Relationship between the Virtual Dynamic Thinning Line and the Self-Thinning Boundary Line in Simulated Plant Populations

The self-thinning rule defines a straight upper boundary line on log-log scales for all possible combinations of mean individual biomass and density in plant populations. Recently, the traditional slope of the upper boundary line, -3/2, has been challenged by -4/3 which is deduced from some new mechanical theories, like the metabolic theory. More experimental or field studies should be carried out to identify the more accurate self-thinning exponent. But it＇s hard to obtain the accurate self-thinning exponent by fitting to data points directly because of the intrinsic problem of subjectivity in data selection. The virtual dynamic thinning line is derived from the competition-density （C-D） effect as the initial density tends to be positive infinity, avoiding the data selection process. The purpose of this study was to study the relationship between the virtual dynamic thinning line and the upper boundary line in simulated plant stands. Our research showed that the upper boundary line and the virtual dynamic thinning line were both straight lines on log-log scales. The slopes were almost the same value with only a very little difference of 0.059, and the intercept of the upper boundary line was a little larger than that of the virtual dynamic thinning line. As initial size and spatial distribution patterns became more uniform, the virtual dynamic thinning line was more similar to the upper boundary line. This implies that, given appropriate parameters, the virtual dynamic thinning line may be used as the upper boundary line in simulated plant stands.

Self-thinning lines and allometric relation in Chinese fir(Cunninghamia lanceolata) stands

We calculated a self-thinning exponent of 1.05 for tree mass using the 3/2 power equation in 93 Cunninghamia lanceolata plots.According to Weller’s allometric model,the self-thinning exponent for tree mass was calculated as 1.28 from the allometric exponents h and d.The both self-thinning exponents were significantly lower than 3/2.The self-thinning exponent of organs was estimated to be 1.42 for stems,0.93 for branches,0.96 for leaves,1.35 for roots and 1.28 for shoots,respectively.The self-thinning exponent of stem mass was not significantly different from 3/2,whereas thinning exponents of trees,branches,leaves and roots were significantly lower than 3/2.The stand leaf mass and stand branch mass were constant regardless of the stand density.The scaling relations among branch,leaf,stem,root and shoot mass（MB,ML,MS,MR and MA,respectively） showed that MB and ML scaled as the3/4 power of MS,whereas MS or MA scaled isometrically with respect to MR.

Riemann Boundary Value Problem of Non-Normal Type on the Infinite Straight Line

Various kinds of Riemann boundary value problems (BVPs) for analytic functions on closed curves or on open arc, doubly periodic Riemann BVPs, doubly quasi-periodic Riemann BVPs, and BVPs for polyanalytic functions have been widely investigated in [1-8]. The main ap- proach is to use the decomposition of polyanalytic functions and their generalization to transform the boundary value problems to their corresponding boundary value problems for analytic functions. Recently, inverse Riemann BVPs for generalized analytic functions or bianalytic functions have been investigated in [9-12]. In this paper, we consider a kind of Riemann BVP of non-normal type on the infinite straight line and discuss the solvable conditions and the general solution for it.

Existence of Solutions for Infinity-Point Nonlinear Fractional Boundary Value Problem at Resonance

A class of the boundary value problem for fractional order nonlinear differential equation with Riemann-Liouville fractional derivative on the half line was studied. By using the coincidence degree theory due to Mawhin and constructing the suitable operators,the existence theorem of at least one solution has been established. An example is given to illustrate our result.

Application of Line Boundary Technique to 2D Tidal Current Simulation

To deal with the problems concerning the shore boundary, moving boundary and engineering boundary which are encountered frequently in 2D tidal current simulation by the finite difference method, the concept of line boundary is introduced and studied here, and then the line boundary technique in common use is proposed in this paper. Analysis of some calculation cases shows that this technique is practical, effective, and simple in 2D tidal current simulation involving different boundaries.

ANALYSIS OF OPEN MICROSTRIP STRUCTURES BY USING DIAKOPTIC METHOD OF LINES COMBINED WITH PERIODIC BOUNDARY CONDITIONS

This paper presents the analysis of open microstrip structures by using diakoptic method of lines (ML) combined with periodic boundary conditions (PBC). The parameters of microstrip patch are obtained from patch current excited by plane wave. Impedance matrix elements are computed by using fast Fourier transform(FFT), and reduced equation is solved by using diakoptic technique. Consequently, the computing time is reduced significantly. The convergence property of simulating open structure by using PBC and the comparison of the computer time between using PBC and usual absorbing boundary condition (ABC) show the validity of the method proposed in this paper. Finally, the resonant frequency of a microstrip patch is computed. The numerical results obtained are in good agreement with those published.

Hilbert Boundary Value Problem with an Unknown Function on Arbitrary Infinite Straight Line

We consider a Hilbert boundary value problem with an unknown parametric function on arbitrary infinite straight line passing through the origin. We propose to transform the Hilbert boundary value problem to Riemann boundary value problem, and address it by defining symmetric extension for holomorphic functions about an arbitrary straight line passing through the origin. Finally, we develop the general solution and the solvable conditions for the Hilbert boundary value problem.

THEORY AND METHOD FOR WETLAND BOUNDARY DELINEATION

Based on the analysis of the subjectivity of wetland boundary criteria and their causes at present, this paper suggested that, under the condition that the mechanism of wetland formation process has not been understood, "black box" method of System Theory can be used to delineate wetland boundaries scientifically. After analyzing the difference of system construction among aquatic habitats, wetlands and uplands, the lower limit of rooted plants was chosen as the lower boundary criterion of wetlands. Because soil diagnostic horizon is the result of the long-term interaction among all environments, and it is less responsive than vegetation to short-term change, soil diagnostic horizon was chosen as the indicator to delineate wetland upper boundary, which lies at the thinning-out point of soil diagnostic horizon. Case study indicated that it was feasible using the lower limit of rooted plants and the thinning-out point of soil diagnostic horizon as criteria to delineate the lower and upper boundaries of wetland. In the study area, the thinning-out line of albic horizon was coincident with the 55.74m contour line, the maximum horizon error was less than 1m, and the maximum vertical error less than 0.04m. The problem on wetland definition always arises on the boundaries. Having delineated wetland boundaries, wetlands can be defined as follows: wetlands are the transitional zones between uplands and deepwater habitats, they are a kind of azonal complex that are inundated or saturated by surface or ground water, with the lower boundary lying at the lower limit of rooted plants, and the upper boundary at the thinning-out line of upland soil diagnostic horizon.

An IBEM solution to the scattering of plane SH-waves by a lined tunnel in elastic wedge space

The indirect boundary element method （IBEM） is developed to solve the scattering of plane SH-waves by a lined tunnel in elastic wedge space. According to the theory of single-layer potential, the scattered-wave field can be constructed by applying virtual uniform loads on the surface of lined tunnel and the nearby wedge surface. The densities of virtual loads can be solved by establishing equations through the continuity conditions on the interface and zero-traction conditions on free surfaces. The total wave field is obtained by the superposition of free field and scattered-wave field in elastic wedge space. Numerical results indicate that the IBEM can solve the diffraction of elastic wave in elastic wedge space accurately and effi- ciently. The wave motion feature strongly depends on the wedge angle, the angle of incidence, incident frequency, the location of lined tunnel, and material parameters. The waves interference and amplification effect around the tunnel in wedge space is more significant, causing the dynamic stress concentration factor on rigid tunnel and the displacement amplitude of flexible tunnel up to 50.0 and 17.0, respectively, more than double that of the case of half-space. Hence, considerable attention should be paid to seismic resistant or anti-explosion design of the tunnel built on a slope or hillside.

Dynamic interaction of twin vertically overlapping lined tunnels in an elastic half space subjected to incident plane waves

The scattering of plane harmonic P and SV waves by a pair of vertically overlapping lined tunnels buried in an elastic half space is solved using a semi-analytic indirect boundary integration equation method. Then the effect of the distance between the two tunnels, the stiffness and density of the lining material, and the incident frequency on the seismic response of the tunnels is investigated. Numerical results demonstrate that the dynamic interaction between the twin tunnels cannot be ignored and the lower tunnel has a significant shielding effect on the upper tunnel for high-frequency incident waves, resulting in great decrease of the dynamic hoop stress in the upper tunnel; for the low-frequency incident waves, in contrast, the lower tunnel can lead to amplification effect on the upper tunnel. It also reveals that the frequency-spectrum characteristics of dynamic stress of the lower tunnel are significantly different from those of the upper tunnel. In addition, for incident P waves in low-frequency region, the soft lining tunnels have significant amplification effect on the surface displacement amplitude, which is slightly larger than that of the corresponding single tunnel.

Moving contact line problem: Advances and perspectives

The solid-liquid interface, which is ubiquitous in nature and our daily life, plays fundamental roles in a variety of physical-chemical-biological- mechanical phenomena, for example in lubrication, crystal growth, and many biological reactions that govern the building of human body and the functioning of brain. A surge of interests in the moving contact line （MCL） problem, which is still going on today, can be traced back to 1970s primarily because of the exis- tence of the ＂Huh-Scriven paradox＂. This paper, mainly from a solid mechanics perspective, describes very briefly the multidisciplinary nature of the MCL problem, then summarizes some major advances in this exciting research area, and some future directions are presented.

Distributed Capacitance of Coaxial Line With Perturbed Walls

Perturbation method of boundary geometry(PMOBG) used in Lapiacian problems is dealt with and the three--term perturbation expression of distributed capacitance of a coaxial line with perturbed walls is obtained. As an example,four-order expression of distributed capacitance of a elliptic coaxial line with small eccentricity is given.

Domain boundaries in silicene:Density functional theory calculations on electronic properties

By using density functional theory(DFT)-based first-principles calculations, the structural stability and electronic properties for two kinds of silicene domain boundaries, forming along armchair edge and zigzag edge, have been investigated. The results indicate that a linkage of tetragonal and octagonal rings(4|8) appears along the armchair edge, while a linkage of paired pentagonal and octagonal rings(5|5|8) appears along the zigzag edge. Different from graphene, the buckling properties of silicene lead to two mirror symmetrical edges of silicene line-defect. The formation energies indicate that the 5|5|8 domain boundary is more stable than the 4|8 domain boundary. Similar to graphene, the calculated electronic properties show that the 5|5|8 domain boundaries exhibit metallic properties and the 4|8 domain boundaries are half-metal.Both domain boundaries create the perfect one-dimensional(1D) metallic wires. Due to the metallic properties, these two kinds of nanowires can be used to build the silicene-based devices.

Identifying boundary between near field and far field in ground vibration caused by surface loading

The boundary between the near and far fields is generally defined as the distance from the vibration source beyond which ground vibrations are mainly dominated by Rayleigh waves. It is closely related to the type of vibration source and the soil properties. Based on the solutions of the Lamb＇s problem, the boundary at the surface between the near and far fields of ground vibration was investigated for a harmonic vertical concentrated load and an infinite line load at the surface of a visco-elastic half-space. Particularly, the variation of the boundary with the material damping was investigated for both cases. The results indicate that the material damping slightly contributes to the attenuation of vibrations in the near-source region, but significantly reduces the vibrations in the region that is at some distance away from the source. When taking the material damping into consideration, the boundary between the near and far fields tends to move towards the vibration source. Compared with the vibrations caused by a concentrated load, the vibrations induced by an infinite line load can affect a larger range of the surrounding environment, and they attenuate more slowly. This means the boundary between the near field and far field should move fitrther away from the source. Finally, the boundaries are defined in terms of R-wave length （2R） and Poisson ratio of the ground （o）. For the case of a point load, the boundary is located at the distance of （5.0-6.0）2R for v≤0.30 and at the distance of （2.0--3.0）2R for v≥0.35. For the case of an infinite line load, the boundary is located at the distance （5.5-6.5）2rt for v≤0.30 and at the distance （2.5--3.5）2R for v≥0.35.

VISUALIZATION OF FLOW STRUCTURES IN A TURBULENT BOUNDARY LAYER USING A NEW TECHNIQUE

In this paper, an experimental investigation on the flow structures in a turbulent bounda- ry layer employing a special laser light sheet-Hydrogen bubble flow visualization technique is described. It is observed that the high/low speed streaks are directly related to the hairpin or horseshoe-like vortices. This observation can give a better understanding of the physical mechanism in the turbulent boundary layer.

A simple method to extract glacier length based on Digital Elevation Model and glacier boundaries for simple basin type glacier

Glacier length is a key morphological element that has many glaciological applications; however, it is often difficult to determine, especially for glaciers that cover larger spatial areas or those that exhibit frequent temporal change. In this paper, we describe a new Arc GIS-based method that can derive glacier flow lines for determining glacier length based on digital elevation model and glacier outlines. This method involves(1) extraction of the highest and lowest points on a glacier,(2) calculation of 10-m contour lines on the glacier from 10 m to 100 m height, and(3) connection of the midpoints of each contour line with the highest and the lowest points in order to create a flow line, which is subsequently smoothed. In order to assess the reliability of this method, we tested the algorithm's results against flow lines calculated using field measurements, analysing data from the Chinese Glacier Inventory, and manual interpretation. These data showed that the new automated method is effective in deriving glacier flow lines when contour lines are relatively large; in particular, when they are between 70 m and 100 m. Nonetheless, a key limitation of the algorithm is the requirement to automatically delete repeated and closed curves in the pre-treatment processes. In addition to calculating glacier flow lines for derivation of glacier length, this method also can be used to effectively determine glacier terminus change.

A Review of the Attachment Line Instability for Hybrid Laminar Flow Control

This paper focuses on the investigation of the attachment line instability for Hybrid Laminar Flow Control(HLFC),one of the most promising drag reduction technologies for modern transport aircraft respect to high Reynolds numbers and large sweep angles.The attachment line instability also plays an important role during laminar-turbulent transition control and HLFC design on a swept wing.The overview of historical research is presented and knowledge gaps are pointed out as the conclusion.

A Method to Determine the Incident Wave Boundary Conditions and Its Application

When studying the harbor water tranquility, cases are often confronted as that the verification point is not located on the generation line or that the angle between the generation line and the isobath is so large that the differences of the wave climates along the generation line can not be ignored. For these cases, the incident boundary conditions are difficult to evaluate. In order to solve this problem, a combined wave model is developed in the present paper based on the Boussinesq equation and the wave action balance equation. Instead of the one-line wave generation method, a multi-line generation method is proposed for the combined model. Application of this method is given to a case that the harbor is designed with two entrances and the angle between the generation line and the isobath is large and the results are shown reasonable. We suggest that the wave generation method on multi-lines might also be introduced to the wave physical model as the replacement for the one-line generation method.

Optimal Valve Closure Operations for Pressure Suppression in Fluid Transport Pipelines

When a valve is suddenly closed in fluid transport pipelines,a pressure surge or shock is created along the pipeline due to the momentum change.This phenomenon,called hydraulic shock,can cause major damage to the pipelines.In this paper,we introduce a hyperbolic partial differential equation(PDE)system to describe the fluid flow in the pipeline and propose an optimal boundary control problem for pressure suppression during the valve closure.The boundary control in this system is related to the valve actuation located at the pipeline terminus through a valve closing model.To solve this optimal boundary control problem,we use the method of lines and orthogonal collocation to obtain a spatial-temporal discretization model based on the original pipeline transmission PDE system.Then,the optimal boundary control problem is reduced to a nonlinear programming(NLP)problem that can be solved using nonlinear optimization techniques such as sequential quadratic programming(SQP).Finally,we conclude the paper with simulation results demonstrating that the full parameterization(FP)method eliminates pressure shock effectively and costs less computation time compared with the control vector parameterization(CVP)method.

POSITIONAL ERROR CURVES BAND OF A PLANAR LINE SEGMENT WITHIN GISs

In this paper, the positional error curve of point features was extended to an error curves band of line segment features. Firstly, the constitution and shape of the error curves band were analyzed. On this basis, the general boundary curve formula of that band was derived. Secondly, the visualizing error curves bands were realized through three exam- ples. Finally,area index has been examined by comparing numerical results from error curves band and error ellipes band.