Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation

Singular perturbation theory of two-time scale expansions was developed both in inviscid and weak viscous fluids to investigate the motion of single surface standing wave in a liquid-filled circular cylindrical vessel, which is subject to a vertical periodical oscillation. Firstly, it is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear evolution equation of slowly varying complex amplitude, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from solvability condition of high-order approximation. It shows that when forced frequency is low, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is high, the influence of surface tension is significant, and can not be neglected. This proved that the surface tension has the function, which causes free surface returning to equilibrium location. Theoretical results much close to experimental results when the surface tension is considered. In fact, the damping will appear in actual physical system due to dissipation of viscosity of fluid. Based upon weakly viscous fluids assumption, the fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates damping term and external excitation, was derived from linearized Navier-Stokes equation. The analytical expression of damping coefficient was determined and the relation between damping and other related parameters (such as viscosity, forced amplitude and depth of fluid) was presented. The nonlinear amplitude equation and a dispersion, which had been derived from the inviscid fluid approximation, were modified by adding linear damping. It was found that the modified results much reasonably close to experimental results. Moreover, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent. Finally, instability of the surface wave is analyzed and properties of the solutions of the modified amplitude equation are determined together with phase-plane trajectories. A necessary condition of forming stable surface wave is obtained and unstable regions are illustrated. (c) 2005 Elsevier SAS. All rights reserved.

Nonlinear Faraday Waves in a Parametrically Excited Circular Cylindrical Container

In the cylindrical coordinate system, a singular perturbation theory of multiple-scale asymptotic expansions was developed to study single standing water wave mode by solving potential equations of water waves in a rigid circular cylinder, which is subjec

Computer Simulation Of Random Sphere Packing In An Arbitrarily Shaped Container

Most simulations of random sphere packing concern a cubic or cylindric container with periodic boundary, containers of other shapes are rarely studied. In this paper, a new relaxation algorithm with pre-expanding procedure for random sphere packing in an arbitrarily shaped container is presented. Boundaries of the container are simulated by overlapping spheres which covers the boundary surface of the container. We find 0.4 similar to 0.6 of the overlap rate is a proper value for boundary spheres. The algorithm begins with a random distribution of small internal spheres. Then the expansion and relaxation procedures are performed alternately to increase the packing density. The pre-expanding procedure stops when the packing density of internal spheres reaches a preset value. Following the pre-expanding procedure, the relaxation and shrinking iterations are carried out alternately to reduce the overlaps of internal spheres. The pre-expanding procedure avoids the overflow problem and gives a uniform distribution of initial spheres. Efficiency of the algorithm is increased with the cubic cell background system and double link data structure. Examples show the packing results agree well with both computational and experimental results. Packing density about 0.63 is obtained by the algorithm for random sphere packing in containers of various shapes.

Surface waves in a vertically excited circular cylindrical container

The nonlinear free surface amplitude equation, which has been derived from the inviscid fluid by solving the potential equation of water waves with a singular perturbation theory in a vertically oscillating rigid circular cylinder, is investigated successively in the fourth-order Runge-Kutta approach with an equivalent time-step. Computational results include the evolution of the amplitude with time, the characteristics of phase plane determined by the real and imaginary parts of the amplitude, the single-mode selection rules of the surface waves in different forced frequencies, contours of free surface displacement and corresponding three-dimensional evolution of surface waves, etc. In addition, the comparison of the surface wave modes is made between theoretical calculations and experimental measurements, and the results are reasonable although there are some differences in the forced frequency.

Instability of the vertically forced surface wave in a circular cylindrical container

The nonlinear amplitude equation, which was derived by Jian Yongjun employing expansion of two-time scales in inviscid fluids in a vertically oscillating circular cylindrical vessel, is modified by introducing a damping term due to the viscous dissipation of this system. Instability of the surface wave is analysed and properties of the solutions of the modified equation are determined together with phase-plane trajectories. A necessary condition of forming a stable surface wave is obtained and unstable regions are illustrated. Research results show that the stable pattern of surface wave will not lose its stability to an infinitesimal disturbance.

Dynamic interaction of an elastic container with fluid

The vibration analysis of an elastic container with partially filled fluid was investigated in this paper. The container is made of a thin cylinder and two circular plates at the ends. The axis of the cylinder is in the horizontal direction. It is difficult to solve this problem because the complex system is not axially symmetric. The equations of motion for this system were derived. An incompressible and ideal fluid model is used in the present work. Solutions of the equations were obtained by the generalized variational method. The solution was expressed in a series of normalized generalized Fourier's functions. This series converged rapidly, and so its approximate solution was obtained with high precision. The agreement of the calculated values with the experimental result is good. It should be mentioned that with our method, the computer time is less than that with the finite-element method.

岷江干旱河谷三种蔷薇植物繁殖更新研究

繁殖更新是植物生活史的重要阶段，在退化生态系统中，植物繁殖更新能力往往较差，是植被恢复的限制环节，因而也成为恢复研究重点和核心。本研究选择岷江干旱河谷广泛分布的三种蔷薇：多苞蔷薇（R. multibracteata）、黄蔷薇（R. hugonis）和川滇蔷薇（R. soulieana）为研究对象，通过野外调查，在查明其生长、繁殖更新状况的基础上，采用控制和模拟实验，对种子和幼苗阶段进行了深入研究，综合分析更新潜力，并提出相对应的促进更新和植被恢复措施。主要结论如下： 1）三种蔷薇在岷江干旱河谷广泛分布，生长和繁殖状况良好，结实量大。各生长指标：株高、基径和冠幅，繁殖指标：结实数量、重量和单果重量都具有显著的空间差异性。基径对多苞蔷薇结实量影响最大；而冠幅对黄蔷薇结实量影响最大。海拔和纬度是对蔷薇生长和繁殖影响最大的环境因素，随着海拔和纬度的升高，植株生长更高大，结实量增加；坡度和坡向对其生长和繁殖也有一定影响，随着坡度 和坡向增加，蔷薇生长和结实受到抑制。 2）三种蔷薇在岷江干旱河谷更新现状不佳, 但更新潜力大。活力种子比率低，动物取食以及两年生幼苗的大量死亡是蔷薇更新的主要限制因素。多苞蔷薇和黄蔷薇的结实率低，川滇蔷薇较高。三种蔷薇种子产量大，但种子质量较差，更新具有充足的种源。三种蔷薇都能形成持久种子库，种子库中种子总量大，但有效种子少，黄蔷薇被动物啃食的比例很高，多苞蔷薇和川滇蔷薇也有一部分种子受到动物破坏。三种蔷薇幼苗库组成特征表现为，当年生幼苗所占比例很高，年龄较大幼苗所占比例小。 3）三种蔷薇都具有不同程度休眠，未经处理种子的发芽率极低。黄蔷薇休眠程度最深，为深度生理休眠；多苞蔷薇为中度生理休眠；川滇蔷薇为非深度生理休眠。三种蔷薇种子在形态上发育成熟，种皮具有透水性。蔷薇果果肉和瘦果中含有抑制物质，其浸泡液抑制了油菜种子萌发，果肉抑制作用更强，果肉和瘦果浸泡液的抑制程度分别为：川滇蔷薇>黄蔷薇>多苞蔷薇。切割和硫酸腐蚀提高了川滇蔷薇种子的发芽能力，而对多苞蔷薇和黄蔷薇没有影响。完全去除瘦果果皮和种皮提高了多苞蔷薇种子发芽率，但对黄蔷薇没有影响。赤霉素和烟水对蔷薇种子萌发没有促进作用。三种蔷薇打破休眠所需低温层积时间分别为：黄蔷薇>多苞蔷薇>川滇蔷薇。对于多苞蔷薇和川滇蔷薇，层积前对种子进行硫酸腐蚀或暖温层积能缩短低温层积时间，提高发芽率。对于多苞蔷薇，变温层积中暖温层积和低温层积具有一定的负补性，即延长暖温层积可以缩短种子萌发对低温层积的需要。 4）多苞蔷薇种子形态特征和种子休眠与萌发在不同海拔梯度间存在较大差异。种子采集时间、采集季节和干藏影响多苞蔷薇和川滇蔷薇的种子休眠。多苞蔷薇果实大小、种子大小和千粒重、种皮厚度随海拔升高而增加，而种子饱满率和活力随海拔升高而降低，种子休眠程度也随海拔升高而增加。种皮厚度与种子大小、千粒重成正相关关系，硫酸腐蚀后的种子经过不同时间的低温层积后，种子发芽率与种皮厚度、种子大小、千粒重、海拔成正相关关系。2006 年采集川滇蔷薇和多苞蔷薇种子休眠程度较2005 年低。种子休眠随种子年龄增加而减弱。高温和干旱能减轻多苞蔷薇和川滇蔷薇种子休眠。 5）三种蔷薇的生长和生物量积累在干旱胁迫条件下受到抑制，而生物量分配、叶片形态特征和水分利用特征等都发生了变化。三种蔷薇的根、茎、叶各器官生物量以及总生物量等在干旱胁迫下明显减小，叶片脱落数量增加。在干旱胁迫条件下，较多的生物量分配到地下部分，从而这使R/S 明显增加。比叶面积（SLA）和冠层面积比（LAR）对干旱胁迫的反应不敏感，仅有部分物种在干旱胁迫条件下发生了变化，并且其变化特点在不同年龄幼苗之间有一定差异。干旱胁迫对WUE 的影响在不同物种间存在差异。多苞蔷薇和黄蔷薇的WUE 随着干旱胁迫的增加而增大， 而川滇蔷薇的WUE 则随干旱胁迫增加而减小。在干旱胁迫条件下，多苞蔷薇和黄蔷薇叶片脱落量和生物量减小幅度较川滇蔷薇大，表明其抗旱能力较强。在干旱胁迫条件，三种蔷薇两年生幼苗的生物量减小幅度较当年生幼苗小，表明两年生幼苗的抗旱能力更强。 6）两种植被恢复措施中，幼苗移栽比播种具有更好的植被恢复效果。播种后，蔷薇种子的发芽率较高，但出苗率都很低，即使出苗，幼苗也几乎在一月内全部死亡。 三种微生境条件下（灌木、半灌木和裸地），种子出苗和幼苗成活没有差异。移栽幼苗总体死亡率都比较低，小于20％。特别是两年生幼苗死亡率更低，小于2％。移栽后的幼苗生长状况良好，在整个生长季中，各生长指标不断增加。生境对幼苗的存活率没有显著影响，但对于幼苗的生长和生物量积累有一定影响，裸地更有利于幼苗生长和生物量积累。与当年生幼苗相比，两年生幼苗具有更高的成活率。总之，三种蔷薇在干旱河谷分布广泛、生长繁殖状况良好，结实量大，具有丰富种源，繁殖更新潜力大，但繁殖更新状况不佳；种子散布后动物对种子的取食、种子的深度休眠过程、种子出苗以及当年生幼苗的存活和定居是更新的主要限制环节。水分是影响结实、种子休眠解除和萌发，幼苗存活和定居的最主要的限制因素。在植被恢复中，应在种子成熟季节大量采集种子，在室内打破休眠后进行人工播种，培育两年生幼苗，通过幼苗移栽方式进行植被恢复。川滇蔷薇应栽种在相对湿润的过渡区，而多苞蔷薇和黄蔷薇可以应用于核心区植被恢复。 Regeneration is an important phase in plant life cycle. It has been a key component of ecological restoration in degradation ecosystem in which plants commonly has poor regeneration. In this paper, we investigated the natural growth, propagation and regeneration status of native three rose species, Rosa multibracteata, R. hugonis and R. soulieana, and analysis the limitation in seed germination and seedling establishment stages. Advice on facilitating the use of these plants in restoration based on the results has been proposed. The results were as follows: 1) Three rose plants widely distributed in the dry valley of the Minjiang River, and made a good performance in growth and propagation. There were significant spatial differences in each growth parameter, such as ramet height, basal diameter, crown diameter and propagation parameters including hip number of a clump, hip mass of a clump and a hip mass. Basa diameter was the most important growth parameter influencing fruit number for R. multibracteata and crown diameter was for R. hugoni. Altitude and latitude had the greatest effect on the growth and propagation of rose plants among environmental conditions. Each parameter of growth and propagation increased with the increase of altitude and latitude. In addition, the increase of slope and aspect limited the growth and propagation. 2) Three rose plants had poor natural regeneration, but great regeneration potential. Low seed viability, predation and higher mortality of current year old seedlings were the limitation in regeneration. R. multibracteata and R. hugonis had higher fruiting rates than R. souliean. All three plants produced a great number of seeds, while their viability was poor. Three rose plants had persistent seed banks, with high total seed number but very low viable seed density. Predation was most severe in R. hugonis, and it also existed to some degree in R. multibracteata and R. soulieana. The seedling age-structure was characteristic of current-year seedlings predominating and few older seedlings were observed. 3) Three rose seeds were dormant and untreated seeds germinated with very low germination percentages. The rose seeds had morphological mature embryos, and achenes were permeable. Some inhabit substances existed in hips and achenes for the extracts of hips and achenes inhibited germination of Brassica campestris. The inhibition effect of the extracts of three rose hip and achenes was R. soulieana>R. hugonis>R. multibracteata. Mechanical and H2SO4 scarification increased R. soulieana germination but had no effect on germination of R. hugonis and R. multibracteata seeds. Full removal of pericarp and testa improved the germination of R. multibracteata but did not affect R. hugonis germination. GA3 and smoke water had no positive effect on rose seed germination. The periods of cold stratification required to released seed dormancy was R. hugonis > R. soulieana >R. multibracteata. H2SO4 scarification and warm stratification shortened cold stratification to release dormancy for R. soulieana and R. multibracteata. Warm stratification had complementary effect for cold stratification, i.e. the longer warm stratification seeds received, the shorter cold stratification were required to obtain the same germination percentage. Three rose seeds had different kinds of dormancy; R. hugonis has deep physiological dormancy, R. multibracteata with intermediate physiological dormancy and R. souliean non-deep physiological dormancy. 4）The seeds traits and dormancy of R. multibracteata showed significant difference across altitudes. Year and season of seed collection had significant effect on seed dormancy for both R. souliean and R. multibracteata. Hip size, seed size, seed weight, seed coat thickness and seed dormancy level increased with the increase of the altitude. There were positive relations between seed coat thickness with seed size and seed weight. Germination percentage of seeds treated with H2SO4 scarification following different periods of cold stratification showed positive relation with seed coat thickness, seed size, seed weight and altitude. Seeds of R. souliean and R. multibracteata collected in 2006 had low dormancy level than those collected in 2005. Seed dormancy decreased with increasing seeds age. High temperature and drought were associated with low dormancy level. 5) Seedling growth, the total dry mass and their components of seedlings were reduced, while leaf senescence accelerated under drought stress. More biomass allocation to root system resulted in higher R/S ratio under drought. Water-use efficiency (WUE) of R. multibracteata and R. hugonis increased, while it declined for R. soulieana under drought stress. R. soulieana seedlings had poor drought-resistance capacity it had more senescent leaves, and its reduction of biomass was stronger than two other rose plants under drought. The reduction degree of one year old seedlings under drought stress was slighter than that of current year seedlings. Therefore, one year old seedling was more drought-resistent compared to current year seedlings. 6）Planting seedlings may have better effect in comparison with direct seeding. Most seeds germinated after seeding, but seedling emergence was very low. More than 80 % seedlings from direct seeding died within a months after emergence. Seedling emergence and survival rate did not show difference among microhabitats. Mortality rates of seedlings artificially planted in microhabitats were general lower than 20 %, and the mortality rate of one year old seedlings was lower than 2 %. Each grow parameter including plant height, leaf number and branch number continually increased after planting. Microhabitat type had effect on the growth parameter and biomass production, but it did not influence the seedling survival. Bare land tended to facilitate seedling growth. One year old seedlings had higher survival rate than current year seedlings. In conculsion, the three rose had wide distribution in the dry valley of the Minjiang River. They produced many seeds and had tolerance to drought stress to some degree. But they had poor regeneration in habitats may be caused by predation, seed dormancy，and high mortality in current year seedlings. We recommend that rose plants should be utilized in restoration by planting two-year old seedlings in spring. A large quantity of seeds should be collected artificially in autumn, release seed dormancy in room, and then cultivate two-year old seedlings by seeding in particular container. R. soulieana seedling probably be planted in transition area, and R. multibracteata and R. hugonis can be used in core area of the dry valley of the Minjiang River.

Electrochemiluminescent microoptoprobe with mini-grid working electrode and self-contained sample container

A new electrochemiluminescence (ECL) microoptoprobe with simple structure. small sampling volume and high efficiency was developed. It was constructed by fixing the transparent gold mini-grid on the end surface of the optical fiber, and by surrounding the fiber with the counter- and reference electrodes to form a self-contained three-electrode system. The use of mini-grid electrode increased the surface area and collection efficiency. which resulted in higher ECL signal and better sensitivity. The counter electrode together with one end of the fiber formed a mini-vessel, which eliminated the need of additional container and allowed to perform ECL detection in a very small volume (about 10 mul). The microoptoprobe obtained was characterized with the Ru(bpy)(3)(2-)-tripropylamine system and was applied for the determination of oxalate and chlorpromazine (CPZ). Detection limits (S/N = 3) were 5 x 10(-7) and 1 x 10(-6) mol l(-1) for oxalate and CPZ. respectively. The linear range for oxalate and CPZ extended from 1 x 10(-6) to 1 x 10(-3) mol l(-1), and from 5 x 10(-6) to 5 x 10(-4) mol l(-1). respectively.

Capillary Effect on Vertically Excited Surface Wave in Circular Cylindrical Vessel

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions was developed in inviscid fluids to investigate the motion of single free surface standing wave including the effect of surface tension.

Simulation of Free-Surface Flow in a Tank Using the Navier-Stokes Model and Unstructured Finite Volume Method

Modelling free-surface flow has very important applications in many engineering areas such as oil transportation and offshore structures. Current research focuses on the modelling of free surface flow in a tank by solving the Navier-Stokes equation. An unstructured finite volume method is used to discretize the governing equations. The free surface is tracked by dynamically adapting the mesh and making it always surface conforming. A mesh-smoothing scheme based on the spring analogy is also implemented to ensure mesh quality throughout the computaiton. Studies are performed on the sloshing response of a liquid in an elastic container subjected to various excitation frequencies. Further investigations are also carried out on the critical frequency that leads to large deformation of the tank walls. Another numerical simulation involves the free-surface flow past as submerged obstacle placed in the tank to show the flow separation and vortices. All these cases demonstrate the capability of this numerical method in modelling complicated practical problems.

Laboratory study on cracks in saturated sands

It has been reported([1]) that when a loosely packed column of saturated sand in a vertical cylindrical container is shock loaded axially by dropping to the floor, large horizontal cracks initiate, grow and eventually fade away in the sand as it settles under gravity. This paper shows that a similar phenomenon can also be observed when shock loading is replaced by forcing water to percolate upward through the sand column. It is believed that our result sheds further light on the physics of formation of these cracks.