含主应力轴旋转的土体一般应力应变关系

本文利用矩阵理论,分析了使主应力轴产生旋转的应力增量特性,并将一般应力增量分解为与应力共主轴部分及使之产生旋转部分。据此,将含主应力轴旋转的复杂三维问题简化为三维应力应变共轴问题和三主值不变绕某一主轴旋转问题的结合,大大简化了分析的难度。文中还结合有关模型给出了一般三维问题的具体计算方法。     

考虑主应力轴旋转的土体本构关系研究进展

对目前国内外考虑主应力轴旋转的试验研究及本构模型研究进行了总结分析,并对进一步研究提出了相应的建议．基于不同的加载条件,从纯主应力轴旋转和耦合主应力轴旋转两个方面,较全面的描述了主应力轴旋转情况下土体的基本变形特性,并对考虑主应力轴旋转的土体变形试验提出了进一步研究的建议．较为系统地评述了当前较有代表性的考虑主应力轴旋转的土体本构模型（边界面模型、多机构模型、运动硬化模型和广义塑性模型）,得出了广义塑性模型更适合用来描述考虑主应力轴旋转的土体变形特性的结论．总结未来考虑主应力轴旋转的土体本构关系研究的主要方向是:把握主应力轴旋转情况下土体变形的本质特性,建立推理严密、形式简单、适用方便的本构模型,并用来指导工程实践．     

Three-parametric robot manipulators with parallel rotational axes

The paper deals with asymptotic motions of 3-parametric robot manipulators with parallel rotational axes. To describe them we use the theory of Lie groups and Lie algebras. An example of such motions are motions with the zero Coriolis accelerations. We will show that there are asymptotic motions with nonzero Coriolis accelerations. We introduce the notions of the Klein subspace, the Coriolis subspace and show their relation to asymptotic motions of robot manipulators. The asymptotic motions are introduced without explicit use of the Levi-Civita connection.     

Some Aspects of Designing Multirim Composite Flywheels

Approximate solutions are given for stresses in a flexible cylindrical interlayer connecting concentric, rigid, cylindrical rims subjected to three loading cases: (i) rotation about the axis of symmetry; (ii) in-plane translation of the rims relative to each other; (iii) out-of-plane rotation of the rims relative to each other. The solutions are important for the multiple filament-wound composite rims used in energy storage flywheels, where the elastomeric interlayer idea has been proposed as a means of preventing high radial tensile stresses, which would otherwise break down the rims at less than optimal speeds. The compliances associated with the second and third loading cases are also given, establishing a simple means of analysis of the critical vibration frequencies of multirim flywheel rotors.     

Joint Distributions for Interacting Fluid Queues

Motivated by recent traffic control models in ATM systems, we analyse three closely related systems of fluid queues, each consisting of two consecutive reservoirs, in which the first reservoir is fed by a two-state (on and off) Markov source. The first system is an ordinary two-node fluid tandem queue. Hence the output of the first reservoir forms the input to the second one. The second system is dual to the first one, in the sense that the second reservoir accumulates fluid when the first reservoir is empty, and releases fluid otherwise. In these models both reservoirs have infinite capacities. The third model is similar to the second one, however the second reservoir is now finite. Furthermore, a feedback mechanism is active, such that the rates at which the first reservoir fills or depletes depend on the state (empty or nonempty) of the second reservoir.The models are analysed by means of Markov processes and regenerative processes in combination with truncation, level crossing and other techniques. The extensive calculations were facilitated by the use of computer algebra. This approach leads to closed-form solutions to the steady-state joint distribution of the content of the two reservoirs in each of the models.     

Optimal control of rigid body motion with the help of rotors using stereographic coordinates

This paper considers the problem of optimal controlling the rotational motion of a rigid body using three independent control torques developed by three rotors attached with the principal axes of inertia of the body and rotate with the help of electric motors rigidly mounted on the body. The optimal control law is given as non-linear function of new parameterizations of the rotation group derived by using the stereographic projection of the Euler parameters. Given a cost function we seek for a stabilizing feedback control law that minimizes this cost and asymptotically stabilizes the rotational motion of the body. The stabilizing properties of the proposed controllers are proved by using the optimal Liapunov function. Numerical examples and simulation study are presented.     

Variable energy blast wave through rotating gas

The aim of the present paper is to study the propagation of a variable energy blast wave (cylindrical) through a gas having solid-body rotation. The modified similarity method has been used to obtain the first, second and third approximation solutions. The analysis shows that the effects of solid-body rotation on the flow are of third order. Variation of pressure, density and radial velocity distributions with initial angular velocity has been discussed.     

Solitary-wave families of the Ostrovsky equation: An approach via reversible systems theory and normal forms

The Ostrovsky equation is an important canonical model for the unidirectional propagation of weakly nonlinear long surface and internal waves in a rotating, inviscid and incompressible fluid. Limited functional analytic results exist for the occurrence of one family of solitary-wave solutions of this equation, as well as their approach to the well-known solitons of the famous Korteweg–de Vries equation in the limit as the rotation becomes vanishingly small. Since solitary-wave solutions often play a central role in the long-time evolution of an initial disturbance, we consider such solutions here (via the normal form approach) within the framework of reversible systems theory. Besides confirming the existence of the known family of solitary waves and its reduction to the KdV limit, we find a second family of multihumped (or N-pulse) solutions, as well as a continuum of delocalized solitary waves (or homoclinics to small-amplitude periodic orbits). On isolated curves in the relevant parameter region, the delocalized waves reduce to genuine embedded solitons. The second and third families of solutions occur in regions of parameter space distinct from the known solitary-wave solutions and are thus entirely new. Directions for future work are also mentioned.     

A note on the dimensions of projections of cells inE n

We answer a question of J. Sternfeld by producing a topological 3-cell in four dimensional Euclidean space whose projection onto the plane of the first two co-ordinate axes is a 2-cell but whose projections onto the 3-spaces determined by the first, second and third as well as the first, second and fourth co-ordinate axes are also 2-cells. We generalize this construction in higher dimensions.     

Multi‐dimensional Lotka–Volterra systems for carcinogenesis mutations

In the paper we consider three classes of models describing carcinogenesis mutations. Every considered model is described by the system of (n+1) equations, and in each class three models are studied: the first is expressed as a system of ordinary differential equations (ODEs), the second—as a system of reaction–diffusion equations (RDEs) with the same kinetics as the first one and with the Neumann boundary conditions, while the third is also described by the system of RDEs but with the Dirichlet boundary conditions. The models are formulated on the basis of the Lotka–Volterra systems (food chains and competition systems) and in the case of RDEs the linear diffusion is considered. The differences between studied classes of models are expressed by the kinetic functions, namely by the form of kinetic function for the last variable, which reflects the dynamics of malignant cells (that is the last stage of mutations). In the first class the models are described by the typical food chain with favourable unbounded environment for the last stage, in the second one—the last equation expresses competition between the pre‐malignant and malignant cells and the environment is also unbounded, while for the third one—it is expressed by predation term but the environment is unfavourable. The properties of the systems in each class are studied and compared. It occurs that the behaviour of solutions to the systems of ODEs and RDEs with the Neumann boundary conditions is similar in each class; i.e. it does not depend on diffusion coefficients, but strongly depends on the class of models. On the other hand, in the case of the Dirichlet boundary conditions this behaviour is related to the magnitude of diffusion coefficients. For sufficiently large diffusion coefficients it is similar independently of the class of models, i.e. the trivial solution that is unstable for zero diffusion gains stability. Copyright © 2009 John Wiley & Sons, Ltd.     

Über drei zwangläufig gegeneinander bewegte Cayley/Klein-Ebenen

If three Euclidean planes move relatively to each other, the three poles of rotation are either identical or pairwise distinct and collinear. In the second case the distances of the poles are in the ratio of the motions' angular velocities. These known facts of Euclidean kinematics can be generalized in a largely uniform way to plane Cayley/Klein motions with finite poles. For the angular velocities we give a representation which is valid for all considered Cayley/Klein motions. Application of the duality principle of the projective plane yields a proposition about concurrent fixed lines. We also generalize the generation of a pair of envelope curves of a Euclidean motion as paths of a point of a third moved plane.

     

A differentiated service scheme to optimize website revenues

We consider a website host server with web quality of service (QoS) capabilities to offer differentiated services. A quantitative modelling framework is set up to analyse the economic benefits of differentiated services and to build optimization models for managing the website host's connection bandwidth to the Internet (which is assumed to be the bottleneck factor determining the QoS). Three models are formulated corresponding to three operational scenarios to provide differentiated services. The first is for the marketing manager to classify visit requests as premium or basic when the information technology (IT) manager has already reserved bandwidths for the two classes, and the second is for the IT manager to allocate the total available bandwidth to each class when the marketing manager has already designated which visit requests are premium and which are basic. The third is for the joint optimization of request classification and bandwidth allocation when centralized coordination is possible. Analytic results are obtained for a special case that corresponds to very impatient customers requesting large amounts of data. Qualitative insights gained and numerical results obtained strongly support the implementation of differentiated services. More interestingly, the decentralized models that use simple and rough-cut rules yield solutions almost as good as the joint optimization model.     

A Geometric Approach to Actuator Failure in Robotic Manipulators

The use of robotic manipulators in remote and sensitive areas calls for more robust solutions when handling joint failure, and the industry demands mathematically robust approaches to handle even the worst case scenarios. Thus, a systematic analysis of the effects of external forces on manipulators with passive joints is presented. In parallel manipulators passive joints can appear as a design choice or as a result of torque failure. In both cases a good understanding of the effects that passive joints have on the mobility and motion of the parallel manipulator is crucial. We first look at the effect that passive joints have on the mobility of the mechanism. Then, if the mobility, considering passive joints only, is not zero we find a condition for which the parallel manipulator is conditionally equilibrated with respect to a specific external force. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Model Equations and Traveling Wave Solutions for Shallow-Water Waves with the Coriolis Effect

In the present study, we start by formally deriving the simplified phenomenological models of long-crested shallow-water waves propagating in the equatorial ocean regions with the Coriolis effect due to the Earth’s rotation. These new model equations are analogous to the Green–Naghdi equations, the first-order approximations of the KdV-, or BBM type, respectively. We then justify rigorously that in the long-wave limit, unidirectional solutions of a class of KdV- or BBM type are well approximated by the solutions of the Camassa–Holm equation in a rotating setting. The modeling and analysis of those mathematical models then illustrate that the Coriolis forcing in the propagation of shallow-water waves can not be neglected. Indeed, the CH-approximation with the Coriolis effect captures stronger nonlinear effects than the nonlinear dispersive rotational KdV type. Furthermore, we demonstrate nonexistence of the Camassa–Holm-type peaked solution and classify various localized traveling wave solutions to the Camassa–Holm equation with the Coriolis effect depending on the range of the rotation parameter.

     

随机二阶锥二次规划逆问题的SAA方法

本文讨论一类随机的二阶锥二次规划逆问题, 该模型是一个含有二阶锥互补约束的随机二次规划模型, 对解释部分实际问题有着一定的优势。为了求解该模型, 本文引入了随机抽样技术和互补约束光滑化近似技术, 得到问题的近似子问题。本文证明, 只要子问题的解是存在且收敛的, 则该极限以概率一是原问题的C-稳定点; 若严格互补条件和二阶必要性条件成立, 则该极限以概率1是原问题的M-稳定点。一个简单的数值实验验证了该算法具有一定的可行性。     

随机二阶锥二次规划逆问题的SAA方法

本文讨论一类随机的二阶锥二次规划逆问题, 该模型是一个含有二阶锥互补约束的随机二次规划模型, 对解释部分实际问题有着一定的优势。为了求解该模型, 本文引入了随机抽样技术和互补约束光滑化近似技术, 得到问题的近似子问题。本文证明, 只要子问题的解是存在且收敛的, 则该极限以概率一是原问题的C-稳定点; 若严格互补条件和二阶必要性条件成立, 则该极限以概率1是原问题的M-稳定点。一个简单的数值实验验证了该算法具有一定的可行性。     

Nonlinear Modeling and Tracking Control of a Hydraulic Rotary Vane Actuator

Rotary vane actuators as rotational drives provide rotational movements directly because they are constructed as a joint and actuator in one. So it is possible to pass on the disadvantageous transmission kinematics used with the so far usual differential cylinders at the arms of large manipulators. However, the use of hydraulic rotary vane actuators is associated with high internal oil leakage and/or high friction. Therefore, a nonlinear dynamic model for such an actuator, driving a rigid robot arm, as well as its nonlinear control are derived. To achieve tracking control a model based control law is set up using fundamental linear differential equations for the tracking error. The control law is implemented and tested on a testbed, the produced experimental results are presented. The same control algorithm can also be used to realize nonlinear disturbance attenuation for hydraulic rotary vane actuators via tracking control. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)