Mathematical analysis of corneal remodelling after intracorneal ring surgery in keratoconus

AIM：To represent mathematically the intersection between the ectatic corneal geometry and the plane of intracorneal ring implants（ICRS）in order to determine the corneal response to ICRS surgery in keratoconus（KC）.Thereafter,to present the concept and early results of a newly derived topography-guided nomogram for ICRS surgery for the treatment of keratectasia. METHODS：The corneal rings plane intersection was modelled to a conic section. Ring effect was the result of：the ring size,position（steep vs flat）,location（distance from the geometric centre of the cornea）,and the discrepancy between the ring＇s curvature and the tunnel＇s curvature.Femtosecond laser was used to create the tunnels and the incision sites were chosen according to the nomogram in order to place the thickest ring in the steepest portion of the cornea regardless of the astigmatism axis of refraction.RESULTS：The conic section had a more prolate shape in the steep area of the cornea than in the flat area,depending on the corneal sagittal curvature. Equal ring size had more flattening effect in the steep area than in the flat area. Thick segment should be implanted under the steep portion of the cornea regardless of the cylinder axis of refraction. Single segment in the steep area was sufficient in early and moderate cases of KC. The new nomogram provided more topographic regularity with significant reduction of astigmatism and better improvement in uncorrected visual acuity（UCVA）and best-corrected visual acuity（BCVA）than the conventional nomogram. CONCLUSION：The newly derived nomogram can produce better results than the conventional nomogram. Moreover,based on this concept,a new nomogram can be integrated into the femtosecond laser software to create topography-guided,customized,elliptical tunnels with modified focal asphericity that allows for customized focal flattening of the irregularly steepened ectatic cornea.

Mathematical analysis of the role of recoil pressure in weld pool dynamics during laser-MIG hybrid welding

A mathematical model was established to simulate the weld pool development and dynamic process in stationary iaser-MlG hybrid welding. Surface tension and buoyancy were considered to calculate liquid metal flow patter, moreover, typical phenomena of MIG welding, such as filler droplets impinging weld pool, electromagnetic force in the weld pool, and typical phenomena of laser beam welding, such as recoil pressure, Inverse Bremsstrahlung absorption, Fresnel absorption were all considered in the model. The laser beam and arc couple effect were introduced into this model by the plasma width during hybrid welding. The role of recoil pressure in the weld formation was discussed. Transient weld pool shape and complicated liquid metal velocity distribution from two kinds weld pool to an unified weld pool were calculated. The simulated weld bead geometry with consideration recoil pressure was in good agreement with experimental measurement.

Prediction and sensitivity analysis of the surface quality in Ni60/WC coatings

For laser cladding a large temperature gradient easily weakened the surface quality by generating cracks and irregular coating surfaces,which in turn affected the bearing capacity and corrosion resistance of coatings in the rapid heating and cooling process.The response surface methodology(RSM)was used to predict coating cracks by changing the powder ratio,energy density,and preheating temperature,which obtained the relevant mathematical model.After that,the sensitivity of the crack length to process parameters was analyzed based on the sensitivity analysis method.The effect of Ni60/WC composite powder process parameters on the surface quality was revealed in laser cladding.The crack length first decreased and then increased,and the Smooth decreased with the increased powder ratio.The crack length and Smooth increased with the increased energy density.The crack length decreased and Smooth increased with the increased preheating temperature.Sensitivity analysis showed that the crack length and Smooth were the most sensitive to the powder ratio.Therefore,the process parameters were reasonably selected to control the surface quality.The mathematical model and sensitivity analysis method in the work could improve the surface quality,which provided a theoretical basis for the prediction and control of laser cladding cracks.

Simulation of Thermophysical Processes at Laser Welding of Alloys Containing Refractory Nanoparticles

Mathematical model is formulated for description of thermophysical processes at laser welding of metal plates for the case when modifying nanoparticles of refractory compounds (nanopowder inoculators – NPI) are introduced into the weld pool. Specially prepared nanoparticles of refractory compounds serve here as crystallization centers, i.e. in fact they are exogenous inoculants on which surface clusters are grouped. This can be used to control the melt crystallization process and formation of its structure, and, therefore, properties of the weld seam. As an example, calculation results of the butt welding of aluminum alloy and steel plates are presented. The results of calculation and experimental data comparison are shown.

Modeling of a Linear Scanning 3D Vision Coordinate Measurement System

This paper theoretically analyzes and researches the coordinate frames of a 3D vision scanning system, establishes the mathematic model of a system scanning process, derives the relationship between the general non-orthonormal sensor coordinate system and the machine coordinate system and the coordinate transformation matrix of the extrinsic calibration for the system.

Using a Gaussian mathematical model to define eruptive stages of young volcanic rocks in Tengchong based on laser 40Ar/39Ar dating

Reconstruction of Quaternary environments,late Cenozoic geodynamics and evaluation of volcanic hazards,all depend on the precise delineation of eruptive stages.In recent years,laser 40Ar/39Ar dating methods have been widely used for dating young volcanic rocks,given their stable automated testing process,very low background level and high sensitivity,which meet the requirements for precise dating of young samples.This paper applied high-precision laser 40Ar/39Ar dating to the main volcanic units in the Tengchong area and obtained ages in the range of 0.025–5.1 Ma using conventional data processing methods.However,conventional dating highlighted issues related to very low radiogenic 40Ar content,accidental errors and poor data stability,which led to huge age deviations.Moreover,lacking a unified timescale,conventional methods were unable to strictly define the stages of the Tengchong volcanic eruptions,leading to ongoing controversy.In this study,we applied a Gaussian mathematical model to deal with all 378 original ages from 13 samples.An apparent age-probability diagram,consisting of three independent waveforms,have been obtained.The corresponding isochron ages of these three waveforms suggest there were three volcanic eruptive stages,namely during the Pliocene(3.78±0.04 Ma),early Middle Pleistocene(0.63±0.03 Ma)and late Middle Pleistocene to early Late Pleistocene(0.139±0.005 Ma).These results accurately define eruptive stages in the Tengchong area.

水轮发电机组碳刷/集电环摩擦副接触电阻计算及仿真验证

碳刷/集电环组件作为水轮发电机组励磁系统的重要组成部分,常因界面接触状态变化而出现碳刷过热、打火、电弧侵蚀等问题.其界面间的接触状态目前无法直接监测,间接监测则成为解决该问题的关键.载流摩擦副间的接触状态常用接触电阻进行表征,因此,本文中基于电接触和传热学的相关理论,建立了接触电阻的数学模型,该模型旨在根据碳刷温度估算接触电阻值.通过碳刷/集电环载流摩擦试验确定模型中的相关参数,计算并分析不同额定电流、转速、弹簧压力条件下,接触电阻的动态变化及关键影响因素.将计算结果代入COMSOL Multiphysics有限元分析软件中,基于其内置的物理场控制方程,仿真模拟碳刷的温度并与试验得到的碳刷的温度作比较,以验证该模型的有效性.计算结果表明:当界面接触压力一定时,接触电阻值随着额定电流的增大而减小;当额定电流一定时,界面接触压力大的碳刷接触电阻值小;当集电环转速增大时,弹簧压力对接触电阻的影响进一步增大.

疫苗环形接种阻断猴痘传播的可行性建模

[目的]探讨在男-男性行为(men sex with men,MSM)人群中开展环形接种从而阻断猴痘传播的可行性.[方法]将人群接触区分为固定与非固定接触两部分,建立描述环形接种的常微分方程猴痘传播数学模型.进而基于该模型的数值模拟,评估并探讨环形接种在群体层面的防传播效果,以及接种过程中涉及的若干环节实施力度的影响.[结果]模拟显示,在基线场景的200 d传播模拟中,仅追踪接种80%和90%密接的环形接种方案可以分别使人群中平均每7.00和9.18 d产生一个病例,二者均大于病例的实际传染期,意味着发生传播阻断.密接追踪比例α1≥0.5时,继续提高α1可以减少疫苗消耗,提高有限疫苗资源的利用率.额外针对次密接的追踪接种将消耗与大规模接种类似的大量疫苗资源,效益较低,仅适用于疫情传播早期病例数极少的情形.[结论]对于猴痘这种自限性疾病,仅针对密切接触者的追踪接种可以很好地控制猴痘传播,同时对局部暴发具有较好的控制效果.然而为进一步减少聚集性暴发带来的额外负担,仍应预先提高MSM人群的疫苗覆盖率.

Mathematical model for light scanning system based on circular laser

A novel light scanning system based on circular laser trajectory for welding robot is developed. With the help of image processing technique, intelligent laser welding could be realized. According to laser triangulation algorithm and Scheimpflug condition, mathematical model for circular laser vision is built. This scanning system projects circular laser onto welded seams and recovers the depth of the welded seams, escapes from shortcomings of less information, explains ambiguity and single tracking direction inherent in “spot” or “line” type laser trajectory. Three-dimensional （3D） model for welded seams could be recognized after depth recovery. The imaging error is investigated also.

SLM成形薄壁件尺寸偏差预测与控制研究

目的 针对选区激光熔化成形薄壁件过程中存在的变形较大、精度低等问题,通过获得最优工艺参数区间来减小薄壁件的变形。方法 利用有限元软件分析薄壁件成形过程中温度场和应力场的演化规律;建立形变量预测模型并进行试验验证,研究工艺参数对薄壁件尺寸偏差的影响,得到激光功率、扫描速度与形变量之间的关系,实现对形变量的预测和控制。结果 随着扫描层数的增加,熔池的最高温度和热影响区也随之增大,等温线越密集,温度梯度越大,最终趋于稳定;薄壁件成形过程中,出现两侧壁边缘向内倾斜、上侧边缘出现内凹的现象,薄壁件的最大应力随层数的增加而减小,最大热应力主要分布在薄壁件底层的两端;形变量随激光功率的增大而增大,随扫描速度的增大而减小,薄壁件的形变量最小约为0.02 mm;试验验证所建立的数学模型误差在10%左右,误差较小,可以对形变量进行良好的预测和控制。结论 激光功率100~200 W、扫描速度800~1 000 mm/s为最优参数区间;降低能量密度可以有效降低薄壁件形变量,提高其精度。

激光熔覆钴基合金涂层稀释率预测数学模型构建

激光熔覆操作过程中,很多参数都会对涂层稀释率具有影响,稀释率过大、过小都会直接关系到激光熔覆涂层质量。基于上述背景,构建激光熔覆钴基合金涂层稀释率预测数学模型。计算影响因素与稀释率之间的灰度关联度,筛选出大于1.0的影响因素作为预测模型的自变量。参照选出的影响因素,通过实验采集样本数据。将样本数据输入到基于多元回归模型当中,估算回归系数,完成预测模型构建。结果表明:所构建的预测模型应用下,激光熔覆钴基合金涂层稀释率预测值与实际值之间的拟合优度均大于0.9,说明所构建的预测模型准确性较高。

光纤影响量子点激光器的运行状态数学模型研究

光纤影响下的量子点激光器运行状态具有非线性,构建基于势能函数分析和双态QDL激子模型的光纤影响量子点激光器的运行状态数学模型。在光纤注入状态下,分析量子点激光器的非线性动力学参数模型,结合非线性动力学态的分布和演化特性,利用时间序列、功率谱及相图分析的方法,在不同参数注入下进行量子点激光器的参数空间及运行状态动力学分布特性分析。以光学能级、光学限制因子以及光学增益因子等为约束参数,进行自由运行状态下的量子点激光器基态和激发态特性分析,实现光纤影响下量子点激光器的运行状态数学模型构建。实验结果表明,该模型能有效获取量子点激光器的最优微波线宽,在电流增加的过程中,自由运行光谱能级谱检测性能较好,研究结果为光纤网络互联和光存储提供理论基础。

激光冲击强化钢的残余应力数学建模分析

为分析钢在激光冲击强化后的残余应力,以SAPH420结构钢为例,进行激光冲击强化处理。用有限元和无限元结合构建钢残余应力的有限元模型,计算残余应力。结果表明:激光冲击的光斑搭接率为75%时,压应力约为814 MPa,激光冲击时间为3 500 ns时,内能、塑性能及弹性能分别约为65、60、10 mJ,激光冲击强化后钢表面平均硬度为350HV0.2,屈服强度和抗拉强度分别超过587.3 MPa和594.4 MPa,疲劳性能提升,残余应力影响的最大深度为0.35 mm,有利于提升钢的使用寿命。

基于LIEF的喷雾数值仿真模型验证

为了进一步探索发动机内部的空气燃料混合特性,基于Converge软件的O Rourke湍流扩散模型与Frossling蒸发模型建立了喷雾蒸发的数值仿真模型,并使用复合激光诱导荧光(LIEF)技术对相同工况下定容弹内喷雾的液气两相浓度进行了同步测量,以对仿真进行验证。验证结果表明,仿真中的液相贯穿距与试验吻合较好,证明了仿真模型的正确性。仿真结果在气相部分出现了较明显的偏差,通过对模型方程进行分析得知,这是由于仿真模型所使用的Frossling单液滴蒸发模型无法考虑多组分与多相流情况的传质与传热,并针对如何提高模型精度给出了修正建议。

拉曼激光放大器特性与影响因子间关系变化的数学模型设计

针对当前数学模型无法描述拉曼激光放大器的特性,设计了拉曼激光放大器特性与影响因子间关系变化的数学模型。首先分析拉曼激光放大器的工作原理,并设定拉曼激光放大器的阈值,然后找到影响拉曼激光放大器特性的影响因子,并采用深度信念网络拟合拉曼激光放大器输出特性与影响因子之间关系,从而建立相应的数学模型,最后分析该模型的性能,结果表明,模型可以准确描述影响因子与拉曼激光放大器特性之间的关系,为设计性能优异的拉曼激光放大器提供了重要支撑,具有重要的实际应用价值。

LIBS成分检测与Ausmelt数模系统协同优化铜熔炼用氧实践

奥斯麦特炉(Ausmelt)熔池熔炼受输入原料、结焦脱落等动态变化因素的影响,炉内熔池温度、冰铜品位和炉渣渣型易发生变化,若炉况调整不及时易造成炉内结壳,严重时甚至会出现死炉。鉴于此,探索了依靠激光诱导击穿光谱(LIBS)技术快速对冰铜和炉渣完成在线成分检测,然后将检测数据人工传输到Metcal冶金数模软件中反馈指导生产的可行性,并就奥斯麦特炉用氧量指标进行仿真及实践效果比对。通过LIBS熔体在线检测设备的长期运行实践,验证了其检测的可靠性和准确性,以X射线荧光光谱仪(XRF)检测结果为基准的LIBS熔体检测偏差在±1.0%以内的为96.2%,固体检测偏差在±1.0%以内的为81.7%,基本可实现以LIBS取代XRF检测。基于高实时性在线检测结果,随机抽取15炉次奥炉平均实际用氧量与LIBS指导数模用氧量,可见偏差由7.65%降低至2.77%,达到了精准调控炉况控制参数的效果,为奥炉稳定生产和节能降耗提供了重要保障。

高强化柴油机活塞环-气缸套边界润滑模型研究

高强化柴油机活塞环-气缸套在上止点处的工作环境恶劣,多处于边界润滑状态,该润滑状态对摩擦副的摩擦磨损性能具有较大影响,然而目前仍缺少相应的数值模型。本研究建立了考虑摩擦膜影响的活塞环-气缸套边界润滑模型,并对其关键参数进行了试验标定,在此基础上,对典型工况下该摩擦副摩擦系数及磨损量进行预测,并与往复摩擦磨损试验机试验结果进行对比,二者偏差小于10%,验证了该模型用于工程评价的有效性。

激光捷联惯性导航系统动态锥动误差建模分析

提出了一种机抖激光陀螺的锥动误差参数建模与补偿方法。首先从机理上分析了锥动误差产生的原因,利用有限元分析方法给出了在不同外界角加速度输入下激光陀螺敏感轴的变形情况;建立了锥动误差的补偿模型,将锥动误差的影响用锥动误差系数表示,该系数仅和激光陀螺自身相关;设计了锥动误差系数的系统级标定方案,利用圆锥运动前后系统的姿态误差与锥动误差系数的关系完成参数标定。然后通过激光陀螺和光纤陀螺的圆锥运动实验,证明了锥动误差的存在;通过系统级的圆锥运动实验,证明了锥动误差的补偿效果。最后通过系统级的振动试验,验证了本文提出的锥动误差补偿方法能够有效地减小振动环境下系统的姿态和速度误差,对提升惯导系统在复杂力学环境下导航精度有着重要作用。

Studies on the mechanisms of powerful terahertz radiations from laser plasmas

A survey on the mechanisms of powerful terahertz （THz） radiation from laser plasmas is presented.Firstly,an analytical model is described,showing that a transverse net current formed in a plasma can be converted into THz radiations at the plasma oscillation frequency.This theory is applied to explain THz generation in a gas driven by two-color laser pulses.It is also applied to THz generation in a tenuous plasma driven by a chirped laser pulse,a few-cycle laser pulse,a DC/AC bias electric field.These are well verified by particle-in-cell simulations,demonstrating that THz radiations produced in these approaches are nearly single-cycles and linear polarized.In the chirped laser scheme and the few-cycle laser scheme,THz radiations with the peak field strength of tens of MV/cm and the peak power of gigawatt can be achieved with the incident laser intensity less than 10 17 W/cm 2.

ABF封装载板激光盲孔斜度提升

高密度封装载板是人工智能、5G、大数据、高性能计算、智能汽车和数据中心等新兴需求应用的CPU、图形处理器(GPU)、FPGA等高端数字芯片的重要载体,业界对其需求量快速增长。产品一般通过在增层树脂膜(ABF树脂)上加工小尺寸盲孔实现层间互联,因此盲孔孔型的控制是影响品质的关键指标,文章从盲孔的孔型出发,阐述采用激光钻孔方式制作高Taper孔型(下孔径比上孔径),高Taper孔型有利于除胶药水清除孔底残留树脂,提升盲孔可靠性。本文采用数学建模,预测达成目标Taper值的影响因子和水平,提出提升激光盲孔Taper值的优化方向。