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On Local Singularities in Ideal Potential Flows with Free Surface

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Chinese Annals of Mathematics,Series B 2019年第6期40卷 925-948页

作者： jian-guo liu Robert L.PEGO Department of Physics and Department of Mathematics Duke UniversityDurhamNC 27708USA Department of Mathematical Sciences and Center for Nonlinear Analysis Carnegie Mellon UniversityPittsburghPennsylvaniaPA 12513USA

Despite important advances in the mathematical analysis of the Euler equations for water waves,especially over the last two decades,it is not yet known whether local singularities can develop from smooth data in well-posed initial value *** ideal free-surface flow with zero surface tension and gravity,the authors review existing works that describe"splash singularities",singular hyperbolic solutions related to jet formation and"flip-through",and a recent construction of a singular free surface by Zubarev and Karabut that however involves unbounded negative *** authors illustrate some of these phenomena with numerical computations of 2D flow based upon a conformal mapping *** tests with a different kind of initial data suggest the possibility that corner singularities may form in an unstable way from specially prepared initial data.

关键词： Incompressible flow Water wave equations Splash singularity Flipthrough Dirichlet hyperbolas Conformal mapping

Some Random Batch Particle Methods for the Poisson-Nernst-Planck and Poisson-Boltzmann Equations

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Communications in Computational Physics 2022年第6期32卷 41-82页

作者： Lei Li jian-guo liu Yijia Tang School of Mathematical Sciences Institute of Natural SciencesMOE-LSCShanghai Jiao Tong UniversityShanghai200240P.R.China Department of Mathematics and Department of Physics Duke UniversityDurhamNC 27708USA School of Mathematical Sciences Shanghai Jiao Tong UniversityShanghai200240P.R.China

We consider in this paper random batch interacting particle methods forsolving the Poisson-Nernst-Planck (PNP) equations, and thus the Poisson-Boltzmann(PB) equation as the equilibrium, in the external unbounded domain. To justify thesimulation in a truncated domain, an error estimate of the truncation is proved inthe symmetric cases for the PB equation. Then, the random batch interacting particle methods are introduced which are O(N) per time step. The particle methods cannot only be considered as a numerical method for solving the PNP and PB equations,but also can be used as a direct simulation approach for the dynamics of the chargedparticles in solution. The particle methods are preferable due to their simplicity andadaptivity to complicated geometry, and may be interesting in describing the dynamics of the physical process. Moreover, it is feasible to incorporate more physical effectsand interactions in the particle methods and to describe phenomena beyond the scopeof the mean-field equations.

关键词： Interacting particle systems Coulomb interaction reflecting stochastic differential equation charge reversal phenomenon singular-regular decomposition

An All-Speed Asymptotic-Preserving Method for the Isentropic Euler and Navier-Stokes Equations

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Communications in Computational Physics 2012年第9期12卷 955-980页

作者： Jeffrey Haack Shi Jin jian-guo liu Department of Mathematics University of Wisconsin-MadisonMadisonWI 53706USA Department of Mathematics University of Texas at AustinAustinTX 78712USA Departments of Physics and Mathematics Duke UniversityDurhamNC 27708USA

The computation of compressible flows becomesmore challengingwhen the Mach number has different orders of *** the Mach number is of order one,modern shock capturing methods are able to capture shocks and other complex structures with high numerical ***,if theMach number is small,the acoustic waves lead to stiffness in time and excessively large numerical viscosity,thus demanding much smaller time step and mesh size than normally needed for incompressible flow *** this paper,we develop an all-speed asymptotic preserving(AP)numerical scheme for the compressible isentropic Euler and Navier-Stokes equations that is uniformly stable and accurate for all Mach *** idea is to split the system into two parts:one involves a slow,nonlinear and conservative hyperbolic system adequate for the use of modern shock capturing methods and the other a linear hyperbolic system which contains the stiff acoustic dynamics,to be solved *** implicit part is reformulated into a standard pressure Poisson projection system and thus possesses sufficient structure for efficient fast Fourier transform solution *** the zero Mach number limit,the scheme automatically becomes a projection method-like incompressible *** present numerical results in one and two dimensions in both compressible and incompressible regimes.

关键词： Low Mach number limit asymptotic preserving schemes incompressible limit projection scheme isentropic Euler equation

AN INTERIOR TRUST REGION ALGORITHM FOR NONLINEAR MINIMIZATION WITH LINEAR CONSTRAINTS

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Journal of Computational Mathematics 2002年第3期20卷 225-244页

作者： jian-guo liu (Department of Mathematics, University of North Texas, Denton, TX 76203, USA) Department of Mathematics University of North Texas 美国 Denton

Presents information on a study which analyzed an interior trust-region-based algorithm for linearly constrained minimization problems. Optimality conditions for the linearly constrained minimization problem presented; Vectors for each updating step in the algorithm proposed; Establishment of the convergence properties of the proposed algorithm.

关键词： Nonlinear programming Linear constraints Trust region algorithms Newton methods Interior algorithms Quadratic convergence

Random Walk Approximation for Irreversible Drift-Diffusion Process on Manifold:Ergodicity,Unconditional Stability and Convergence

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Communications in Computational Physics 2023年第6期33卷 132-172页

作者： Yuan Gao jian-guo liu Department of Mathematics Purdue UniversityWest LafayetteINUSA Departments of Mathematics and Physics Duke UniversityDurhamNCUSA

Irreversible drift-diffusion processes are very common in biochemical *** have a non-equilibrium stationary state(invariant measure)which does not satisfy detailed *** the corresponding Fokker-Planck equation on a closed manifold,using Voronoi tessellation,we propose two upwind finite volume schemes with or without the information of the invariant *** schemes possess stochastic Q-matrix structures and can be decomposed as a gradient flow part and a Hamiltonian flow part,enabling us to prove unconditional stability,ergodicity and error *** on the two upwind schemes,several numerical examples–including sampling accelerated by a mixture flow,image transformations and simulations for stochastic model of chaotic system–are *** two structurepreserving schemes also give a natural random walk approximation for a generic irreversible drift-diffusion process on a *** makes them suitable for adapting to manifold-related computations that arise from high-dimensional molecular dynamics simulations.

关键词： Symmetric decomposition non-equilibrium thermodynamics enhancement by mixture exponential ergodicity structure-preserving numerical scheme

On Energy Stable Runge-Kutta Methods for the Water Wave Equation and its Simplified Non-Local Hyperbolic Model

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Communications in Computational Physics 2022年第6期32卷 222-258页

作者： Lei Li jian-guo liu Zibu liu Yi Yang Zhennan Zhou School of Mathematical Sciences Institute of Natural SciencesMOE-LSCShanghai Jiao Tong UniversityShanghai200240P.R.China Department of Mathematics and Department of Physics Duke UniversityDurhamNC 27708USA Department of Mathematics Duke UniversityDurhamNC 27708USA Nanjing Research Institute of Electronics Technology NanjingP.R.China Beijing International Center for Mathematical Research Peking UniversityP.R.China

Although interest in numerical approximations of the water wave equationgrows in recent years, the lack of rigorous analysis of its time discretization inhibits thedesign of more efficient algorithms. In practice of water wave simulations, the tradeoff between efficiency and stability has been a challenging problem. Thus to shed lighton the stability condition for simulations of water waves, we focus on a model simpli-fied from the water wave equation of infinite depth. This model preserves two mainproperties of the water wave equation: non-locality and hyperbolicity. For the constantcoefficient case, we conduct systematic stability studies of the fully discrete approximation of such systems with the Fourier spectral approximation in space and generalRunge-Kutta methods in time. As a result, an optimal time discretization strategy isprovided in the form of a modified CFL condition, i.e. ∆t = O(√∆x). Meanwhile,the energy stable property is established for certain explicit Runge-Kutta *** CFL condition solves the problem of efficiency and stability: it allows numericalschemes to stay stable while resolves oscillations at the lowest requirement, which onlyproduces acceptable computational load. In the variable coefficient case, the convergence of the semi-discrete approximation of it is presented, which naturally connectsto the water wave equation. Analogue of these results for the water wave equationof finite depth is also discussed. To validate these theoretic observation, extensive numerical tests have been performed to verify the stability conditions. Simulations of thesimplified hyperbolic model in the high frequency regime and the water wave equation are also provided.

关键词： Runge-Kutta methods non-locality hyperbolicity

Hydrothermal Synthesis,Crystal Structure and Thermal Analysis of a Dinuclear Complex Cd_2(3,5-Dinitrobenzoate)_4(pyridine)_4

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Chinese Journal of Structural Chemistry 2006年第11期25卷 1297-1302页

作者： guo Jin-Yu ZHANG Tong-Lai ZHANG jian-guo liu Yan-Hong QIAO Xiao-Jing YANG Li State Key Laboratory of Explosion Science and Technology Beij＇ing Institute of Technology Beij＇ing 100081 China

A dinuclear complex Cd2（dnba）4（pyridine）4 （dnba = 3,5-dinitrobenzoate） has been synthesized by hydrothermal method and characterized by X-ray single-crystal diffraction, elemental analysis, FT-IR spectroscopy, DSC and TG-DTG techniques. The complex with empirical formula C48H32Cd2NI2024 （Mr = 692.83） crystallizes in monoclinic, space group P21/n with a - 12.0344（14）, b = 10.5752（13）, c = 21.578（3） A, β = 104.150（2）°, V = 2662.8（6） A^3, Z = 2, D, = 1.728 g/cm^3,μ（MoKa） = 0.897 mm^-1, F（000） = 1384, S = 1.016 and （△/σ）max = 0.001. R = 0.0638 and wR = 0.0737 for all data; the final R = 0.0337 and wR = 0.0644. In this complex, four carboxylates are bidentate-or chelate-coordinated with the Cd（Ⅱ） centers to give the dinuclear structure. The other coordination positions of Cd（Ⅱ） are occupied by the lone pair electrons from N of four pyridines. Thermal analyses DSC and TG-DTG have been used to determine the thermal decomposition mechanism of the title complex.

关键词： hydrothermal synthesis dinuclear complex crystal structure thermal analysis

An FFT Based Fast Poisson Solver on Spherical Shells

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Communications in Computational Physics 2011年第3期9卷 649-667页

作者： Yin-Liang Huang jian-guo liu Wei-Cheng Wang Department of Applied Mathematics National University of TainanTainan 70005Taiwan Department of Physics and Department of Mathematics Duke UniversityDurhamNC 27708USA Department of Mathematics National Tsing Hua UniversityHsinchu 30013Taiwan

We present a fast Poisson solver on spherical *** a special change of variable,the radial part of the Laplacian transforms to a constant coefficient differential *** a result,the Fast Fourier Transform can be applied to solve the Poisson equation with O(N^(3) logN)*** examples have confirmed the accuracy and robustness of the new scheme.

关键词： Poisson equation spherical coordinate FFT spectral-finite difference method fast diagonalization high order accuracy error estimate trapezoidal rule Euler-Maclaurin formula Bernoulli numbers

Micromorphology and physicochemical properties of hydrophobic blasting dust in iron mines

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International Journal of Minerals,Metallurgy and Materials 2019年第6期26卷 665-672页

作者： jian-guo liu Long-zhe Jin Jia-ying Wang Sheng-nan Ou Jing-zhong guo Tian-yang Wang School of Civil and Resource Engineering University of Science and Technology BeijingBeijing 100083China Key Laboratory of High-Efficient Mining and Safety of Metal Mines of the Ministry of Education University of Science and Technology BeijingBeijing 100083China Mine Emergency Technology Research Center University of Science and Technology BeijingBeijing 100083China College of Safety Engineering North China Institute of Science and TechnologyYanjiao 101601China

The micromorphology and physicochemical properties of hydrophobic blasting dust(HBD)from an iron mine were comprehensively analyzed by laser particle size analysis(LPSA),scanning electron microscopy(SEM),X-ray diffraction(XRD),and X-ray photoelectron spectroscopy(XPS).The results show that the HBD particles can be classified into three types based on their particle size(PS):larger particles(PS>10μm),medium particles(1μm≤PS≤10μm),and nanoparticles(PS<1μm).The cumulative volume of respirable dust(PS≤10μm)was 84.45%.In addition,three shapes of HBD were observed by SEM:prism,flake,and *** particular,the small particles were mostly flaky,with a greater possibility of being ***,the body and surface chemical compounds of HBD were determined by XRD and XPS,*** adipate(C6H16N2O4)was the only organic compound in the body of HBD,but its mass fraction was only 13.4%.However,the content of organic C on the surface of HBD was 85.35%.This study demonstrated that the small-particle size and large amount of organic matter on the surface of HBD are the main reasons for its hydrophobicity,which can provide important guidance for controlling respirable dust in iron mines.

关键词： iron mine dust respirable dust hydrophobic blasting dust microstructure physicochemical properties particle size