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A Third Order Accurate in Time,BDF-Type Energy Stable Scheme for the Cahn-Hilliard Equation

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Numerical mathematics(Theory,methods and Applications) 2022年第2期15卷 279-303页

作者： Kelong Cheng Cheng Wang steven m.wise Yanmei Wu School of Science Southwest University of Science and TechnologyMianyangSichuan 621010P.R.China Department of mathematics The University of MassachusettsNorth DartmouthMA 02747USA Department of mathematics The University of TennesseeKnoxvilleTN 37996USA

In this paper we propose and analyze a backward differentiation formula(BDF)type numerical scheme for the Cahn-Hilliard equation with third order temporal *** Fourier pseudo-spectral method is used to discretize *** surface diffusion and the nonlinear chemical potential terms are treated implicitly,while the expansive term is approximated by a third order explicit extrapolation formula for the sake of *** addition,a third order accurate Douglas-Dupont regularization term,in the form of−A_(0)△t^(2)△_( N)(φ^(n+1)−φ^(n)),is added in the numerical *** particular,the energy stability is carefully derived in a modified version,so that a uniform bound for the original energy functional is available,and a theoretical justification of the coefficient A becomes *** a result of this energy stability analysis,a uniform-in-time L_(N)^(6)bound of the numerical solution is *** also,the optimal rate convergence analysis and error estimate are provided,in the L_(△t)^(∞)(0,T;L_(N)^(2))∩L^(2)_(△ t)(0,T;H_(h)^(2))norm,with the help of the L_(N)^(6)bound for the numerical solution.A few numerical simulation results are presented to demonstrate the efficiency of the numerical scheme and the third order convergence.

关键词： Cahn-Hilliard equation third order backward differentiation formula unique solvability energy stability discrete L6 N estimate optimal rate convergence analysis

Benchmark Computations of the Phase Field Crystal and Functionalized Cahn-Hilliard Equations via Fully Implicit,Nesterov Accelerated Schemes

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Communications in Computational Physics 2023年第2期33卷 367-398页

作者： Jea-Hyun Park Abner J.Salgado steven m.wise Department of mathematics University of California Santa BarbaraCA 93106USA Department of mathematics University of Tennessee KnoxvilleTN 37996USA.

We introduce a fast solver for the phase field crystal(PFC)and functionalized Cahn-Hilliard(FCH)equations with periodic boundary conditions on a rectangular domain that features the preconditioned Nesterov’s accelerated gradient descent(PAGD)*** discretize these problems with a Fourier collocation method in space,and employ various second-order schemes in *** observe a significant speedup with this solver when compared to the preconditioned gradient descent(PGD)*** the PAGD solver,fully implicit,second-order-in-time schemes are not only feasible to solve the PFC and FCH equations,but also do so more efficiently than some semi-implicit schemes in some cases where accuracy issues are taken into *** computations of four different schemes for the PFC and FCH equations are conducted and the results indicate that,for the FCH experiments,the fully implicit schemes(midpoint rule and BDF2 equipped with the PAGD as a nonlinear time marching solver)perform better than their ImEX versions in terms of computational cost needed to achieve a certain *** the PFC,the results are not as conclusive as in the FCH experiments,which,we believe,is due to the fact that the nonlinearity in the PFC is milder nature compared to the FCH *** also discuss some practical matters in applying the *** introduce an averaged Newton preconditioner and a sweeping-friction strategy as heuristic ways to choose good preconditioner *** sweeping-friction strategy exhibits almost as good a performance as the case of the best manually tuned parameters.

关键词： Phase field crystal functionalized Cahn-Hilliard preconditioning Nesterov acceleration nonlinear solver.

A Second Order Accurate in Time, Energy Stable Finite Element Scheme for the Flory-Huggins-Cahn-Hilliard Equation

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Advances in Applied mathematics and mechanics 2022年第6期14卷 1477-1508页

作者： maoqin Yuan Wenbin Chen Cheng Wang steven m.wise Zhengru Zhang School of Science&Arts China University of Petroleum-Beijing at KaramayKaramayXinjiang 834000China Shanghai Key Laboratory of mathematics for Nonlinear Sciences School of Mathematical SciencesFudan UniversityShanghai 200433China Department of mathematics The University of MassachusettsNorth DartmouthMA 02747USA Department of mathematics The University of TennesseeKnoxvilleTN 37996USA School of mathematical Sciences Beijing Normal University and Laboratory of Mathematics and Complex SystemsMinistry of EducationBeijing 100875China

In this paper, we propose and analyze a second order accurate in time, masslumped mixed finite element scheme for the Cahn-Hilliard equation with a logarithmic Flory-Huggins energy potential. The standard backward differentiation formula (BDF)stencil is applied in the temporal discretization. In the chemical potential approximation,both the logarithmic singular terms and the surface diffusion term are treatedimplicitly, while the expansive term is explicitly updated via a second-order Adams-Bashforth extrapolation formula, following the idea of the convex-concave decompositionof the energy functional. In addition, an artificial Douglas-Dupont regularizationterm is added to ensure the energy dissipativity. In the spatial discretization, the masslumped finite element method is adopted. We provide a theoretical justification of theunique solvability of the mass lumped finite element scheme, using a piecewise linearelement. In particular, the positivity is always preserved for the logarithmic argumentsin the sense that the phase variable is always located between -1 and 1. In fact, thesingular nature of the implicit terms and the mass lumped approach play an essentialrole in the positivity preservation in the discrete setting. Subsequently, an unconditionalenergy stability is proven for the proposed numerical scheme. In addition, theconvergence analysis and error estimate of the numerical scheme are also *** numerical experiments are carried out to verify the theoretical properties.

关键词： Cahn-Hilliard equations Flory Huggins energy potential mass lumped FEm convexconcave decomposition energy stability positivity preserving.

A modified Crank-Nicolson Numerical Scheme for the Flory-Huggins Cahn-Hilliard model

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Communications in Computational Physics 2022年第1期31卷 60-93页

作者： Wenbin Chen Jianyu Jing Cheng Wang Xiaoming Wang steven m.wise Shanghai Key Laboratory for Contemporary Applied mathematics Fudan UniversityShanghai 200433P.R.China School of mathematical Sciences Fudan UniversityShanghai 200433P.R.China mathematics Department University of MassachusettsNorth DartmouthMA 02747USA International Center for mathematics and Department of mathematics and Guangdong Provincial Key Laboratory of Computational Science and Material Designand National Center for Applied Mathematics ShenzhenSouthern University of Science and TechnologyShenzhen 518055P.R.China mathematics Department University of TennesseeKnoxvilleTN 37996USA

In this paper we propose and analyze a second order accurate numericalscheme for the Cahn-Hilliard equation with logarithmic Flory Huggins energy potential. A modified Crank-Nicolson approximation is applied to the logarithmic nonlinear term, while the expansive term is updated by an explicit second order AdamsBashforth extrapolation, and an alternate temporal stencil is used for the surface diffusion term. A nonlinear artificial regularization term is added in the numerical scheme,which ensures the positivity-preserving property, i.e., the numerical value of the phasevariable is always between -1 and 1 at a point-wise level. Furthermore, an unconditional energy stability of the numerical scheme is derived, leveraging the special formof the logarithmic approximation term. In addition, an optimal rate convergence estimate is provided for the proposed numerical scheme, with the help of linearizedstability analysis. A few numerical results, including both the constant-mobility andsolution-dependent mobility flows, are presented to validate the robustness of the proposed numerical scheme.

关键词： Cahn-Hilliard equation Flory Huggins energy potential positivity preserving energy stability second order accuracy optimal rate convergence estimate

Clinical implications of interleukins-31, 32, and 33 in gastric cancer

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World Journal of Gastrointestinal Oncology 2022年第9期14卷 1808-1822页

作者： Qing-Hua Liu Ji-Wei Zhang Lei Xia steven G wise Brett David Hambly Kun Tao Shi-San Bao Department of Pathology Xuzhou Medical UniversityXuzhou 221004Jiangsu ProvinceChina Department of Surgery The Central Hospital of Songjiang DistrictShanghai Jiaotong UniversityShanghai 201699ShanghaiChina Faculty of medicine and Health School of Medical SciencesUniversity of SydneySydney 2006NSWAustralia Department of Pathology Tongren HospitalShanghai 200336China

BACKGROUND Gastric cancer(GC) is one of the most common malignancies in China with a high morbidity and *** To determine whether interleukin(IL)-31, IL-32, and IL-33 can be used as biomarkers for the detection of GC, via evaluating the correlations between their expression and clinicopathological parameters of GC *** Tissue array(n = 180) gastric specimens were utilised. IL-31, IL-32, and IL-33 expression in GC and non-GC tissues was detected immunohistochemically. The correlations between IL-31, IL-32, and IL-33 expression in GC and severity of clinicopathological parameters were evaluated. Survival curves were plotted using the Kaplan-meier method/Cox regression. Circulating IL-31, IL-32, and IL-33 were detected by *** We found that the expression levels of IL-31, IL-32, and IL-33 were all lower in GC than in adjacent non-GC gastric tissues(P m L, P male patients(P m I-II stage. Univariate/multivariate analysis revealed that IL-32 was an independent prognostic factor for GC in the T4 stage subgroup. Circulating IL-33 was significantly lower in GC patients at TNm stage IV than in healthy people(P may provide new insights into the roles of IL-31, IL-32, and IL-33 in the carcinogenesis of GC and demonstrate their relative usefulness as prognostic markers for GC. The underlying mechanism of IL-31, IL-32, and IL-33 actions in GC should be further explored.

关键词： Diagnosis and therapy Gastric cancer Immune cell interactions Interleukin-31 Interleukin32 Interleukin-33

Transport model for shale gas well leakage through the surrounding fractured zones of a longwall mine

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International Journal of mining Science and Technology 2020年第5期30卷 635-641页

作者： Kayode m.Ajayi steven J.Schatzel Centers for Disease Control and Prevention National Institute for Occupational Safety and HealthPittsburghPA 15236USA

The environmental risks associated with casing deformation in unconventional(shale)gas wells positioned in abutment pillars of longwall mines is a concern to many in the mining and gas well *** the recent interest in shale exploration and the proximity to longwall mining in Southwestern Pennsylvania,the risk to mine workers could be catastrophic as fractures in surrounding strata create pathways for transport of leaked ***,this research by the National Institute for Occupational Safety and Health(NIOSH)presents an analytical model of the gas transport through fractures in a low permeable *** derived equations are used to conduct parametric studies of specific transport conditions to understand the influence of stratum geology,fracture lengths,and the leaked gas properties on subsurface *** results indicated that the prediction that the subsurface gas flux decreases with an increase in fracture length is specifically for a non-gassy *** sub-transport trend could be significantly impacted by the stratum gas generation rate within specific fracture lengths,which emphasized the importance of the stratum *** findings provide new insights for improved understanding of subsurface gas transport to ensure mine safety.

关键词： Subsurface gas transport Longwall mining Shale gas well Analytical modeling Environmental risk Shale gas casing failure

Assessing the reproductive health of men with occupational exposures

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Asian Journal of Andrology 2014年第1期16卷 23-30页

作者： steven m Schrader Katherine L marlow Centers for Disease Control and Prevention National Institute for Occupational Safety and Health Division of Applied Research and Technology Cincinnati OH USA.

The earliest report linking environmental （occupational） exposure to adverse human male reproductive effects dates back to1775 when an English physician, Percival Pott, reported a high incidence of scrotal cancer in chimney sweeps. This observation led to safety regulations in the form of bathing requirements for these workers. The fact that male-mediated reproductive harm in humans may be a result of toxicant exposures did not become firmly established until relatively recently, when Lancranjan studied lead-exposed workers in Romania in 1975, and later in 1977, when Whorton examined the effects of dibromochloropropane （DBCP） on male workers in California. Since these discoveries, several additional human reproductive toxicants have been identified through the convergence of laboratory and observational findings. many research gaps remain, as the pool of potential human exposures with undetermined effects on male reproduction is vast. This review provides an overview of methods used to study the effects of exposures on male reproduction and their reproductive health, with a primary emphasis on the implementation and interpretation of human studies. Emphasis will be on occupational exposures, although much of the information is also useful in assessing environmental studies, occupational exposures are usually much higher and better defined.

关键词： accessory glands endocrine epidemiology semen sexual function sperm testis toxicology

Earth system history / steven m. Stanley. United States：

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Strigolactones redefine plant hormones

1999年

作者： steven m. Stanley.

来源：畅想之星图书光盘版（南... 畅想之星图书光盘版（南... 评论

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Science China(Life Sciences) 2016年第10期59卷 1083-1085页

作者： Lu Wang steven m.Smith School of Biological Sciences University of Tasmania Institute of Genetics and Developmental Biology Chinese Academy of sciences

A commonly accepted view of plant growth hormones is that their interaction with the cognate receptor protein is reversible, so that each hormone molecule can potentially interact multiple times with a receptor and so either amplify the hormone signal or maintain it over an extended period of time. The signal can be ＇cancelled＇ by degrading the hormone. Strigolactones present us with a potentially new paradigm. The receptor is a serine hydrolase-type protein which attacks the strigolactone resulting in covalent modi- fication of the receptor, while at the same time destroying the hormone. Strigolactone is apparently a one-use ＇dispos- able＇ hormone.

关键词：植物激素受体蛋白定义植物生长激素相互作用激素信号酸水解