DYNAMIC MODEL OF CROP GROWTH SYSTEM AND NUMERICAL SIMULATION OF CROP GROWTH PROCESS UNDER THE MULTI-ENVIRONMENT EXTERNAL FORCE ACTION

IntroductionAccordingtobiomechanics,thegrowthsystemoffarmlandcropistheartificiallyecologicalsystemthatchangestheenvironmentalresourcefactors(light,temperature,soilwaterandcarbondioxideetc .)intothefarmlandprimaryproductivity .Thesystemisactedbytheexternalforcevariablesofenvironment,inabroadsense,whichincludeslightintensity ,thetemperaturemaintenanceaction ,soilwater,andtheeffectiveuserateofnutrientsetc.Withinsystemisalsoactedbybiologicalvariableswhichincludethecropleafindex ,rootvolume ,biomas…     

《中国大百科全书·力学》在编写中

中国历来是巨型类书之乡,誉满四海.明清之时,类书更出类拔萃,搜罗广宏,分类辑录,引证详明,便于查览,诸子百家,兼收并蓄,各自立论,编者不褒贬偏弃.近代的科学文化,迅速发展,知识犹如汪洋大海,更兼层出不穷,若无适当的指南和工具书,广大读者常 ...     

Improving Our Life and Bettering Our Industry through Particuology

Everyonereadingthisjournalmayhavehisownvisionaboutparticles,sand,sugar,grains,flour,dust,fineandultrafinepowders,evennanocrystals,inourdailylifeandindustriesincludingthehightechnologies.Progressinhumancivilizationhasbeenchangingwithadvancesinprocessing,manufacturingandutilizationofparticlesofalldimensions.Numerousexamplescanbefoundinhistorytosupportsuchremark,e.g.,humanfoodsfromcoarseprimarygrainstofinepowders,andindustrialmaterialsfromthefinenessinsieveclassificationtothoseinmicronorevennanom…     

第七届全国周培源大学生力学竞赛报名总人数逾万

第七届全国周培源大学生力学竞赛报名工作圆满完成,在第六届报名总数9 736人的基础上,本届全国周培源大学生力学竞赛报名总人数共计11688人,遍布全国29个省、直辖市及自治区,各地具体报名人数如下:安徽省437人,北京市815人,重庆市270人,辽宁省543人,福建省316人,甘肃省219人,广东省242人,广西壮族自治区68人,贵州省64人,海南省17人,河北省229人,河南省527人,黑龙江省554人,湖北省642人,湖南省     

ADAPTIVE GENERALIZED PREDICTIVE CONTROL OF SWITCHED SYSTEMS

IntroductionSwitchedsystemsariseinvariedcontextsinmanufacturing ,communicationnetworks,autopilotdesign ,computersynchronization ,trafficcontrol,chemicalprocesses,andsoon .Switchedsystemsareaspecialclassofhybriddynamicalsystemswhichconsistofafamilyofsubsystemsandaswitchinglawspecifyingtheswitchingbetweenthesubsystems.Inrecentyears ,therehasbeenincreasinginterestinthecontrolofswitchedsystemsduetotheirsignificancebothintheoryandapplications.Generalizedpredictivecontrol (GPC) ,asoneofthemostpopu…     

Seasonal variations and sources of mass and chemical composition for PM10 aerosol in Hangzhou,China

Aerosol observation was conducted for four seasons from September 2001 to August 2002 at five sampling sites in Hangzhou, South China, on PM10 mass, 22 elements （Na, Mg, AI, Si, P, S, K, Ca, Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, As. Se, Br, Cd, Ba, and Pb）, 5 major ions （F^-, Cl^ , NO3^-, SO4^2- , and NH4^＋）, and organic and elemental carbon （OC and EC）, showing that PM10 mass ranged from 46.7 to 270.8 μg/m^3, with an annual average of 119.2 μg/m^3. Na, AI, Si, S, K, Ca, and Fe were the most abundant elements in PM10, most of S being in the form of SO4^2- . SO4^2-, NO3^-, and NH4^＋ were the major ions, which contributed to about 20% of the PM10 mass. The mean seasonal concentrations for SO4^2- , averaged over all sites, were found to be 18.0, 18.5, 24,Z and 21.4 μg/m^3, for spring, summer, autumn, and winter, respectively, while the corresponding loadings for NO3^- were 7.2, 4.7, 7.1, and 11.2 μg/m^3, and for NH4^＋ were 6.0, 5.9, 8.2, and 9.3 μg/m^3, in the form mostly of NH4NO3 in spring, autumn, and winter, and mostly of （NH4）2SO4 in summer. The low NO3^-/SO4^2- ratio found indicates coal combustion as the major source throughout the year. The mean annual concentrations of OC and EC in PM10 were found to be 21.4, and 4.1 μg/m^3, respectively. Material balance calculation indicated that fugitive dust, the secondary aerosol, and carbonaceous matter were the most abundant species in PM10 for the four seasons, as is characteristic for cities in South China.     

Seasonal variations and sources of mass and chemical composition for PM10 aerosol in Hangzhou,China

Aerosol observation was conducted for four seasons from September 2001 to August 2002 at five sampling sites in Hangzhou, South China, on PM10 mass, 22 elements (Na, Mg, Al, Si, P, S, K, Ca, Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, As, Se, Br, Cd, Ba, and Pb), 5 major ions (F-, Cl-, NO3-, SO42-, and NH4+), and organic and elemental carbon (OC and EC), showing that PM10 mass ranged from 46.7 to 270.8 μg/m3, with an annual average of 119.2 μg/m3. Na, AI, Si, S. K, Ca, and Fe were the most abundant elements in PM10, most ors being in the form of SO42-. SO42-, NO4-, and NH4+ were the major ions, which contributed to about 20%; of the PM10 mass. The mean seasonal concentrations for SO42- , averaged over all sites, were found to be 18.0, 18.5, 24.Z and 21.4 μg/m3. for spring, summer, autumn, and winter, respectively, while the corresponding Ioadings for NO3- were 72, 4.7, 7.1, and 11.2μg/m3. and for NH4+ were 6.0, 5.9, 8.2. and 9.3 μg/m3, in the form mostly of NH4NO3 in spring, autumn, and winter, and mostly of (NH4)2SO4 in summer. The low NO3-/SO42- ratio found indicates coal combustion as the major source throughout the year. The mean annual concentrations of OC and EC in PM10 were found to be 21A, and 4.1 μg/m3, respectively. Material balance calculation indicated that fugitive dust, the secondary aerosol, and carbonaceous matter were the most abundant species in PM10 for the four seasons, as is characteristic for cities in South China.     

ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR NONLINEAR SYSTEM WITH MULTIPLE DELAYS

IntroductionInthispaper,westudyT_periodicsolutionsofthefollowingnonlinearsystemwithmultipledelays x(t) =f(t,x(t) ,x(t-τ1(t) ) ,… ,x(t -τm(t) ) ) ,(1 )wherex(t) ∈C(R ,R) ,fiscontinuous,f(t+T ,·) =f(t,·) ,τi(t) (i=1 ,2 ,… ,m)arecontinuousperiodicfunctionsofperiodT .AlemmaisintroducedfordiscussingtheexistenceofT_periodicsolutionofsystem (1 ) .LetXbeaBanachSpace ,considerthefollowingoperatorequation :Lx =λNx　　 (λ∈ [0 ,1 ] ) ,whereL :DomL∩X→Xisalinearoperator,λ∈ [0 ,1 ]isapa…     

半硬半软岩隧道塌方的力学特性及处理方法分析

由于蛟岭隧道出口横断面一半为硬岩,结构完整,而另一半为软岩,为风化岩层,且较为破碎,所以在隧道开挖时,硬岩一侧刚度较大,变形较小,自稳能力大;软岩一侧与之相反,遇水软化,流变性明显,所以在软硬岩交界面处,产生滑移,导致塌方,从而在软岩一侧采取了地表加固和掌子面管棚注浆的处理,形成了与硬岩接近的强度,使隧道周围形成一个承载环,并对处理段进行了监测,监测数据分析表明处理后迅速达到稳定。     

THE FRACTAL STRUCTURE OF ATTRACTOR FOR THE GENERALIZEDKURAMOTO-SIVASHINSKY EQUATIONS

I.IntroductionSincethereexistspectralbarriersandspectralgapconditions,theexistenceofaninertialmanifoldformanynonlineardissipativeevolutionequationsisstillamystery.Recently,Edenetal[5]havediscoveredthatfornonlinearsemigroup,definedbynonlineardissipativeevolutionequationsincludingZDNavier-Stokesequations,thereexistsatinliefractaldimensionalinertialsetwhichmayberepresentedbyaunionoffractillsetsandattractor,ifitisLipschitzcontinuousandissqueezingonacompacti,ositiveinvariantset.Ontileotherhand,S…     

三维势流场的比例边界有限元求解方法

比例边界有限元法(SBFEM)是线性偏微分方程的一种新的数值求解方法。该方法只对计算域边界利用Galerkin方法进行数值离散,相对于有限元方法(FEM)减少了一个空间坐标的维数,而在减少的空间坐标方向利用解析方法进行求解;相对于边界元法(BEM),比例边界有限元方法不需要基本解,避免了奇异积分的计算,所以它结合了有限元和边界元方法的优点。本文建立了利用比例边界有限元法求解三维Laplace方程的数值模型并用于计算三维物体周围的水流场,将计算结果与解析解和边界元方法进行了对比,结果表明此方法可以很好地模拟水流场,且具有较高的计算精度。     

Analysis of a two-grid method for semiconductor device problem

The mathematical model of a semiconductor device is governed by a system of quasi-linear partial differential equations.The electric potential equation is approximated by a mixed finite element method,and the concentration equations are approximated by a standard Galerkin method.We estimate the error of the numerical solutions in the sense of the Lqnorm.To linearize the full discrete scheme of the problem,we present an efficient two-grid method based on the idea of Newton iteration.The main procedures are to solve the small scaled nonlinear equations on the coarse grid and then deal with the linear equations on the fine grid.Error estimation for the two-grid solutions is analyzed in detail.It is shown that this method still achieves asymptotically optimal approximations as long as a mesh size satisfies H=O(h^1/2).Numerical experiments are given to illustrate the efficiency of the two-grid method.     

Two-grid methods for semi-linear elliptic interface problems by immersed finite element methods

In this paper, two-grid immersed finite element(IFE) algorithms are proposed and analyzed for semi-linear interface problems with discontinuous diffusion coefficients in two dimension. Because of the advantages of finite element(FE) formulation and the simple structure of Cartesian grids, the IFE discretization is used in this paper. Two-grid schemes are formulated to linearize the FE equations. It is theoretically and numerically illustrated that the coarse space can be selected as coarse asH= O(h~(1/4))(orH=O(h~(1/8))), and the asymptotically optimal approximation can be achieved as the nonlinear schemes. As a result, we can settle a great majority of nonlinear equations as easy as linearized problems. In order to estimate the present two-grid algorithms, we derive the optimal error estimates of the IFE solution in theL pnorm. Numerical experiments are given to verify the theorems and indicate that the present two-grid algorithms can greatly improve the computing efficiency.     

The Dual-Reciprocity Boundary Element Analysis for Hydraulically Fractured Shale Gas Reservoirs Considering Diffusion and Sorption Kinetics

This work presents a new application of boundary element method (BEM) to model fluid transport in unconventional shale gas reservoirs with discrete hydraulic fractures considering diffusion, sorption kinetics and sorbed-phase surface diffusion. The fluid transport model consists of two governing partial differential equations (PDEs) written in terms of effective diffusivities for free and sorbed gases, respectively. Boundary integral formulations are analytically derived using the fundamental solution of the Laplace equation for the governing PDEs and Green’s second identity. The domain integrals arising due to the time-dependent function and nonlinear terms are transformed into boundary integrals employing the dual-reciprocity method. This transformation retains the domain-integral-free, boundary-integral-only character of standard BEM approaches. In the proposed solution, the free- and sorbed-gas flow in the shale matrix is solved simultaneously after coupling the fracture flow equation of free gas. Well production performance under the effect of relaxation phenomenon due to delayed responses of sorbed gas under nonequilibrium sorption condition is rigorously captured by imposing the zero-flux condition at fracture–matrix interface for the sorbed-gas transport equation. The validity of proposed solution is verified using several case studies through comparison against a commercial finite-element numerical simulator.

     

加性非平稳激励下结构速度响应的FPK方程降维

结构在随机激励下的非线性响应分析是具有高度挑战性的困难问题. 对于白噪声或过滤白噪声激励,求解FPK方程将获得结构响应 的精确解. 遗憾的是,对于非线性多自由度系统,FPK方程难以直接求解. 事实上,其数值解法严重受限于方程维度,而解析求解 则仅适用于少数特定的系统,且多是稳态解. 因此,将FPK方程进行降维,是求解高维随机动力响应分析问题的重要途径. 本文针 对幅值调制的加性白噪声激励下多自由度非线性结构的非平稳随机响应分析问题,将联合概率密度函数满足的高维FPK方程进行降 维. 针对结构速度响应概率密度函数求解,通过引入等价漂移系数,原FPK方程可转化为一维FPK型方程. 建议了构造等价漂移系数 的条件均值函数方法. 进而,采用路径积分方法求解降维FPK型方程,得到速度概率密度函数的数值解答. 结合单自由度Rayleigh 振子、十层线性剪切型框架和非线性剪切型框架结构在幅值调制的加性白噪声激励下的非平稳速度响应求解,讨论了本文方法的精 度和效率,验证了其有效性.      

Simulation of the Action of a Permeable Barrier on an Ideal Incompressible Channel Flow

Plane ideal incompressible flow in a rectangular channel partitioned by a thin permeable barrier (lattice) is considered. In flowing through the lattice the stream suddenly (jumpwise) changes direction and loses energy. The flow is assumed to be vortical; the vorticity is discontinuous on the lattice. A mathematical formulation of the problem for the stream function is proposed in the form of a nonlinear elliptic equation with coefficients discontinuous on the lattice line. A numerical solution is constructed using the finite-element iteration method. The results of the numerical simulation show how the flow velocity profile in the channel can be controlled by means of permeable barriers.     

A non‐iterative implicit algorithm for the solution of advection–diffusion equation on a sphere

A numerical algorithm for the solution of advection–diffusion equation on the surface of a sphere is suggested. The velocity field on a sphere is assumed to be known and non‐divergent. The discretization of advection–diffusion equation in space is carried out with the help of the finite volume method, and the Gauss theorem is applied to each grid cell. For the discretization in time, the symmetrized double‐cycle componentwise splitting method and the Crank–Nicolson scheme are used. The numerical scheme is of second order approximation in space and time, correctly describes the balance of mass of substance in the forced and dissipative discrete system and is unconditionally stable. In the absence of external forcing and dissipation, the total mass and L₂‐norm of solution of discrete system is conserved in time. The one‐dimensional periodic problems arising at splitting in the longitudinal direction are solved with Sherman–Morrison's formula and Thomas's algorithm. The one‐dimensional problems arising at splitting in the latitudinal direction are solved by the bordering method that requires a prior determination of the solution at the poles. The resulting linear systems have tridiagonal matrices and are solved by Thomas's algorithm. The suggested method is direct (without iterations) and rapid in realization. It can also be applied to linear and nonlinear diffusion problems, some elliptic problems and adjoint advection–diffusion problems on a sphere. Copyright © 2015 John Wiley & Sons, Ltd.     

On Vertical Diffusion of Gases in a Horizontal Reservoir

Exact and approximate solutions to vertical diffusion in gravity-stable, ideal gas mixtures in gas reservoirs, depleted oil reservoirs, or drained aquifers are presented, and characteristic times of diffusion are obtained. Our solutions also can be used to test numerical simulators that model diffusion after gas injection. First, we consider isothermal, countercurrent vertical diffusion of carbon dioxide and methane in a horizontally homogeneous reservoir. Initially, the bottom part of the reservoir, with no flow boundaries at the top and bottom, is filled with CO₂ and the upper part with CH₄. At time equal zero, the two gases begin to diffuse. We obtain the exact solution to the initial and boundary-value problem using Fourier series method. For the same problem, we also obtain an approximate solution using the integrated mass balance method. The latter solution has a particularly simple structure, provides a good approximation and retains the important features of the exact solution. Its simplicity allows one to perform calculations that are difficult and non-transparent with the Fourier series method. It also can be used to test numerical algorithms. Furthermore, we consider diffusion of CO₂ with partitioning into connate water. We show that at reservoir pressures the CO₂ retardation by water cannot be neglected. The diffusion-retardation problem is modelled by a non-linear diffusion equation whose self-similar solution is obtained. Finally, we obtain a self-similar solution to a nonlinear diffusion problem. This solution is a good approximation at early times, before the diffusing gases reach considerable concentrations at the top and bottom boundaries of the reservoir.     

Diffusion-based coarse graining in hybrid continuum–discrete solvers: Theoretical formulation and a priori tests

Coarse graining is an important ingredient in many multi-scale continuum–discrete solvers such as CFD–DEM (computational fluid dynamics–discrete element method) solvers for dense particle-laden flows. Although CFD–DEM solvers have become a mature technique that is widely used in multiphase flow research and industrial flow simulations, a flexible and easy-to-implement coarse graining algorithm that can work with CFD solvers of arbitrary meshes is still lacking. In this work, we proposed a new coarse graining algorithm for continuum–discrete solvers for dense particle-laden flows based on solving a transient diffusion equation. Via theoretical analysis we demonstrated that the proposed method is equivalent to the statistical kernel method with a Gaussian kernel, but the current method is much more straightforward to implement in CFD–DEM solvers. A priori numerical tests were performed to obtain the solid volume fraction fields based on given particle distributions, the results obtained by using the proposed algorithm were compared with those from other coarse graining methods in the literature (e.g., the particle centroid method, the divided particle volume method, and the two-grid formulation). The numerical tests demonstrated that the proposed coarse graining procedure based on solving diffusion equations is theoretically sound, easy to implement and parallelize in general CFD solvers, and has improved mesh-convergence characteristics compared with existing coarse graining methods. The diffusion-based coarse graining method has been implemented into a CFD–DEM solver, the results of which are presented in a separate work.     

A monotone finite volume scheme for advection–diffusion equations on distorted meshes

A new monotone finite volume method with second‐order accuracy is presented for the steady‐state advection–diffusion equation. The method uses a nonlinear approximation for both diffusive and advective fluxes that guarantee the positivity of the numerical solution. The approximation of the diffusive flux is based on nonlinear two‐point approximation, and the approximation of the advective flux is based on the second‐order upwind method with proper slope limiter. The second‐order convergence rate for concentration and the monotonicity of the nonlinear finite volume method are verified with numerical experiments. Copyright © 2011 John Wiley & Sons, Ltd.