Ancient Chinese algorithm: The Ying Buzu Shu (method of surplus and deficiency) vs Newton iteration method

Air exploratory discussion of an ancient Chinese algorithm, the Ying Buzu Shu, in about 2nd century BC, known as the rule of double false position in the West is given. In addition to pointing out that the rule of double false position is actually a translation version of the ancient Chinese algorithm, a comparison with well-known Newton iteration method is also made. If derivative is introduced, the ancient Chinese algorithm reduces to the Newton method. A modification of the ancient Chinese algorithm is also proposed, and some of applications to nonlinear oscillators are illustrated.

A Study of Composite Beam with Shape Memory Alloy Arbitrarily Embedded under Thermal and Mechanical Loadings

The constitutive relations and kinematic assumptions on the composite beam with shape memory alloy (SMA) arbitrarily embedded are discussed and the results related to the different kinematic assumptions are compared. As the approach of mechanics of materials is to study the composite beam with the SMA layer embedded, the kinematic assumption is vital. In this paper, we systematically study the kinematic assumptions influence on the composite beam deflection and vibration characteristics. Based on the different kinematic assumptions, the equations of equilibrium/motion are different. Here three widely used kinematic assumptions are presented and the equations of equilibrium/motion are derived accordingly. As the three kinematic assumptions change from the simple to the complex one, the governing equations evolve from the linear to the nonlinear ones. For the nonlinear equations of equilibrium, the numerical solution is obtained by using Galerkin discretization method and Newton-Rhapson iteration method. The analysis on the numerical difficulty of using Galerkin method on the post-buckling analysis is presented. For the post-buckling analysis, finite element method is applied to avoid the difficulty due to the singularity occurred in Galerkin method. The natural frequencies of the composite beam with the nonlinear governing equation, which are obtained by directly linearizing the equations and locally linearizing the equations around each equilibrium, are compared. The influences of the SMA layer thickness and the shift from neutral axis on the deflection, buckling and post-buckling are also investigated. This paper presents a very general way to treat thermo-mechanical properties of the composite beam with SMA arbitrarily embedded. The governing equations for each kinematic assumption consist of a third order and a fourth order differential equation with a total of seven boundary conditions. Some previous studies on the SMA layer either ignore the thermal constraint effect or implicitly assume that the SMA is symmetrically embedded. The composite beam with the SMA layer asymmetrically embedded is studied here, in which symmetric embedding is a special case. Based on the different kinematic assumptions, the results are different depending on the deflection magnitude because of the nonlinear hardening effect due to the (large) deflection. And this difference is systematically compared for both the deflection and the natural frequencies. For simple kinematic assumption, the governing equations are linear and analytical solution is available. But as the deflection increases to the large magnitude, the simple kinematic assumption does not really reflect the structural deflection and the complex one must be used. During the systematic comparison of computational results due to the different kinematic assumptions, the application range of the simple kinematic assumption is also evaluated. Besides the equilibrium study of the composite laminate with SMA embedded, the buckling, post-buckling, free and forced vibrations of the composite beam with the different configurations are also studied and compared.

A Continuation Method of Parameter Inversion for Non-Equilibrium Convection-Dispersion Equation

Based on the homotopy mapping, a globally convergent method of parameter inversion for non-equilibrium convection-dispersion equations (CDEs) is developed. Moreover, in order to further improve the computational efficiency of the algorithm, a properly smooth function, which is derived from the sigmoid function, is employed to update the homotopy parameter during iteration. Numerical results show the feature of global convergence and high performance of this method. In addition, even the measurement quantities are heavily contaminated by noises, and a good solution can be found.

Vibration of an Adhered Microbeam Under a Periodically Shaking Electrical Force

The vibration analysis of an adhered S-shaped microbeam under alternating sinusoidal voltage is presented. The shaking force is the electrical force due to the sinusoidal voltage. During vibration, both the microbeam deflection and the adhesion length keep changing. The microbeam deflection and adhesion length are numerically determined by the iteration method. As the adhesion length keeps changing, the domain of the equation of motion for the microbeam (unadhered part) changes correspondingly, which results in changes of the structure natural frequencies. For this reason, the system can never reach a steady state. The transient behaviors of the microbeam under different shaking frequencies are compared. We deliberately choose the initial conditions to compare our dynamic results with the existing static theory. The paper also analyzes the changing behavior of adhesion length during vibration and an asymmetric pattern of adhesion length change is revealed, which may be used to guide the dynamic de-adhering process. The abnormal behavior of the adhered microbeam vibrating at almost the same frequency under two quite different shaking frequencies is also shown. The Galerkin method is used to discretize the equation of motion and its convergence study is also presented. The model is only applicable in the case that the peel number is equal to 1. Some other model limitations are also discussed.

Influence of Surface Stress on Frequency of Microcantilever-Based Biosensors (vol 10, pg 307, 2004)

Microcantilever-based biosensors have been found increasing applications in physical, chemical, and biological fields in recent years. When biosensors are used in those fields, surface stress and mass variations due to bio-molecular binding can cause the microcantilever deform or the shift of frequency. These simple biosensors allow biologists to study surface biochemistry on a micro or nano scale and offer new opportunities in developing microscopic biomedical analysis with unique characteristics. To compare and illustrate the influence of the surface stress on the frequency and avoid unnecessary and complicated numerical solution of the resonance frequency, some dimensionless numbers are derived in this paper by making governing equations dimensionless. Meanwhile, in order to analyze the influence of the general surface stress on the frequency, a new model is put forward, and the frequency of the microcantilever is calculated by using the subspace iteration method and the Rayleigh method. The sensitivity of microcantilever is also discussed. (19 refs.)

Pull-In Instability Of Micro-Switch Actuators: Model Review

The existing three widely used pull-in theoretical models (i.e., one-dimensional lumped model, linear supposition model and planar model) are compared with the nonlinear beam mode in this paper by considering both cantilever and fixed-fixed type micro and nano-switches. It is found that the error of the pull-in parameters between one-dimensional lumped model and the nonlinear beam model is large because the denominator of the electrostatic force is minimal when the electrostatic force is computed at the maximum deflection along the beam. Since both the linear superposition model and the slender planar model consider the variation of electrostatic force with the beam's deflection, these two models not only are of the same type but also own little error of the pull-in parameters with the nonlinear beam model, the error brought by these two models attributes to that the boundary conditions are not completely satisfied when computing the numerical integration of the deflection.

Compact finite difference - Fourier spectral method for three-dimensional incompressible Navier-Stokes equations

A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported.

Influence of convections on dopant segregation in floating-zone crystal-growth system

The steady and axisymmetric crystal growth process of floating zone model was studied numerically to concern with the influence of convection and phase change on effective segregation. An iteration method of numerical simulation considering both thermocapillary and buoyancy effects for GaAs crystal growth gave the effective segregation coefficient, which was compared with the space experiment of GaAs on board the Chinese recoverable satellite. The calculated segregation coefficient of a two-dimensional model was found to be smaller than the one suggested by space experiment with the simplified assumption of an one-dimensional model.

Optoelectronic quotient-selected modified signed-digit division

A novel optoelectronic quotient-selected modified signed-digit division technique is proposed. This division method generates one quotient digit per iteration involving only one shift operation, one quotient selection operation and one addition/subtraction operation. The quotient digit can be selected by observing three most significant digits of the partial remainder independent of the divisor. Two algorithms based on truth-table look-up and binary logic operations are derived. For optoelectronic implementation, an efficient shared content-addressable memory based architecture as well as compact logic array processor based architecture with an electron-trapping device is proposed. Performance evaluation of the proposed optoelectronic quotient-selected division shows that it is faster than the previously reported convergence division approach. Finally, proof-of-principle experimental results are presented to verify the effectiveness of the proposed technique. (C) 2001 Society of Photo-Optical Instrumentation Engineers.

Photon iterative numerical technique for steady-state simulation of gain-clamped semiconductor optical amplifiers

The photon iterative numerical technique, which chooses the outputs of the amplified spontaneous emission spectrum and lasing mode as iteration variables to solve the rate equations, is proposed and applied to analyse the steady behaviour of conventional semiconductor optical amplifiers (SOAs) and gain-clamped semiconductor optical amplifiers (GCSOAs). Numerical results show that the photon iterative method is a much faster and more efficient algorithm than the conventional approach, which chooses the carrier density distribution of the SOAs as the iterative variable. It is also found that the photon iterative method has almost the same computing efficiency for conventional SOAs and GCSOAs.

一种风险驱动的迭代开发需求优先级排序方法

需求优先级排序是指系统参与者为需求指定实现的优先次序,是迭代开发过程中开发者制定项目迭代计划的基础.现存的需求优先级排序方法对系统参与者之间的协商和调整优先级的支持能力不足,导致根据需求优先级所制定的迭代计划难以作出符合需求变更和环境改变的调整.提出一种风险驱动的需求优先级自适应排序方法.该方法将自适应计划方法学与风险驱动相结合,将风险作为排序决策的依据,以自适应的过程为迭代开发排序需求优先级.该方法能够改善需求优先级排序过程中系统参与者之间的协商和调整需求优先级的能力,增强在迭代开发中对需求的控制,降低因需求导致项目失败的可能性.

缺陷驱动的软件过程量化管理方法研究

随着软件应用范围的不断扩大和复杂程度的不断提高，软件开发过程越来越难以控制，软件质量也越来越难以保障。质量管理的思想和理念，已经从单纯的以面向软件产品的检验为主要手段的质量控制，发展到更加成熟、更加主动地对软件产品生产过程进行管理的质量保障。 作为高成熟度软件过程的特征，量化过程管理逐渐被软件组织接受并实施。通过实施量化管理，能够刻画项目或过程目标的满足程度，找到造成过程或产品重大偏差的根本原因。然而，在量化过程管理实施期间，软件组织面对不同的软件开发过程、众多的过程性能度量指标、复杂的统计分析方法，既要考虑量化管理方法的合理性和复杂程度，又要权衡量化管理的实施成本，这使得实施有效的量化过程管理充满挑战。本文以缺陷数据为中心，提出了一种缺陷驱动的量化过程管理框架，以及基于该框架的两个量化管理方法，支持软件组织收集量化过程管理所需数据，建立过程性能基线和过程性能模型，量化管理软件项目。该框架适合迭代、瀑布等不同的开发方法，支持项目全生命周期的量化管理。 本文主要贡献包括： 提出了一种缺陷驱动的量化过程管理框架(Defect-driven Quantitative Process Management framework, DefQPM)。量化管理中，保障软件质量是核心。质量和缺陷密切相关，软件开发过程中各类工程活动（如：需求、设计、编码、测试等）都伴随着缺陷的注入、排除和遗留。DefQPM框架以缺陷数据作为量化管理的出发点，自底向上的通过数据层、模型层、使用层来指导软件组织分析过程性能，识别度量指标间的相关性，建立符合自身情况的过程性能基线和过程性能模型，有效的实施量化过程管理。DefQPM框架给出了实施量化管理的过程和机制。基于DefQPM框架，可以建立针对特定应用场景的量化管理方法，以及针对特定软件组织的量化管理解决方案。 提出了一种基于DefQPM的迭代项目量化管理方法(process performance Baseline based Defect-driven iteration management, BiDefect)。迭代开发方法由于其灵活性和管理需求变更的能力，得到了广泛应用。然而，如何对迭代项目实施量化管理依然充满挑战。迭代项目中，各种活动多次并行执行，难以找到合适的控制点，也缺乏针对迭代项目的度量指标及分析方法。基于DefQPM框架，本文研究了迭代开发项目典型的量化管理需要（例如：通过控制每次迭代工作产品的质量来保障最终交付软件产品的质量），提出了一种针对迭代项目的量化管理方法，解决了量化管理迭代项目的几个主要挑战。该方法关注缺陷的注入、排除、遗留情况，指导项目策划期间建立整体估算和度量，在项目执行期间评价软件过程执行情况及软件产品的质量，及时识别异常并采取纠正措施，进而为项目后续工作中成本、进度、质量等方面提供估算、控制方面的指导。 提出了一种基于DefQPM的测试过程量化管理方法(Quantitatively Managing Testing process, TestQM)。测试是重要的质量控制活动，对于高成熟度软件组织来说也是需要进行量化管理的活动。缺陷检测和缺陷修复是测试过程的两类主要活动，需要不同技能的人员执行。目前流行的软件估算方法多是将缺陷检测和缺陷修复的工作量和进度统一纳入测试活动中进行估算和管理，不够准确。基于DefQPM框架，本文提出了一种专门针对测试过程的量化管理方法。该方法关注缺陷按注入阶段分布情况，缺陷与修复工作量的相关性，以及缺陷与修复进度的相关性，指导在早期项目建立测试过程的估算，在测试过程中根据缺陷按注入阶段分布情况调整缺陷修复工作量和进度，使得测试过程受控。同时，介绍了TestQM针对Web应用开发项目的经验模型。 最后，介绍了上述量化管理方法在国内软件组织中的应用，包括BiDefect方法在迭代开发项目中的应用，以及TestQM方法在Web应用开发项目中的应用。软件组织实施量化过程管理前后的过程性能变化表明，应用本文方法能够对项目进行有效的估算、度量、重新估算和控制，进而提高产品质量，改善客户满意度。

A finite-element algorithm for modeling variably saturated flows

A general numerical algorithm in the context of finite element scheme is developed to solve Richards’ equation, in which a mass-conservative, modified head based scheme (MHB) is proposed to approximate the governing equation, and mass-lumping techniques are used to keep the numerical simulation stable. The MHB scheme is compared with the modified Picard iteration scheme (MPI) in a ponding infiltration example. Although the MHB scheme is a little inferior to the MPI scheme in respect of mass balance, it is superior in convergence character and simplicity. Fully implicit, explicit and geometric average conductivity methods are performed and compared, the first one is superior in simulation accuracy and can use large time-step size, but the others are superior in iteration efficiency. The algorithm works well over a wide variety of problems, such as infiltration fronts, steady-state and transient water tables, and transient seepage faces, as demonstrated by its performance against published experimental data. The algorithm is presented in sufficient detail to facilitate its implementation.

PREDICTION OF VORTEX-INDUCED VIBRATION OF FLEXIBLE RISER USING AN IMPROVED WAKE-OSCILLATOR MODEL

Based on improving the wake-oscillator model, an analytical model for vortex-induced vibration (VIV) of flexible riser under non-uniform current is presented, in which the variation of added mass at lock-in and the nonlinear relationship between amplitude of response and reduced velocity are considered. By means of empirical formula combining iteration computation, the improved analytical model can be conveniently programmed into computer code with simpler and faster computation process than CFD so as to be suitable to application of practical engineering. This model is validated by comparing with experimental result and numerical simulation. Our results show that the improved model can predict VIV response and lock-in region more accurately. At last, illustrative examples are given in which the amplitude of response of flexible riser experiencing VIV under action of non-uniform current is calculated and effects of riser tension and flow distribution along span of riser are explored. It is demonstrated that with the variation of tension and flow distribution, lock-in region of mode behaves in different way, and thus the final response is a synthesis of response of locked modes.