Numerical analysis of superposed GSPNs

The numerical analysis of various modeling formalisms profits from a structured representation for the generator matrix Q of the underlying continuous-time Markov chain, where Q is described by a sum of tensor (Kronecker) products of much smaller matrices. In this paper, we describe such a representation for the class of superposed generalized stochastic Petri nets (GSPNs), which is less restrictive than in previous work. Furthermore a new iterative analysis algorithm is proposed. It pays special attention to a memory-efficient representation of iteration vectors as well as to a memory-efficient structured representation of Q in consequence the new algorithm is able to solve models which have state spaces with several million states, where other exact numerical methods become impracticable on a common workstation     

Binary superposed quantum decision diagrams

Binary superposed decision diagrams (BSQDDs) are a new type of quantum decision diagram that can be used for representing arbitrary quantum superpositions. One major advantage of BSQDDs is that they are dependent on the types of gates used in synthesis and a BSQDD can be used to efficiently generate a quantum array that will initialize the quantum superposition that the BSQDD represents. Transformation rules for BSQDDs allow BSQDDs to be reduced into simpler BSQDDs that represent the same quantum superposition. Canonical forms exist for a broad class of BSQDDs. This allows BSQDDs to be used for synthesizing quantum arrays that are capable of initializing arbitrary quantum superpositions.     

Transient analysis of acyclic markov chains

Continuous-time Markov chains are commonly used insystem reliability modeling. In this paper, we discuss a method for automatically deriving transient solutions that are symbolic in t for acyclic Markov chains. Our method also includes parametric sensitivity analysis of the transient solution and several cumulative measures associated with Markov chain behavior. We include three examples, one to show the use of our method in evaluating approximate solution techniques, one showing parametric sensitivity analysis of a large Markov model, and one demonstrating the computation of cumulative measures for an acyclic Markov reward process.     

Transient analysis of stochastic fluid models

We analyze the transient behavior of stochastic fluid flow models in which the input and output rates are controlled by a finite homogeneous Markov process. Such models are used in asynchronous transfer mode (ATM) to evaluate the performance of fast packet switching and in manufacturing systems for the performance of producers and consumers coupled by a buffer. The transient analysis of such models has already been considered in earlier works and solutions have been obtained by the use of Laplace transform. We derive in this paper a new transient solution only based on recurrence relations. We show that this solution is particularly interesting for its numerical properties. The limiting behavior of the solution is also considered. We empirically show that the algorithm for computing the transient solution can be stopped when some stationary behavior is detected.     

Character of superposed states under deterministic LOCC

In this paper we investigate the effect of superposition of states on local conversion of pure bipartite states under deterministic LOCC. We are able to form a bridge between comparable and incomparable classes of states through the linear superposition of states. For example, if we consider two pairs of incomparable states, then their superposition may result into a comparable pair of states. We investigate many such cases and provide some of the results in tabular form. We also investigate the entanglement behavior of such classes of states, specifically their monotone nature. Finally we provide some bounds of different measures of entanglement based on the idea of comparability and incomparability under deterministic LOCC.     

Transient analysis of structures by stiffly stable methods

The equation of motion for a general structure can be cast as a system of second order ordinary differential equations in discretized form. The locus of the roots for the homogeneous form of these equations is analyzed and related to the stability region for general, stiffly stable, linear multistep methods. The problem of recasting the second order system as a first order system is analyzed, noting that the final system to be solved is no larger than the original system. A discussion of error control is included and some specific formulas are given. Finally, a new family of third order formulas with a number of advantages over previously published formulas is given.     

Transient dynamic analysis of ferro-fluid bearing spindle motor

 With areal recording density of hard disk drives (HDD) historically growing at an average of 60% per year and fast spindle speed to continue to reduce access time, it is becoming increasingly more difficult to maintain the precise positioning required of the GMR heads to read and write data. Any unexpected vibration will cause the data written to a wrong data track. Consequently, the dynamic behaviors of HDD spindle systems and their potential influences on track misregistration are key issues in disk drive design. With rapid advances in the emerging consumer device market, the fluid bearing spindle motors, which have low NRRO, low acoustic noise and high damping, are being developed as next generation spindles. This paper is to study transient dynamic performance of HDD ferro-fluid bearing spindle systems. The FEA based component mode synthesis method is used to reduce the overall spindle system dimensions. The effect of the unbalanced magnetic pulls (UMP) due to two different types of motor configurations (balanced and unbalanced configurations) on the dynamic behaviors of spindle system was investigated. The simulated results show that the motor with balanced configuration provides better spindle dynamic performance due to absence of UMP. The UMP derived from the unbalanced configuration can result in some frequency resonance interactions and adversely affect the HDD servo-tracking system. Received: 5 July 2001/Accepted: 17 October 2001     

Classical and superposed learning for quantum weightless neural networks

A supervised learning algorithm for quantum neural networks (QNN) based on a novel quantum neuron node implemented as a very simple quantum circuit is proposed and investigated. In contrast to the QNN published in the literature, the proposed model can perform both quantum learning and simulate the classical models. This is partly due to the neural model used elsewhere which has weights and non-linear activations functions. Here a quantum weightless neural network model is proposed as a quantisation of the classical weightless neural networks (WNN). The theoretical and practical results on WNN can be inherited by these quantum weightless neural networks (qWNN). In the quantum learning algorithm proposed here patterns of the training set are presented concurrently in superposition. This superposition-based learning algorithm (SLA) has computational cost polynomial on the number of patterns in the training set.     

Transient state analysis of separated flow around a sphere

Transient state solutions of the Navier-Stokes equations were obtained for incompressible flow around a sphere accelerating from zero initial velocity to its terminal free falling velocity. By assuming rotational symmetry about the axis in the direction of motion, the Navier-Stokes equations and the continuity equation were simplified in terms of vorticity and stream function. The instantaneous acceleration of the falling sphere was calculated by considering the difference between the gravitational force and the drag force in a transient state. A set of implicit finite difference equations was developed. In order to obtain accurate information around the body, an exponential transformation along the radial direction was used to provide finer meshes in the vicinity of the surface of the sphere. The vorticity equation was solved by an alternating direction implicit (ADI) method while the stream function equation was solved by a successive over-relaxation (SOR) method. Simultaneous solutions were obtained. Transient state solutions were compared with steady state solutions for Reynolds numbers up to 300. Separations first occurred at a Reynolds number 20 for steady state flows and at Reynolds numbers 22·46 and 28·24 for transient state flows with terminal Reynolds numbers of 100 and 300, respectively. Separation angles, sizes of separation regions, and drag coefficents were calculated for both steady and unsteady states. Good agreement was obtained with existing experimental data in the steady state.     

Transient and steady-state MSE analysis of the IMPNLMS algorithm

Several techniques have been proposed in the literature to accelerate the convergence of adaptive algorithms for the identification of sparse impulse responses (i.e., with energy concentrated in a few coefficients). Among these techniques, the improved μ-law proportionate normalized least mean squares (IMPNLMS) algorithm is one of the most effective. This paper presents an accurate transient analysis of this algorithm and derives an estimate of its steady-state MSE, without requiring the assumption of white Gaussian input signals.     

Transient performance analysis in robust nonlinear adaptive control

This paper deals with the problem of controlling unknown linear systems in the presence of strictly proper unmodelled dynamics and bounded disturbances. Adaptive controllers that ensure the closed-loop global (uniform) stability and asymptotic performances can be designed following either the backstepping approach or the certainty-equivalence method. The main shortcoming of the involved controllers is that they do not allow quantification of the closed-loop transient behaviour. In this paper, the transient issue is addressed for backstepping adaptive controllers. A L_∞ bound on the tracking error is explicitly given as a function of the design parameters. This shows that the error can be made arbitrarily small by sufficiently increasing the design gains.     

Transient analysis and simulation of nonuniform lossy transmission lines

A new formulation of equations of the nonuniform lossy transmission line, in the form of integral equations based on the method of characteristics, has been introduced. Two methods of solution of these equations are presented, the first based on discretization of the integrals and, the second, a method of successive approximations, are presented and the results are compared. The presented integral equations of the line have interesting circuit representations and exhibit wave processes such as reflection, distortion, and attenuation. © 1992 John Wiley & Sons, Inc.     

Transient analysis of non-Markovian models using stochastic state classes

The method of stochastic state classes approaches the analysis of Generalised Semi Markov Processes (GSMPs) through the symbolic derivation of probability density functions over supports described by Difference Bounds Matrix (DBM) zones. This makes steady state analysis viable, provided that at least one regeneration point is visited by every cyclic behaviour of the model.We extend the approach providing a way to derive transient probabilities. To this end, stochastic state classes are extended with a supplementary timer that enables the symbolic derivation of the distribution of time at which a class can be entered. The approach is amenable to efficient implementation when model timings are given by expolynomial distributions, and it can be applied to perform transient analysis of GSMPs within any given time bound. In the special case of models underlying a Markov Regenerative Process (MRGP), the method can also be applied to the symbolic derivation of local and global kernels, which in turn provide transient probabilities through numerical integration of generalised renewal equations. Since much of the complexity of this analysis is due to the local kernel, we propose a selective derivation of its entries depending on the specific transient measure targeted by the analysis.     

汽车乘员舱空调制冷CFD瞬态分析

为提高汽车乘员舱的热舒适性,缩短空调制冷系统的开发周期,降低开发成本,对某车型乘员舱空调制冷过程进行30 min的CFD瞬态计算.由管道流量分配和总压分布可知,各管道流量分配较均匀,总压分布合理,没有压力损失过大的区域.由气流速度分布和温度场随时间变化情况可知,空调开启15 min后乘员舱温度基本稳定不变,达到人体舒适温度,但舱内后排中间位置温度偏低.计算得到的舱内监控点温度曲线与试验所测温度曲线基本吻合,证明该数值仿真方案有效.     

Transient hydrodynamic analysis of the transition process of bulb hydraulic turbine

In this paper, a semi-implicit method for solving pressure coupled equations used to calculate the flow field, and dynamic mesh were employed to simulate the three-dimensional dynamic turbulent flow of whole flow channels, in start transition process and runaway transition process of bulb hydraulic turbine. In above processes, the transition process of pressure field and flow field were realistically modeled and simulated, which reflects the influence of water flow state, after passing through guide vanes on the inflow of the runner blades, and reveals the flow field variations in the transition process. The numerical results show that: during the start transition process, with the increase of guide vane opening, the flow circulation produced by water flowing through the guide vanes becomes smaller; therefore, the rotational acceleration of the runner decreases and the rotational speed value reduces. In the runaway transition process, the hydraulic turbine operating with load has a sudden load rejection and then, the hydraulic turbine rotational speed is rising with the guide vane closing, leading to pressure pulsations and severe vortex phenomenon, which will cause significant vibrations of swings.     

Transient analysis of sharp thermal gradients using coarse finite element meshes

This paper investigates the application of the generalized finite element method with global–local enrichments (GFEM^gl) to problems of transient heat transfer involving localized features. The GFEM^gl is utilized in order to numerically construct general, specially-tailored shape functions yielding high levels of accuracy on coarse FEM meshes. The use of time-dependent shape functions requires that the system of equations be discretized temporally first, and then spatially in order to properly account for the time-dependency. The standard α-method is used for the time integration scheme. The transient three-dimensional GFEM^gl is then applied to a laser heating example in order to demonstrate its ability to resolve localized, transient features on a fixed, coarse mesh. Convergence analysis of the proposed method as well as applications to heterogeneous materials, and moving heat sources are also provided.     

激光加工聚合物微流道暂态弹性热应力分析

激光直写聚合物微流道是非常有效的加工方法,但是,由于激光烧蚀聚合物的热流密度很高,在小的热影响区产生过大的集中热应力,热应力导致产生微裂纹,降低材料的强度和疲劳寿命,严重的引起材料破坏性失效.为了预测激光烧蚀时的热应力大小随时间空间的变化规律,根据烧蚀模型推出了三维弹性热应力模型.首先由烧蚀模型预测温度场分布和烧蚀流道外形,根据流道轮廓和温度场计算弹性热应力场与烧蚀过程的关系.分析结果表明弹性热应力位于低于或平行于烧蚀表面的一定厚度层内,这也许是引起表面微裂纹的原因.     

Transient analysis including the low- and the medium-frequency ranges of engineering structures

This paper deals with a computational method for transient dynamic analysis which enables one to cover both the low- and medium-frequency ranges. This is a frequency approach in which the low-frequency part is obtained through a classical technique while the medium-frequency part is handled through the Variational Theory of Complex Rays (VTCR) initially introduced for vibrations. The aim of this paper is to show the capabilities of the method for transient analyses of complex engineering structures submitted to impact loadings.     

Transient analysis of multi-server queues with Markov-modulated Poisson arrivals and overload control

This paper studies the transient behavior of a Markov-molulated Poisson arrival queue under overload control. The queue has finite or infinite buffer capacity with multiple exponential servers. A Markov-modulated Poisson process is used to represent an aggregated voice or video packet arrival process in integrated service networks. By overload control, we mean to properly adapt the arrival process once the buffer contents exceed a designated level. The probability distribution of queue length as a function of time is obtained. The temporal effect of the overload control is measured in two forms. While in overload, we measure the amount of time for the queue to fall into underload. While in underload, we measure the amount of time for the queue to rise to overload. A proper design of the control will not only reduce the fall time but also increase the rise time. We also explore the transient queueing behavior as affected by time stochastic properties of the underlying Markov chain for the arrival process.