Free vibration behavior of a thermally post-buckled FG Timoshenko beam under large deflection using a tangent stiffness-based method

For thermally postbuckled configurations, the free vibration behavior of functionally graded (FG) Timoshenko beams are investigated. The postbuckling configurations are obtained through a geometrically nonlinear static problem. The free vibration problem around the postbuckled configuration is formulated using its tangent stiffness. The energy based governing equations are solved following the Ritz method. The elements of the tangent stiffness matrix are obtained using the Ritz coefficients. The results are shown to exhibit the effects of FG material, material profile parameter, and length-thickness ratio. The comparative results are presented for both the cases of the physical neutral surface and the geometrical neutral surface.     

双光束激光焊匙孔动态特征分析

文中研究了高功率单光束激光焊与双光束激光焊过程中匙孔动态特征的差别. 结果表明，单光束激光焊及双光束激光焊接过程中匙孔均处于从产生到湮灭的剧烈波动的过程，不同于单光束激光焊匙孔的形成、长大、维持、缩小、湮灭过程，双光束激光焊的匙孔还存在分离长大及合并缩小的过程；在相同的焊接参数及焊缝具有相同熔深的条件下，双光束激光焊匙孔的波动频率约为单光束激光焊的2/3，单光束激光焊匙孔的开口面积均值约为双光束激光焊匙孔开口面积的1/2，开口面积的波动变异系数约为单光束激光的2倍，即双光束激光焊过程中匙孔较单光束激光焊的具有较高稳定性.     

用宽带超表面产生阵列贝塞尔光束

通过在空间光调制器（SLM）上加载相位图或通过光刻加工微型圆锥状结构可以产生贝塞尔光束阵列。然而，典型空间光调制器具有比波长大一个数量级的像素尺寸，这限制了相位梯度的可用范围，用光刻法加工的微型锥透镜的顶端不是标准的圆锥，这影响了贝塞尔光束的质量。为了克服这些缺点，将复杂的相位图加载到电介质超表面上，设计了一种可以产生阵列贝塞尔光束（在波长700 nm处，NA=0.3）的超表面器件。该器件可以宽波段工作，其单元结构在波长580~800 nm范围内的偏振转换效率均超过57%。利用时域有限差分算法（FDTD）对该器件（厚度为380 nm，直径仅为40 μm）进行了仿真，所产生的阵列光束都垂直于超表面器件。所提出的阵列贝塞尔光束发生器具有纳米级别的厚度和几十微米的直径，这对于未来的集成光学领域具有很大的应用前景。     

Machining accuracy improvement for a dual-spindle ultra-precision drum roll lathe based on geometric error analysis and calibration

This paper performs a comprehensive analysis and calibration on the geometric error of the ultra-precision drum roll lathe with dual-spindle symmetrical structure and cross slider layout. Firstly, the volumetric error model which contains all geometric errors of the dual-spindle ultra-precision drum roll lathe (DSUPDRL) is developed based on the combination of the homogenous transfer matrix (HTM) and multi-body system (MBS) theory. Secondly, sensitivity analysis for the volumetric error model is conducted to identify the sensitive geometric error components of the DSUPDRL using an improved Sobol method based on the quasi-Monte Carlo algorithm. The result of sensitivity analysis laid the foundation for the subsequent geometric error calibration. Then, some sensitive error components along the X and Z directions are calibrated using a laser interferometer and a pair of inductance displacement probes. Besides the volumetric error model, the concentricity error caused by dual-spindle symmetrical structure is proposed and calibrated by the on-machine measurement using a classic reversal method. Finally, a large-scale roller mold with a diameter of 250 mm and a length of 600 mm is machined using the DSUPDRL after calibration. The experimental result shows that 1.4 μm/600 mm generatrix accuracy is obtained, which validate the effectiveness of the geometric error analysis and calibration.     

Supply chain network design under the risk of uncertain disruptions

Facility disruptions in the supply chain often lead to catastrophic consequences, although they occur rarely. The low frequency and non-repeatability of disruptive events also make it impossible to estimate the disruption probability accurately. Therefore, we construct an uncertain programming model to design the three-echelon supply chain network with the disruption risk, in which disruptions are considered as uncertain events. Under the constraint of satisfying customer demands, the model optimises the selection of retailers with uncertain disruptions and the assignment of customers and retailers, in order to minimise the expected total cost of network design. In addition, we simplify the proposed model by analysing its properties and further linearise the simplified model. A Lagrangian relaxation algorithm for the linearised model and a genetic algorithm for the simplified model are developed to solve medium-scale problems and large-scale problems, respectively. Finally, we illustrate the effectiveness of proposed models and algorithms through several numerical examples.     

An expectation operator for belief functions in the Dempster–Shafer theory*

ABSTRACT

The main contribution of this paper is a new definition of expected value of belief functions in the Dempster–Shafer (D–S) theory of evidence. Our definition shares many of the properties of the expectation operator in probability theory. Also, for Bayesian belief functions, our definition provides the same expected value as the probabilistic expectation operator. A traditional method of computing expected of real-valued functions is to first transform a D–S belief function to a corresponding probability mass function, and then use the expectation operator for probability mass functions. Transforming a belief function to a probability function involves loss of information. Our expectation operator works directly with D–S belief functions. Another definition is using Choquet integration, which assumes belief functions are credal sets, i.e. convex sets of probability mass functions. Credal sets semantics are incompatible with Dempster's combination rule, the center-piece of the D–S theory. In general, our definition provides different expected values than, e.g. if we use probabilistic expectation using the pignistic transform or the plausibility transform of a belief function. Using our definition of expectation, we provide new definitions of variance, covariance, correlation, and other higher moments and describe their properties.     

On the approximation of the canard explosion point in singularly perturbed systems without an explicit small parameter

A canard explosion is the dramatic change of period and amplitude of a limit cycle of a system of nonlinear ODEs in a very narrow interval of the bifurcation parameter. It occurs in slow–fast systems and is well understood in singular perturbation problems where a small parameter epsilon defines the time-scale separation. We present an iterative algorithm for the determination of the canard explosion point which can be applied for a general slow–fast system without an explicit small parameter. We also present assumptions under which the algorithm gives accurate estimates of the canard explosion point. Finally, we apply the algorithm to the van der Pol equations, a Templator model for a self-replicating system and a model for intracellular calcium oscillations with no explicit small parameters and obtain very good agreement with results from numerical simulations.     

Focusing characteristics of the relativistic electron beam transmitting in ion channel

Based on the beam–plasma system model established in this paper, the trajectory of the electron beam in the ion channel is studied quantitatively through the envelope equation. Under different initial system parameters, the focusing transmission conditions of the beam in the ion channel are discussed. Then, a series of particle-in-cell simulations are performed, which generally versifies the theoretical results and shows some further details of the focusing behavior of the beam. It is found that the deceleration of some electrons around the focusing point or the beam–plasma interaction at the ion channel boundary will result in the generation of the residual electrons,which forms the electron return current that leads to the new instabilities influencing the focusing characteristics of the beam.     

Fabrication of highly sensitive MnO2/F-MWCNT/Ta hybrid nanocomposite sensor with different MnO2 overlayer thickness for H2O2 detection

In this work, we report the development of MnO₂/F-MWCNT/Ta hybrid nanocomposite sensor with different MnO₂ overlayer thickness for the detection of H₂O₂ in real samples. A novel two-step process using e-beam evaporation and spray pyrolysis deposition was adopted for the synthesis of hybrid MnO₂/F-MWCNT/Ta electrodes. SE morphology revealed smaller-sized, compact grains of MnO₂ infiltrated on the outermost walls of MWCNTs. Raman analysis confirmed the existence of carbon nanotubes with abundant structural defects of MnO₂ in the composite. The cyclic voltammetry results displayed a high peak current and narrowed over potential towards the reduction of H₂O₂. The sensor displayed a fast response (<5?s), wide linear range (2–1510?μM) and a low limit of detection (0.04?μM) with significant anti-interfering properties, promising for the development of highly sensitive and reproducible biosensors. The three dimensional nanocomposite sensor also exhibited good recovery (> 98%), thus providing a favourable tool for analysis of H₂O₂ in milk samples.     

Designing the framework of technological entrepreneurship ecosystem: A grounded theory approach in the context of Iran

The ecosystem approach, as a comprehensive way of understanding multi-aspect environments, has recently gained so much attention in entrepreneurship and innovation studies. The application of this approach has led to the introduction of the currently available ecosystem frameworks that are dealing with some issues such as infirm structure and heterogeneity of components. In this research, by adopting the grounded theory approach in the context of Iran, we defined a novel and comprehensive framework for the technological entrepreneurship ecosystem (TEE). Twenty-six in-depth and semi-structured interviews have been conducted and analysed through a modified grounded theory procedure. Seventy-four secondary sources were added to the study to expand the breadth of our analysis and reach a stronger saturation. The concluded framework comprised of four interconnected layers representing environmental conditions, entity domains, functional realms, and tech-entrepreneurial agents. In addition, we identified some general principles and rules as important underlying aspects of this framework. The inferred components and structure of this novel framework not only could enable us to design the relations between the ecosystem components, but also prompt and support further research on each dimension of the ecosystem.