THE INTERIOR LAYER FOR A NONLINEAR SINGULARLY PERTURBED DIFFERENTIAL-DIFFERENCE EQUATION

In this article, the interior layer for a second order nonlinear singularly perturbed differential-difference equation is considered. Using the methods of boundary function and fractional steps, we construct the formula of asymptotic expansion and point out that the boundary layer at t = 0 has a great influence upon the interior layer at t = a. At the same time, on the basis of differential inequality techniques, the existence of the smooth solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of our result. The result of this article is new and it complements the previously known ones.

THE INTERIOR LAYER PHENOMENA FOR A CLASS OF SINGULARLY PERTURBED DELAY-DIFFERENTIAL EQUATIONS

In this article, we study a kind of vector singularly perturbed delay-amerenum equation. Using boundary layer function method and geometric analysis skill, the asymptotic expression of the system is constructed and the uniform validity of asymptotic solution is also proved.

A CLASS OF STRONGLY NONLINEAR SINGULARLY PERTURBED INTERIOR LAYER PROBLEMS

In this paper, a class of strongly nonlinear singularly perturbed interior layer problems are considered by the theory of differential inequalities and the corrective theory of interior layer. The existence of solution is proved and the asymptotic behavior of solution for the boundary value problems are studied. And the satisfying result is obtained.

THE INTERIOR LAYER SOLUTION TO NONLOCAL REACTION DIFFUSION EQUATIONS

An initial boundary value problem of semilinear nonlocal reaction diffusion equations is considered.Under some suitable conditions,using the asymptotic theory,the existence and asymptotic behavior of the interior layer solution to the initial boundary value problem are studied.

High Order Compact Difference Scheme and Multigrid Method for 2D Elliptic Problems with Variable Coefficients and Interior/Boundary Layers on Nonuniform Grids

In this paper, a high order compact difference scheme and a multigrid method are proposed for solving two-dimensional (2D) elliptic problems with variable coefficients and interior/boundary layers on nonuniform grids. Firstly, the original equation is transformed from the physical domain (with a nonuniform mesh) to the computational domain (with a uniform mesh) by using a coordinate transformation. Then, a fourth order compact difference scheme is proposed to solve the transformed elliptic equation on uniform girds. After that, a multigrid method is employed to solve the linear algebraic system arising from the difference equation. At last, the numerical experiments on some elliptic problems with interior/boundary layers are conducted to show high accuracy and high efficiency of the present method.

Persistent mixing bursts in the equatorial Pacific thermocline induced by persistent equatorial waves

A recent study by Liu et al.(2020)suggested that due to the saturation of equatorially trapped planetary waves with different dynamical types,temporal periods,meridional and baroclinic modes,complex layer structures of vertical velocity shear and hence turbulent mixing could frequently occur in the thermocline of the eastern equatorial Pacific.We investigated the occurrence of the interior turbulent mixing as indicated by shear instabilities,above the Equatorial Undercurrent(EUC)core at three equatorial sites along 140°W,170°W,and 165°E,respectively,based mainly on data from the Tropical Atmosphere and Ocean(TAO)mooring array.We found that turbulent mixing bursts persisted in the thermocline of all three sites.Specifically,the interior turbulent mixing layers(ITMLs)could occur in probability of approximately 68%,53%,and 48%at the three sites,respectively.The overall occurrence probability shows obvious and similar biannual variations at 140°W and 170°W,which is higher in boreal from late summer to winter and lower in spring.Vertically,the ITMLs are primarily located above the EUC core and prevail in deeper(shallower)layers from late summer to winter(spring).Most ITMLs(70%)lasted for hours to 3 days,and a few of them(15%)for more than 7 days.The thicknesses of ITMLs were concentrated between 15 and 55 m.At 165°E,the vertical distribution of ITML occurrence probability was different from that at 140°W and 170°W,as it did not show a preference for depths;the durations of ITMLs are short(also from hours to several days)and their thicknesses were between 5 and 25 m.These properties,particularly the high occurrence probability,and short durations demonstrated the persistence of thermocline mixing in the western to eastern equatorial Pacific thermocline and confirmed the generation mechanism by persistent equatorial waves as well.

挂具球形设计在塑料电镀中的应用

随着汽车行业的蓬勃发展,汽车客户对于汽车内外饰件提出了越来越高的要求。为了解决塑料电镀整槽零件的镀层厚度均匀性不一致的问题,本文进行了多次实验设计并开展了相关测试。结果表明:通过对挂具进行合理设计,在挂具上相对电流密度不同的位置,设计长短不同的挂钩,电流密度低的位置,挂钩长,电流密度高的位置,挂钩短,即将挂具整体外观设计为半球面形状,可以确保挂具上不同位置的零件上的电流密度分布大致相同,从而使得不同位置上零件的镀层厚度更为均匀。该设计有效的提高了电镀产品的合格率,既不增加电镀成本,又可满足主流主机厂对汽车零部件质量更高的要求。

不同施肥措施对太子参产量与品质的影响

【目的】探明不同施肥措施对太子参产量和品质的影响,为太子参的合理施肥提供科学依据。【方法】于2019—2021年通过田间定位试验,研究不同施肥措施〔施单层复合肥(T_(1))、施单层有机肥+复合肥(T_(2))、施双层复合肥(T_(3))、施双层有机肥+复合肥(T_(4))〕处理太子参的药材产量、生物总量、单株块根数、块根单重、块根长度及块根最大直径的变化,太子参药材优形指数和等级得率,折干率、水分、总灰分及浸出物的含量,进而分析双层施肥技术对太子参生长的影响。【结果】不同施肥措施对太子参产量和品质的影响不同,T_(2)和T_(4)对太子参生物总量(23.1 g/株、24.7 g/株)、折干率(37.7%、38.9%)和浸出物(37.1%、37.7%)影响显著,分别较T_(1)和T_(3)的生物总量显著提高17.9%、9.5%和26.0%、17.1%,折干率显著提高7.4%、6.5%和10.8%、9.9%,浸出物显著提高5.7%、5.1%和7.4%、6.8%;双层施肥的T_(3)和T_(4)对太子参产量(601.8 kg/667m^(2)、688.4 kg/667m^(2))、单株块根数(17.5块/株、18.1块/株)、块根长度(4.7 cm、4.6 cm)、块根最大直径(2.9 mm、3.2 mm)、优形指数(6.1、6.9)及一等品得率(11.2%、15.7%)影响显著,产量分别较T_(1)和T_(2)增产9.9%、0.8%和25.7%、15.3%,单株块根数增加18.2%、8.7%和22.3%、12.4%,块根长度降低9.6%、11.5%和7.8%、9.8%,块根最大直径增加26.1%、39.1%和16.0%、28.0%,优形指数增加38.6%、24.5%和56.8%、40.8%,一等品得率增加25.8%、76.4%和17.9%、65.3%。双层施肥较常规施肥显著降低太子参上层块根的长宽比、统货得率,增加上层块根一等品得率、折干率与浸出物,使上下层块根在形态及品质上更趋于一致。【结论】双层施肥有助于提高太子参产量及优品率,配施有机肥与复合肥则有助于提高太子参内在品质,采用双层施肥技术配施有机肥与复合肥适宜于太子参种植生产。

一类具有非单调内层性态的半线性边值问题(英文)

本文运用内层校正方法和微分不等式理论研究了一类半线性边值问题.在一定的条件下,我们获得了两类非单调内层性态:尖层性态或非单调过渡层性态的解的一致有效复合展开式.

两参数非线性奇摄动燃烧问题的渐近解

讨论了一类两参数奇摄动燃烧Dirichlet边值问题.利用伸长变量,构造了问题解的边界层和内部层,并且得到了原问题的形式渐近解.再利用微分不等式证明了解的一致有效性.

一类非线性奇摄动问题激波位置的转移

用一个特殊而简单的方法来讨论一类非线性奇摄动问题的激波位置· 得出了在一定的情况下,当边界条件作微小的变化时,激波的位置将作较大的偏移。

具有二阶转向点的大参数奇摄动方程

讨论了一类二阶常微分方程并具有高阶转向点的大参数的奇异摄动问题.首先将方程同时作自变量和因变量的Liouville-Green变换,得到问题的外部解.然后引入伸展变量变换,并利用1/4和-1/4阶Bessel函数,构造在转向点附近的内层解.最后从解在不同区域的表示式,利用匹配原理适当地选取任意常数,将外部解和内层解进行匹配得到问题解的匹配条件.从而得到在整个区域内的一致有效的渐近解的不同表示式.

一类反应扩散方程内部冲击层解

研究了一类具有跳跃的初始条件的奇摄动反应扩散方程.利用摄动方法构造了问题解的形式渐近展开式,再利用极值原理证明了解的渐近表示式的一致有效性.

SHIFT OF SHOCK POSITION FOR A CLASS OF NONLINEARSINGULARLY PERTURBED PROBLEMS

The shift of shock position for a class of nonlinear singularly perturbed problems is considered using a special and simple method. The location of the shock wave will be larger moved, even from interior layer to the boundary layer when the boundary conditions change smaller.

奇摄动边值问题中的衔接法

在奇摄动内层问题的研究中提出一种构造性方法,称为衔接法.并用它分别研究奇摄动非线性边值问题中的角层和激波层两类内层性态.通过分别构造内层两边解的近似,然后将对应的曲线光滑地衔接起来,从而形成整个区间上解的近似式.

一类奇摄动边值问题的边界层

讨论一类最高阶导数项带有小参数的二阶半线性方程奇摄动D irichlet边值问题.通过直接展开法,构造了问题解的外部展开式,并引用伸长变量分别在区域内部和边界层附近构造了内层解和边界层解.利用匹配原理将对应的外部解、内层解和边界层解分别进行匹配,构造解的合成展开式.得到了原奇摄动边值问题解在整个区间内一致有效的渐近展开式.

具有空间对照结构渐近解的构造(Ⅰ)

对具有快慢变量非线性方程组的边值问题(μ是小参数) ■本文讨论了产生空间对照结构时的渐近解构造,“啪”型内部层解位置的确定及给出了渐近解的误差估计.

西部凹陷基底结构及油气成藏特征

针对西部凹陷基底各构造层的地质结构特点,深化基底各构造层特征研究,深入探讨基岩油气藏成藏特征及分布规律,创新地质认识,取得了良好的勘探效果。通过研究,建立了变质岩、碳酸盐岩内幕成藏模式以及基底多层结构成藏模式,有效地指导了勘探实践。陈古2、兴古9等14口预探井和风险探井——赵古1井的成功钻探,有望在该区带形成亿吨级储量规模。

一类非线性奇摄动问题的激波解

利用边界层理论和匹配原理,讨论了一类非线性方程的激波问题,分别对区域的两个端点和内部进行了分析,得出了与边界条件相对应的激波位置及解的不同表达式．

一类三阶非线性Robin问题的内层现象

本文研究带有Robin边界条件的一类三阶非线性常微分方程的内层问题。应用高阶微分不等式理论得到了摄动问题解的存在性,描述了摄动问题的解及其导函数的渐近性态。