On Nonlinear Evolution of C-type Instability in Nonparallel Boundary Layers

The process of evolution, especially that of nonlinear evolution, of C-type instability of laminar-turbulent flow transition in nonparallel boundary layers are studied by means of a newly developed method called parabolic stability equations （PSE）. Initial conditions, which are very important for the nonlinear problem, are investigated by computing initial solution of the harmonic waves, modifying the mean-flow-distortion, and giving initial value of TS wave and its subharmonic waves at initial station by solving linear PSE. A numerical method with high-order accuracy are developed in the text, the key normalization conditions in the PSE are satisfied, and nonlinear PSE are solved efficiently and implemented stably by the spatial marching. It has been shown that the computed process of nonlinear evolution of C-type instability in Blasius boundary layer is in good agreement with the experimental results.

Overburden fracture evolution laws and water-controlling technologies in mining very thick coal seam under water-rich roof

Considering the danger of water inrush in mining very thick coal seam under water-rich roof in Majialiang Coal Mine,the universal discrete element(UDEC)software was used to simulate the overburden fracture evolution laws when mining 4#coal seam.Besides,this study researched on the influence of face advancing length,speed and mining height on the height of the water flowing fractured zones(HWFFZ),and analyzed the correlation of face advancing length and change rules of aquifer water levels and goaf water inflow.Based on those mentioned above,this research proposed the following water-controlling technologies:draining the roof water before mining,draining goaf water,reasonable advancing speed and mining thickness.These water-controlling technologies were successfully used in the feld,thus ensured safely mining the very thick coal seam under water-rich roof.

Grain Boundary Distribution Evolution of 00Cr12Ti FSS during Annealing

The texture and grain boundary of 00Cr12 Ti FSS have a close correlation with properties and should be controlled to optimize the performance of steel sheets. In this paper, the macrotexture evolution during recrystallization annealing was investigated by XRD, the microtexture and grain boundary distribution evolution during recrystallization annealing were investigated by EBSD. The results showed that the γ fiber texture were mainly generated by replacing α fiber texture in recrystallization process. But with the holding time extending,γ fiber texture transferred to other texture after the holding time got to a certain degree. The major CSLs in 00Cr12 Ti FSS after recrystallization are Σ3 and the frequency of Σ3 climb up and then decline with the holding time extending.Σ11 plays an important role in the process of recrystallized γ fiber texture formation.

Effect of TbF_(3)diffusion on the demagnetization behavior and domain evolution of sintered Nd-Fe-B magnets by electrophoretic deposition

We studied the magnetic properties and domain evolution of annealed and TbF3-diffused sintered Nd-Fe-B magnets using the electrophoretic deposition method.After TbF_(3)diffusion,the coercivity increased significantly by 9.9 kOe and microstructural analysis suggested that Tb favored the formation of the(Nd,Tb)_(2)Fe_(14)B shell phase in the outer region of the matrix grains.The first magnetization reversal and the dynamic successive domain propagation process were detected with a magneto-optical Kerr microscope.For the TbF_(3)-diffused magnet,the magnetization reversal appeared at a larger applied field and the degree of simultaneous magnetization reversal decreased compared with an annealed magnet.During demagnetization after full magnetization,the occurrence of domain wall motion(DWM)in the reproduced multi-domain regions was observed by the step method.The maximum polarization change resulting from the reproduced DWM was inversely related to the coercivity.The increased coercivity for the diffused magnet was mainly attributed to the more difficult nucleation of the magnetic reversed region owing to the improved magneto-crystalline anisotropy field as a result of Tb diffusion.

GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS TO A NONLOCAL EVOLUTION p-LAPLACE SYSTEM WITH NONLINEAR BOUNDARY CONDITIONS

In this paper, the authors discuss the global existence and blow-up of the solution to an evolution p-Laplace system with nonlinear sources and nonlinear boundary condition. The authors first establish the local existence of solutions, then give a necessary and sufficient condition on the global existence of the positive solution.

EVOLUTION OF A 2-D DISTURBANCE IN A SUPERSONIC BOUNDARY LAYER AND THE GENERATION OF SHOCKLETS

Through direct numerical simulation,the evolution of a 2-D disturbance in a supersonic boundary layer has been investigated.At a chosen location,a small amplitude T-S wave was fed into the boundary layer to investigate its evolution. Characteristics of non-linear evolution have been found. Two methods were applied for the detection of shocklets,and it was found that when the amplitude of the disturbance reached a certain value, shocklets would be generated, which should be taken into consideration when nonlinear theory of hydrodynamic stability for compressible flows is to be established.

INITIAL-BOUNDARY VALUE PROBLEM AND CAUCHY PROBLEM FOR A QUASILINEAR EVOLUTION EQUATION

In the present paper,the local existence of classical solutions to the periodic boundary problem and the Cauchy problem of a quasilinear evolution equation are studied under the assumptions that do not require the monotonicity of σi(s) (i= 1,…, n). The nonexistence of global solutions to the initial-boundary value problem of the equation is also discussed, a blowup theorem is proved and a concrete example is given.

BOUNDARY LAYER AND VANISHING DIFFUSION LIMIT FOR NONLINEAR EVOLUTION EQUATIONS

In this paper, we consider an initial-boundary value problem for some nonlinear evolution equations with damping and diffusion. The main purpose is to investigate the boundary layer effect and the convergence rates as the diffusion parameter α goes to zero.

NONLINEAR EVOLUTION ANALYSIS OF T-S DISTURBANCE WAVE AT FINITE AMPLITUDE IN NONPARALLEL BOUNDARY LAYERS

The nonlinear evolution problem in nonparallel boundary layer stability was studied. The relative parabolized stability equations of nonlinear nonparallel boundary layer were derived. The developed numerical method, which is very effective, was used to study the nonlinear evolution. of T-S disturbance wave at finite amplitudes. Solving nonlinear equations of different modes by using predictor-corrector and iterative approach, which is uncoupled between modes, improving computational accuracy by using high order compact differential scheme, satisfying normalization condition I determining tables of nonlinear terms at different modes, and implementing stably the spatial marching, were included in this method. With different initial amplitudes, the nonlinear evolution of T-S wave was studied. The nonlinear nonparallel results of examples compare with data of direct numerical simulations (DNS) using full Navier-Stokes equations.

Blow-up vs.Global Finiteness for an Evolution p-Laplace System with Nonlinear Boundary Conditions

In this paper, the authors consider the positive solutions of the system of the evolution p-Laplacian equationswith nonlinear boundary conditionsand the initial data （u0, v0）, where Ω is a bounded domain in Rn with smooth boundary δΩ, p 〉 2, h（·,·） and s（·,· ） are positive C1 functions, nondecreasing in each variable. The authors find conditions on the functions f, g, h, s that prove the global existence or finite time blow-up of positive solutions for every （u0, v0）.

Formation of I1 stacking fault by deformation defect evolution from grain boundaries in Mg

I_(1)stacking faults(SFs)in Mg alloys are regarded as the nucleation sites of<c+a>dislocations that are critical for these alloys to achieve high ductility.Previously it was proposed that the formation of I_(1)SFs requires the accumulations of a large number of vacancies,which are difficult to achieve at low temperatures.In this study,molecular dynamics(MD)and molecular statics(MS)simulations based on empirical interatomic potentials were applied to investigate the deformation defect evolutions from the symmetric tilt grain boundaries(GBs)in Mg and Mg-Y alloys under external loading along<c>-axis.The results show the planar faults(PFs)on Pyramidal I planes first appear due to the nucleation and glide of(1/2 c+p)partial dislocations from GBs,where p=1/3(1010).These partial dislocations with pyramidal PFs interact with other defects,including pyramidal PFs themselves,GBs,and ppartial dislocations,generating a large amount of I_(1)SFs.Detailed analyses show the nucleation and growth of I_(1)SFs are achieved by atomic shuffle events and deformation defect reactions without the requirements of vacancy diffusion.Our simulations also suggest the Y clusters at GBs can reduce the critical stress for the formation of pyramidal PFs and I_(1)SFs,which provide a possible reason for the experimental observations that Y promotes the<c+a>dislocation activities.

Advanced development of grain boundaries in TMDs from fundamentals to hydrogen evolution application

Grain boundary(GB),as a kind of lattice defect,widely exists in two-dimensional transition metal dichalcogenides(2D TMDs),which has complex and diverse influences on the physical/chemical properties of 2D TMDs.GBs are universally considered to be a double-edged sword,although some electrical and mechanical properties of 2D TMDs would be adversely affected leading to the reduced overall quality,certain structure-oriented applications could be realized based on its unique properties.In this review,we first detailed the atomic structure characteristics of GBs and the corresponding techniques,then we systematically summarized the methods of introducing GBs into 2D TMDs.Next,we expounded unique electrical,mechanical,and chemical properties of the GBs in 2D TMDs and clarified its internal relationship with the atomic structure.Moreover,the application of GB structure in hydrogen evolution reaction(HER)is also discussed.In the end,we make a conclusion and put forward outlooks,hoping to further promote the basic research of GB and boost the wide application of 2D TMDs.

Inverse Optimal Control of Evolution Systems and Its Application to Extensible and Shearable Slender Beams

An optimal(practical) stabilization problem is formulated in an inverse approach and solved for nonlinear evolution systems in Hilbert spaces. The optimal control design ensures global well-posedness and global practical K∞-exponential stability of the closed-loop system, minimizes a cost functional,which appropriately penalizes both state and control in the sense that it is positive definite(and radially unbounded) in the state and control, without having to solve a Hamilton-Jacobi-Belman equation(HJBE). The Lyapunov functional used in the control design explicitly solves a family of HJBEs. The results are applied to design inverse optimal boundary stabilization control laws for extensible and shearable slender beams governed by fully nonlinear partial differential equations.

鄂尔多斯盆地东部边界的构造学分析:以石楼北地区为例

通常认为鄂尔多斯东部边界带由晋西挠褶带和离石断裂组成,但这一边界为残余边界,并非原始的沉积边界。文中以石楼北区域为例,过该区域构建了1条鄂尔多斯盆地东部盆-山尺度的区域地质大剖面,运用2D-Move软件进行构造演化的反演与正演模拟,对其构造变形进行定量分析,并根据研究结果对鄂尔多斯盆地东部边界进行重新厘定。研究认为:(1)石楼北地区在加里东晚期受深部基底断裂活动影响,奥陶系膏盐岩层中形成盐滑脱褶皱,之后沉积石炭系—白垩系,至燕山期受到东西向的挤压应力,地层整体发生掀斜,最终在新生代吕梁隆起加速隆升,遭受差异风化剥蚀形成现今构造格局。(2)构建的区域地质大剖面现今长度为263.76 km,海拔最高可达2000 m,从加里东晚期到白垩纪地层缩短量为3.14 km,缩短率为1.18%,地层抬升高度为3.82 km。(3)根据地层、构造、演化特征对燕山运动期鄂尔多斯盆地的东部边界进行重新厘定,认为东部边界应向东延伸至吕梁隆起东侧。该成果可为鄂尔多斯盆地东缘范围、构造变形研究以及晋西挠褶带煤层气勘探开发提供参考与新思路。

塔里木盆地西南部晚白垩世——早古新世沉积环境演化:来自皮山PBX1井的地化证据

【研究目的】白垩纪与古近纪之交发生过地质历史上重大的灾变和异常事件,致使K/Pg界线成为全球最重要的地质界线之一。通过对塔里木盆地晚白垩世—早古新世沉积环境的研究,有助于重建特提斯北部盆地群塔里木盆地的古环境。【研究方法】本文通过塔里木盆地西南部PBX1井岩心的地球化学元素敏感指标研究K/Pg上下环境的变化。【研究结果】晚白垩世晚期古气候属于干热型,早古新世呈现短暂温湿型。古盐度由晚白垩世正常海洋环境向早古新世半咸水、海陆过渡盐湖环境转换,K/Pg界线位置处,古盐度达到最低值。氧化-还原环境由晚白垩世富氧→贫氧的弱氧化-弱还原环境经历了K/Pg事件之后短暂向早古新世富氧环境转化,而后整体上由贫氧的弱氧化-弱还原环境向极贫氧的还原环境演化。【结论】PBX1井地球化学元素敏感指标揭示了中生代—新生代之交灾变异常事件在塔里木盆地响应特征,也是特提斯洋北部盆地群晚白垩世—早古新世沉积环境演化的有效证据。

发展方程的完美匹配边界层模型

在有界区域上使用数值方法模拟无界区域上的偏微分方程时,要求在有界区域边界上添加人工边界条件。构造的人工边界条件必须能消除边界上不必要的反射,完美匹配边界层是非常有效的人工吸收边界条件之一。本研究采用复值坐标拉伸的方法,在不分离变量的前提下对发展方程推导出了完美匹配边界层模型。通过平面波分析可知,波在初始求解区域边界上无反射,且在有界的完美匹配边界层上振幅是指数衰减的。

Global and Blow-up Solutions to a p-Laplace Equation with Nonlocal Source and Nonlocal Boundary Condition

This paper deals with an evolution p-Laplace equation with nonlocal source subject to weighted nonlocal Dirichlet boundary conditions. We give sufficient conditions for the existence of global and non-global solutions.

Analytical investigation of the boundary-triggered phase transition dynamics in a cellular automata model with a slow-to-start rule

Previous studies suggest that there are three different jam phases in the cellular automata automaton model with a slow-to-start rule under open boundaries.In the present paper,the dynamics of each free-flow-jam phase transition is studied.By analysing the microscopic behaviour of the traffic flow,we obtain analytical results on the phase transition dynamics.Our results can describe the detailed time evolution of the system during phase transition,while they provide good approximation for the numerical simulation data.These findings can perfectly explain the microscopic mechanism and details of the boundary-triggered phase transition dynamics.

基于边界规整的矩形PCB排样优化算法

随着国内电子行业的快速发展,国内各厂商对PCB的需求量与日俱增,材料价格上涨较快,如何尽可能地提高母板板材利用率、子板规整率和类聚度已经成为各PCB制造厂商急需解决的问题,提出了一种基于边界规整的矩形PCB排样算法。算法基于对PCB子板边界规整度和类聚度进行表征,与板材利用率进行加权构造出优化目标函数并使用差分进化算法对排样序列进行优化。实验表明,算法在PCB排样的板材利用率、子板规整率和类聚度的综合效果上有较大提高。

青藏高原周缘的河流纵剖面特征及其对构造地貌演化的启示

河流水系是改造地表地貌的主要外动力,其形态样式记录了造山带和高原的生长和演化。目前对于青藏高原周缘的河流剖面研究主要集中在南缘、东南缘及东缘。相比而言,对于流经高原其他边缘河流的纵剖面特征仍然缺乏分析,不同位置的高原边缘河流发育是否存在相似性或差异性及其内在原因尚未开展相关研究。选取青藏高原北缘西昆仑—阿尔金地区、东北缘祁连山地区、东南缘三江地区和南缘喜马拉雅等典型区域,通过开展河流地貌对比研究,利用河流纵剖面的关键地貌参数定量分析了高原周边地貌边界带的空间特征及相关的构造与气候因素。结果表明,在青藏高原周缘地貌边界带上,河流陡峭度指数最大值与区域地形起伏最大区域一致,河流流经高原边缘时陡峭度有显著升高,而在高原边缘两侧陡峭度均相对较低,且河流向高原内部的溯源侵蚀十分有限,而且河流裂点均出现在区域地形起伏较高的地貌部位。其中青藏高原北缘、东北缘与南缘,地形起伏最大的区域与构造边界所围限的高原边界一致,并大致对应最新构造活动的强隆升区,而青藏高原东南缘的高原边界较模糊,地形起伏度变化最明显的区域出现在雅砻逆冲断裂两侧,与前人提出的古高原边界一致,暗示该区河流裂点的形成可能与雅砻逆冲断裂的早期活动有关。基于研究结果认为,对于青藏高原这样大尺度或经历长时间构造演化过程的地貌单元,基于稳态假设下的河流形态分析高原隆升时间可能存在较大偏差。青藏高原东南缘的高海拔低起伏地貌面可能是在较平缓的内流水系作用下形成的,在随后的河流袭夺等过程中演变为现今的外流河状态。