滚珠丝杠中回珠器的几何结构(续)

前文[1]对回珠器进行了几何学结构的分析,给出了回珠器的近似计算方法.本文在此基础上考察有倒角的丝杠中回珠器的几何结构,使前文的结果成为本文的极限情形.为简略起见,仍采用前文的记号,并且接着前文(包括公式的编号)来叙述.     

热力学理论与空化现象

有关空化现象的理论研究大多建立在1917年由Rayleigh[1]开始的,后由Plesset等人发展起来的单个空泡运动理论的基础上.该理论仅从流体动力学的某些观点出发,考虑了力的作用,对诸如水下爆炸等问题的讨论,无疑是合适的.由于忽视了空泡生长或消失过程中气、液两相间的物质交换及能量转化,因此对空化现象的讨论则认为是不完备的. 本文主要从热力学观点.分析高速水流中的空化现象、空泡形成条件、空化数以及讨论空化模型实验的相似性问题.     

边界和算子双摄动的高阶椭圆型方程一般边值问题解的渐近式

本文在文[1]和[2]的基础上研究边界和算子双摄动的高阶椭圆型方程一般边值问题的奇摄动,建立含两参数的渐近解表达式,导出求渐近解的迭代过程,给出余项估计,改进和拓广了前文的工作.     

随机定向收缩及其应用*

作为Altman的定向收缩理论[4,5]和Lee,Padgett的随机收缩理论[1,2]的推广,本文对非线性集值随机算子引入了随机定向收缩概念,利用这一新概念和超限归纳法,我们证明了非线性集值随机算子方程随机解的几个存在性定理.这些定理分别改进和推广了[1,2,4,5,11]中相应的结果.其次,给出了我们的结果对非线性随机积分和微分方程的某些应用.     

指定根的最小树形图的一个算法

文[1]给出了求有向图的最小树形图的算法,[2]中给出了求有指定根的最小树形图的算法.本文采用了[1]和[2]中的收缩回路的方法,给出了求有指定根的最小树形图的一个算法.设有向图G=(X,U),其中X={x_1,x_2,…,x_n}是顶点的集合,     

非线性膨胀型映射的不动点定理

王尚志等在[1]中就B.E.Rhoades在[2]中所归纳出的某些压缩型映射给出了相应的膨胀型映射的定义及不动点定理。本文在此基础上对部分膨胀型映射继续讨论其不动点的存在性,唯一性及不动点集的性质。     

多边形与多面体的优美定值

文[1],[2]分别给出了正三角形和正四面体、正方形和正方体的定值性质.文[3]将结论做了进一步推广,给出了平行四边形和平行六面体的类似定值性质.笔者在此将上述结论作更进一步推广,并就文[2]和文[3]性质的证明中笔者认为值得商榷的地方作一说明.     

关于随机变量期望方差的两个注记

文献[1]中给出了有关条件期望与三个随机变量独立的两个充要条件,本文通过几个反例说明其充分性是不成立的.分析了文献[4]中一个定理证明存在的错误,并给出了新的证明.     

搭接焊缝内的准确应力分布

本文给出了受弯矩M作用的搭接焊缝内的准确应力分布,结合前文[1]所给出的受集中力P作用的搭接焊缝内的应力分布准确解,使搭接焊缝的设计可以建立在准确的理论解基础之上。     

Führer f在不同环中分解的理论(Ⅱ)

<正> 引言本文目的是把作者在前文[1]中所获得的结果作出更一般的研究.设 o 是合有么元且满足理想约束极小条件的一个整区,(?)是合有与 o 相同么元且包含 o 的一个整区,并且假设(?)是代数整封闭的.记 Q(?)与 Q(o)如前文[1]中那样分别为(?)及 o 的商体,并且满足 Q(?):Q(?)=n<∞ 的条件.因此在(?)中以(?)的非零理想     

Vortex shedding behind a rising bubble and two-bubble coalescence: A numerical approach

In this work, we present the computational results on the wake instability in wobbling bubble regime as well as on the coalescence of two bubbles in different shape regimes. This is a continuation of our previous studies on the dynamics of a single gas bubble rising in a viscous liquid (see [A. Smolianski, H. Haario, P. Luukka, Computational Study of Bubble Dynamics, Research Report 86, Lappeenranta University of Technology, Finland]), and we use the same, finite-element/level-set/operator-splitting method that was proposed in [A. Smolianski, Numerical Modeling of Two-Fluid Interfacial Flows, Ph.D. Thesis, University of Jyväskylä, 2001]. The numerical method allows to simulate a wide range of flow regimes, accurately capturing the shape of the deforming interface of the bubble and the surface tension effect, while maintaining a good mass conservation. Due to the highly unstable and small-scale nature of the considered problems there are very few experimental investigations, but the comparison with available experimental data confirms a good accuracy of our numerical predictions. Our studies show that plausible results can be obtained with two-dimensional numerical simulations, when a single buoyant bubble or a coalescence of two bubbles is considered.     

Nonlinear Dynamics of a Bubble Contrast Agent Oscillating near an Elastic Wall

Contrast agent microbubbles, which are encapsulated gas bubbles, are widely used to enhance ultrasound imaging. There are also several new promising applications of the contrast agents such as targeted drug delivery and noninvasive therapy. Here we study three models of the microbubble dynamics: a nonencapsulated bubble oscillating close to an elastic wall, a simple coated bubble and a coated bubble near an elastic wall.We demonstrate that complex dynamics can occur in these models. We are particularly interested in the multistability phenomenon of bubble dynamics. We show that coexisting attractors appear in all of these models, but for higher acoustic pressures for the models of an encapsulated bubble.We demonstrate how several tools can be used to localize the coexisting attractors. We provide some considerations why the multistability can be undesirable for applications.     

VECTORIAL EKELAND VARIATIONAL PRINCIPLE AND CYCLICALLY ANTIMONOTONE EQUILIBRIUM PROBLEMS

In this article, we extend the cyclic antimonotonicity from scalar bifunctions to vector bifunctions. We find out a cyclically antimonotone vector bifunction can be regarded as a family of cyclically antimonotone scalar bifunctions. Using a pre-order principle(see Qiu, 2014), we prove a new version of Ekeland variational principle(briefly, denoted by EVP), which is quite different from the previous ones, for the objective function consists of a family of scalar functions. From the new version, we deduce several vectorial EVPs for cyclically antimonotone equilibrium problems, which extend and improve the previous results. By developing the original method proposed by Castellani and Giuli, we deduce a number of existence results(no matter scalar-valued case,or vector-valued case), when the feasible set is a sequentially compact topological space or a countably compact topological space. Finally, we propose a general coercivity condition. Combining the general coercivity condition and the obtained existence results with compactness conditions, we obtain several existence results for equilibrium problems in noncompact settings.     

Transport equation with boundary conditions for free surface localization

Summary. During the filling stage of an injection moulding process, which consists in casting a melt polymer in order to manufacture plastic pieces, the free interface between polymer and air has to be precisely described. We set this interface as a zero level set of an unknown function. This function satisfies a transport equation with boundary conditions, where the velocity field has few regularity properties. In a first part, we obtain existence and uniqueness result for these equations, under weaker regularity assumptions than C. Bardos [Bar70], and C. Bardos, Y. Leroux and J.C. Nedelec [BLN79] in previous articles, but stronger assumptions than R.J. DiPerna and P.L. Lions [DL89b] who studied the case without boundary condition. We also study some regularity properties of the interface. A second part is devoted to an application to injection molding of melt polymer. We give a numerical experiment which shows that our method leads to an accurate localization of interface, which is robust, since it easily handles changes of topology of the free interface, as bubble formation or fusion of two fronts of melt polymer. Received November 1, 1997 / Revised version received December 9, 1998 / Published online September 24, 1999     

On the performance of West’s bubble test: A simulation approach

In this research we examine the ability of West’s bubble test [1] in detecting speculative bubbles using Brock’s (1982) [2] intertemporal general equilibrium model of asset pricing as the basis for a simulation study. In this setting, (1) the economy, by construction is efficient and produces the maximally possible amount of welfare for society, and (2) asset prices reflect the utility-maximizing behavior of consumers and the profit-maximizing behavior of firms. We find that the West’s bubble test flag as “bubbles” in the simulated data yet the data is produced from an economy in which markets are efficient in welfare production.     

Mixed boundary value problems with a shift for a pair of metaanalytic and analytic functions

In this article, we reconsider the mixed boundary value problem on the unit circle for a pair of metaanalytic and analytic functions as in Du and Wang (2008) [9]. By adopting appropriate transformations, we convert the problem into two independent boundary value problems for analytic functions. We then obtain expressions of solution and condition of solvability for the mixed boundary value problem. The forms of the solutions and the condition of solvability here are rather dissimilar to those in Du and Wang (2008) [9]. But the equivalence is established at the end of this article.     

Numerical study of dynamics of single bubbles and bubble swarms

A systematic computational study of the dynamics of gas bubbles rising in a viscous liquid is presented. Two-dimensional simulations are carried out. Both the dynamics of single bubbles and small groups of bubbles (bubble swarms) are considered. This is a continuation of our previous studies on the two-bubble coalescence and vortex shedding [A. Smolianski, H. Haario, P. Luukka, Vortex shedding behind a rising bubble and two-bubble coalescence: a numerical approach, Appl. Math. Model. 29 (2005) 615–632]. The proposed numerical method allows us to simulate a wide range of flow regimes, accurately capturing the shape of the deforming interface of the bubble and the surface tension effect, while maintaining the mass conservation. The computed time-evolution of bubble’s position and rise velocity shows a good agreement with the available experimental data. At the same time, the results on the dynamics of bubble interface area, which are, up to our knowledge, presented for the first time, show how much the overall mass transfer would be affected by the interface deformation in the case of the bubble dissolution. Another set of experiments that are of interest for chemical engineers modelling bubbly flows concerns the bubble swarms and their behavior in different bubble-shape regimes. The ellipsoidal and spherical shape regimes are considered to represent, respectively, the coalescing and non-coalescing bubble swarms. The average rise velocities of the bubble swarms are computed and analyzed for both regimes.     

Variational Formulation and Numerical Implementation of Diffusion in Hydrogels at Finite Strains

Hydrogels are polymeric materials with a cross-linked network which can absorb water. Due to their bio-compatibility, hydrogels have many applications in biology and medicine. Recently modeling the mechanical behavior of hydrogels has attracted a great deal of attention among researchers, see e.g., [1] and [2]. Following our previous works [3], [4] and [5] we now present a variational framework for swelling phenomenon in hydrogels. The variational formulation of the problem can be done using a saddle-point principle or a minimization principle. Saddle-point principle has to fulfill the Ladyzhenskaya-Babuška-Brezzi (LBB) condition in order to lead to a stable finite element scheme. The key aspect of our proposed minimization principle is its advantage with regard to an unconstrained fem implementation. In this work we aim to compare the numerical performance of these two variational formulations for swelling of hydrogels. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical study of formation of a series of bubbles at a submerged orifice

Bubble formation from a submerged orifice is widely applied in bio-process and chemical reaction systems. In this study, the effects of different orifice diameters and contact angles in Period-I and Period-II regimes are studied systematically on a 2D axisymmetric domain. Simulation results are presented from the formation of the first bubble and explained by means of the surrounding fluid field, bubble interaction, and bubble aspect ratio.The orifice diameter is varied from 0.6 mm to 3 mm. The numerical results show that the detachment time of all bubbles remains constant (in time) for smaller orifice diameters (d_a ≤ 1.5 mm), while the detachment time of the first bubble is different from the rest of the bubbles for larger orifice diameters (d_a ≥ 2 mm), which is due to the different surrounding flow field. Contact angles from 60° to 165° are considered for the gas flow rates in the regime of bubble pairing, and it is observed that the bubble detachment time decreases when the contact angle increases, and it converges to a constant value when the contact angle is larger than 135°. In addition, the transition from period doubling to deterministic chaos (in which there is a variable number of bubbles within each period) is observed.A new scenario of inserting a submerged tube upward into the liquid is considered and compared to the previous cases. It is observed that when the tube is vertically inserted into the liquid, the bubble detachment time is even smaller because of higher influence from the surrounding liquid field, leading to a different phenomenon from the non-inserted tube cases.     

Equilibrium and perfection in discounted supergames

In this paper, we discuss equilibrium and perfect equilibrium in a simplified model of the supergame. We assume that players can observe the mixed moves employed by all players at each previous stage. For this model, we obtain a complete characterization of the set of equilibrium outcomes, and a fairly weak sufficient condition for this set to coincide with the set of perfect equilibrium outcomes.Inter alia, simple proofs of the Folk Theorem and the result that the requirement of perfection does not eliminate any equilibrium outcomes for the undiscounted supergame are presented.