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.

Mechanical behaviours of bedded sandstone under hydromechanical coupling

The combination of the dipping effect and hydromechanical(H-M)coupling effect can easily lead to water inrush disasters in water-rich roadways with different dip angles in coal mines.Therefore,H-M coupling tests of bedded sandstones under identical osmotic pressure and various confining pressures were conducted.Then,the evolution curves of stress-strain,permeability and damage,macro-and mesoscopic failure characteristics were obtained.Subsequently,the mechanical behaviour was characterized,and finally the failure mechanism was revealed.The results showed that:(1)The failure of the sandstone with the bedding angle of 45°or 60°was the structure-dominant type,while that with the bedding angle of 0°,30°or 90°was the force-dominant type.(2)When the bedding angle was in the range of(0°,30°)or(45°,90°),the confining pressure played a dominant role in influencing the peak strength.However,withinβ∈(30°,45°),the bedding effect played a dominant role in the peak strength.(3)With the increase in bedding angle,the cohesion increased first,then decreased and finally increased,while the internal friction angle was the opposite.(4)When the bedding angle was 0°or 30°,the“water wedging”effect and the“bedding buckling”effect would lead to the forking or converging shear failure.When the bedding angle was 45°or 60°,the sliding friction effect would lead to the shear slipping failure.When the bedding angle was 90°,the combination of the“bedding buckling”effect and shear effect would lead to the mixed tension-shear failure.The above conclusions obtained are helpful for the prevention of water inrush disasters in water-rich roadways with different dips in coal mines.

When Fleeing Matters:Differences in Escape Behaviours of Three Northeast Asian Anurans

Prey species may have their own optimal escape strategy to balance predation risks and the energetic cost of fleeing.Some species have an advantage when maintaining a short fleeing distance,while others may favour an earlier escape based on microhabitat,size,or body condition.Here,we examined the escape behaviour of the three syntopic Northeast Asian anuran species:Mongolian toads(Strauchbufo raddei),Amur brown frogs(Rana amurensis),and Japanese treefrogs(Dryophytes japonicus)in Mongolia,Russia,China and DPR Korea.We examined flight initiation distance(FID;the distance from a potential predator to the point when the individual starts to flee)and distance fled(DF;distance between flight initiation and flight termination points)of each species and the effects of microhabitat,sex,and body size.Strauchbufo raddei and R.amurensis had a longer FID than D.japonicus,and S.raddei also had a longer DF than D.japonicus.These trends remained similar when dividing FID and DF by a size proxy(snout-vent length)for all individuals.This suggests that the treefrog D.japonicus used a strategy to stay immobile even when they were detected,and the toad S.raddei reacted quicker and more sensitively to predators despite the presence of toxin.Female S.raddei had a significantly longer FID than males suggesting that females are more sensitive to predation risk in this species,but body size was not significant for any of the three species.Our results indicate that the three sympatric species have different escaping strategies,likely related to differences in physiology and crypticity.

Suicidal Behaviours in Sickle Cell Patients at the Douala Sickle Cell Care Centre in Cameroon

Introduction: Sickle cell anaemia is a hereditary disease that combines physical and psychological manifestations, including suicidal tendencies. So far, to our knowledge, no study has been conducted on suicidal behaviours among people with sickle cell disease in Cameroon. This is what justifies our study on the prevalence and factors related to suicidal behaviors in our study population. Methods: We conducted a cross-sectional, analytical study of 171 sickle cell patients aged from 12 years upwards who came to the sickle cell disease care service of the Laquintinie Hospital in Douala, over a period of 6 months, that is, from 1 January to 31 June 2022. Data were collected using a structured questionnaire with questions on suicidal behaviours based on the “MINI” (Mini International Neuropsychiatric Interview). The data were processed using the SPSS 26.0 software. The related factors were studied in both a bivariate and multivariate analysis. Results: Female sickle cell patients accounted for 60.2% of the sample. The mean age was 23.36 ± 8.42 years. Suicidal ideation was prevalent in 56% of cases and 13% attempted suicide. The factors most associated with suicidal ideation were: primary level of education (OR = 0.08 (0.09 - 0.79);p = 0.03), feeling unworthy of life (OR = 0.40 (0.08 - 1.96);p = 0.02), not often being considered by those around them (OR = 2.97 (1.26 - 6.99);p = 0.01), lack of family support (OR = 0.34 (0.15 - 0.77);p = 0.01). Meanwhile, the factors associated with suicide attempts were: the fact of being rarely exposed to suicide-related media (OR = 4.17 (1.40 - 71.80);p = 0.03), and a constant feeling of sadness when returning home (OR = 18.02 (1.59 - 20.55);p = 0.01). Conclusion: More than half of sickle cell patients had had suicidal thoughts and 1/6 had made at least one suicide attempt, women and young adults being the most concerned. It is therefore necessary to ensure optimum psychological care for patients with sickle cell disease.

Train post‑derailment behaviours and containment methods:a review

Railway accidents,particularly serious derailments,can lead to catastrophic consequences.Therefore,it is essential to prevent derailment escalation to reduce the likelihood of severe derailments.Train post-derailment behaviours and containment methods play a critical role in preventing derailment escalation and providing passive safety protection and accident prevention in the event of a derailment.However,despite the increasing attention on this field from academia and industry in recent years,there is a lack of systematic exploration and summarization of emerging applications and containment methods in train post-derailment research.For this reason,this paper presents a comprehensive review of existing studies on train post-derailment behaviours,encompassing various topics such as post-derailment contact-impact models,dynamic modelling and simulation techniques,and the primary factors influencing post-derailment behaviours.Significantly,this review introduces and elucidates substitute guidance mechanisms(SGMs),which serve as railway-specific passive safety protection and accident prevention measures.The various types of SGMs are depicted,and their ongoing developments and applications are explored in depth.The review additionally points out several unresolved challenges including the adverse effects of SGMs,and proposes future research directions to advance the theoretical understanding and practical application of train post-derailment behaviours and containment methods.This review seeks to be a valuable reference for railway industry professionals in preventing catastrophic derailment consequences through post-derailment containment methods.

A novel model of drug cue-induced behaviours in rhesus macaque subjected to chronic ketamine exposure

To the Editor,Non-human primate(NHP)models are advantageous for mimicking human addiction with high behavioural validity.1 However,current NHP drug addiction models(eg,self-administration)often require a comprehensive behavioural training paradigm,relatively expensive apparatus and invasive surgical procedures.

A Numerical Investigation Based on Exponential Collocation Method for Nonlinear SITR Model of COVID-19

In this work,the exponential approximation is used for the numerical simulation of a nonlinear SITR model as a system of differential equations that shows the dynamics of the new coronavirus(COVID-19).The SITR mathematical model is divided into four classes using fractal parameters for COVID-19 dynamics,namely,susceptible(S),infected(I),treatment(T),and recovered(R).The main idea of the presented method is based on the matrix representations of the exponential functions and their derivatives using collocation points.To indicate the usefulness of this method,we employ it in some cases.For error analysis of the method,the residual of the solutions is reviewed.The reported examples show that the method is reasonably efficient and accurate.

基于Triple-Collocation多源地表温度数据融合方法研究

为充分利用多源地表温度数据,提高区域尺度下地表温度精度,改善地表温度遥感产品的适用性。以淮河流域为研究区,Triple-Collocation(TC)方法为基础,采用最小二乘法,由中分辨率光谱成像仪(MODIS)地表温度与风云三号可见光红外扫描辐射计(FY-3C/VIRR)地表温度遥感产品,结合地面观测站实测数据,研究多源数据融合方法。将淮河流域39个气象站点分为融合站点与验证站点,由融合站点采用反距离插值(IDW)算法得到区域连续地表温度数据,与FY-3C/VIRR地表温度数据、MODIS地表温度数据,融合得到淮河流域地表温度。与地面验证站点对比分析表明,融合后的地表温度,其R^(2)、RMSE和MAE分别为0.98、1.10 K、0.88 K,优于MODIS地表温度的0.92、2.59 K、2.18 K和FY-3C地表温度产品的0.84、6.68 K、5.35 K,精度得到了显著的提高。淮河流域不同月份的温度变化季节性规律明显,且变化主要出现在中部及东部地区,最高温度变化值都达到了20 K以上。

BITS: an efficient transport solver based on a collocation method with B-spline basis

A B-spline Interpolation Transport Solver(BITS) based on a collocation method is developed. It solves transport equations as a generalized interpolation problem, taking the first-order accuracy in time and the second-order accuracy in space along with a predictor–corrector or under-relaxation iteration method. Numerical tests show that BITS can solve one-dimensional transport equations for tokamak plasma more accurately without additional computation cost, compared to the finite difference method transport solver which is widely used in existing tokamak transport codes.

Shear behaviours and roughness degeneration based on a quantified rock joint surface description

The asperity wear of rock joints significantly affects their shear behaviour.This study discusses the wear damage of the asperities on the joint surface,highlighting the roughness degradation characteristics during the shear process.The direct shear experiment of artificial specimens containing rock joints was conducted under different normal stresses based on three-dimensional scanning technology.These experimental results showed the contribution of joint wear to roughness degeneration,such as the height,zone,and volume of asperity degeneration.The wear coefficient of the rock joint was obtained based on the volume wear of asperities in the laboratory experiment.The functional relationship between the friction coefficient and wear coefficient is subsequently determined.To quantitatively analyse the wear damage of a joint surface,a calculation method for determining the wear depth of the rock joint after shearing was proposed based on wear theory.The relationship between the ultimate dilation and wear depth was analysed.A coefficient m,which can describe the damage degree of the joint surface,and a prediction method of joint surface roughness after shearing are established.Good agreement between analytical predictions and measured values demonstrates the capability of the developed model.Lastly,the sensitivity factors on the wear depth are explored.

Finite Element Orthogonal Collocation Approach for Time Fractional Telegraph Equation with Mamadu-Njoseh Polynomials

Finite element method (FEM) is an efficient numerical tool for the solution of partial differential equations (PDEs). It is one of the most general methods when compared to other numerical techniques. PDEs posed in a variational form over a given space, say a Hilbert space, are better numerically handled with the FEM. The FEM algorithm is used in various applications which includes fluid flow, heat transfer, acoustics, structural mechanics and dynamics, electric and magnetic field, etc. Thus, in this paper, the Finite Element Orthogonal Collocation Approach (FEOCA) is established for the approximate solution of Time Fractional Telegraph Equation (TFTE) with Mamadu-Njoseh polynomials as grid points corresponding to new basis functions constructed in the finite element space. The FEOCA is an elegant mixture of the Finite Element Method (FEM) and the Orthogonal Collocation Method (OCM). Two numerical examples are experimented on to verify the accuracy and rate of convergence of the method as compared with the theoretical results, and other methods in literature.

A Comparative Study on Verb-Noun Collocation Errors of Chinese EFL Learners with Different Language Proficiency

This study presents a comparative analysis of verb-noun collocation errors made by Chinese EFL learners with different language proficiency.Linguistic data from two sub-corpora of CLEC(Chinese Learner English Corpus,Gui&Yang,1999)consist of the compositions written freely by Chinese senior high school students(ST2)and the 3rd-and 4th-year English majors of Chinese universities(ST6).The study results show that four types of verb-noun collocation errors are frequently made due to incorrect L1 translation,misuse of relative synonyms,misuse of delexical verbs,and misuse of part of speech;the number of errors decreases with the development of language proficiency,especially errors by incorrect L1 translation and relative synonyms.And for both ST2 and ST6 EFL learners,errors resulted from incorrect L1 translation account for nearly a half with the same high-frequency words.It is also found that ST6 learners’competence in collocation and synonym identification doesn’t grow with the increase of their vocabulary,as is shown in the case of overusing delexical verbs in collocation,the same error made by ST2 learners,who have a significantly weaker command of delexical verbs.Implications of the findings are also discussed with the purpose of raising the awareness of collocation pedagogy and enhancing EFL learners’collocation competence.

Risk behaviours associated with HIV and AIDS among couples in Rwamiko Sector, Gicumbi District, Rwanda

Background:Risk behaviours have been linked to the spread of the Human Immunodeficiency Virus(HIV)epidemic in both urban and rural areas.Despite the progress made in the fight against HIV,it remains a public health concern worldwide.Risk behaviours such as not using condoms,having multiple sexual partners,and engaging in early sexual activity increase the risk of HIV infection.Therefore,it is important to assess these risk behaviours and understand the relationship between different factors and HIV,specifically among couples,in order to better understand the dynamics of the epidemic.The main objective of this study was to assess risk behaviours for HIV and AIDS among couples in Rwamiko sector,Gicumbi District,and suggest appropriate interventions for this group.Methods:This cross-sectional survey aimed to assess associated HIV and AIDS risk behaviours among couples in Rwamiko Sector,Gicumbi District,in order to determine the dynamics of the epidemic in this group and suggest appropriate interventions.Data was collected using a self-administered questionnaire and a multistage cluster random sampling technique.The collected data was then computed,analyzed,and presented in the form of tables and figures.Descriptive statistics were used to analyze all variables.Multivariate logistic regression was used to calculate odds ratios and 95%confidence intervals(CI)to investigate the relationship between the assessed factors,such as independent and dependent variables.The association between the studied factors was described using odds ratios with 95%CIs.Results:The majority of respondents were in the age group of 30-39 years.All respondents were married,and approximately 45%had completed primary education.The majority of respondents were unemployed.Respondents reported receiving HIV information from multiple sources,including radio,TV,films,school,church,health workers,parents,and friends.The findings of this study showed that some participants had knowledge about HIV transmission and prevention,while others did not.The proportion of respondents with a high level of HIV and AIDS knowledge was 30.61%(n=60),while moderate knowledge accounted for 53.57%(n=105).Furthermore,the proportion of respondents with a low level of knowledge on HIV and AIDS was 15.81%(n=31).The attitude towards HIV and AIDS was positive for 58.16%(n=114)of respondents,while 41.83%(n=82)had a negative attitude.None of the respondents reported using injection drugs.Significant associations were found between age(P-value=0.002,odds ratio(OR)=3.4,95%CI=1.59-7.67),gender(p=0.001,OR=2.6,95%CI=1.44-4.68),and alcohol consumption.There was also an association between age(P=0.001,OR=5.13,95%CI=2.04-12.91)and having multiple sexual partners.Conclusion:The majority of couples in Rwamiko Sector,Gicumbi District have a moderate level of knowledge and a positive attitude towards HIV and AIDS.However,the proportions of respondents with a low level of knowledge and a negative attitude should not be overlooked.The results of this study suggest the need to improve communication messages related to HIV,its transmission risks,and safer sexual behavior,particularly among couples in Rwamiko Sector,Gicumbi District.

Exploring“Enabling Behaviours”of Wives of Persons with Substance Use Disorder in Chapter 8 of the Big Book of Alcoholic Anonymous

Substance use disorder has a damaging effect on the family members of alcoholics and drug users.On the other hand,the reactions and behaviours of family members may negatively influence a person with substance use disorder.The behaviours of significant others of a person with substance use disorder that contribute to the maintenance of substance use disorder are called enabling.This study aimed to explore enabling behaviours of wives of persons with substance use disorder in Chapter 8 of Alcoholic Anonymous’Big Book by utilising qualitative content analysis.Alcoholics Anonymous(AA)is one of the most commonly used programs for recovery from alcoholism.The current study sought to help mental health professionals get a better understanding of the views and premises of the AA program in reference to enabling behaviours of wives by conducting a qualitative content analysis of the AA Big Book.The study also discusses the healthy behaviours suggested by the authors of the Big Book and the comprehensiveness of the text for the readers.

滥用数据优势行为的竞争法规制

数字经济时代滥用数据优势行为不仅诱发了直接排斥效应、供给挤压效应和市场封锁效应等竞争损害,而且阻滞了创新要素流通利用,不利于数据要素价值充分释放。我国《反垄断法》与《反不正当竞争法》均已围绕新兴业态开展数字化变革,但如何协调两者关系以塑造体系化数据竞争规则,迄今尚缺乏定论。我国宜以市场支配地位和相对交易优势地位的分层建构规制滥用数据优势行为,同时由反垄断法调整排他性滥用行为,并以保证特定数据的可获取性为重点;由反不正当竞争法调整剥削性滥用行为,以保障公平交易权为重点。

同情聚焦疗法对脑卒中偏瘫患者认知功能与病耻感的影响

目的 探讨同情聚焦疗法对脑卒中偏瘫患者认知功能与病耻感的影响。方法 选择本院收治的100例脑卒中偏瘫患者作为研究对象,其中2020年12月至2021年12月收治的50例作为对照组,2022年1月至2023年1月收治的50例作为观察组。对照组予以认知行为疗法干预,观察组在对照组的基础上予以同情聚焦疗法干预。比较干预前后两组患者羞耻感、认知功能、自我批评情况。结果 干预后观察组患者病耻感水平评分低于对照组,认知功能评分低于对照组,自我批评水平得分低于对照组,两组比较,差异具有统计学意义(均P<0.05)。结论 同情聚焦疗法可降低脑卒中偏瘫患者自我批评水平、羞耻感,促进患者认知功能恢复。

代际支持视角下脑卒中失能患者就医行为的影响因素研究

目的研究脑卒中失能患者就医行为现状及主要影响因素,探讨代际支持对脑卒中失能患者就医行为的影响,为促进其合理就医行为提供理论依据。方法采用便利抽样法,于2023年1月至3月对608例脑卒中防治工程管理专项数据库中的患者进行网络问卷调查,问卷内容包括患者一般资料、失能程度、代际支持情况、就医行为现况4个方面,并使用多因素线性回归分析脑卒中失能患者就医行为的影响因素。结果608例脑卒中失能患者就医行为得分为(30.30±5.22)分、代际支持得分为(16.91±0.83)分。多因素线性回归分析结果显示,年龄、月收入、就医距离、子代陪护照料、就医接送、情感交流程度及情感交流频次为脑卒中失能患者就医行为的影响因素(P<0.05),可解释总变异的41.6%。结论脑卒中失能患者就医行为总体较为合理,代际照料支持和代际情感支持对脑卒中失能患者就医行为呈正向促进作用,应重点关注高龄、低收入水平、居住偏远地区的失能患者,同时制定合适的措施增加子女代际支持能力,以期改善患者就医行为。

“互联网+健康管理”模式在健康体检外阴阴道假丝酵母菌病检出人群的干预效果分析

目的外阴阴道假丝酵母菌病(VVC)是当前育龄期女性常见的一种下生殖道感染性疾病,VVC除了对患者生殖器官和功能造成一定的损害外,还因其反复发作、顽固难愈引发了患者心理健康、生活质量和社会功能等一系列相关问题。为加强VVC患者对疾病的防治意识,提高卫生服务质量和妇女的生殖健康水平,现探讨应用“互联网+健康管理”模式对健康体检外阴阴道假丝酵母菌病(VVC)检出人群的干预效果。方法选择2019年7月—2020年3月医院200例被确诊为VVC的育龄期女性为研究对象,按照组间基本特征具有可比性的原则分为观察组和对照组,各100例。对照组采用常规基本的健康体检管理方式,发放体检结果及健康指导建议、建立健康体检档案,电话或短信提醒患者按时复诊等;观察组在对照组基础上应用“互联网+健康管理”模式,建立管理小组,搭建医患沟通平台,健康科普宣教,健康风险评估,个性化干预,定期健康随访。比较两组患者干预前后疗效、VVC复发率、遵医行为及VVC相关知识得分情况。结果干预3个月、6个月后,观察组患者各项VVC相关知识评分高于同期对照组,差异有统计学意义(P<0.05)。干预后观察组患者的遵医行为、临床总有效率及VVC复发率据低于对照组,差异有统计学意义(P<0.05)。结论“互联网+健康管理”模式可促进健康体检VVC检出人群健康生活方式的养成,提高患者治疗依从性,延缓患者VVC发展,降低VVC的复发率,实现了预期的管理目标。在防治VVC的发展起到了“治未病,防患于未然”的作用。该管理模式具有高效率、广覆盖、低成本的特点,适宜在健康管理和临床护理领域应用。

行人过街事件网联HUD预警系统对驾驶行为的影响

为探索行人过街事件网联环境下平视显示预警系统在不同天气条件下对驾驶行为的影响,以论证预警系统的有效性。文中首先设计基线条件(Baseline)、低头显示(HDD)、平视显示(HUD)3种预警系统,依托驾驶模拟平台开发晴天和雾天天气条件下城市道路网联场景,通过实验测试提取驾驶行为参数;然后,从微观层面刻画行人过街事件网联HUD预警系统作用下驾驶行为的整个空间变化过程,分析预警系统和天气状况两种因素对驾驶行为的作用规律,构建包含避险阶段和恢复阶段的驾驶行为影响模式,提出了反映避险阶段安全水平、恢复阶段恢复水平以及全过程稳定水平等3个层面的综合指标体系,包括首次制动距离、最小冲突距离、恢复稳定时间、速度恢复量、最大减速度和最大加速度;最后,量化不同预警系统(Baseline/HDD/HUD)、天气状况(晴天/雾天)以及两因素间交互作用对驾驶行为的影响。结果表明:行人过街网联HUD预警系统对驾驶人在避险阶段和恢复阶段中的驾驶行为存在显著性作用,显著提高避险阶段驾驶行为的安全水平,同时对恢复阶段恢复效率具有明显的提升作用,也显著影响全过程运行特性的稳定水平;在雾天条件下行人过街网联HUD预警系统表现出更为明显的优势。

老年在线声乐学习的需求、行为特征与促进策略

老年在线声乐学习是教育数字化转型下的实践场域,其有助于提升老年人的幸福感和生命价值。通过选取参与在线声乐学习的老年群体开展问卷和访谈调研,探明了老年群体参与在线声乐学习的缘由、学习行为特征和学习障碍等;发现老年用户在线声乐学习行为特征匹配五类学习需求——应对需求、表达需求、贡献需求、影响需求和超越需求。探明了促进老年在线学习的有效策略,即提供老年在线学习支持和代际互助、发展老年用户粘性、构建学习共同体、实施平台无障碍设计及适老化改造、提供适合老年用户的优秀教师等。