Review of Collocation Methods and Applications in Solving Science and Engineering Problems

The collocation method is a widely used numerical method for science and engineering problems governed by partial differential equations.This paper provides a comprehensive review of collocation methods and their applications,focused on elasticity,heat conduction,electromagnetic field analysis,and fluid dynamics.The merits of the collocation method can be attributed to the need for element mesh,simple implementation,high computational efficiency,and ease in handling irregular domain problems since the collocation method is a type of node-based numerical method.Beginning with the fundamental principles of the collocation method,the discretization process in the continuous domain is elucidated,and how the collocation method approximation solutions for solving differential equations are explained.Delving into the historical development of the collocation methods,their earliest applications and key milestones are traced,thereby demonstrating their evolution within the realm of numerical computation.The mathematical foundations of collocation methods,encompassing the selection of interpolation functions,definition of weighting functions,and derivation of integration rules,are examined in detail,emphasizing their significance in comprehending the method’s effectiveness and stability.At last,the practical application of the collocation methods in engineering contexts is emphasized,including heat conduction simulations,electromagnetic coupled field analysis,and fluid dynamics simulations.These specific case studies can underscore collocation method’s broad applicability and effectiveness in addressing complex engineering challenges.In conclusion,this paper puts forward the future development trend of the collocation method through rigorous analysis and discussion,thereby facilitating further advancements in research and practical applications within these fields.

Anchanling reduces pathology in a lactacystin-induced Parkinson's disease model

A rat model of Parkinson＇s disease was induced by injecting lactacystin stereotaxically into the left mesencephalic ventral tegmental area and substantia nigra pars compacta. After rats were intragastrically perfused with Anchanling, a Chinese medicine, mainly composed of magnolol, for 5 weeks, when compared with Parkinson’s disease model rats, tyrosine hydroxylase expression was increased, α-synuclein and ubiquitin expression was decreased, substantia nigra cell apoptosis was reduced, and apomorphine-induced rotational behavior was improved. Results suggested that Anchanling can ameliorate Parkinson＇s disease pathology possibly by enhancing degradation activity of the ubiquitin-proteasome system.

Aeroheating CFD analysis of missile slots

This paper develops a hypersonic aerothermal simulation method for missile slot flow. The finite volume method of structure grid solver is developed for solving Euler and Navier-Stokes equations. The solver includes Park＇s two temperature model and the air multi-species reaction model. The second-order accuracy TVD numerical method was deduced to compute the hypersonic aeroheating which improves the computational efficiency. Computational results are given to show the high accuracy comparing to the existing experimental data.

A spatiotemporal analysis of the impact of lockdown and coronavirus on London’s bicycle hire scheme:from response to recovery to a new normal

The coronavirus pandemic that started in 2019 has had wide-ranging impacts on many aspects of people’s daily lives.At the peak of the outbreak,lockdown measures and social distancing changed the ways in which cities function.In particular,they had profound impacts on urban transportation systems,with public transport being shut down in many cities.Bike share systems(BSS)were widely reported as having experienced an increase in demand during the early stages of the pandemic before returning to pre-pandemic levels.However,the studies published to date focus mainly on the first year of the pandemic,when various waves saw continual relaxing and reintroductions of restrictions.Therefore,they fall short of exploring the role of BSS as we move to the post-pandemic period.To address this gap,this study uses origin-destination(O-D)flow data from London’s Santander Cycle Hire Scheme from 2019-2021 to analyze the changing use of BSS throughout the first two years of the pandemic,from lockdown to recovery.A Gaussian mixture model(GMM)is used to cluster 2019 BSS trips into three distinct clusters based on their duration and distance.The clusters are used as a reference from which to measure spatial and temporal change in 2020 and 2021.In agreement with previous research,BSS usage was found to have declined by nearly 30%during the first lockdown.Usage then saw a sharp increase as restrictions were lifted,characterized by longer,less direct trips throughout the afternoon rather than typical peak commuting trips.Although the aggregate number of BSS trips appeared to return to normal by October 2020,this was against the backdrop of continuing restrictions on international travel and work from home orders.The period between July and December 2021 was the first period that all government restrictions were lifted.During this time,BSS trips reached higher levels than in 2019.Spatio-temporal analysis indicates a shift away from the traditional morning and evening peak to a more diffuse pattern of working hours.The results indicate that the pandemic may have had sustained impacts on travel behavior,leading to a“new normal”that reflects different ways of working.

有晶状体眼后房型人工晶状体植入术后视觉质量的研究进展

随着有晶状体眼后房型人工晶状体植入术的发展及可植入式接触镜(ICL)设计、功能及材料的不断改进,ICL植入术目前已经成为矫正中高度近视的主流术式之一,然而近视患者对术后视觉质量的要求也日益提高,不仅要求摘掉框架眼镜后的视力达到预期矫正视力,还要求视力达到高清视觉效果。因此本文就ICL植入术后视觉质量的研究进行综述。

Cell Polarity Signaling： Focus on Polar Auxin Transport

Polar auxin transport, which is required for the formation of auxin gradients and directional auxin flows that are critical for plant pattern formation, morphogenesis, and directional growth response to vectorial cues, is mediated by polarized sub-cellular distribution of PIN-FORMED Proteins （PINs, auxin efflux carriers）, AUX1/AUXI-like proteins （auxin influx facilitators）, and multidrug resistance P-glycoproteins （MDR/PGP）. Polar localization of these proteins is controlled by both developmental and environmental cues. Recent studies have revealed cellular （endocytosis, transcytosis, and endosomal sorting and recycling） and molecular （PINOID kinase, protein phosphatase 2A） mechanisms underlying the polar distribution of these auxin transport proteins. Both TIR1-mediated auxin signaling and TIRl-independent auxinmediated endocytosis have been shown to regulate polar PIN localization and auxin flow, implicating auxin as a selforganizing signal in directing polar transport and directional flows.

ICL-V4c植入对人工晶状体度数计算的影响

目的:观察中央孔型有晶状体眼后房型人工晶状体ICL-V4c植入对人工晶状体(IOL)度数计算的影响。方法:前瞻性临床研究。选取2020年12月至2021年6月在新疆军区总医院北京路医疗区行ICL-V4c植入术并符合本研究纳排标准的患者40例(80眼),在术前及术后1 d、1周、1个月、3个月使用IOLMaster 500测量每例患者角膜屈光度、眼轴、前房深度(ACD),并通过SRK-T、HolladayⅠ、Haigis、Hoffer-Q公式计算得出IOL度数。采用重复测量方差分析进行数据分析。结果:角膜屈光度(K1、K2)术前及术后各时间点测量值之间的差异有统计学意义(F=34.23,P<0.001;F=14.64,P<0.001)。K1术后各时间点测量值均明显小于术前测量值(均P<0.001),术后各时间点测量值呈逐渐上升趋势;K2术后1 d、1周、1个月、3个月测量值均明显大于术前测量值(均P<0.05),术后各时间点测量值呈逐渐降低趋势。ACD在术前及术后各时间点测量值之间的差异有统计学意义(F=36.90,P<0.001),术后各时间点测量值均明显小于术前测量值(均P<0.001),术后各时间点测量值之间两两比较差异均无统计学意义,呈平稳趋势。眼轴在术前及术后各时间点测量值之间的差异无统计学意义,各时间点测量值两两比较差异均无统计学意义。使用SRK-T、HolladayⅠ、Haigis、Hoffer-Q公式计算获得的IOL度数在术前及术后各时间点的差异无统计学意义(均P>0.05)。结论:角膜屈光度及ACD的测量可能受ICL-V4c植入的影响,IOLMaster 500通过SRK-T、HolladayⅠ、Haigis、Hoffer-Q公式计算IOL度数不受ICL-V4c的植入的影响。