颤振分析中的特征值排序问题

颤振分析中判断颤振临界速度的重要依据是系统V-g和V-f图,即系统特征值随参数的变化曲线.在几乎所有商用软件及自编程序的输出结果中,有时会出现所谓的"窜支"现象,这给颤振临界速度和颤振穿越分支及耦合形式的判断带来很大不便.通过隐函数定理可以证明,除重特征值点以外,系统特征值连续依赖于系统参数变化.依据多元向量值函数连续性,建立对特征值的排列算法,给出系统特征根轨迹的正确曲线,再输出V-g和V-f图数据,从而避免"窜支"现象.编制应用程序,通过几个典型算例对算法进行了验证.该工作能够有效简化颤振分析的后处理工作,提高分析效率.     

Creep of polymer concrete in the nonlinear region

Two polyester-based polymer concretes with various volume content of diabase as an extender and aggregate are tested in creep under compression at different stress levels. The phenomenological and structural approaches are both used to analyze the experimental data. Common features of changes in the instantaneous and creep compliances are clarified, and a phenomenological creep model which accounts for the changes in the instantaneous compliance and in the retardation spectrum depending on the stress level is developed. It is shown that the model can be used to describe the experimental results of stress relaxation and creep under repeated loading. Modeling of the composite structure and subsequent solution of the optimization problem confirm the possibility of the existence of an interphase layer more compliant than the binder. A direct correlation between the interphase volume content and the instantaneous compliance of the composite is revealed. It is found that the distinction in nonlinearity of the viscoelastic behavior of the two polymer concretes under investigation can be due to the difference in their porosity. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000.) Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 147–164, 2000.     

A model for predicting the shear bearing capacity of FRP-strengthened beams

The shear failure of reinforced concrete beams needs more attention than the bending failure since no or only small warning precedes the failure. For this reason, it is of utmost importance to understand the shear bearing capacity and also to be able to undertake significant rehabilitation work if necessary. In this paper, a design model for the shear strengthening of concrete beams by using fiber-reinforced polymers (FRP) is presented, and the limitations of the truss model analogy are highlighted. The fracture mechanics approach is used in analyzing the bond behavior between the FRP composites and concrete. The fracture energy of concrete and the axial rigidity of the FRP are considered to be the most important parameters. The effective strain in the FRP when the debonding occurs is determined. The limitations of the anchorage length over the cross section are analyzed. A simple iterative design method for the shear debonding is finally proposed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 357–372, May–June, 2008.     

Variation of the structure and permeability of tensioned fiber layers during impregnation with a thermoplastic polymer melt

The influence of displacements of tensioned fibers on the impregnation of fibrous layers with a polymer melt and on the final composite structure is studied. Using computer simulation, it is shown that, during impregnation, the structure of tensioned fibrous layers changes considerably depending on the initial arrangement and tensioning of fibers. The consolidated regions formed under the melt front move inside the impregnated layer with the advancing melt front. Displacement of the tensioned fibers as well as the formation of “washouts” favors the impregnation of internal layers, but cause significant inhomogeneity of the polymer structure. The surface (on the side of the melt flow) regions are more saturated with the polymer than the internal ones. A difference in the melt percolation mechanisms at various impregnation regimes is revealed. The effective permeability coefficients of a tensioned fiber layer are not constant but depend on the conditions and regimes of impregnation. Submitted to the 11th Conference on the Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 259–270, March–April, 2000.     

Exact and stable least squares solution to the linear programming problem

A linear programming problem is transformed to the finding an element of polyhedron with the minimal norm. According to A. Cline [6], the problem is equivalent to the least squares problem on positive ortant. An orthogonal method for solving the problem is used. This method was presented earlier by the author and it is based on the highly developed least squares technique. First of all, the method is meant for solving unstable and degenerate problems. A new version of the artifical basis method (M-method) is presented. Also, the solving of linear inequality systems is considered.     

Testing Ten Theories

Using the most comprehensive data set now available, this investigation tests the precision of all exchange theories that now contend. Beyond precision, the investigation focuses on broad issues of effectiveness including consistency, parsimony, and whether the theories can be applied to structures larger than normally studied in the lab. Seeking greater parsimony, this investigation introduces a new model by combining parts of two contending theories. We find that all ten theories have scientific merit for all can predict with some effectiveness for the exchange structures experimentally investigated. Nevertheless, the ten vary in precision. Elementary Theory is the most precise. The new Expected-value Resistance model ranks second in precision and is the simplest. Both apply to large networks as well as the best of the other theories.     

Unsteady motion of a spherical bubble in a complex fluid: Mathematical modelling and simulation

The nonlinear response of an oscillatory bubble in a complex fluid is studied. The bubble is immersed in a Newtonian liquid, which may have a dilute volume fraction of anisotropic additives such as fibers or few ppm of macromolecules. The constitutive equation for the fluid is based on a Maxwell model with an extensional viscosity for the viscous contribution. The model is considered new in the study of bubble dynamics in complex fluids. The numerical computation solves a system of three first order ordinary differential equations, including the one associated with the solution of the convolution integral, using a fifth order Runge–Kutta scheme with appropriated time steps. Asymptotic solutions of governing equation are developed for small values of the pressure forcing amplitude and for small values of the elastic parameter. A study of the bubble collapse radius is also presented. We compare the results predicted by our model with other model in the literature and a good agreement is observed. The calculated asymptotic solutions are also used to test the results of the numerical simulations. In addition, the orientation of the additives is considered. The angular probability density function is assumed to be a normal distribution. The results show that the model based on the fully aligned additives with the radial direction overestimates the tendency of the additives to stabilize the bubble motion, since the effect of extensional viscosity occurs due to the particle resistance to the movement throughout its longitudinal direction.     

拍卖机制设计在区块链中的应用与挑战

区块链是新一代信息技术的重要组成部分,是分布式网络、加密技术、智能合约等多种技术集成的新型数据库软件。过去的十多年,区块链技术在全球范围内产生广泛影响。如今的区块链技术,已从最初的关注于解决货币和支付的去中心化问题,转入到解决市场的去中心化问题。智能合约的出现使得基于区块链技术的去中心化金融进入高速发展状态,也涌现出区块链环境下的各类拍卖场景。本文首次从机制设计角度,以区块链交易费机制,非同质化代币(Non-Fungible Token,NFT)拍卖和矿工可提取价值(Miner-Extractable Value,MEV)交易位置拍卖为主要对象,总结和剖析近些年来区块链上特有的拍卖机制;并针对区块链特性,提出区块链上拍卖机制设计所面临的挑战和未来亟待解决的问题。     

考虑服务和退货的双渠道供应链定价问题研究

在考虑零售服务和消费者退货情况下,运用两阶段优化方法分别探究了集中式和分散式两种双渠道供应链的最优定价策略。研究发现零售服务有助于提高零售商的渠道权力,并始终使制造商获益,但只有当服务水平小于某一临界值时,才使制造商和零售商同时得到帕累托改进。零售价格和直销价格与退货率正相关,而与服务水平的关系受渠道结构的影响。服务水平的提高加剧了供应链的“双重边际化”效应,制造商通过生产与消费者需求相匹配的产品来降低退货风险可以减弱这种效应,从而提高供应链效率。     

Gaussian Versus Optimal Integration of Analytic Functions

We consider error estimates for optimal and Gaussian quadrature formulas if the integrand is analytic and bounded in a certain complex region. First, a simple technique for the derivation of lower bounds for the optimal error constants is presented. This method is applied to Szeg?-type weight functions and ellipses as regions of analyticity. In this situation, the error constants for the Gaussian formulas are close to the obtained lower bounds, which proves the quality of the Gaussian formulas and also of the lower bounds. In the sequel, different regions of analyticity are investigated. It turns out that almost exclusively for ellipses, the Gaussian formulas are near-optimal. For classes of simply connected regions of analyticity, which are additionally symmetric to the real axis, the asymptotic of the worst ratio between the error constants of the Gaussian formulas and the optimal error constants is calculated. As a by-product, we prove explicit lower bounds for the Christoffel-function for the constant weight function and arguments outside the interval of integration. September 7, 1995. Date revised: October 25, 1996.     

On the hyperbolicity of the period-doubling fixed point

We give a new proof of the hyperbolicity of the fixed point for the period-doubling renormalization operator using the local dynamics near a semi-attractive fixed point (in a Banach space) and the theory of holomorphic motions. We also give a new proof of the exponential contraction of the Feigenbaum renormalization operator in the hybrid class of the period-doubling fixed point: our proof uses the non-existence of invariant line fields in the period-doubling tower (C. McMullen), the topological convergence (D. Sullivan), and a new infinitesimal argument.

     

Numerical study on the dynamics of a jet-vortex interaction

The interaction of a vortex and a jet plays an important role for many industrial processes such as carbon black formation or combustion in diesel engines. The knowledge of physics of these phenomena is crucial for engineers, but also for scientists who wish to study this complex flow pattern. In this research, we numerically investigate cases where a cylindrical reactor is charged with gas injected through five ports. The first one is located along the main axis of the cylinder and this leads to the formation of the main jet. The other four ports are situated along the side walls such that the gas entering the cylinder tangentially through them causes a vortex to be formed. The objective of this paper is to show the fundamental physical phenomena and also how the initial and boundary conditions influence the results. It is shown how the process is influenced not only by modifying the velocity of injected gas, but also by the orientation and position of the vortex inlet nozzles.     

制造企业服务化程度、服务化模式和服务化收益研究

制造企业在推进服务化的过程中出现的绩效下滑和“去服务化”现象引起了学术界的广泛关注并催生了“服务化悖论”的相关研究。本文从需求侧视角出发,将这一问题转化为不同需求侧特征下服务化程度、服务化模式对服务化收益的影响,并构建了考虑需求侧特征的制造企业服务化程度决策模型;在此基础上研究了不同服务化模式下服务化程度与服务化收益之间的关系;最后,结合仿真分析的结果确定了制造企业服务化路径。研究表明:(1)制造企业服务化是一个双向的动态可逆过程,并非所有企业都适合开展服务化活动,企业应根据当前的服务化状态选择相应服务化路径。(2)除独立服务化模式外,合作服务化和外包服务化两种模式下服务化程度的高低更多的受到合作伙伴属性的影响,企业很难单独决定服务化程度。(3)需求侧特征的变动会对服务化收益产生重要影响,不同服务化模式对应不同的需求侧特征。研究结论为服务化悖论的分析提供了新的视角,也为企业推进服务化战略提供了借鉴。     

Dynamical Spin Susceptibility in the t–J Model in the Superconducting Phase

Dynamical spin susceptibility is calculated for the t–J model in the superconducting phase using the memory function method in terms of the Hubbard operators. The self-consistent system of equations for the memory function is obtained within the mode-coupling approximation. Both itinerant hole excitations and localized spin fluctuations contribute to the memory function. Moreover, the itinerant contribution itself consists of two parts, i.e., the contribution of Bogoliubov quasiparticles and that of Cooper pairs. The spin dynamics is diffusive in the hydrodynamic limit, but the itinerant part does not contribute to the spin diffusion. In the high frequency region, spin–wave-like excitations continue to exist. We discuss our analytic results in the light of neutron scattering experiments performed on the cuprate superconductors.     

Adiabatic divergence of the chaotic layer width and acceleration of chaotic and noise-induced transport

We show that, in spatially periodic Hamiltonian systems driven by a time-periodic coordinate-independent (AC) force, the upper energy of the chaotic layer grows unlimitedly as the frequency of the force goes to zero. This remarkable effect is absent in any other physically significant systems. It gives rise to the divergence of the rate of the spatial chaotic transport. We also generalize this phenomenon for the presence of a weak noise and weak dissipation. We demonstrate for the latter case that the adiabatic AC force may greatly accelerate the spatial diffusion and the reset rate at a given threshold.     

Model-based estimation of the stress-strain curve of metal strips

The identification of the stress-strain curve of metal strips is a common task in the metals industry. As an alternative to commonly used tensile test machines, an inexpensive, model-based optical measurement method is presented. Particular importance was placed on the cost and usability of the method. The indirect approach computes the stress-strain curve based on a measured strip bending line. For the measurement, a metal strip is bent over a solid roll. A defined weight can be mounted at the end of the strip to control the local bending moment in the strip. The bending line of the strip is optically measured by a camera. The identification is carried out based on an optimization problem, where the quadratic error between the measured and the modelled strip bending line is minimized. Experimental results and measurements from a tensile test machine show a good agreement and thus verify the proposed identification method.     

Optimal component selection based on cohesion & coupling for component based software system under build-or-buy scheme

Component based software system approach is concerned with the system development by integrating components. The component based software construction primarily focuses on the view that software systems can be built up in modular fashion. The modular design is a logical collection of several independent developed components that are assembled with well defined software architecture. These components can be developed in-house or can be obtained commercially from outside market making build versus buy decision an important consideration in development process. Cohesion and coupling (C&C) plays a major role in determining the system quality in terms of reliability, maintainability and availability. Cohesion is defined as the internal interaction of components within the module. On the other hand, coupling is the external interaction of the module with other modules i.e. interaction of components amongst the modules of the software system. High cohesion and low coupling is one of the important criteria for good software design. Intra-modular coupling density (ICD) is a measure that describes the relationship between cohesion and coupling of modules in a modular software system and its value lies between zero and one. This paper deals with the selection of right mix of components for a modular software system using build-or-buy strategy. In this paper, fuzzy bi-criteria optimization model is formulated for component selection under build-or-buy scheme. The model simultaneously maximizes intra-modular coupling density (ICD) and functionality within the limitation of budget, reliability and delivery time. The model is further extended by incorporating the issue of compatibility amongst the components of the modules. A case study is devised to explain the formulated model.     

Finding Optimal Targets for Change Agents: A Computer Simulation of Innovation Diffusion

We introduce a diffusion of innovation model based on a network threshold approach. Realistic network and threshold data were gathered regarding the diffusion of new software tools within part of a large organization. Novel model features are a second threshold for innovation rejection and a memory that allows actors to take trends into account. Computer simulations produce expected outcomes, such as the S-shaped diffusion curve, but also diffusion breakdown and oscillations. We define and compute the quality of change agent targets in terms of the impact targeted actors have on the diffusion process. Our simulations reveal considerable variance in the quality of actors as change agent targets. Certain actors can be singled out as especially important to the diffusion process. Small changes in the distribution of thresholds and changes in some parameters, such as the sensitivity for trends, lead to significant changes in the target quality measure. To illustrate these interdependencies we outline how the impact of an actor targeted by a change agent spreads through the network. We thus can explain why a good change agent target does not necessarily need to be an opinion leader. Simulations comparing the effectiveness of randomly selected targets versus a group of good change agent targets indicate that the selection of good targets can accelerate innovation diffusion.     

Thermomechanical behaviour of a damageable beam in contact with two stops

A model for the thermomechanical behaviour of a beam which allows for the general evolution of material damage is presented and investigated. One end of the beam is fixed while the other is constrained to move between two stops. The contact of the free tip with the stops is modelled by the normal compliance condition. The thermal interaction between the stops and the free tip is described by a heat exchange condition where the heat transfer coefficient is a general function of the gaps between the tip and the stops. The effects on the mechanical properties of the material due to crack expansion are described by a damage field, which measures the decrease in the load-bearing capacity of the material. The damage evolves as a constrained diffusion process in which the microcracks that develop may grow or disappear. The mathematical model consists of a coupled system of energy--elasticity equations together with a nonlinear parabolic inclusion for the damage field. The existence of a local solution is established using truncation, penalization, and a priori estimates.     

考虑决策单元竞争合作动态变化的DEA博弈交叉效率方法

利用DEA方法进行相对效率评估时,决策单元通常需要考虑多重目标,且随着目标的变化,决策单元间竞争合作状态也会发生动态变化。传统竞合模型虽然考虑了决策单元间竞争与合作同时存在的现象,但忽视了竞争合作关系动态变化的过程。本文以竞争合作对策为切入点,将多目标规划中的优先因子引入传统DEA博弈交叉效率模型中,提出了带有优先等级的多目标DEA博弈交叉效率模型,即动态竞合博弈交叉效率模型。该模型充分体现了不同目标下决策单元间竞争合作关系的动态变化,其焦点由传统竞合模型对多重最优权重现象的改善,转向对最优效率得分的直接寻找。利用DEA动态竞合博弈交叉效率模型,本文对环境污染约束下2014年长三角地区制造业投入产出绩效进行了客观的评估。分析结果表明:DEA动态竞合博弈交叉效率模型收敛速度优于传统DEA博弈交叉效率模型,其交叉效率得分收敛于唯一的纳什均衡点;不同目标重要性的差异程度,对最终排名结果不产生明显影响,不需要确切指出。