割点图的Avalanche多项式

利用图的常返构形与支撑树的关系,研究有割点图的avalanche大小及其avalanche多项式.

Advances in ice avalanches on the Tibetan Plateau

As some of the greatest natural disasters in the cryosphere,ice avalanches(IAs)seriously threaten lives and cause catastrophic damage to the resource environment,but a comprehensive overview of the state of knowledge on IAs remains lacking.We summarized 63 IAs on the Tibetan Plateau(TP)since the 20th century,of which,over 20 IAs occurred after the 21st century.The distributions of IAs are mainly concentrated in the southeastern and northwestern TP,and the occurrence time of IAs is mostly concentrated from July to September.We highlight recent advances in mechanical properties and genetic mechanisms of IAs and emphasize that temperature,rainfall,and seismicity are the inducing factors.The failure modes of IAs are summarized into 6 categories by examples:slip pulling type,slip toppling type,slip breaking type,water level collapse type,cave roof collapse type,and wedge failure type.Finally,we deliver recommendations concerning the risk assessment and prediction of IAs.The results provide important scientific value for addressing climate change and resisting glacier-related hazards.

Numerical simulation for the initial state of avalanche in polydisperse particle systems

Numerical simulation is employed to investigate the initial state of avalanche in polydisperse particle systems.Nucleation and propagation processes are illustrated for pentadisperse and triadisperse particle systems,respectively.In these processes,particles involved in the avalanche grow slowly in the early stage and explosively in the later stage,which is clearly different from the continuous and steady growth trend in the monodisperse system.By examining the avalanche propagation,the number growth of particles involved in the avalanche and the slope of the number growth,the initial state can be divided into three stages:T1(nucleation stage),T2(propagation stage),T3(overall avalanche stage).We focus on the characteristics of the avalanche in the T2 stage,and find that propagation distances increase almost linearly in both axial and radial directions in polydisperse systems.We also consider the distribution characteristics of the average coordination number and average velocity for the moving particles.The results support that the polydisperse particle systems are more stable in the T2 stage.

Dynamic Characteristics of the Long Runout Rock-ice Avalanche at High Altitude——A Case from the Zelongnong Basin,Eastern Himalayan Syntaxis,China

Rock-ice avalanches have frequently occurred in the Eastern Himalayan Syntaxis region due to climate change and active tectonic movements.These events commonly trigger catastrophic geohazard chains,including debris flows,river blockages,and floods.This study focuses on the Zelongnong Basin,analyzing the geomorphic and dynamic characteristics of high-altitude disasters.The basin exhibits typical vertical zonation,with disaster sources initiating at elevations exceeding 4000 m and runout distances reaching up to 10 km.The disaster chain movement involves complex dynamic effects,including impact disintegration,soil-rock mixture arching,dynamic erosion,and debris deposition,enhancing understanding of the flow behavior and dynamic characteristics of rock-ice avalanches.The presence of ice significantly increases mobility due to lubrication and frictional melting.In the disaster event of September 10,2020,the maximum flow velocity and thickness reached 40 m/s and 43 m,respectively.Furthermore,continuous deformation of the Zelongnong glacier moraine was observed,with maximum cumulative deformations of 44.68 m in the distance direction and 25.96 m in the azimuth direction from March 25,2022,to August 25,2022.In the future,the risk of rock-ice avalanches in the Eastern Himalayan Syntaxis region will remain extremely high,necessitating a focus on early warning and risk mitigation strategies for such basin disasters.

Evidence of ancient rock-ice avalanches along the China-Bhutan Chomolhari Range,and their implications for demise of the summit

Large-scale rock-ice avalanches resulting from the interaction of tectonics and climate are characterized with high mobility,huge volumes of sediment,and rapid denudation,being a major agent of landscape evolution in high altitude mountainous regions.Specifically,the extreme glaciated slope failures often transform into extraordinarily large and mobile debris flows,resulting in disastrous consequences such as sedimentation and desertification.Due to a dearth of on-site observation data and experimental data collection,our comprehension of the geomorphic and kinematic characteristics of rock-ice avalanches remains poor.Here we report a cluster of ancient rock-ice avalanches spreading along the Chomolhari range of the China-Bhutan Himalayas.By integrating remote sensing image interpretation with detailed field investigations,we demonstrate the geomorphic and sedimentary characteristics of four events among the avalanches.The estimated volumes of the four are 23.73 Mm³,39.69 Mm³,38.43 Mm³,and 38.25 Mm³,respectively.The presence of pre-existing moraines or alluvial fans constrained their movement,resulting in deposition features such as marginal digitated lobes at higher elevations and large depressed areas in the interior.Applying the Savage-Hutter theory,we calculate the basal friction angle and travel angle of these ancient rock-ice avalanches that are both less than 10°,affirming the similarity of these avalanches in the study area to those occurring in other regions.Our study significantly contributes to understanding the geomorphic and kinematic characteristics of rock-ice avalanches in high-altitude mountainous regions,providing valuable insights into their response to the disproportionate growth of Himalayan peaks.

Mantle avalanches in a Venus-like stagnant lid planet

Stagnant lid planets are characterized by a globe-encircling,conducting lid that is thick and strong,which leads to reduced global surface heat flows.Consequently,the mantles of such planets can have warmer interiors than Earth,and interestingly,a pyrolitic mantle composition under warmer conditions is predicted to have a distinctly different mantle transition zone compared to the present-day Earth(Hirose,2002;Stixrude and Lithgow-Bertelloni,2011;Ichikawa et al.,2014;Dannberg et al,2022).Instead of olivine primarily transforming into its higher-pressure polymorphs such as wadsleyite and then ringwoodite,at pressures corresponding to 410 km and 520 km depth in Earth,respectively,it instead transforms into a mineral assemblage of wadsleyite,majorite,and ferropericlase(WMF),and then to majorite+ferropericlase(MF),before finally transforming into bridgmanite at pressures corresponding to 660 km depth in Earth(Stixrude and Lithgow-Bertelloni,2011;Ichikawa et al.,2014).Convective motions in stagnant lid planets are dominated by small-scale instabilities(cold drips)forming within the mobile rheological sublayer under the rigid lid.Using ASPECT and a thermodynamic model of a pyrolitic mantle composition generated by HeFESTo,we show that under certain conditions,the small drips can pond atop the WMF-MF mineral phase transition.The barrier to convective flow arises from the WMF mineral phase assemblage having an effective negative thermal expansivity(Stixrude and Lithgow-Bertelloni,2022).Although large-scale downwellings that typically occur within mobile lid planets are able to pass through the WMF zone without difficulty(Dannberg et al.,2022;Li RP et al.,2024),the smaller and less negatively buoyant nature of downwelling drips in stagnant lid planets are more susceptible to these effects,which leads to an ephemeral layering of the mantle.Our numerical models show that in stagnant lid planets with mantle potential temperatures that exceed 1900 K,the smaller,cold drips from the lid continue to pile up until enough of them have coalesced that they collectively avalanche as a larger instability into the deeper interior.

Topographic seismic effects and avalanche hazard:A case study of Mount Siella(L’Aquila,Central Italy)

In mountainous areas,snow avalanches could be triggered by the shaking produced by earthquakes.The forces induced by the earthquake can cause an irregular increase of shear strength load down the slope,for the presence of complex surface and buried morphologies.Topographic irregularities generate maximum effects of waves amplification linked to wavelengths comparable to the horizontal dimension of the topographic feature.For this reason,the selected time-histories represent an appropriate input for the two-dimensional numerical response analyses when a dynamic phenomenon produce the resonant motion of a whole mountain.This represents an important earthquake-induced hazard in snow-covered mountain areas with high probability of seismic events.Some valleys are located in regions with scare ground motion data and investments on infrastructures are not always accompanied by adequate protection against earthquake-induced avalanches.The paper points out a simple deterministic approach for selecting a set of real accelerograms applied to a real case of Siella Mountain(Central Italy)where a large avalanche destroying a tourist facility of Rigopiano resort on 18 January 2017.The selected time histories were used as input for the two-dimensional numerical model of the subsoil to evaluate the topographic seismic amplification in ridge and compare it with the results of other authors.These methods suggest that morphology-related inertial effects should be considered as an overload action on snow layers when controlling multi-hazard studies and spatial planning.

Protective effect of retaining wall on rock avalanche:A case study of Nayong rock avalanche in China

Rock avalanches are generally difficult to prevent and control due to their high velocities and the extensive destruction they cause.However,barrier structures constructed along the path of a rock avalanche can partially mitigate the magnitudes and consequences of such catastrophic events.We selected a rock avalanche in Nayong County,Guizhou Province,China as a case to study the effect of the location and height of a retaining wall on the dynamic characteristics of rock avalanche by using both actual terrain-based laboratory-model tests and coupled PFC3D-FLAC3D numerical simulations.Our findings demonstrate that a retaining wall can largely block a rock avalanche and its protective efficacy is significantly influenced by the integrity of the retaining wall.Coupled numerical simulation can serve as a powerful tool for analyzing the interaction between a rock avalanche and a retaining wall,facilitating precise observations of its deformation and destruction.The impact-curve characteristics of the retaining wall depend upon whether or not the rock avalanche-induced destruction is taken into account.The location of the retaining wall exerts a greater influence on the outcome compared to the height and materials of the retaining wall,while implementing a stepped retaining-wall pattern in accordance with the terrain demonstrates optimal efficacy in controlling rock avalanche.

基于RAMMS-AVALANCHE模型的雪崩模拟参数敏感性分析

以巩乃斯大陆性气候雪崩危险区为研究背景,建立三维数字地形模型对雪崩运动过程进行模拟。研究RAMMS雪崩数值模拟结果的影响因素,分析计算网格分辨率、雪层断裂深度、摩擦系数3种参数值对模拟结果的影响程度及敏感性。通过单因素分析法对比不同参数下模拟结果进而得出3种参数的影响程度,采用灰色关联法分析参数对模拟结果的敏感性。结果表明:选择合适的计算网格分辨率能提高模拟结果的准确性;雪层断裂深度每减少10%,流动高度变化率在5%~7%;流动速度变化率在1%~2%;冲击力变化率在2%~3%;而摩擦系数的大小主要对堆积区特征值和雪崩停止时间产生较大影响,对运动过程中的特征值影响较小。在此基础上进行敏感度计算,根据计算结果确定各特征值最大影响性时参数的主次关系。研究结果明晰了雪崩模拟各输入参数的敏感性,可有效提高雪崩数值模拟参数选取的合理性和计算结果的准确性,为雪崩灾害危险程度分析提供依据。

基于多项式混沌展开的电力系统概率可用输电能力评估

大规模开发和利用风能有利于实现电力系统清洁低碳转型,是实现国家“碳达峰、碳中和”战略目标的重要技术手段,但风电出力的强不确定性对电力系统区域间可用输电能力(available transfer capability,ATC)评估带来了全新的挑战,传统用于求解计及风电出力不确定性的概率ATC评估模型在计算效率和计算精度方面均存在一定的不足。为此,该文提出一种基于多项式混沌展开(polynomialchaos expansion,PCE)的电力系统概率ATC评估方法,该方法首先构建基于机会约束的电力系统概率ATC评估模型;然后,根据风电出力预测误差的概率分布特征,选择对应的正交多项式为基函数以近似风电出力预测误差及电力网络中与之相关联的其他随机变量;进一步,借助Galerkin投影和基于一阶矩、二阶矩的机会约束转化方法,将所构建的机会约束模型的概率约束转化为确定性约束,实现基于机会约束的概率ATC评估模型向易于求解的确定性优化模型的转化;进而,将概率ATC评估模型的求解问题转化为ATC的最优多项式逼近系数的求解问题,根据求得的最优多项式逼近系数和选取的基函数计算电力系统ATC的概率分布特征;最后,通过修改后的PJM-5节点测试系统、IEEE-118节点测试系统及吉林西部电网实际算例验证了所提基于多项式混沌展开的电力系统概率ATC评估方法的准确性和有效性。

基于多项式代理模型的车顶绝缘子背风侧沿面压力优化研究

高速气流下,车顶绝缘子背风侧出现低气压会使得闪络电压降低,影响列车安全运行,为了改善车顶绝缘子背风侧的低气压现象,使用代理模型对车顶绝缘子结构参数进行优化。在车顶绝缘子结构参数上选取了伞裙上、下倾角以及伞裙间距作为因子,以绝缘子背风侧沿面压力的最小值作为响应,采用全因子试验设计方法获取样本数据,并对因子的主效应和交互效应进行分析,在此基础上建立多项式代理模型,进一步得到最佳的结构参数,最后进行闪络试验验证其有效性。结果表明:伞裙上、下倾角的主效应与伞裙间距相比更加显著,各因子之间没有显著的交互效应;最佳参数:伞裙上、下倾角分别为8°和0°,伞裙间距为45mm,背风侧沿面压力最小值提高了25.62%,同时压力平均值提高了42.47%;在100m/s的风速条件下,车顶绝缘子的闪络电压提高了16.80%。研究结果可以为车顶绝缘子结构设计提供参考。

纽结琼斯多项式与整系数多项式

主要研究纽结琼斯多项式与整系数多项式之间的关系.利用纽结琼斯多项式的性质以及在某些点的特殊值,给出了宽度不同的整系数多项式为纽结琼斯多项式的成立条件.首先,给出了整系数多项式是某纽结Jones多项式的充分必要条件,给出了宽度为6的多项式是某一组结Jones多项式的充分必要条件.其次,主要研究Jones多项式与十一次整系数多项式的关系,研究宽度为9的十一次整系数多项式是琼斯多项式的必要条件,进而给出了某些纽结的Arf不变量.

基于多项式Chirplet变换的线性调频引信干扰波形设计方法

针对现代战场环境下线性调频引信干扰技术的迫切需求,提出多项式Chirplet变换的方法实现低信噪比下对调频连续波无线电引信的信号参数估计,并针对调频连续波引信重构了干扰信号。基于线性小波变换原理,选取适当的核函数,将无线电引信信号经过旋转与平移操作后进行短时傅里叶变换,再利用遗传算法求得变换核的最优参数,实现对调频连续波信号的参数估计,并重构干扰信号。仿真对比结果表明,该方法可以在较低信噪比下实现对调频连续波无线电引信信号载波频率、调制周期、最大频偏等参数进行精准估计,相较于周期调制类干扰,重构干扰信号能够以更低功率对调频引信产生较好的干扰效果。

基于多项式混沌展开的交直流系统全纯嵌入概率潮流计算方法

为快速、准确量化分析风电出力不确定性对交直流电力系统潮流分布的影响,提出一种基于多项式混沌展开(PCE)的交直流电力系统全纯嵌入概率潮流计算方法。该方法首先根据风电出力的概率分布特征选择最优正交基函数,构造近似风电出力概率分布特征的PCE表达式;其次,将该PCE表达式引入交直流电力系统的全纯嵌入潮流方程中,构建基于PCE的交直流电力系统全纯嵌入概率潮流计算模型;再次,通过Galerkin投影将所构建的全纯嵌入概率潮流计算模型转化为高维确定性全纯嵌入潮流计算模型;然后,借助确定性全纯嵌入潮流模型求解方法,实现对所转化的高维确定性全纯嵌入潮流模型的求解,并根据所得PCE逼近系数计算交直流电力系统潮流的概率分布特征;最后,通过修改的PJM 5节点、IEEE 30节点和IEEE 118节点交直流测试系统算例验证所提方法的准确性和有效性。

集合论、笛卡尔乘积和多项式定理在生命表研究中的应用:以取食玉米粒和茶树叶片的棉铃虫生命表为例

【目的】自我重复取样技术(bootstrap technique)广泛用于计算生命表各参数的方差、标准误和置信区间(confidence interval),而配对自我重复取样检验(paired bootstrap test,PBT)则用于检测处理间的生命表参数差异。本研究以取食玉米粒和茶树叶片的棉铃虫Helicoverpa armigera生命表为例,进一步解释集合论、笛卡尔乘积和多项式定理在害虫种群生物学研究中的应用。【方法】利用年龄-龄期两性生命表对取食玉米粒和茶树叶片的棉铃虫种群参数进行分析,利用集合论、笛卡尔乘积和多项式定理将种群统计分析以明确数学的方法呈现,以检测所有可能的自我重复取样样本、精确计算种群参数置信区间以及处理之间差异的置信区间,计算可育和不育样本的概率。【结果】取食茶树叶片的棉铃虫其成虫前期存活率、内禀增长率(r)、周限增长率(λ)、净增殖率(R_(0))、平均世代周期(T)均显著低于取食玉米粒的,说明茶树叶片不是棉铃虫的适宜寄主植物。因取食茶树叶片棉铃虫种群不育样本数较多,利用bootstrap重复取样接受可育与不育样本时,其结果与不用bootstrap技术计算的差异小于5%;若取样时仅接受可育样本,结果与原数值差异显著,误差较大(>5%)。使用笛卡尔配对检验(Cartesian paired test,CPT)比较取食两种食物的棉铃虫种群的R0的差异时,可计算两种处理bootstrap抽样结果所有可能差异的精确置信区间,而使用自我重复取样检验通常会导致置信区间的估值过高或过低,尤其是自我重复取样数较小时。多项式定理可以揭示可育和不育样本的自我重复取样结果。自我重复取样抽样记录必须保留,以便在后续分析中进一步应用。【结论】本研究进一步明确了两性生命表理论的数学基础,也为昆虫学研究中的生命表技术的应用提供数学支撑。

排叉链环的琼斯多项式与零点分布

该文利用纽结琼斯多项式的性质研究了排叉结的多项式的零点问题.首先,给出了纽结的多项式和排叉结的基本性质;其次,研究了排叉链环■的琼斯多项式的零点性质,讨论了当2≤n≤5时,排叉链环■的琼斯多项式的零点性质.

实系数多项式实根范围的探讨

针对实系数多项式方程,在已知一个实根的条件下,给出了其余实根上、下界的估计.然后将结论推广至已知多个实根的情形,并通过例题加以说明.

基于混合蒙特卡洛/多项式混沌展开方法的多参数随机等离子体不确定性分析

多项式混沌展开(polynomial chaos expansion, PCE)方法对于分析随机等离子体电磁传播不确定性已经展示出了相当大的潜力。然而,由于构建多项式混沌模型的计算量随着不确定性输入维数的增加呈指数增长,数值模拟耗时长,导致“维数灾难”问题。因此,本文基于非侵入式多项式混沌(non-intrusive polynomial chaos,NIPC)方法,采用混合蒙特卡洛(Monte Carlo, MC)/PCE方法研究了多层等离子体平板电子密度不确定性对透射系数的影响,并验证了所提出方法的实用性。与MC方法相比,本文方法可以大大加快仿真的速度,有效缓解了多项式展开项的数量随着随机变量维数的增加而快速增加的缺点,同时大大降低了MC方法的仿真次数,有利于电磁模型的多参数不确定性分析。

准晶问题多项式应力函数及其在有限元中的应用

本文基于广义Lekhnitskii各向异性弹性理论,提出了一种确定准晶问题多项式应力函数的系统性方法,并将之应用于杂交应力函数(HSF)单元的构造.结果表明,对于准晶平面问题,任意齐n次多项式应力函数至多存在6个独立的多项式,且多项式应力函数的一般表达式可以显式地给出.所得的多项式作为解析试函数用于构造准晶问题的新型八节点HSF单元,与传统的有限元相比,HSF单元具有更高的精度和更优异的性能.

高质量加工五次多项式速度规划算法研究

通过分析直线、指数、S曲线以及正弦函数几种常用的加减速算法,针对传统的速度规划算法存在的加工曲线不连续以及加工过程出现振荡、加工精度低等问题,提出适用于高质量加工的五次多项式速度规划算法,将整个加工过程分段,细化每一段的方程,并介绍对于待定的NURBS曲线使用五次多项式速度规划算法进行插补的过程,针对快速插补和实时插补两个阶段进行优化。结尾根据仿真加工实验图像得出结论,该算法实现了加工过程中运动曲线的连续变化、柔性变化。并将加工精度控制在理想范围之内,适应于高质量的加工。