Predicted Critical State Based on Invariance of the Lyapunov Exponent in Dual Spaces

Critical states in disordered systems,fascinating and subtle eigenstates,have attracted a lot of research interests.However,the nature of critical states is difficult to describe quantitatively,and in general,it cannot predict a system that hosts the critical state.We propose an explicit criterion whereby the Lyapunov exponent of the critical state should be 0 simultaneously in dual spaces,namely the Lyapunov exponent remains invariant under the Fourier transform.With this criterion,we can exactly predict a one-dimensional quasiperiodic model which is not of self-duality,but hosts a large number of critical states.Then,we perform numerical verification of the theoretical prediction and display the self-similarity of the critical state.Due to computational complexity,calculations are not performed for higher dimensional models.However,since the description of extended and localized states by the Lyapunov exponent is universal and dimensionless,utilizing the Lyapunov exponent of dual spaces to describe critical states should also be universal.Finally,we conjecture that some kind of connection exists between the invariance of the Lyapunov exponent and conformal invariance,which can promote the research of critical phenomena.

Application of the Conditional Nonlinear Local Lyapunov Exponent to Second-Kind Predictability

In order to quantify the influence of external forcings on the predictability limit using observational data,the author introduced an algorithm of the conditional nonlinear local Lyapunov exponent(CNLLE)method.The effectiveness of this algorithm is validated and compared with the nonlinear local Lyapunov exponent(NLLE)and signal-to-noise ratio methods using a coupled Lorenz model.The results show that the CNLLE method is able to capture the slow error growth constrained by external forcings,therefore,it can quantify the predictability limit induced by the external forcings.On this basis,a preliminary attempt was made to apply this method to measure the influence of ENSO on the predictability limit for both atmospheric and oceanic variable fields.The spatial distribution of the predictability limit induced by ENSO is similar to that arising from the initial conditions calculated by the NLLE method.This similarity supports ENSO as the major predictable signal for weather and climate prediction.In addition,a ratio of predictability limit(RPL)calculated by the CNLLE method to that calculated by the NLLE method was proposed.The RPL larger than 1 indicates that the external forcings can significantly benefit the long-term predictability limit.For instance,ENSO can effectively extend the predictability limit arising from the initial conditions of sea surface temperature over the tropical Indian Ocean by approximately four months,as well as the predictability limit of sea level pressure over the eastern and western Pacific Ocean.Moreover,the impact of ENSO on the geopotential height predictability limit is primarily confined to the troposphere.

The Dual of the Two-Variable Exponent Amalgam Spaces (Lq(),lp())(Ω)

Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of Wiener. In this paper: we first introduce a two-variable exponent amalgam space (Lq(),lp())(Ω). Secondly, we investigate some basic properties of these spaces, and finally, we study their dual.

TWO DISJOINT AND INFINITE SETS OF SOLUTIONS FOR AN ELLIPTIC EQUATION INVOLVING CRITICAL HARDY-SOBOLEV EXPONENTS

In this paper,by an approximating argument,we obtain two disjoint and infinite sets of solutions for the following elliptic equation with critical Hardy-Sobolev exponents■whereΩis a smooth bounded domain in RN with 0∈?Ωand all the principle curvatures of?Ωat 0 are negative,a∈C1(Ω,R*+),μ>0,0<s<2,1<q<2 and N>2(q+1)/(q-1).By2*:=2N/(N-2)and 2*(s):(2(N-s))/(N-2)we denote the critical Sobolev exponent and Hardy-Sobolev exponent,respectively.

Solutions for Schrodinger-Poisson system involving nonlocal term and critical exponent

In this paper,we consider the following Kirchhoff-Schrodinger-Poisson system:{−(a+b∫_(R^(3))|∇u|^(2))△u+u+ϕu=μQ(x)|u|^(q-2)u+K(x)|u|^(4)u,in R^(3),−△ϕ=u^(2) the nonlinear growth of|u|^(4)u reaches the Sobolev critical exponent.By combining the variational method with the concentration-compactness principle of Lions,we establish the existence of a positive solution and a positive radial solution to this problem under some suitable conditions.The nonlinear term includes the nonlinearity f(u)~|u|^(q-2)u for the well-studied case q∈[4,6),and the less-studied case q∈(2,3),we adopt two different strategies to handle these cases.Our result improves and extends some related works in the literature.

General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts:Mobility edges and Lyapunov exponents

We establish a general mapping from one-dimensional non-Hermitian mosaic models to their non-mosaic counterparts.This mapping can give rise to mobility edges and even Lyapunov exponents in the mosaic models if critical points of localization or Lyapunov exponents of localized states in the corresponding non-mosaic models have already been analytically solved.To demonstrate the validity of this mapping,we apply it to two non-Hermitian localization models:an Aubry-Andre-like model with nonreciprocal hopping and complex quasiperiodic potentials,and the Ganeshan-Pixley-Das Sarma model with nonreciprocal hopping.We successfully obtain the mobility edges and Lyapunov exponents in their mosaic models.This general mapping may catalyze further studies on mobility edges,Lyapunov exponents,and other significant quantities pertaining to localization in non-Hermitian mosaic models.

不同建筑环境下平均风速剖面的数值模拟

基于计算流体力学(CFD)方法对具有不同建筑环境参数的城市上空的风场进行系统性的数值模拟,并对平均风速剖面指数的变化规律进行讨论。研究结果表明,建筑平均高度对平均风速剖面指数的影响较大,建筑密度对平均风速剖面指数的影响较小。文中还给出了以建筑平均高度和建筑密度为自变量的平均风速剖面指数经验公式。

基于观测与预报数据融合的森林火险预报

针对气象因子日变化波动大容易引起森林火险气象等级预报变动大这一问题,参考布龙-戴维斯方案森林火险气象预报模型的构建思路,利用2016—2020年广西1785个森林火灾样本和气象观测数据,建立森林火险气象指数模型(简称“模型”)。将气象观测数据输入模型,计算出每日森林火险气象监测指数,同时,将智能网格预报数据输入模型,计算出每日森林火险气象预报指数,然后利用加权算法将每日森林火险气象监测指数和每日森林火险气象预报指数进行融合计算,得到森林火险气象融合预报指数。利用2021年6月—2023年6月789个火灾样本,对林火险气象融合预报指数进行验证,结果表明:融合后未来1~7 d森林火险等级预报准确率从82%~56%,较融合前预报准确率提升1%~3%,基本满足目前广西森林火险气象等级预报业务应用。

一类本原双色有向图的指数界

对一类相对特殊的双色本原有向图给出了本原条件,结合圈矩阵给出了本原指数的上下界,并刻画了取得指数上下界时所对应的极图。

分数阶立方映射的混沌行为

本文研究了分数阶立方映射的混沌特征.首先,在立方映射基础上,本文定义了分段常数分数阶微分方程,进而对其进行离散化处理得到分数阶立方映射.然后,通过研究映射的分岔和Lyapunov指数,本文揭示了分数阶立方映射通过倍周期分岔进入混沌,且相较传统立方映射具有更加丰富的混沌行为.此外本文还研究了更具普适性的时滞分数阶立方映射,发现该映射的混沌分岔点会随着参数的变化而变化.

单位圆内高阶非齐次微分方程复振荡与解及其任意阶导数的不动点

本文研究一类单位圆内有穷迭代级解析系数的高阶非齐次线性微分方程的复振荡与解及其任意阶导数的不动点问题,得到解的迭代增长级,迭代级零点收敛指数的更精细的估计,并得到解的不动点与解的任意阶导数的不动点分布的精确估计.所得结果是已有相关结果的推广.

基于二维离散混沌系统和DNA的图像加密方案

为丰富低维离散混沌系统的动力学特性以及克服脱氧核糖核酸(deoxyribonucleic acid,DNA)编码的引入使混沌图像加密系统安全性易于降低的问题,基于Arnold映射构建具有恒定正Lyapunov指数的2维离散混沌系统,并将其与DNA编码结合,设计一个混沌图像加密方案.所设计的混沌系统模型中不含非线性项,系统具有超混沌动力学行为;加密方案中用于加密的混沌序列为明文图像像素与密钥的加取模运算结果,图像按4×4大小予以分块,扩散算法中的DNA加减、异或、同或等运算分别基于DNA编码规则1、规则4和规则7.仿真实验和性能分析结果表明:加密方案的密钥空间达到2^(266),信息熵为7.9993 bit,密钥灵敏度达到10^(−15),平均像素变化率(number of pixel change rate,NPCR)、统一平均变化强度(unified average change intensity,UACI)、块平均变化强度(block average change intensity,BACI)分别为99.6092%、33.4664%、26.7718%.

融入智能网联汽车的混行交通流混沌特性

为了研究混行交通流混沌特性、辨析影响混行车队混沌程度的因素,在传统交通流理论基础上,利用Cao方法和改进的Cao方法确定混行交通流延迟时间和嵌入维数,对混行交通流序列进行相空间重构并通过计算最大Lyapunov指数判定其混沌特性.对混行交通流中智能网联汽车(intelligent connected vehicle,ICV)协同自适应巡航(cooperative adaptive cruise control,CACC)车辆比例及延迟时间关键参数进行影响分析.结果表明:在跟驰过程中车头间距序列的最大Lyapunov指数小于0时,混行交通流存在混沌;CACC车辆比例增加能够减弱混沌的时间区域,比如当CACC车辆比例达到0.6时,跟驰系统趋于稳定;CACC车辆的延迟时间对混沌的影响显著,保持低通信延迟才能发挥CACC车辆的作用,从而有效抑制混沌.

炭黑对CMDB推进剂燃烧性能的影响

采用燃烧–靶线法分析了炭黑的种类、含量及粒径对复合改性双基(CMDB)推进剂燃烧性能的影响。结果表明:在压强为1~8MPa时,添加炭黑可以提高推进剂的燃速,Y1炭黑可以有效减小推进剂配方的压强指数;当Y1炭黑在推进剂配方中含量较低时,推进剂样品在压强为3~8MPa时具有平台燃烧特性,小粒径的Y1炭黑有利于推进剂配方压强指数的降低。

长相关随机模型FBM对光伏发电短期预测

针对光伏发电功率具有较强的波动性、间歇性输出,光伏功率预测精度较低,且难于给出具体预测时间长度等问题,提出了一种长相关随机模型分数阶布朗运动(fractional Brownian motion,FBM),用于光伏功率预测。首先,采用重标极差法计算长相关(long-range dependence,LRD)参数-Hurst指数,Hurst指数用于判断光伏功率数据是否满足长相关性,并通过最大李雅普诺夫指数(Lyapunov)计算出模型最大可预测时间尺度;其次,采用随机微分法建立FBM光伏功率预测模型,同时估计FBM预测模型参数值;最后,选取澳大利亚沙漠知识太阳能中心(Desert Knowledge Australia Solar Center,DKASC)、美国国家可再生能源实验室(National Renewable Energy Laboratory,NREL)以及北京国能日新科技有限公司的光伏功率数据集,从不同的地理环境、不同的气候特征、不同的规模大小电站进行验证。仿真结果表明,该模型较传统的Kalman、LSTM模型具有更高的预测精度,可为光伏并网的稳定和安全运行提供更好的理论支持,对电网调度部门具有较高的参考价值。

伪抛物型p-Kirchhoff方程的爆破解

该文研究了一类具有变指数的伪抛物型p-Kirchhoff方程的齐次Dirichlet初边值问题.首先,采用改进的势阱法和辅助函数法,对初始能量进行最优分类,得到解的爆破和整体存在的判据.其次,分别得到了解的爆破时间估计和整体解的大时间性态.

铁路悬索桥车致纵向运动混合阻尼减振研究

针对铁路悬索桥在列车过桥时梁端纵向运动响应控制问题,提出了一种创新的混合阻尼减振方案,采用多种类型的阻尼器控制梁端位移,以满足不同的减振需求.以某在建大跨铁路悬索桥为工程背景,建立了空间桁架精细模型和等效单梁简化模型,系统研究了混合阻尼减振方案不同阻尼器参数对减振效果的影响.该方案将低指数黏滞阻尼器纵向安装于桥塔与加劲梁之间,同时在桥台与加劲梁之间纵向安装电涡流阻尼器.鉴于桥台结构的特殊性,电涡流阻尼器被设计为仅能承受压力的装置,并通过样机试验进行了验证.为了进一步提升减振性能,电涡流阻尼器还配备了摩擦耗能元件.该混合阻尼减振方案能够有效控制列车过桥时梁端的纵向运动响应,显著提高桥梁结构的安全性和耐久性,在类似工程中具有重要的参考价值和借鉴意义.

基于活化能特征指数的变压器绝缘状态评估方法

基于活化能这一理化特征参量,从微观角度定量研究变压器的缺陷检测与老化评估技术,建立了泄漏电流、活化能与老化时间的定量关系模型,研制出基于活化能特征指数的变压器绝缘系统状态评估装置。实例分析表明,本方法具有较高的适用性。

三阶三次幂非线性混沌电路的自适应反馈控制和H_(∞)控制

针对三阶三次幂非线性混沌电路,研究其控制问题.首先,给出系统的Lyapunov指数和混沌吸引子,验证系统存在复杂的混沌现象;其次,用自适应反馈控制方法和H_(∞)状态反馈控制方法,设计参数已知和参数未知的自适应反馈控制器以及H_(∞)状态反馈控制器,将混沌系统状态稳定到平衡点上;最后,通过MATLAB软件进行数值仿真验证控制器的有效性,并对两种控制器的控制效果进行比较.

基于毫米波通信技术的超高清视频传输方法研究

为了提高对超高清视频传输能力,提出基于毫米波通信的超高清视频传输方法。采用多频调制通信组网技术构建超高清视频传输的信道模型,建立超高清视频毫米波通信传输的自适应图像信息交互和采集模型;结合Lyapunov指数谱密度特征分析,实现谱特征分解和信道均衡模型构建;建立视频传输的视景转换和高阶谱特征提取模型;采用毫米波通信技术,实现滤波补偿和反馈增益调节;采用联合自相关的统计特征分析方法,得到动态均衡迭代函数,通过复杂信道环境下的抗干扰抑制和均衡调度,实现对超高清视频的无损传输和编码解码。实验结果表明,该方法进行超高清视频传输的误码率较低,平均为0.058 2,传输时延较低,平均为248.4 ms,峰值信噪比为49 dB。