustness across different domains.

关键词： massive data clustering psychological observation Weber–Fechner law cognitive interpretability computational scalability

Unlabeled data driven cost-sensitive inverse projection sparse representation-based classification with 1/2 regularization

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Science China(Information Sciences) 2022年第8期65卷 39-56页

作者： Xiaohui YANG Zheng WANG Jian SUN Zongben XU Henan Engineering Research center for Artificial Intelligence Theory and Algorithms School of Mathematics and StatisticsHenan University National Engineering Laboratory for Big data analytics School of Mathematics and StatisticsXi'an Jiaotong University

Sparse representation-based classification(SRC) has been widely used because it just relies on simple linear regression ideas to do classification, and it does not need learning. However, the performance of SRC is limited by needing sufficient labeled samples per class and the sensitivity to class imbalance. For tackling these problems, an improved SRC model is constructed in this paper. For alleviating the problem of insufficient labeled samples, an unlabeled data-driven inverse projection sparse representation-based classification model is constructed to achieve effective and stable representation and recognition results. The L1/2 and S1/2 regularizations are introduced to capture the sparsity of 1-D and 2-D, and to make the model have good statistical properties. Moreover, the cost-sensitive strategy is integrated into the model’s classification criteria to improve the imbalance of class distribution adaptively, especially for multiclass imbalanced data.A solver utilizing the mixed Gauss-Seidel and Jacobian ADMM algorithm is developed to obtain the approximate solution. Experiments on common public test databases show that the proposed model achieves competitive results compared with the latest published results and some deep-learning algorithms.

关键词： unlabeled-data driven 1/2 regularization cost-sensitive inverse projection sparse representation-based classification

Generating geologically realistic 3D reservoir facies models using deep learning of sedimentary architecture with generative adversarial networks

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Petroleum Science 2019年第3期16卷 541-549页

作者： Tuan-Feng Zhang Peter Tilke Emilien Dupont Ling-Chen Zhu Lin Liang William Bailey Applied Math and data analytics Schlumberger-Doll Research Cambridge MAUSA Schlumberger Technology Innovation center Menlo Park CA USA Reservoir Geosciences Schlumberger-Doll Research Cambridge MA USA

This paper proposes a novel approach for generating 3-dimensional complex geological facies models based on deep generative *** can reproduce a wide range of conceptual geological models while possessing the flexibility necessary to honor constraints such as well *** with existing geostatistics-based modeling methods,our approach produces realistic subsurface facies architecture in 3D using a state-of-the-art deep learning method called generative adversarial networks(GANs).GANs couple a generator with a discriminator,and each uses a deep convolutional neural *** networks are trained in an adversarial manner until the generator can create "fake" images that the discriminator cannot distinguish from "real" *** extend the original GAN approach to 3D geological modeling at the reservoir *** GANs are trained using a library of 3D facies *** the GANs have been trained,they can generate a variety of geologically realistic facies models constrained by well data *** geomodelling approach using GANs has been tested on models of both complex fluvial depositional systems and carbonate reservoirs that exhibit progradational and aggradational *** results demonstrate that this deep learning-driven modeling approach can capture more realistic facies architectures and associations than existing geostatistical modeling methods,which often fail to reproduce heterogeneous nonstationary sedimentary facies with apparent depositional trend.

关键词： Geological facies Geomodeling data conditioning Generative adversarial networks

In silico assessment of household level closed water cycles:Towards extreme decentralization

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Environmental Science and Ecotechnology 2022年第2期10卷 1-11页

作者： Arjen Van de Walle Elena Torfs Dorien Gaublomme Korneel Rabaey center for Microbial Ecology and Technology Ghent UniversityCoupure Links 6539000GhentBelgium center for Advanced Process Technology for Urban Resource Recovery(CAPTURE) Coupure Links 6539000GhentBelgium BIOMATH Department of Data Analysis and Mathematical ModellingGhent UniversityCoupure links 6539000GhentBelgium

Water management in most of the developed world is currently practiced in a highly centralized manner,leading to major infrastructure and energy costs to transport *** decrease the impacts of water scarcity and climate change,the decentralization of water can increase local *** extremis,decentralization can involve building or house level water supply and ***,we constructed a MATLAB/Simulink model for two decentralized water management configurations at the household level,assuming the socio-environmental setting of Flanders,*** from the potable water grid and sewer system was pursued through rainwater harvesting,reuse of wastewater streams fitfor-purpose,and discharge via *** mass balance for water was calculated over the system boundaries showing high potential for independence from the grid with a reasonable treatment train and storage ***,the risk of contaminant accumulation within the circular system was assessed,showing a key limitation on decentralized system performance necessitating a system *** to 59%of system rainwater usage was due to the replacement of this *** treatment units with high(95%)contaminant rejection efficiencies eliminated contaminant accumulation *** raw model output was quantitatively assessed by constructing four newly proposed key performance indicators(KPIs),quantifying system independence,circularity,drought tolerance and local water body recharge,which allowed for facilitated system comparison and communication to stakeholders.A sensitivity analysis was performed in which the effect of input parameter variability and uncertainty on system performance was *** sensitivity analysis showed the importance of water recovery and contaminant removal efficiencies of the applied treatment technologies on system performance when contaminant accumulation in the system forms an *** systems not severely affected by pollutant accumulation,para

关键词： Extreme decentralization Household-scale Water reuse Simulations

Slip effects on unsteady mixed convection of hybrid nanofluid flow near the stagnation point

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Applied Mathematics and Mechanics(English Edition) 2022年第4期43卷 547-556页

作者： N.A.ZAINAL R.NAZAR K.NAGANTHRAN I.POP Department of mathematical Sciences Faculty of Science and TechnologyUniversiti Kebangsaan MalaysiaBangi 43600Malaysia Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan Universiti Teknikal Malaysia MelakaHang Tuah JayaDurian Tunggal 76100Malaysia Institute of mathematical Sciences Faculty of ScienceUniversiti MalayaKuala Lumpur 50603Malaysia center for data analytics Consultancy and ServicesFaculty of ScienceUniversiti MalayaKuala Lumpur 50603Malaysia Department of Mathematics Babes-Bolyai UniversityR-400084 Cluj-NapocaRomania

The unsteady mixed convection of the Al_(2)O_(3)-Cu/H_(2)O hybrid nanofluid flow near the stagnation point past a vertical plate is *** bvp4c technique is used to solve the resulting ordinary differential *** combined effects of the velocity and thermal slip are *** effects of different relevant physical parameters are studied *** results show that the heat transfer rate is reduced when the volume fraction of the nanoparticles increases,while the unsteadiness parameter has an opposite effect in the opposing *** presence of the slip parameter is proven to increase the skin friction coefficient while reduce the local Nusselt number in the buoyancy opposing flow.A contradictory result is observed in the buoyancy assisting ***,the heat transfer rate is reduced in the buoyancy of the assisting and opposing flows when the thermal slip effect is considered.

关键词： hybrid nanofluid mixed convection unsteady flow stagnation point