MEMS Huygens Clock Based on Synchronized Micromechanical Resonators

With the continuous miniaturization of electronic devices,microelectromechanical system(MEMS)oscillators that can be combined with integrated circuits have attracted increasing attention.This study reports a MEMS Huygens clock based on the synchronization principle,comprising two synchronized MEMS oscillators and a frequency compensation system.The MEMS Huygens clock improved shorttime stability,improving the Allan deviation by a factor of 3.73 from 19.3 to 5.17 ppb at 1 s.A frequency compensation system based on the MEMS oscillator’s temperature-frequency characteristics was developed to compensate for the frequency shift of the MEMS Huygens clock by controlling the resonator current.This effectively improved the long-term stability of the oscillator,with the Allan deviation improving by 1.6343105 times to 30.9 ppt at 6000 s.The power consumption for compensating both oscillators simultaneously is only 2.85 mW·℃^(-1).Our comprehensive solution scheme provides a novel and precise engineering solution for achieving high-precision MEMS oscillators and extends synchronization applications in MEMS.

δ函数在标量Huygens原理推导过程中的作用

通过在一定边界条件下解非齐次项为δ函数的Helmholtz方程得到三类Green函数,按照无界空间以及Dirichlet边界条件和Neumann边界条件对Green函数分类.明确它们的物理意义.它们是所考察区域内的单位点源在一定的边界条件下所产生的场.从而在Green函数分类的基础上理解Kirchhoff以及第一和第二RayleighSommerfeld 3个衍射积分公式之间的关系.

关于双曲函数的Huygens型不等式及应用

给出了关于双曲函数的Huygens型不等式,并得到了双曲函数的Wilker型不等式的加强.定义了一类新的Seiffert型平均,给出两个有关不等式.

关于一般正规双曲型方程组的不完全Huygens现象

在文献中我们给出了双曲型方程的不完全Huygens现象。本文将这一概念推广到一般正规双曲型方程组上,并给出了一些基本定理和例子。

与三角函数和双曲函数Huygens不等式有关的几个结果

利用积分恒等式、积分不等式和单调性的L'Hospital法则,给出几个与三角函数的Huygens不等式和双曲函数的Huygens不等式有关的结果。

波函数的Huygens原理

利用偏微分算子的方法 ,从描述粒子波动的Schr¨odinger方程出发 ,证明波函数具有类似波动光学中Huygens原理的性质 ,并将波函数表示成类似Kirchhoff公式的形式 。

关于一类双曲型方程的Huygens原理

给出一类双曲型方程发生Huygens原理的充要条件,从而推广了Stellmacher的结果。[1]

High Performance Electrically Small Huygens Rectennas Enable Wirelessly Powered Internet of Things Sensing Applications:A Review

Far-field wireless power transfer(WPT)is a major breakthrough technology that will enable the many anticipated ubiquitous Internet of Things(IoT)applications associated with fifth generation(5G),sixth generation(6G),and beyond wireless ecosystems.Rectennas,which are the combination of rectifying circuits and antennas,are the most critical components in far-field WPT systems.However,compact application devices require even smaller integrated rectennas that simultaneously have large electromagnetic wave capture capabilities,high alternating current(AC)-to-direct current(DC)(AC-to-DC)conversion efficiencies,and facilitate a multifunctional wireless performance.This paper reviews various rectenna miniaturization techniques such as meandered planar inverted-F antenna(PIFA)rectennas;miniaturized monopole-and dipole-based rectennas;fractal loop and patch rectennas;dielectric-loaded rectennas;and electrically small near-field resonant parasitic rectennas.Their performance characteristics are summarized and then compared with our previously developed electrically small Huygens rectennas that are proven to be more suitable for IoT applications.They have been tailored,for example,to achieve batteryfree IoT sensors as is demonstrated in this paper.Battery-free,wirelessly powered devices are smaller and lighter in weight in comparison to battery-powered devices.Moreover,they are environmentally friendly and,hence,have a significant societal benefit.A series of high-performance electrically small Huygens rectennas are presented including Huygens linearly-polarized(HLP)and circularly-polarized(HCP)rectennas;wirelessly powered IoT sensors based on these designs;and a dual-functional HLP rectenna and antenna system.Finally,two linear uniform HLP rectenna array systems are considered for significantly larger wireless power capture.Example arrays illustrate how they can be integrated advantageously with DC or radio frequency(RF)power-combining schemes for practical IoT applications.

关于二变元双曲型方程具有不完全Huygens现象的注记

本文给出二变元双曲型方程具有不完全Ｈｕｙｇｅｎｓ现象时，通解在任意四条特征线的交点处的相关性。

Superdirective Circular Arrays of Electric and Huygens Dipole Elements

Uniform circular arrays(UCAs)provide both omnidirectional(360°)and directive(sector)coverage of the azimuthal plane.Superdirective versions with unidirectional,high front-to-back ratio(FTBR)properties could provide the radiated field char-acteristics being pursued for NextG wireless networks and their perceived applications.Typical UCA configurations–full,semi-circular,and sector–that radiate vertically-polarized(VP)fields and are composed of either omnidirectional electric dipole ele-ments or unidirectional Huygens dipole elements are analyzed first with conventional methods as reference cases.These omni-and uni-directional element configurations are then treated with several optimization techniques:the classic Rayleigh-quotient(RQ)method and its unidirectional-constrained version;the eigenbeam decomposition and synthesis(EBDS)technique used to design su-perdirective acoustic receiving arrays;and the Bessel-azimuthal multipole(BEAM)approach developed herein.Several arrays are identified as being superdirective with extremely high FTBR values.The performance characteristics of the arrays of unidirectional elements are demonstrated to be superior in general.Moreover,it is shown that larger radius arrays with RQ-specified excitation amplitudes are robust to changes in them whereas the outcomes of the corresponding small radius versions are not.On the other hand,the BEAM-optimized densely-packed small-radius superdirective arrays are quite tolerant to those variations while generating unidirectional pseudo-needle beams.

一类双曲型方程的Huygens原理

通过双曲型方程的Hadamard基本解理论,将Huygens算子识别问题转化为双曲型方程的系数满足的关系,找出了更多的Huygens算子,从而推广了Stellmacher的结果,并解析了Veselov和Berest给出的一类Huygens算子与Stellmacher算子的关系．

Low-profile microwave lens antenna based on isotropic Huygens＇ metasurfaces

An isotropic electromagnetic （EM） lens based on Huygens＇ metasurface is proposed for 28.0 GHz lens antenna design. The lens consists of a series of non-resonant and subwavelength metallic patterns etched on both sides of an ultrathin dielectric substrate. Both electric and magnetic responses are introduced to realize desired abrupt phase change and high-efficiency transmission for the secondary wavelets in the incident wavefront. Then, a substrate-integrated waveguide （SIW） fed patch antenna is combined with the lens as the primary feed to form a low-profile lens antenna system. The simulated and measured results coincide with each other, and demonstrate that the prototype realizes 8.8 dB-12.6 dB gain increment and low side-lobe levels over the bandwidth of 26.7 GHz-30.0 GHz. The novel design leads to a low-profile, light weight, and low-cost antenna solution in a wireless communication system.

圆形平顶高斯光束阵列在湍流大气传输中的M^2因子

应用Wigner分布函数的二阶矩定义和拓展Huygens-Fresnel原理研究了圆形平顶高斯光束阵列在湍流大气传输中的光束性质,得到其传输质量因子(M^2因子)的解析表达式,进行了相应的数值计算和模拟。结果表明:在湍流大气中传输时,圆形平顶高斯光束阵列的传输质量因子随传播距离、湍流大气结构常数的增大和束腰宽度的减小而增大;当光束阵列阶数一定,阵列个数不断增加时,其传输质量因子先保持不变,然后开始减小,最后不再减小而保持这个定值不变;当光束阵列的个数一定,阶数不断增加时,其传输质量因子减小,最后不再减小而保持不变。在自由空间中传输时,圆形平顶高斯光束阵列的传输质量因子保持不变。

惠更斯的14个概率命题研究

目的系统探讨和分析惠更斯在《论赌博中的计算》中所给出的14个概率命题,以揭示其概率思想。方法历史分析和文献考证。结果惠更斯首次提出数学期望的概念,创立了“惠更斯分析法”,第一次把概率论建立在公理、命题和问题上而构成一个较完整的理论体系,第一次将以往概率论知识系统化、公式化及一般化。结论惠更斯的概率思想奠定了概率论的基础,且对今日数学创造仍有重要启发意义。

sinx/x的较强上下界估计及其应用

借助于级数理论,给出了sinx/x的形如(a+bcos x)/(c+dcos x)(其中a+b=c+d)的较强上下界估计,并借此得到两正数的Seiffert平均的较强上下界。

大气湍流中孔径限制下高斯光束的传播特性

在扩展Huygens-Fresnel原理和Rytov近似的基础上,得到了孔径限制下湍流大气中高斯光束平均光强的积分表达式,利用数值模拟方法分析了轴上和接收面上平均光强的分布,并得到了波阵面半径、传播距离、湍流强度和波长与平均光强的关系曲线图。结果表明在湍流大气中波长、传播距离、发射孔径和波阵面半径的改变会引起平均光强重心的漂移,传播距离增加会导致光束的展宽。

树冠火生长蔓延模型的改进与实时仿真

现有林火研究多偏重于火焰蔓延的数值模拟以及简单可视化,存在火焰细节丢失和蔓延过程不精确的问题,本文通过深入分析地表火向树冠火的转换过程,完成树冠火生长蔓延模型的改进,并进行实时仿真。首先,为解决火焰蔓延过程中火焰运动缺乏真实感及细节丢失问题,引入脉动风场重新构建树冠火生长蔓延模型,丰富火焰细节,提高火焰运动真实性;其次,应用能量守恒定律,建立树冠火随温度场动态变化模型,提高地表火向树冠火生长转换过程精确性;最后,通过纹理映射技术模拟烧焦现象,采用Huygens原理结合树冠火生长蔓延模型对火焰蔓延进行优化仿真,保证实时性。实验对比和分析表明,能够实时仿真出树冠火生长蔓延过程。

基于ArcGIS的火灾模拟系统研究与设计——以贵州雷山县西江镇为例

本文作为贵州大学青年基金项目的研究成果,选取贵州省雷山县西江镇为研究区域,以惠更斯原理(Huygens)和罗塞迈尔(Rothermel)林火蔓延模型为依据,并结合西江镇的地形、气象、植被等参数,在ArcGIS 9.2平台上通过二次开发进行农村火灾模拟系统的模型架构,此外,本文还使用ArcEngine组件开发了相应的动态模拟模块。

基于WebGIS的林火蔓延模拟研究

我国森林资源分布不均,且大量分布在人口较少的山区和边疆,交通不便。森林火灾一直对森林构成严重的威胁,对待林火只能加强预防。资料显示,在已发生的森林火灾中人为因素占了绝大部分。面临突发性火灾时及时部署扑救方案显得极为重要,而进行方案部署的依据是分析林火蔓延的态势。本文结合王正非模型和Huygens原理,通过WebGIS平台来对森林火灾进行蔓延模拟展开研究。希望能借助WebGIS的一些特性和优点对林火蔓延模拟工作有所帮助。