Blowup criterion for Navier–Stokes equation in critical Besov space with spatial dimensions d ≥ 4

This paper is concerned with the blowup criterion for mild solution to the incompressible Navier–Stokes equation in higher spatial dimensions $d\ge 4$. By establishing an ? regularity criterion in the spirit of [11], we show that if the mild solution u with initial data in ${\dot{B}}_{p,q}^{?1+d/p}({\mathbb{R}}^d)$, $d<p,q<\infty$ becomes singular at a finite time $T_{?}$, then$\underset{t\to T_{?}}{\lim \sup }{6u(t)6}_{{\dot{B}}_{p,q}^{?1+d/p}({\mathbb{R}}^d)}=\infty .$ The corresponding result in 3D case has been obtained in [24]. As a by-product, we also prove a regularity criterion for the Leray–Hopf solution in the critical Besov space, which generalizes the results in [17], where blowup criterion in critical Lebesgue space $L^d({\mathbb{R}}^d)$ is addressed.     

Bunch evolution study in optimization of Me V ultrafast electron diffraction

Megaelectronvolt ultrafast electron diffraction（UED） is a promising detection tool for ultrafast processes.The quality of diffraction image is determined by the transverse evolution of the probe bunch. In this paper, we study the contributing terms of the emittance and space charge effects to the bunch evolution in the MeV UED scheme, employing a mean-field model with an ellipsoidal distribution as well as particle tracking simulation. The small transverse dimension of the drive laser is found to be critical to improve the reciprocal resolution, exploiting both smaller emittance and larger transverse bunch size before the solenoid. The degradation of the reciprocal spatial resolution caused by the space charge effects should be carefully controlled.     

Enhancing water level prediction through model residual correction based on Chaos theory and Kriging

Hydrodynamic models based on the physical processes are indispensable tools for predicting water levels in ocean environment. Nonetheless, their accuracies are limited by various factors such as simplifying assumptions, complex ocean bathymetry, and so on. Residual correction, as one of the data assimilation techniques, can extract information from observation and assimilate it into a numerical model to correct the model output directly. Such correction is often performed in two steps: prediction of the model residuals at measured stations followed by spatial distribution at non‐measured locations. For long‐term residual forecast, the accuracy of prediction usually deteriorates with the forecast horizon. In addition to the residual correction at measurement locations, in this paper, we address the critical question as to how to effectively update outputs for computational points without measurements. We develop a hybrid data assimilation procedure, which combines a modified local model (MLM) and an approximated ordinary kriging (AOK). This technique improves the forecasts over a long horizon over the entire computational domain. Using the proposed residual correction technique, the hybrid procedure is examined on a case study of Singapore Regional Model for correcting the water level outputs at locations with and without measurements. In order to provide a comparison, the analysis is carried out throughout prediction horizon of model residuals, tidal residuals, and sea level anomaly, respectively. The comparisons show that the proposed method can successfully assimilate and forecast all variables. Results indicate that resulting prediction accuracy can be significantly improved for all locations of interest independently of the forecast horizon. Copyright © 2014 John Wiley & Sons, Ltd.     

Potential of multiparametric characterization of foodstuffs by nuclear magnetic resonance to better predict microbial behavior

Numerous predictive microbiology models have been proposed to describe bacterial population behaviors in foodstuffs. These models depict the growth kinetics of particular bacterial strains based on key physico-chemical parameters of food matrices and their storage temperature. In this context, there is a prominent issue to accurately characterize these parameters, notably pH, water activity (a_w), and NaCl and organic acid concentrations. Usually, all these product features are determined using one destructive analysis per parameter at macroscale (>5 g). Such approach prevents an overall view of these characteristics on a single sample. Besides, it does not take into account the intra-product microlocal variability of these parameters within foods. Nuclear magnetic resonance (NMR) is a versatile non-invasive spectroscopic technique. Experiments can be recorded successively on a same collected sample without damaging it. In this work, we designed a dedicated NMR approach to characterize the microenvironment of foods using 10-mg samples. The multiparametric mesoscopic-scale approach was validated on four food matrices: a smear soft cheese, cooked peeled shrimps, cold-smoked salmon, and smoked ham. Its implementation in situ on salmon fillets enabled to observe the intra-product heterogeneity and to highlight the impact of process on the spatial distribution of pH, NaCl, and organic acids. This analytical development and its successful application can help address the shortcomings of monoparametric methods traditionally used for predictive microbiology purposes.     

Ant Colony System Optimization for Spatiotemporal Modelling of Combined EEG and MEG Data

Electroencephalography/Magnetoencephalography (EEG/MEG) source localization involves the estimation of neural activity inside the brain volume that underlies the EEG/MEG measures observed at the sensor array. In this paper, we consider a Bayesian finite spatial mixture model for source reconstruction and implement Ant Colony System (ACS) optimization coupled with Iterated Conditional Modes (ICM) for computing estimates of the neural source activity. Our approach is evaluated using simulation studies and a real data application in which we implement a nonparametric bootstrap for interval estimation. We demonstrate improved performance of the ACS-ICM algorithm as compared to existing methodology for the same spatiotemporal model.     

基于复杂分子结构模型建构的项目教学案例*——探秘血红素

本研究基于可视化软件VESTA和生物大分子空间结构数据库(PDB)将血红蛋白的结构模型可视化,切割出其功能单元“血红素”并将其晶胞内分数坐标转化为可供学生搭建的三维直角坐标。在课堂上尽可能还原了科学家破解复杂分子结构的一般方法及步骤,学生在项目实施过程中动手搭建血红素原子位置模型,利用键长数据判断原子间的成键关系,并利用模型解释血红蛋白载氧和中毒的机理,发展了证据推理与模型认知等学科核心素养。     

An evolve‐then‐filter regularized reduced order model for convection‐dominated flows

In this paper, we propose a new evolve‐then‐filter reduced order model (EF‐ROM). This is a regularized ROM (Reg‐ROM), which aims to add numerical stabilization to proper orthogonal decomposition (POD) ROMs for convection‐dominated flows. We also consider the Leray ROM (L‐ROM). These two Reg‐ROMs use explicit ROM spatial filtering to smooth (regularize) various terms in the ROMs. Two spatial filters are used: a POD projection onto a POD subspace (Proj) and a POD differential filter (DF). The four Reg‐ROM/filter combinations are tested in the numerical simulation of the three‐dimensional flow past a circular cylinder at a Reynolds number Re=1000. Overall, the most accurate Reg‐ROM/filter combination is EF‐ROM‐DF. Furthermore, the spatial filter has a higher impact on the Reg‐ROM than the regularization used. Indeed, the DF generally yields better results than Proj for both the EF‐ROM and L‐ROM. Finally, the CPU times of the four Reg‐ROM/filter combinations are orders of magnitude lower than the CPU time of the DNS. Copyright © 2017 John Wiley & Sons, Ltd.     

空间竞争视角下奥特莱斯模式研究

奥特莱斯已演变成为一种新型的零售业态，在实践中取得巨大成功，但相关学术理论成果还相对缺乏。本研究以空间竞争理论为基础，从传统购物中心和奥特莱斯间的博弈出发，在消费者的偏好不确定的情况下，探究了奥特莱斯的区位选择、建设规模以及商品定价问题，试图为奥特莱斯投资人提供决策依据。研究结果表明，最优区位选择和建设规模依赖于消费者的聚集程度，消费者聚集程度较低时，奥特莱斯应紧邻消费者，投资者应尽可能扩大其建设规模，聚集程度较高时，可适当远离消费者，且选址越远，建设规模越大。另外，奥特莱斯中各零售商的商品售价不会偏离购物中心指导价。     

注意力缺陷多动障碍（ADHD）儿童的空间知觉失认研究

空间知觉是对物体距离、形状、大小、方位等空间特性的知觉.空间知觉失认的患者往往会出现写字左右颠倒、间架结构处理混乱、对数量关系不易理解等缺陷,从而无法准确地感知物体的各种特性,难以形成良好的推理能力.对ADHD儿童空间知觉的研究目前还存在很大的空缺,虽已有学者将视觉本顿图形测试运用于ADHD儿童的空间知觉研究中,证明了ADHD儿童存在空间认知失认,但这是唯一一项应用于该领域的研究,尚缺乏普遍性.本文通过分析现有的视觉空间研究理论和实验方法,指出今后在ADHD儿童空间知觉研究中还需使用更多的实验方法,使对ADHD患儿在空间知觉失认的研究具有普遍性.笔者将研究内容进行了细化,分别从形状知觉、长度-距离知觉、方位知觉、大小知觉等方面进行具体、深入的论证.     

Asymptotic and other estimates for semilinear parabolic problem in semi-infinite cylinder

The spatial decay of solutions to initial-boundary value problems for a semilinear parabolic equation in a semi-infinite cylinder of variable cross-section subject to zero condition on the lateral boundaries is investigated. A second-order differential inequality that shows the spatial decay O(exp(−z ²/(4(t+t ₀)))) for an L ^2p cross-sectional measure of the solution is obtained. A first-order differential inequality leading to growth or decay is also derived. In the case of growth, an upper bound for blow-up in space is obtained, while in the case of decay an upper bound for the total energy in terms of data is obtained.