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A Variational Neural Network Approach for Glacier Modelling with nonlinear rheology

Communications in Computational Physics 2023年第9期34卷 934-954页

作者： Tiangang Cui Zhongjian Wang Zhiwen Zhang School of Mathematics and Statistics University of SydneyNSW 2006Australia Division of Mathematical Sciences School of Physical and Mathematical SciencesNanyang Technological University21 Nanyang LinkSingapore 637371 Department of Mathematics The University of Hong KongPokfulam RoadHong Kong SARChina

We propose a mesh-free method to solve the full Stokes equation for modeling the glacier dynamics with nonlinear *** by the Deep-Ritz method proposed in[13],we first formulate the solution to the non-Newtonian Stokes equation as the minimizer of a variational problem with boundary ***,we approximate its solution space by a deep neural *** loss function for training the neural network is a relaxed version of the variational form,in which penalty terms are used to present soft constraints due to mixed boundary *** of introducing mesh grids or basis functions to evaluate the loss function,our method only requires uniform sampling from the physical domain and ***,we introduce a re-normalization technique in the neural network to address the significant variation in the scaling of real-world ***,we illustrate the performance of our method by several numerical experiments,including a 2D model with the analytical solution,the Arolla glacier model with realistic scaling and a 3D model with periodic boundary *** results show that our proposed method is efficient in solving the non-Newtonian mechanics arising from glacier modeling with nonlinear rheology.

关键词： Deep learning method variational problems mesh-free method non-Newtonian mechanics nonlinear rheology glacier modelling

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Structural and Rheological Properties of PP/EPR/PE Alloys

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Chinese Journal of Polymer Science 2023年第2期41卷 240-249页

作者： Jia-Qi Zhang Yan-Jie Zhang Chun-Yu Zhang Quan Chen State Key Laboratory of Polymer Physics and Chemistry Changchun Institute of Applied ChemistryChinese Academy of SciencesChangchun130022China University of Science and Technology of China Hefei230026China School of Polymer Science and Engineering Qingdao University of Science&TechnologyQingdao266042China

Linear and non-linear rheological properties were examined for in-reactor alloy samples composed of isotactic polypropylene(iPP),ethylene-propylene rubber(EPR),and polyethylene(PE).The samples were prepared through two-or three-stage sequential polymerization,where iPP,as the majority,was synthesized in the first stage,and either EPR or PE,as the minority,was synthesized in the second or third *** Tm of both PE and iPP,the linear viscoelasticity shows two relaxation processes,where the fast and slow processes are attributable to the relaxation of the iPP component and that of the EPR/PE domains,*** the damping behavior upon applying the step-strain measurements and the shear-thinning behavior under the shear-rate sweep measurements are strongly related to the different degrees of nonlinearity of the two relaxation processes.

关键词： Polypropylene alloy Structure nonlinear rheology

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Models of plate tectonics with the Lattice Boltzmann Method

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Artificial Intelligence in Geosciences 2023年第1期4卷 47-58页

作者： Peter Mora Gabriele Morra David A.Yuen Geosciences Department College of Petroleum Engineering and GeosciencesKing Fahd University of Petroleum and MineralsDhahran31261Saudi Arabia Department of Physics University of Louisiana at LafayetteLafayetteLA70504USA Department of Applied Physics and Applied Mathematics Columbia UniversityNew YorkNY10027USA Department of Information Science and Engineering and College of Marine Geosciences Ocean University of ChinaQingdao266100China

Modern geodynamics is based on the study of a large set of models,with the variation of many parameters,whose analysis in the future will require Machine Learning to be *** introduce here for the first time how a formulation of the Lattice Boltzmann Method capable of modeling plate tectonics,with the introduction of plastic non-linear rheology,is able to reproduce the breaking of the upper boundary layer of the convecting mantle in *** simulation of the earth’s mantle and lithospheric plates is a challenging task for traditional methods of numerical solution to partial differential equations(PDE’s)due to the need to model sharp and large viscosity contrasts,temperature dependent viscosity and highly nonlinear *** rheologies such as plastic or dislocation creep are important in giving mantle convection a past *** present a thermal Lattice Boltzmann Method(LBM)as an alternative to PDE-based solutions for simulating time-dependent mantle dynamics,and demonstrate that the LBM is capable of modeling an extremely nonlinear plastic *** nonlinear rheology leads to the emergence plate tectonic like behavior and history from a two layer viscosity *** results demonstrate that the LBM offers a means to study the effect of highly nonlinear rheologies on earth and exoplanet dynamics and evolution.

关键词： Lattice Boltzmann Method Mantle convection simulation Plate tectonics simulation nonlinear rheology Extreme plasticity

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