On the threshold problem for Latin boxes

Let m ≤ n ≤ k. An m × n × k 0‐1 array is a Latin box if it contains exactly m n ones, and has at most one 1 in each line. As a special case, Latin boxes in which m = n = k are equivalent to Latin squares. Let be the distribution on m × n × k 0‐1 arrays where each entry is 1 with probability p, independently of the other entries. The threshold question for Latin squares asks when contains a Latin square with high probability. More generally, when does support a Latin box with high probability? Let ε > 0. We give an asymptotically tight answer to this question in the special cases where n = k and , and where n = m and . In both cases, the threshold probability is . This implies threshold results for Latin rectangles and proper edge‐colorings of K_n,n.     

Physics-based plasticity model incorporating microstructure changes for severe plastic deformation

During machining processes, materials undergo severe deformations that lead to different behavior than in the case of slow deformation. The microstructure changes, as a consequence, affect the materials properties and therefore influence the functionality of the component. Developing material models capable of capturing such changes is therefore critical to better understand the interaction process–materials. In this paper, we introduce a new physics model associating Mechanical Threshold Stress (MTS) with Dislocation Density (DD) models. The modeling and the experimental results of a series of large strain experiments on polycrystalline copper (OFHC) involving sequences of shear deformation and strain rate (varying from quasi-static to dynamic) are very similar to those observed in processes such as machining. The Kocks–Mecking model, using the mechanical threshold stress as an internal state variable, correlates well with experimental results and strain rate jump experiments. This model was compared to the well-known Johnson–Cook model that showed some shortcomings in capturing the stain jump. The results show a high effect of rate sensitivity of strain hardening at large strains. Coupling the mechanical threshold stress dislocation density (MTS–DD), material models were implemented in the Abaqus/Explicit FE code. The model shows potentialities in predicting an increase in dislocation density and a reduction in cell size. It could ideally be used in the modeling of machining processes.     

Hyperparameter on-line learning of stochastic resonance based threshold networks

Aiming at training the feed-forward threshold neural network consisting of nondifferentiable activation functions, the approach of noise injection forms a stochastic resonance based threshold network that can be optimized by various gradient-based optimizers. The introduction of injected noise extends the noise level into the parameter space of the designed threshold network, but leads to a highly non-convex optimization landscape of the loss function. Thus, the hyperparameter on-line learning procedure with respective to network weights and noise levels becomes of challenge. It is shown that the Adam optimizer, as an adaptive variant of stochastic gradient descent, manifests its superior learning ability in training the stochastic resonance based threshold network effectively. Experimental results demonstrate the significant improvement of performance of the designed threshold network trained by the Adam optimizer for function approximation and image classification.     

Evolution of vortices in the wake of an ARJ21 airplane: Application of the lift-drag model

Wake separation is crucial to aircraft landing safety and is an important factor in airport operational efficiency. The near-ground evolution characteristics of wake vortices form the foundation of the wake separation system design. In this study, we analysed the near-ground evolution of vortices in the wake of a domestic aircraft ARJ21 initialised by the lift-drag model using large eddy simulations based on an adaptive mesh. Evolution of wake vortices formed by the main wing, flap and horizontal tail was discussed in detail. The horizontal tail vortices are the weakest and dissipate rapidly, whereas the flap vortices are the strongest and induce the tip vortex to merge with them. The horizontal tail and flap of an ARJ21 do not significantly influence the circulation evolution, height change and movement trajectory of the wake vortices. The far-field evolution of wake vortices can therefore be analysed using the conventional wake vortex model.     

基于多通道盲识别的自适应光学图像事后处理

为实时恢复天文或空间目标的湍流退化成像,提出一种适应大气湍流动态变化的多通道自适应光学图像恢复方法.以自适应光学校正后不同时刻的目标成像作为多个通道,建立求解系统点扩散函数的线性方程,根据解出的点扩散函数利用超拉普拉斯算法,求解待观测目标的估计值.结果表明:不同时刻的点扩散函数之间存在互质关系,满足多通道盲识别的理论要求.利用建立的线性方程求解出的点扩散函数与原点扩散函数的均方误差在10^-30~10^-27量级,采用超拉普拉斯算法恢复出的目标成像与原始目标之间的均方误差在10^-5~10^-4量级.本文研究为湍流退化图像的实时恢复提供了理论基础.     

The energy-critical nonlinear wave equation with an inverse-square potential

We study the energy-critical nonlinear wave equation in the presence of an inverse-square potential in dimensions three and four. In the defocussing case, we prove that arbitrary initial data in the energy space lead to global solutions that scatter. In the focusing case, we prove scattering below the ground state threshold.     

中国出境旅游的外交效应

2000年以来，中国出境旅游高增长、高消费，影响力不断增大，成为国家外交战略的重要内容，外交效应逐渐显现。通过辨析中国出境旅游外交效应的概念、表现形式和结果，基于10个中国主要出境目的国的旅游互动数据，采用DIF-GMM计量经济模型，实证检验了中国出境旅游外交效应。结果表明，中国通过有序推进ADS协议、加强经济援助、举办“旅游年”活动、实施旅游“制裁”，并积极参与国际制度建设等旅游外交行为，促进了与世界各国的友好交往，维护了自身核心利益，提升了外交软实力和国际影响力。国际旅游反作用于国际关系，对国际关系具有显著的正向促进作用，不仅是国际关系的结果，而且是其重要动因之一。中国出境旅游与政治、经济、社会、文化等联动，多方面提升了中国的国际影响力。     

Influence of temperature and alloying elements on the threshold displacement energies in concentrated Ni–Fe–Cr alloys

Concentrated solid-solution alloys(CSAs) have demonstrated promising irradiation resistance depending on their compositions. Under irradiation, various defects can be produced. One of the most important parameters characterizing the defect production and the resulting defect number is the threshold displacement energies(E_d). In this work, we report the results of E_dvalues in a series of Ni–Fe–Cr concentrated solid solution alloys through molecular dynamics(MD)simulations. Based on several different empirical potentials, we show that the differences in the E_dvalues and its angular dependence are mainly due to the stiffness of the potential in the intermediate regime. The influences of different alloying elements and temperatures on E_dvalues in different CSAs are further evaluated by calculating the defect production probabilities. Our results suggest a limited influence of alloying elements and temperature on E_dvalues in concentrated alloys. Finally, we discuss the relationship between the primary damage and E_dvalues in different alloys. Overall, this work presents a thorough study on the E_dvalues in concentrated alloys, including the influence of empirical potentials,their angular dependence, temperature dependence, and effects on primary defect production.