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International journal of Biomathematics 2019年第1期12卷 1-31页

作者： R.Ishwariya j.j.h.miller S.Valarmathi Department of Mathematics Bishop Heber College TiruchirappalliTamil NaduIndia Institute for Numerical Computation and A nalysis Dublin Ireland

In this paper,a class of linear parabolic systems of singularly perturbed second-order differential equations of reaction-diffusion type with initial and Robin boundary conditions is *** components of the solution u→ of this system are smooth,whereas the components of αu→/αx exhibit parabolic boundary layers.A numerical method composed of a classical finite difference scheme on a piecewise uniform Shishkin mesh is *** method is proved to be first-order convergent in time and essentially first-order convergent in the space variable in the maximum norm uniformly in the perturbation parameters.

关键词： Singular perturbations boundary layers linear parabolic differential equations Robin boundary conditions finite difference schemes Shishkin meshes parameter uniform convergence

AN ACCURATE NUMERICAL SOLUTION OF A TWO DIMENSIONAL hEAT TRANSFER PROBLEM WITh A PARABOLIC BOUNDARY LAYER

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journal of Computational Mathematics 1998年第1期16卷 27-39页

作者： C.Clavero j.j.h.miller E.O'Riordan G.I.Shishkin Universidad de Zaragoza 西班牙 Trinity College 爱尔兰 Dublin City University 爱尔兰 Institute of Mathematics and Mechanics 俄罗斯

A singularly perturbed linear convection-diffusion problem for heat transfer in two dimensions with a parabolic boundary layer is solved numerically The numerical method consists of a special piecewise uniform mesh condensing in a neighbourhood of the parabolic layer and a standard finite difference operator satisfying a discrete maximum principle. The numerical computations demonstrate numerically that the method is epsilon-uniform in the sense that the Fate of convergence and error constant of the method are independent of the singular perturbation parameter epsilon. This means that no matter how small the singular perturbation parameter epsilon is, the numerical method produces solutions with guaranteed accuracy depending solely on the number of mesh points used.

关键词： linear convection-diffusion parabolic layer piecewise uniform mesh finite difference

Analytic and Experimental Studies of the Errors in Numerical Methods for the Valuation of Options

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Numerical Mathematics(Theory,Methods and Applications) 2008年第2期1卷 150-164页

作者： P.Lin j.j.h.miller G.I.Shishkin Department of Mathematics National University of Singapore Department of Mathematics Trinity College Dublin Institute for Mathematics and Mechanics Russian Academy of Science Ekaterinburg

The value of a European option satisfies the Black-Scholes equation with appropriately specified final and boundary *** transform the problem to an initial boundary value problem in dimensionless *** are two parameters in the coefficients of the resulting linear parabolic partial differential *** a range of values of these parameters,the solution of the problem has a boundary or an initial *** initial function has a discontinuity in the first-order derivative,which leads to the appearance of an interior *** construct analytically the asymptotic solution of the equation in a finite *** on the asymptotic solution we can determine the size of the artificial boundary such that the required solution in a finite domain in x and at the final time is not affected by the ***,we study computationally the behaviour in the maximum norm of the errors in numerical solutions in cases such that one of the parameters varies from finite (or pretty large) to small values,while the other parameter is fixed and takes either finite (or pretty large) or small values. Crank-Nicolson explicit and implicit schemes using centered or upwind approximations to the derivative are *** present numerical computations,which determine experimentally the parameter-uniform rates of *** note that this rate is rather weak,due probably to mixed sources of error such as initial and boundary layers and the discontinuity in the derivative of the solution.

关键词： Options singularities finite difference methods monotone robust method

A functional tacrolimus-releasing nerve wrap for enhancing nerve regeneration following surgical nerve repair

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Neural Regeneration Research 2025年第1期20卷 291-304页

作者： Simeon C.Daeschler Katelyn j.W.So Konstantin Feinberg Marina Manoraj jenny Cheung jennifer Zhang Kaveh Mirmoeini jPaul Santerre Tessa Gordon Gregory hBorschel SickKids Research Institute Neuroscience and Mental Health ProgramTorontoONCanada Institute of Biomaterials and Biomedical Engineering University of TorontoTorontoONCanada Indiana University School of Medicine IndianapolisINUSA Division of Plastic and Reconstructive Surgery the Hospital for Sick ChildrenTorontoONCanada Translational Biology and Engineering Program Ted Rogers Centre for Heart ResearchInstitute of Biomedical EngineeringFaculty of DentistryUniversity of TorontoTorontoONCanada

Axonal regeneration following surgical nerve repair is slow and often incomplete,resulting in poor functional recovery which sometimes contributes to lifelong ***,there are no FDA-approved therapies available to promote nerve *** accelerates axonal regeneration,but systemic side effects presently outweigh its potential benefits for peripheral nerve *** authors describe herein a biodegradable polyurethane-based drug delivery system for the sustained local release of tacrolimus at the nerve repair site,with suitable properties for scalable production and clinical application,aiming to promote nerve regeneration and functional recovery with minimal systemic drug *** is encapsulated into co-axially electrospun polycarbonate-urethane nanofibers to generate an implantable nerve wrap that releases therapeutic doses of bioactive tacrolimus over 31 *** and drug loading are adjustable for applications in small and large caliber nerves,and the wrap degrades within 120 days into biocompatible *** released from the nerve wrap promotes axon elongation in vitro and accelerates nerve regeneration and functional recovery in preclinical nerve repair models while off-target systemic drug exposure is reduced by 80%compared with systemic *** its surgical suitability and preclinical efficacy and safety,this system may provide a readily translatable approach to support axonal regeneration and recovery in patients undergoing nerve surgery.

关键词： biodegradable local drug delivery nerve injury nerve regeneration nerve wrap tacrolimus

A PARAMETER-UNIFORM TAILORED FINITE POINT METhOD FOR SINGULARLY PERTURBED LINEAR ODE SYSTEMS＊

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journal of Computational Mathematics 2013年第4期31卷 422-438页

作者： houde han j.j.h. miller Min Tang Department of Mathematical Sciences Tsinghua University Beijing 100084 China Department of Mathematics Trinity College Dublin 2 Ireland Key Laboratory of Scientific and Engineering Computing Department of Mathematics and Institute of Natural Sciences Shanghai Jiao Tong University Shanghai 200240 China

In scientific applications from plasma to chemical kinetics, a wide range of temporal scales can present in a system of differential equations. A major difficulty is encountered due to the stiffness of the system and it is required to develop fast numerical schemes that are able to access previously unattainable parameter regimes. In this work, we consider an initial-final value problem for a multi-scale singularly perturbed system of linear ordi- nary differential equations with discontinuous coefficients. We construct a tailored finite point method, which yields approximate solutions that converge in the maximum norm, uniformly with respect to the singular perturbation parameters, to the exact solution. A parameter-uniform error estimate in the maximum norm is also proved. The results of numerical experiments, that support the theoretical results, are reported.

关键词： Tailored finite point method Parameter uniform Singular perturbation ODEsystem.

On an isotropic porous solid cylinder:the analytical solution and sensitivity analysis of the pressure

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Applied Mathematics and Mechanics(English Edition) 2024年第9期45卷 1499-1522页

作者： h.ASGhARI L.miller R.PENTA j.MERODIO Departamento de Matematica Aplicada a las TIC ETS de Ingenieria de Sistemas InformaticosUniversidad Politecnica de MadridMadrid 28031Spain School of Mathematics and Statistics University of GlasgowGlasgow G128QQU.K.

Within this work,we perform a sensitivity analysis to determine the influence of the material input parameters on the pressure in an isotropic porous solid *** provide a step-by-step guide to obtain the analytical solution for a porous isotropic elastic cylinder in terms of the pressure,stresses,and elastic *** obtain the solution by performing a Laplace transform on the governing equations,which are those of Biot's poroelasticity in cylindrical polar *** enforce radial boundary conditions and obtain the solution in the Laplace transformed domain before reverting back to the time *** sensitivity analysis is then carried out,considering only the derived pressure *** analysis finds that the time t,Biot's modulus M,and Poisson's ratio ν have the highest influence on the pressure whereas the initial value of pressure P_(0) plays a very little role.

关键词： sensitivity analysis Laplace transform cylindrical polar coordinate Biot's modulus cylinder

Dynamics and mechanisms of permethrin resistance in a field population of the horn fly, haematobia irritans irritans

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Insect Science 2009年第2期16卷 175-184页

作者： Andrew Y. Li Kimberly h. Lohmeyer j. Allen miller USDA ARS Knipling-Bushland US Livestock Insects Research Laboratory 2700 Fredericksburg Road Kerrville TX 78028 USA

A study was conducted at the Pressler ranch, near Kerrville, Texas, USA between 2002 and 2006 to determine the dynamics and mechanisms of resistance to permethrin in a field population of the horn fly, haematobia irritans irritans （L.）. Changes of resistance to pyrethroid insecticide associated with use of a pour-on formulation of cyfluthrin in 2002 and use of diazinon ear tags in subsequent years were studied using a filter paper bioassay technique and a polymerase chain reaction assay that detects two sodium channel mutations, kdr and super-kdr resistance alleles. A maximum of 294-fold resistance to permethrin was observed in the summer of 2002. A significant decrease in the resistance level was observed in spring 2003, and resistance continued to decline after animals were treated with diazinon ear tags. In response to pyrethroid treatments, the allelic kdr and super-kdr frequency increased from 56.3% to 93.8% and from 7.5% to 43.8%, respectively in 2002, and decreased significantly in 2003 when the pyrethroid insecticide was no longer used to treat animals. Females were found to have a higher allelic super-kdr frequency than males in 2002, while no difference was detected between males and females in the allelic kdr frequency. There was a significant positive correlation between frequencies of the sodium channel mutations and levels ofpermethrin resistance, suggesting that the sodium channel mutations, kdr and super-kdr, are the major mechanisms of resistance to pyrethroids in this horn fly population. Results of synergist bioassays also indicated possible contributions of two metabolic detoxification mechanisms, the mixed function oxidases （MFO） and glutathione S-trans- ferases （GST）. Compared to a horn fly infestation of an untreated herd, treatments with the pyrethroid pour-on formulation failed to control horn flies at the Pressler ranch in 2002. Sustained control of horn flies was achieved with the use of diazinon ear tags in 2003 and subsequent years.

关键词： efficacy horn fly insecticide resistance PCR permethrin pyrethroids

Plasma density measurement and downstream etching of silicon and silicon oxide in Ar/NF3 mixture remote plasma source

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Plasma Science and Technology 2019年第6期21卷 52-57页

作者： h j YEOM D h ChOI Y S LEE j h KIM D j SEONG S j YOU h C LEE Korea Research Institute of Standards and Science(KRISS) Daejeon 34113 Republic of Korea Department of Physics Chungnam National University Daejeon 34134 Republic of Korea

In this study,plasma density measurements were performed near the plume region of the remote plasma source (RPS) in Ar/NF3 gas mixtures using a microwave cutoff *** measured plasma density is in the range of 1010-1011 cm-3 in the discharge conditions with RPS powers of 2-4 kW and gas pressures of 0.87-4 *** plasma density decreased with increasing gas pressures and RPS powers under various Ar/NF3 mixing *** decrease in the plasma density measured at the fixed measurement position (plume region) can be understood by the reduction of the electron energy relaxation length with increases in the gas pressures and mixing ratio of NF3/(Ar/NF3).We also performed downstream etching of silicon and silicon oxide films in this *** etch rate of the silicon films significantly increases while the silicon oxide is slightly etched with the gas pressures and *** was also found that the etch rate strongly depends on the wafer position on the processing chamber electrode,and that the etch selectivity reached 96-131 in the discharge conditions of RF powers (3730-4180 W) and gas pressures (3.6-4 Torr).

关键词： remote plasma source electron density cutoff probe downstream etch

Optimal use of mobile cooling units in a deep-level gold mine

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International journal of Mining Science and Technology 2020年第4期30卷 547-553页

作者： h.j.van Staden j.F.van Rensburg h.j.Groenewald Centre for Research and Continued Engineering Development North-West UniversityPretoria 0081South Africa

The South African gold mining sector remains a significant contributor to the country’s *** several challenges that hinder the realisation of South Africa’s full mineral potential,the sector’s sustainability and profitability can be enhanced through implementing operational improvement *** cooling units(MCUs)were identified as a potential focus area for operational *** are used as tertiary or in-stope cooling in hot underground *** this paper,a method was presented to characterise the performance of existing MCUs based on three key performance indicators(KPIs),namely,the wet-bulb temperature ratio(WTR),efficiency and *** strategies were then elected and implemented based on these *** implementation of this method in a South African gold mine attained a reduction in pumped water volumes,reduced operating costs through electricity cost savings and improvements in underground ventilation air temperatures.

关键词： Mobile cooling units Optimisation Mine cooling performance Electricity cost savings Spot cooling

A structural topological optimization method for multi-displacement constraints and any initial topology configuration

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Acta Mechanica Sinica 2010年第5期26卷 735-744页

作者： j. h. Rong j. h. Yi School of Automotive and Mechanical Engineering Changsha University of Science and TechnologyChangsha 410076 China

In density-based topological design, one expects that the final result consists of elements either black （solid material） or white （void）, without any grey areas. Moreover, one also expects that the optimal topology can be obtained by starting from any initial topology configuration. An improved structural topological optimization method for multidisplacement constraints is proposed in this paper. In the proposed method, the whole optimization process is divided into two optimization adjustment phases and a phase transferring step. Firstly, an optimization model is built to deal with the varied displacement limits, design space adjustments, and reasonable relations between the element stiffness matrix and mass and its element topology variable. Secondly, a procedure is proposed to solve the optimization problem formulated in the first optimization adjustment phase, by starting with a small design space and advancing to a larger deign space. The design space adjustments are automatic when the design domain needs expansions, in which the convergence of the proposed method will not be affected. The final topology obtained by the proposed procedure in the first optimization phase, can approach to the vicinity of the optimum topology. Then, a heuristic algorithm is given to improve the efficiency and make the designed structural topology black/white in both the phase transferring step and the second optimization adjustment phase. And the optimum topology can finally be obtained by the second phase optimization adjustments. Two examples are presented to show that the topologies obtained by the proposed method are of very good 0/1 design distribution property, and the computational efficiency is enhanced by reducing the element number of the design structural finite model during two optimization adjustment phases. And the examples also show that this method is robust and practicable.

关键词： Topological optimization Displacement constraint Continuum structure Design space adjustment Rational approximation material model