Reconstruction of the acoustic impedance profile in a plate using an inverse spectral procedure

An inverse spectral procedure was applied to reconstruct the acoustic impedance profile along the thickness direction of a plate using its thickness resonance frequencies, density and thickness. For a successful reconstruction, the material-property profile must be symmetric about the mid-plane of the plate. Several cases of numerical simulations, including plates with a few layers and with a high number of layers are described. The calculated resonance frequencies were used to reconstruct the acoustic impedance profile, a process that was successful for all cases. We assume that a plate with a high number of layers, each with a different but constant acoustic impedance, simulates a plate with a smoothly varying acoustic impedance profile. It can be concluded that such a plate, which generates small, virtually undetectable, internally reflected waves, can also be reconstructed. In the special case of a plate of unknown thickness and unknown but constant density, the method is still useful, because a relative variation of the material property can be reconstructed using only the resonance frequencies. An experiment using a resonance-mode electromagnetic acoustic transducer (resonance-mode EMAT) is also described. EMAT is a non-contact ultrasonic method that can measure thickness resonance frequencies, making it appropriate for this method. Some examples of applications are measurement of the temperature profile inside a rolled metal sheet, measurement of a clad metal plate, and monitoring of a metal casting.     

具有态守恒赝隙的光子晶体中两能级原子自发辐射的增强与抑制

论证了在赝带隙光子晶体中存在一个全频率域态总数守恒规则，在完全带隙光子晶体中还存在一个局域态总数守恒规则.态总数守恒规则指出，如果一个光子晶体的态密度在某些频率范围存在相对于等效介质态密度的谷，则一定由其他频率范围内相对于等效介质态密度的峰来补偿.使用符合态总数守恒规则的态密度模型，解释了态密度调制导致的自发辐射谱增强、抑制、变窄、红移、蓝移以及谱分裂等光子晶体中的量子光学现象.该理论比较适合研究在具有赝带隙的光子晶体中大量随机分布的发光原子或分子的自发辐射行为. 关键词： 光子晶体 自发辐射 态密度 光子赝带隙     

From wave-particle duality to wave-particle-mixedness triality: an uncertainty approach

The wave-particle duality, as a manifestation of Bohr’s complementarity, is usually quantified in terms of path predictability and interference visibility. Various characterizations of the wave-particle duality have been proposed from an operational perspective, most of them are in forms of inequalities, and some of them are expressed in forms of equalities by incorporating entanglement or coherence. In this work, we shed different insights into the nature of the wave-particle duality by casting it into a form of information conservation in a multi-path interferometer, with uncertainty as a unified theme. More specifically, by employing the simple yet fundamental concept of variance, we establish a resolution of unity, which can be interpreted as a complementarity relation among wave feature, particle feature, and mixedness of a quantum state. This refines or reinterprets some conventional approaches to wave-particle duality, and highlights informational aspects of the issue. The key idea of our approach lies in that a quantum state, as a Hermitian operator, can also be naturally regarded as an observable, with measurement uncertainty (in a state) and state uncertainty (in a measurement) being exploited to quantify particle feature and wave feature of a quantum state, respectively. These two kinds of uncertainties, although both are defined via variance, have fundamentally different properties and capture different features of a state. Together with the mixedness, which is a kind of uncertainty intrinsic to a quantum state, they add up to unity, and thus lead to a characterization of the wave-particle-mixedness complementarity. This triality relation is further illustrated by examples and compared with some popular wave-particle duality or triality relations.     

Brownian motion on a manifold

The question of the existence and correct form of equations describing Brownian motion on a manifold cannot be answered by mathematics alone, but requires a study of the underlying physics. As in classical mechanics, manifolds enter through the transformation of variables needed to account for the presence of constraints. The constraints are either due to a physical agency that forces the motion to remain on a manifold, or they represent conserved quantities of the equation of motion themselves. Also the Brownian motion is described either by a Smoluchowski diffusion equation or by a Kramers equation. The four cases lead to the following conclusions, (i) Smoluchowski diffusion with a conserved quantity reduces to a diffusion equation on the manifold; (ii) The same is true for diffusion with a physical constraint in three dimensions, but in more dimensions it may happen thatno autonomous equation on the manifold results; (iii) A Kramers equation with a conserved quantity reduces to an equation on the manifold, but in general not of the form of a Kramers equation; (iv) The Kramers equation with a physical constraint reduces to an autonomous Kramers equation on the manifold only for a special shape of that constraint. Throughout, only a certain type of physical constraints has been envisaged, and global questions are ignored. Finally, the customary heuristic construction of a Fokker-Planck equation for a mechanical system on a manifold is demonstrated for the case of Brownian rotation of a rigid body, and its shortcomings are emphasized.     

组合非球面太阳能聚光镜的光学设计

提出了一种组合非球面反射型太阳能聚光镜并给出了设计方法。聚光镜由38片非球面组成,每一片非球面都由一组特定系数C,a₂,a₄,a₆,a₈,a₁₀的偶次非球面方程决定,是此特定非球面的一部分。根据非球面方程和光反射定律矢量形式,导出了非球面内壁上太阳反射光束的方向矢量与非球面系数C,a₂,a₄,a₆,a₈,a₁₀的关系,适当地选择这些非球面系数,即适当地调整非球面面型,可以使太阳反射光束具有特定的方向矢量,使入射到非球面内壁上的太阳光束反射后全部聚焦在某一特定的区域内,形成小的光斑。每组特定系数都用粒子群优化算法求得,并经计算机模拟和实验证明其聚焦效果。聚光镜的光束压缩比为330：1,其聚焦光斑可作为一种高温热源,而此聚光镜可以用在太阳能加热装置中。     

2kV高稳定度高压脉冲电源设计

在一些光学精密仪器的应用场合中,不仅需要脉冲电源在时间上能够提供精确的控制,而且需要具有高稳定度的输出,以提高光电系统的探测性能;运用基于高压开关的两级式方法,采用单级高功率MOSFET开关结合具有高稳定输出的直流电源的结构,设计了输出辐度可达2kV的高稳定负脉冲电源;测试结果表明,在输出脉冲宽度为8 μs时,脉冲前沿约为48 ns,系统延迟时间约为140 ns,负脉冲超调参数约为1%。该系统具有结构简单、可靠性高、高稳定性输出等优点,可以为特定的光电器件提供优质的控制方式。     

Wrinkling of a bilayer resting on a soft substrate under in-plane compression

The wrinkling problem of a bilayer film resting on a soft substrate under in-plane compression is investigated via theoretical analysis and numerical simulations. Such a system may undergo two different wrinkling modes, namely surface wrinkling of the top single layer on a composite substrate or bilayer wrinkling on a homogeneous substrate, depending on the geometric and material parameters. In the present paper, a theoretical solution is first derived for the former case, while a solution available in the literature is applied for the latter. The solution derived here can degenerate both to the classical solution for a stiff layer resting on a semi-infinite soft substrate and that for a stiff layer lying on a compliant substrate of finite thickness. A series of finite element simulations are performed to demonstrate the accuracy of the theoretical solution. In addition, it is found that, at a given compressive strain, a certain change in the elastic modulus of the intermediate layer may lead to a dramatic surface pattern transformation between the two wrinkling modes, indicating a novel approach to realise surface pattern switching.     

Crossed gratings: A theory and its applications

We introduce a rigorous formulation for the problem of the diffraction by a finitely-conducting, bi-periodic surface. The formationon is based on a coordinate transformation which maps the grating surface onto a plane. The transformed Maxwell equations are resolved using an iterative technique. The numerical implementation is tested against a number of criteria, including a comparison with two recently developed formalisms. As well, it is shown to give results in agreement with the Reciprocity Theorem, which is derived for efficiencies of crossed gratings in unpolarized light. The method has been shown to work throughout the whole range of values of surface conductivity. We investigate the effect of a surface-corrugation on the solar absorptance of a metallic mirror. We discuss a useful equivalence property linking the behaviour of crossed gratings with that of classical gratings. We exhibit for the first time a grating in a highly-reflecting metal capable of totally absorbing unpolarized incident light. On leave from the Department of Theoretical Physics, School of Physics, University of Sydney, Sydney, N.S.W., 2006, Australia     

Trees at an Interface

A lattice tree at an interface between two solvents of different quality is examined as a model of a branched polymer at an interface. Existence of the free energy is shown, and the existence of critical lines in its phase diagram is proven. In particular, there is a line of first order transitions separating a positive phase from a negative phase (the tree being predominantly on either side of the interface in these phases), and a curve of localization–delocalization transitions which separate the delocalized positive and negative phases from a phase where the tree is localized at the interface. This model is generalized to a branched copolymer which is examined in a certain averaged quenched ensemble. Existence of a thermodynamic limit is shown for this model, and it is also shown that the model is self-averaging. Lastly, a model of branched polymers interacting with one another through a membrane is considered. The existence of a limiting free energy is shown, and it is demonstrated that if the interaction is strong enough, then the two branched polymers will adsorb on one another.     

The shape gradient of the least-squares objective functional in optimal shape design problems of radiative heat transfer

Optimal shape design problems of steady-state radiative heat transfer are considered. The optimal shape design problem (in the three-dimensional space) is formulated as an inverse one, i.e., in the form of an operator equation of the first kind with respect to a surface to be optimized. The operator equation is reduced to a minimization problem via a least-squares objective functional. The minimization problem has to be solved numerically. Gradient minimization methods need the gradient of a functional to be minimized. In this paper the shape gradient of the least-squares objective functional is derived with the help of the shape sensitivity analysis and adjoint problem method. In practice a surface to be optimized may be (or, most likely, is to be) given in a parametric form by a finite number of parameters. In this case the objective functional is, in fact, a function in a finite-dimensional space and the shape gradient becomes an ordinary gradient. The gradient of the objective functional, in the case that the surface to be optimized is given in a finite-parametric form, is derived from the shape gradient. A particular case, that a surface to be optimized is a “two-dimensional” polyhedral one, is considered. The technique, developed in the paper, is applied to a synthetic problem of designing a “two-dimensional” radiant enclosure.     

单电子在含有双能级原子的空腔中的输运行为

本文构造了一个含有双能级原子的空腔系统,用来模拟一个含有双能级量子点的微腔系统, 并研究其对电子输运行为的影响.通过对该系统输运方程的求解,给出了系统输运系数的具体表达式,然后通过调整空腔及原子的本征特性以及两者的耦合性质,研究了电子在腔体中的输运行为对腔体本征属性的依赖关系. 这些结果可以为如何操控电子在微观结构器件中的输运特性提供一定的理论支持.     

污染气体扫描成像红外被动遥测技术研究

傅里叶变换红外光谱技术可实现大气中污染气体的远程被动遥测。而污染气团的位置和分布,对于有害气体泄露情况下泄露位置勘查和污染扩散态势的评估来说是至关重要的。据此设计了一套红外被动成像遥测系统,系统由傅里叶变换光谱仪、数据采集处理软件、扫描系统、可见光成像系统和计算机组成。以六氟化硫为示踪气体,开展了遥测验证实验。通过非线性最小二乘算法结合辐射传输计算反演获得了目标气体的柱浓度,并用伪彩色图显示其分布情况,最后以可见光图像叠加伪彩色柱浓度分布图的形式显示结果。实验分析表明,该系统具有高探测灵敏度,并以可视化和定量的方式显示污染的空间分布情况。     

On the Role of the Excitation/Inhibition Balance of Homeostatic Artificial Neural Networks

Homeostatic models of artificial neural networks have been developed to explain the self-organization of a stable dynamical connectivity between the neurons of the net. These models are typically two-population models, with excitatory and inhibitory cells. In these models, connectivity is a means to regulate cell activity, and in consequence, intracellular calcium levels towards a desired target level. The excitation/inhibition (E/I) balance is usually set to 80:20, a value characteristic for cortical cell distributions. We study the behavior of these homeostatic models outside of the physiological range of the E/I balance, and we find a pronounced bifurcation at about the physiological value of this balance. Lower inhibition values lead to sparsely connected networks. At a certain threshold value, the neurons develop a reasonably connected network that can fulfill the homeostasis criteria in a stable way. Beyond the threshold, the behavior of the artificial neural network changes drastically, with failing homeostasis and in consequence with an exploding number of connections. While the exact value of the balance at the bifurcation point is subject to the parameters of the model, the existence of this bifurcation might explain the stability of a certain E/I balance across a wide range of biological neural networks. Assuming that this class of models describes the self-organization of biological network connectivity reasonably realistically, the omnipresent physiological balance might represent a case of self-organized criticality in order to obtain a good connectivity while allowing for a stable intracellular calcium homeostasis.     

Modelling of a closed two-dimensional reactor bounded by a wavy wall

In this paper, we propose a model for a two-dimensional closed reactor bounded by a wavy wall. The left, right and top walls of the reactor are assumed to be flat surfaces while the bottom wall is a wavy surface. In order to formulate a model for such a reactor, we introduce a coordinate transformation into the dimensionless equations of a rectangular closed domain. Then the resulting equations illustrate the phenomena for a closed reactor bounded by a wavy wall. We solve these equations using the finite difference method. The astonishing results are that the intensity of streamlines and the maximum temperature within the reactor significantly increase with an increase of the number of waves in the bottom wall, the amplitude of waves and the Frank-Kamenetskii number. Converse characteristics are observed for higher values of the enlargement of a wave. Moreover, larger Rayleigh number induces stronger vortices in the flow field and reduces the maximum temperature. The Nusselt number at the bottom wavy wall is found to increase for higher values of the Frank-Kamenetskii number and the amplitude of a wave. A transition from the steady-state to the oscillatory convection is identified for a certain value of the Frank-Kamenetskii number. However, for a low value of the Rayleigh number, there occurs a transition from the steady-state to an explosion for increasing value of the Frank-Kamenetskii number. Results also demonstrate that the critical value of the Frank-Kamenetskii number, for which a transition from the steady-state to the oscillatory convection occurs, is higher for increasing values of the number of waves, the enlargement of a wave and the amplitude of a wave.     

Lyapunov function as potential function： A dynamical equivalence

For a physical system, regardless of time reversal symmetry, a potential function serves also as a Lyapunov function, providing convergence and stability information. In this paper, the converse is constructively proved that any dynamics with a Lyapunov function has a corresponding physical realization: a friction force, a Lorentz force, and a potential function. Such construction establishes a set of equations with physical meaning for Lyapunov function and suggests new approaches on the significant unsolved problem namely to construct Lyapunov functions for general nonlinear systems. In addition, a connection is found that the Lyapunov equation is a reduced form of a generalized Einstein relation for linear systems, revealing further insights of the construction.     

Properties of a simple bilinear stochastic model: Estimation and predictability

We analyze the properties of arguably the simplest bilinear stochastic multiplicative process, proposed as a model of financial returns and of other complex systems combining both nonlinearity and multiplicative noise. By construction, it has no linear predictability (zero two-point correlation) but a certain nonlinear predictability (non-zero three-point correlation). It can thus be considered as a paradigm for testing the existence of a possible nonlinear predictability in a given time series. We present a rather exhaustive study of the process, including its ability to produce fat-tailed distributions from Gaussian innovations, the unstable characteristics of the inversion of the key nonlinear parameters and of the two initial conditions necessary for the implementation of a prediction scheme and an analysis of the associated super-exponential sensitivity of the inversion of the innovations in the presence of a large impulse. Our study emphasizes the conditions under which a degree of predictability can be achieved and describe a number of different attempts, which overall illuminates the properties of the process. In conclusion, notwithstanding its remarkable simplicity, the bilinear stochastic process exhibits remarkably rich and complex behavior, which makes it a serious candidate for the modeling of financial time series among others.     

Equality and Freedom as Uncertainty in Groups

In this paper, I investigate a connection between a common characterisation of freedom and how uncertainty is managed in a Bayesian hierarchical model. To do this, I consider a distributed factorization of a group’s optimization of free energy, in which each agent is attempting to align with the group and with its own model. I show how this can lead to equilibria for groups, defined by the capacity of the model being used, essentially how many different datasets it can handle. In particular, I show that there is a “sweet spot” in the capacity of a normal model in each agent’s decentralized optimization, and that this “sweet spot” corresponds to minimal free energy for the group. At the sweet spot, an agent can predict what the group will do and the group is not surprised by the agent. However, there is an asymmetry. A higher capacity model for an agent makes it harder for the individual to learn, as there are more parameters. Simultaneously, a higher capacity model for the group, implemented as a higher capacity model for each member agent, makes it easier for a group to integrate a new member. To optimize for a group of agents then requires one to make a trade-off in capacity, as each individual agent seeks to decrease capacity, but there is pressure from the group to increase capacity of all members. This pressure exists because as individual agent’s capacities are reduced, so too are their abilities to model other agents, and thereby to establish pro-social behavioural patterns. I then consider a basic two-level (dual process) Bayesian model of social reasoning and a set of three parameters of capacity that are required to implement such a model. Considering these three capacities as dependent elements in a free energy minimization for a group leads to a “sweet surface” in a three-dimensional space defining the triplet of parameters that each agent must use should they hope to minimize free energy as a group. Finally, I relate these three parameters to three notions of freedom and equality in human social organization, and postulate a correspondence between freedom and model capacity. That is, models with higher capacity, have more freedom as they can interact with more datasets.     

Two-channel IR gas sensor with two detectors based on LiTaO3 single-crystal wafer

An infrared (IR) single-element detector based on a lithium tantalate (LiTaO₃) single-crystal wafer has been successfully fabricated. The preparation and design of the device are discussed and analyzed in detail. The processing of a thin LiTaO₃ wafer, the characterization of an IR filter window, and the assembly of the wafer and filter are explained. A LiTaO₃ sensor element, a CMOS amplifier, a narrow-band filter (which can be selected to operate within the appropriate spectral region), and the read-out circuits are set into a TO-18 vessel. Each TO-18-type detector offers a single channel (a single detection wavelength). Two TO-18 detectors with different filters, one acting as a detection channel and the other as a reference, a broadband light source, a circuit board and a flake of wire gauze are assembled and integrated into a gilded gas cell for the purpose of detecting ethene gas.