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A dive into spectral inference networks: improved algorithms for self-supervised learning of continuous spectral representations

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Applied Mathematics and Mechanics(English Edition) 2023年第7期44卷 1199-1224页

作者： j.wu S.F.WANG P.PERDIKARIS Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA 19104U.S.A. Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania PhiladelphiaPA 19104U.S.A.

We propose a self-supervising learning framework for finding the dominant eigenfunction-eigenvalue pairs of linear and self-adj.int *** represent target eigenfunctions with coordinate-based neural networks and employ the Fourier positional encodings to enable the approximation of high-frequency *** formulate a self-supervised training obj.ctive for spectral learning and propose a novel regularization mechanism to ensure that the network finds the exact eigenfunctions instead of a space spanned by the ***,we investigate the effect of weight normalization as a mechanism to alleviate the risk of recovering linear dependent modes,allowing us to accurately recover a large number of *** effectiveness of our methods is demonstrated across a collection of representative benchmarks including both local and non-local diffusion operators,as well as high-dimensional time-series data from a video *** results indicate that the present algorithm can outperform competing approaches in terms of both approximation accuracy and computational cost.

关键词： spectral learning partial differential equation(PDE) neural network slow features analysis

Particulate Flow Simulation via a Boundary Condition-Enforced Immersed Boundary-Lattice Boltzmann Scheme

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Communications in Computational Physics 2010年第4期7卷 793-812页

作者： j.wu C.Shu Department of Mechanical Engineering National University of Singapore10 Kent Ridge CrescentSingapore 119260

A boundary condition-enforced immersed boundary-lattice Boltzmannmethod (IB-LBM) for the simulation of particulate flows is presented in this paper. Ingeneral, the immersed boundary method (IBM) utilizes a discrete set of force densityto represent the effect of boundary. In the conventional IB-LBM, such force density ispre-determined, which cannot guarantee exact satisfaction of non-slip boundary condition. In this study, the force density is transferred to the unknown velocity correctionwhich is determined by enforcing the non-slip boundary condition. For the particulateflows, accurate calculation of hydrodynamic force exerted on the boundary of particlesis of great importance as it controls the motion of particles. The capability of presentmethod for particulate flows is depicted by simulating migration of one particle in asimple shear flow and sedimentation of one particle in a box and two particles in achannel. The expected phenomena and numerical results are achieved. In addition,particle suspension in a 2D symmetric stenotic artery is also simulated.

关键词： Lattice Boltzmann method immersed boundary method non-slip boundary condition particulate flow two-dimensional

Material and structural instabilities of single-wall carbon nanotubes

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Acta Mechanica Sinica 2008年第3期24卷 285-288页

作者： j.wu K.C.Hwang j.Song Y.Huang FML Department of Engineering MechanicsTsinghua UniversityBeijing 100084China Department of Mechanical Science and Engineering University of Illinois1206 W.Green StreetUrbanaIL 61801USA Department of Civil and Environmental Engineering and Department of Mechanical Engineering Northwestern UniversityEvanstonIL 60208USA

The nonlinear atomistic interactions usually involve softening behavior. Instability resulting directly from this softening are called the material instability, while those unrelated to this softening are called the structural instability. We use the finite-deformation shell theory based on the interatomic potential to show that the tension instability of single-wall carbon nanotubes is the material instability, while the compression and torsion instabilities are structural instability.

关键词： Carbon nanotubes Instability

A stabilized complementarity formulation for nonlinear analysis of 3D bimodular materials

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Acta Mechanica Sinica 2016年第3期32卷 481-490页

作者： L.Zhang H.W.Zhang j.wu B.Yan Department of Engineering Mechanics College of AerospaceEngineering Chongqing University State Key Laboratory of Structural Analysis for IndustrialEquipment Dalian University of Technology

Bi-modulus materials with different mechanical responses in tension and compression are often found in civil,composite, and biological engineering. Numerical analysis of bimodular materials is strongly nonlinear and convergence is usually a problem for traditional iterative schemes. This paper aims to develop a stabilized computational method for nonlinear analysis of 3D bimodular materials. Based on the parametric variational principle, a unified constitutive equation of 3D bimodular materials is proposed, which allows the eight principal stress states to be indicated by three parametric variables introduced in the principal stress *** original problem is transformed into a standard linear complementarity problem（LCP） by the parametric virtual work principle and a quadratic programming algorithm is developed by solving the LCP with the classic Lemke＇s algorithm. Update of elasticity and stiffness matrices is avoided and, thus, the proposed algorithm shows an excellent convergence behavior compared with traditional iterative *** examples show that the proposed method is valid and can accurately analyze mechanical responses of 3D bimodular materials. Also, stability of the algorithm is greatly improved.

关键词： Bimodular materials Non-smooth stressstrain relationship Parametric variational principle Complementarity

A Hybrid Lattice Boltzmann Flux Solver for Simulation of Viscous Compressible Flows

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Advances in Applied Mathematics and Mechanics 2016年第6期8卷 887-910页

作者： L.M.Yang C.Shu j.wu State Key Laboratory of Aerodynamics China Aerodynamics Research and Development CenterMianyang 621000China Department of Aerodynamics College of Aerospace EngineeringNanjing University of Aeronautics and AstronauticsYudao StreetNanjing 210016China Department of Mechanical Engineering National University of Singapore10 Kent Ridge CrescentSingapore 119260Singapore

In this paper,a hybrid lattice Boltzmann flux solver(LBFS)is proposed for simulation of viscous compressible *** the solver,the finite volume method is applied to solve the Navier-Stokes *** from conventional Navier-Stokes solvers,in this work,the inviscid flux across the cell interface is evaluated by local reconstruction of solution using one-dimensional lattice Boltzmann model,while the viscous flux is still approximated by conventional smooth function *** present work overcomes the two maj.r drawbacks of existing LBFS[28–31],which is used for simulation of inviscid *** first one is its ability to simulate viscous flows by including evaluation of viscous *** second one is its ability to effectively capture both strong shock waves and thin boundary layers through introduction of a switch function for evaluation of inviscid flux,which takes a value close to zero in the boundary layer and one around the strong shock *** experiments demonstrate that the present solver can accurately and effectively simulate hypersonic viscous flows.

关键词： Lattice Boltzmann flux solver hybrid 1D lattice Boltzmann model switch function

Basic Engineering Circuit Analysis j. David Irwin, Chwan-Hua wu 6th ed.

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Basic Engineering Circuit Analysis J. David Irwin, Chwan-Hua...

Photocatalytic properties of hierarchical CuO nanosheets synthesized by a solution phase method

1999年

作者： j. David Irwin Chwan-Hua wu

来源：畅想之星图书光盘版（南... 评论

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j.urnal of Environmental Sciences 2018年第7期30卷 115-124页

作者： Martha Purnachander Rao j.rry j.wu Abdullah M.Asiri Sambandam Anandan Muthupandian Ashokkumar Nanomaterials and Solar Energy Conversion Lab Department of Chemistry National Institute of Technology Department of Environmental Engineering and Science Feng Chia University The Center of Excellence for Advanced Materials Research King Abdulaziz University School of Chemistry University of Melbourne

CuO nanomaterials were synthesized by a simple solution phase method using cetyltrimethylammonium bromide（CTAB） as a surfactant and their photocatalytic property was determined towards the visible-light assisted degradation of Reactive Black-5 dye. A detailed mechanism for the formation of CuO nanostructures has been *** effect of various experimental parameters such as catalyst amount, dye concentration,p H and oxidizing agent on the dye degradation efficiency was studied. About 87% dye was degraded at p H 2 in the presence of CuO nanosheets under visible light. The enhanced photocatalytic activity of CuO nanosheets can be ascribed to good crystallinity, grain size,surface morphology and a strong absorption in the visible region. CuO is found to be a promising catalyst for industrial waste water treatment.

关键词： CuO Photocatalytic degradation Visible light Reactive Black-5 Reusability

Development and Comparative Studies of Three Non-free Parameter Lattice Boltzmann Models for Simulation of Compressible Flows

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Advances in Applied Mathematics and Mechanics 2012年第4期4卷 454-472页

作者： L.M.Yang C.Shu j.wu Department of Aerodynamics College of Aerospace EngineeringNanjing University of Aeronautics and AstronauticsYudao StreetNanjing 210016JiangsuChina Department of Mechanical Engineering National University of Singapore10 Kent Ridge CrescentSingapore 119260Singapore

This paper at first shows the details of finite volume-based lattice Boltzmann method(FV-LBM)for simulation of compressible flows with shock *** the FV-LBM,the normal convective flux at the interface of a cell is evaluated by using one-dimensional compressible lattice Boltzmann model,while the tangential flux is calculated using the same way as used in the conventional Euler *** paper then presents a platform to construct one-dimensional compressible lattice Boltzmann model for its use in *** platform is formed from the conservation forms of *** the platform,both the equilibrium distribution functions and lattice velocities can be determined,and therefore,non-free parameter model can be *** paper particularly presents three typical non-free parameter models,D1Q3,D1Q4 and *** performances of these three models for simulation of compressible flows are investigated by a brief analysis and their application to solve some one-dimensional and two-dimensional test *** results showed that D1Q3 model costs the least computation time and D1Q4 and D1Q5 models have the wider application range of Mach *** the results,it seems that D1Q4 model could be the best choice for the FVLBM simulation of hypersonic flows.

关键词： FV-LBM non-free parameter models compressible inviscid flows

Development of Lattice Boltzmann Flux Solver for Simulation of Incompressible Flows

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Advances in Applied Mathematics and Mechanics 2014年第4期6卷 436-460页

作者： C.Shu Y.Wang C.j.Teo j.wu Department of Mechanical Engineering National University of Singapore10 Kent Ridge CrescentSingapore 119260 Department of Aerodynamics College of Aerospace EngineeringNanjing University of Aeronautics and AstronauticsNanjing 210016China

A lattice Boltzmann flux solver(LBFS)is presented in this work for simulation of incompressible viscous and inviscid *** new solver is based on Chapman-Enskog expansion analysis,which is the bridge to link Navier-Stokes(N-S)equations and lattice Boltzmann equation(LBE).The macroscopic differential equations are discretized by the finite volume method,where the flux at the cell interface is evaluated by local reconstruction of lattice Boltzmann solution from macroscopic flow variables at cell *** new solver removes the drawbacks of conventional lattice Boltzmann method such as limitation to uniform mesh,tie-up of mesh spacing and time interval,limitation to viscous *** is validated by its application to simulate the viscous decaying vortex flow,the driven cavity flow,the viscous flow past a circular cylinder,and the inviscid flow past a circular *** obtained numerical results compare very well with available data in the literature,which show that LBFS has the second order of accuracy in space,and can be well applied to viscous and inviscid flow problems with non-uniform mesh and curved boundary.

关键词： Chapman-Enskog analysis flux solver incompressible flow Navier-Stokes equation lattice Boltzmann equation