In-plane vibrations of an elastically cantilevered circular arc with a tip mass

Upper and lower bounds are determined for the fundamental frequency of in-plane, transverse vibration of the structural system described in the title in the case of constant cross-section and moment of inertia. The upper bound is determined by approximating the fundamental mode shape with a polynomial co-ordinate function in the angular co-ordinate which includes an exponential optimization parameter. The fundamental frequency equation is generated by means of the Rayleigh-Ritz method and the resulting upper bound is minimized with respect to the previously mentioned exponential parameter. The lower bound for the frequency coefficient is obtained by means of an extension of Dunkerley's method. It is felt that the methodologies developed in the present study are especially useful in the case of variable cross-section of the arch structure, presence of internal supports, etc.     

Upper and lower bounds for fundamental natural frequency of beams

A better upper bound than the Rayleigh quotient is the Timoshenko quotient, the evaluation of which depends on a pair of compatible admissible moment and displacement functions. Based on both Rayleigh and Timoshenko quotients, a lower bound is readily computed. By means of an iteration procedure, both the upper and lower bound converge to the fundamental natural frequency.     

An integral equation approach to the fundamental frequency of vibrating beams

An approximation to the lowest natural frequency of vibrating beams is obtained analytically by applying eigenvalue, eigenfunction theory to the defining integral equation. The method produces successively closer values for both upper and lower bounds to the fundamental frequency. It is found that the second lower bound provides in itself a good approximation to published values and a graph is derived which provides a bound for the error in this approximation without further computation. The application of integral equations to the formulation of mechanical engineering problems is increasing and one aim of the paper is to draw attention to the possibility of obtaining analytical solutions.     

A note on forced vibrations of a rectangular plate embedded in a non-homogeneous foundation

The title problem is solved for the case where the plate is subjected to a uniformly distributed, sinusoidally varying excitation. The plate dynamic amplitude is approximated by means of a polynomial co-ordinate function which contains an undetermined parameter as an exponent. The governing functional is minimized with respect to the unknown coefficient of the coordinate function and with respect to the exponential parameter. Good agreement with known results is shown to exist.     

Achievable accuracy of parameter estimation for multidimensional NMR experiments

A fundamental issue in NMR spectroscopy is the estimation of parameters such as the Larmor frequencies of nuclei, J coupling constants, and relaxation rates. The Cramer-Rao lower bound provides a method to assess the best achievable accuracy of parameter estimates resulting from an unbiased estimation procedure. We show how the Cramer-Rao lower bound can be calculated for data obtained from multidimensional NMR experiments. The Cramer-Rao lower bound is compared to the variance of parameter estimates for simulated data using a least-squares estimation procedure. It is also shown how our results on the Cramer-Rao lower bound can be used to analyze whether an experimental design can be improved to provide experimental data which can result in parameter estimates with higher accuracy. The concept of nonuniform averaging in the indirect dimension is introduced and studied in connection with nonuniform sampling of the data.     

First-principles calculations of the Urbach tail in the optical absorption spectra of silica glass

We present density-functional theory calculations of the optical absorption spectra of silica glass for temperatures up to 2400?K. The calculated spectra exhibit exponential tails near the fundamental absorption edge that follow the Urbach rule in good agreement with experiments. We discuss the accuracy of our results by comparing to hybrid exchange correlation functionals. We show that the Urbach rule holds in a frequency interval where optical absorption is Poisson distributed with very large statistical fluctuations. In this regime, a direct relation between the optical absorption coefficient and electronic density of states is derived, which provides a link between photoemission and absorption spectra and is used to determine the lower bound to the Urbach frequency regime.     

参数不确定统一混沌系统的鲁棒分数阶比例-微分控制

针对含参数不确定的整数阶统一混沌系统, 提出一种鲁棒分数阶比例-微分(PD^μ)控制. 通过变换将受控统一混沌系统转换成等效被控对象及其等效控制器. 针对等效被控对象, 基于一种改进Monje-Vinagre方法并考虑到求解性能约束方程组的复杂度, 设计了鲁棒PD^μ控制器. 通过基于最小相角边界传递函数和最大增益边界传递函数的设计约束来保证受控统一混沌系统对参数不确定性的鲁棒性能. 数值仿真验证了所提出方法的有效性.     

太赫兹无损检测的多特征参数神经网络分析技术

提出一种基于太赫兹无损检测的多特征参数神经网络分析技术,用于分析耐高温复合材料的粘贴质量无损检测.采用抽片式方法设计了一种耐高温复合材料的脱粘缺陷样品,抽片厚度为0.1mm.采用太赫兹时域光谱无损检测技术对耐高温复合材料的多层脱粘缺陷进行了检测试验研究,对比了上下脱粘缺陷所对应的太赫兹时域波形及频谱信息的异同,针对性地建立了耐高温复合材料粘贴质量的上层脱粘参数、下层脱粘参数、频域吸收质心参数等多特征参数,将特征参数进行优化作为反向传播神经网络的输入并对其进行上下脱粘分类识别.通过对反向传播神经网络的训练测试,实现了耐高温复合材料上层脱粘0.1mm、下层脱粘0.1mm的脱粘缺陷的识别.     

Upper bound for the time derivative of entropy for a stochastic dynamical system with double singularities driven by non-Gaussian noise

A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker--Plank equation of the system is obtained through the path-integral approach and the method of transformation. Based on the definition of Shannon's information entropy and the Schwartz inequality principle, the upper bound for the time derivative of entropy is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculations can be used to interpret the effects of the system dissipative parameter, the system singularity strength parameter, the noise correlation time and the noise deviation parameter on the upper bound.     

一种改进的奇异值降噪阶次选取方法用于紫外光谱信号去噪的研究

光谱去噪是光谱检测的重要环节。针对光谱信号易受光谱仪热噪声、现场机械振动以及随机噪声等因素影响,而在线监测系统要求减少人为参数选择对去噪效果的影响,提出利用奇异值分解(SVD)理论对光谱信号去噪。提出一种改进的降噪阶次选取方法：指定奇异值差分谱最大峰值点θ₁为所选阶次下界;利用奇异值、奇异值差分谱综合信息选取阶次上界θ₂;将区间θ₁～θ₂定义为模糊区域,通过模糊C均值聚类求取隶属度,赋予模糊区域内奇异值相应的权重系数。用所提方法对不同信噪比下SO₂紫外光谱信号去噪,将信噪比、均方根误差、波形相似系数、平滑度指标用于去噪效果的评价。去噪结果表明：所提方法完全基于数据驱动,具有较好的去噪效果,能够真实的恢复原始信号。     

Entropy and action bounds for charged black holes

The entropy upper bound for a charged black hole in equilibrium with thermal radiation is derived by means of a general model-independent approach. This bound in some ways improves that proposed by Bekenstein by taking into account the energy of the electrical field. The corresponding lower bound for the Euclidean action is also obtained. The particular role of black-hole physics in the context under consideration is discussed.     

单轴晶体包层抛物型渐变光纤中基模功率分析

研究了以单轴晶体为包层,纤芯为各向同性非均匀材料光纤的功率传输特性.在纤芯满足弱渐变条件的假定下,按矢量场法进行了分析.针对基模讨论了包层的轴向与横向的介电常量比τ对光纤截面上功率分布的影响.结果表明,τ对低频情况影响显著,而对高频情况则影响很小.当此种结构的光纤用做单模光纤时,选用τ较大的包层材料有利于提高传输效率.     

Probing the speed of light with radio waves at extremely low frequencies

The speed of light, a fundamental physical constant and thought to be independent of frequency, is tested here with naturally occurring radio waves in the atmosphere at extremely low frequencies. It is shown that the speed of light in the frequency range 5-50 Hz is known with an accuracy determined by perturbations of the ionospheric reflection height associated with space weather phenomena, which place an upper limit on the photon rest mass mgamma < or approximately 4 x 10(-52) kg to date.     

电各向异性色散介质电磁散射时域有限差分分析的半解析递推卷积方法

利用坐标系转换矩阵给出实验室系中磁化等离子体介质的频域极化率张量, 采用部分分式展开方法通过傅里叶逆变换得到极化率张量的时域指数函数形式, 应用数字信号处理中的半解析递归卷积算法, 给出适用于处理任意外磁场方向情形下磁化等离子体目标电磁散射的半解析递归卷积-时域有限差分计算方法. 计算了磁化等离子体球的同极化和交叉极化后向雷达散射截面, 结果表明了算法的正确有效性. 关键词： 半解析递归卷积 磁化等离子体 电磁散射 时域有限差分方法     

Upper and lower bounds for the speed of pulled fronts with a cut-off

We establish rigorous upper and lower bounds for the speed of pulled fronts with a cut-off. For all reaction terms of KPP type a simple analytic upper bound is given. The lower bounds however depend on details of the reaction term. For a small cut-off parameter the two leading order terms in the asymptotic expansion of the upper and lower bounds coincide and correspond to the Brunet-Derrida formula. For large cut-off parameters the bounds do not coincide and permit a simple estimation of the speed of the front.     

束缚磁极化子的性质

采用线性组合算符和幺正变换方法分别导出弱、强耦合情形下束缚磁极化子的振动频率和基态能量.结果表明库仑场的存在使得磁极化子的基态能量的绝对值变小.     

Vibration and buckling of rectangular plates under in-plane hydrostatic loading

Numerical solutions are presented for the fundamental natural frequency and mode shape of a rectangular plate loaded by in-plane hydrostatic forces for a wide variety of aspect ratios, boundary conditions, and load magnitudes. All six possible combinations of simply supported and clamped edges are considered. The limiting conditions of unloaded vibration and buckling are discussed in detail, with emphasis on the preferred mode shape. Design curves and approximate formulae are presented which provide a simple means of determining the fundamental frequency parameter.     

色噪声驱动的双奇异随机系统随时间演化的熵变化率上界

通过变换的方法讨论了一类高斯色噪声驱动的双奇异随机系统所对应的Fokker-Planck方程, 并结合Shannon信息熵的定义及Schwartz不等式原理给出了经变换后该系统随时间演化的熵变化率上界的精确表达式. 分析了奇异性强度参数、噪声相关时间与耗散参数对熵变化率上界的显著影响.     

Spontaneous-emission suppression on arbitrary atomic transitions

We propose a very simple scheme to slow down the usual exponential decay of upper state population in an atomic two-level system considerably. The scheme uses an additional possibly intense field with frequency lower than the total decay width of the atomic transition. This allows for additional decay channels with the exchange of one or more low-frequency photons during an atomic transition. These channels may then interfere with each other. The intensity and frequency of the low-frequency field are shown to act as two control parameters modifying duration and amount of the population trapping. An extension of the scheme to include transitions to more than one lower state is straightforward.     

Quasibound states in the continuum in a two channel quantum wire with an adatom

We report the prediction of quasibound states (resonant states with very long lifetimes) that occur in the eigenvalue continuum of propagating states for certain systems in which the continuum is formed by two overlapping energy bands. We illustrate this effect using a quantum wire system with two channels and an attached adatom. When the energy bands of the two channels overlap, a would-be bound state that lays just below the upper energy band is slightly destabilized by the lower energy band and thereby becomes a resonant state with a very long lifetime (a second such state lays above the lower energy band). Unlike the bound states in continuum predicted by von Neumann and Wigner, these states occur for a wide region of parameter space.