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.     

Synthesis of magnetic systems producing field with maximal scalar characteristics

A method of synthesis of the magnetic systems (MSs) consisting of uniformly magnetized blocks is proposed. This method allows to synthesize MSs providing maximum value of any magnetic field scalar characteristic. In particular, it is possible to synthesize the MSs providing the maximum of a field projection on a given vector, a gradient of a field modulus and a gradient of a field energy on a given directing vector, a field magnitude, a magnetic flux through a given surface, a scalar product of a field or a force by a directing function given in some area of space, etc. The synthesized MSs provide maximal efficiency of permanent magnets utilization. The usage of the proposed method of MSs synthesis allows to change a procedure of projecting in principal, namely, to execute it according to the following scheme: (a) to choose the sizes, a form and a number of blocks of a system proceeding from technological (economical) reasons; (b) using the proposed synthesis method, to find an orientation of site magnetization providing maximum possible effect of magnet utilization in a system obtained in (a). Such approach considerably reduces a time of MSs projecting and guarantees maximal possible efficiency of magnets utilization. Besides it provides absolute assurance in “ideality” of a MS design and allows to obtain an exact estimate of the limit parameters of a field in a working area of a projected MS.The method is applicable to a system containing the components from soft magnetic material with linear magnetic properties.     

Physical adsorption and surface plasmons

The quantum mechanical formulation of the screening of a point charge by surface plasmons is extended to describe the coupling of a fluctuating atomic dipole with a metallic surface of planar, spherical or cylindrical shape. This allows for the calculation of the nonretarded Van der Waals attraction of an atom by a solid surface in the three different geometries. Applications of the theoretical formulae are made to obtain numerical values of the dispersion energy by a spherical particle, a spherical pore, a thin film, a slot-like prore, a cylindrical fiber or a cylindrical pore.     

The analysis of impact forces in randomly vibrating elastic systems

This work is concerned with the characteristics of the impact force produced when two randomly vibrating elastic bodies collide with each other, or when a single randomly vibrating elastic body collides with a stop. The impact condition includes a non-linear spring, which may represent, for example, a Hertzian contact, and in the case of a single body, closed form approximate expressions are derived for the duration and magnitude of the impact force and for the maximum deceleration at the impact point. For the case of two impacting bodies, a set of algebraic equations are derived which can be solved numerically to yield the quantities of interest. The approach is applied to a beam impacting a stop, a plate impacting a stop, and to two impacting beams, and in each case a comparison is made with detailed numerical simulations. Aspects of the statistics of impact velocity are also considered, including the probability that the impact velocity will exceed a specified value within a certain time.     

Instability of traveling waves in an optical waveguide

Instability of traveling IR waves within a waveguide structure is discussed. A practical model of a traveling wave amplifier of a solid state is proposed, utilizing an optical waveguide. The mechanism of instability is interpreted in terms of an interaction between a plasmon wave and a circuit one under a constraining boundary condition. Properties of the traveling amplification and related problems are discussed, with appropriately suggested semiconductor materials and device designs. The features of the amplifier are a simple structure, a low DC biasing power dissipation for room-temperature operation, unidirectionality, and a wide wavelength range from IR or submillimeter order, suited to various applications.     

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     

The scanning acoustic microprobe: II. Application to the measurement and characterization of a piston reflector

In a pulsed ultrasound beam, echoes detected from a flat, circular piston of arbitrary size depend on the time-space characteristics of the entire pulse-echo measurement system, being a function of as many parameters as it takes to accurately define the system. In the limiting case of a target that is small relative to the spatial extent of an interrogating plane wave, an echo pattern is known to be a relatively simple function of the dimensionless product k0b, where k0 is the wave number and b is the radius of the target. In a companion paper preceding this one [F. E. Barber, J. Acoust. Soc. Am. 90, 8-17 (1991)], the author has described the scanning acoustic microprobe, a pulse-echo system in which the time-space properties of the interrogating waves are specified completely by k0 and a single additional parameter s0, which is the characteristic radius of a spherically symmetric, Gaussian-distributed scattering volume. In this system, the reflection pattern of a flat, circular piston of any arbitrary size is thus a function of two dimensionless parameters, namely k0b and b/s0. In this paper, this functional relationship is derived, a physical system is described, and analytical and experimental results are reported. It is shown that the diameter, orientation, and impedance mismatch properties of this simple target can be measured unambiguously over a range of target sizes from about a wavelength (2 pi/k0) to a beam diameter (about 3s0). For a typical ultrasound system, this is about a 5-1 range; i.e., a range extending to target sizes about five times smaller than can be detected in a simple B-mode imaging system.(ABSTRACT TRUNCATED AT 250 WORDS)     

Theory of chiral imprinting

We present a continuum model for a nematic elastomer network formed in a chiral environment, for instance, in the presence of a chiral solvent. When this environment is removed, the network can retain some memory of its chiral genesis. We predict the residual chiral order for a number of possible scenarios, and examine the robustness (stability) of the imprinted chirality. We show that a twist-untwist transition can take place, which determines whether the imprinting has been successful. A transition is via a coarsening of the helical director pattern and a lengthening of its pitch. Finally, the effect due to a subsequent swelling by an achiral solvent, or by a solvent of differing chirality, is considered.     

Evolution of Classical and Quantum States in the Groupoid Picture of Quantum Mechanics

The evolution of states of the composition of classical and quantum systems in the groupoid formalism for physical theories introduced recently is discussed. It is shown that the notion of a classical system, in the sense of Birkhoff and von Neumann, is equivalent, in the case of systems with a countable number of outputs, to a totally disconnected groupoid with Abelian von Neumann algebra. The impossibility of evolving a separable state of a composite system made up of a classical and a quantum one into an entangled state by means of a unitary evolution is proven in accordance with Raggio’s theorem, which is extended to include a new family of separable states corresponding to the composition of a system with a totally disconnected space of outcomes and a quantum one.     

Some non-abelian phase spaces in low dimensions

A non-abelian phase space, or a phase space of a Lie algebra, is a generalization of the usual (abelian) phase space of a vector space. It corresponds to a para-Kähler structure in geometry. Its structure can be interpreted in terms of left-symmetric algebras. In particular, a solution of an algebraic equation in a left-symmetric algebra which is an analogue of classical Yang–Baxter equation in a Lie algebra can induce a phase space. In this paper, we find that such phase spaces have a symplectically isomorphic property. We also give all such phase spaces in dimension 4 and some examples in dimension 6. These examples can be a guide for a further development.     

Quantum dots in a fractal multilayer system

The stochastic behavior of the strain fields of coupled systems (a fractal layer, a nanotrap, and quantum dots in a fractal multilayer nanosystem) is studied theoretically and numerically. As the semiaxes of a quantum dot shorten, the amplitude of the primary peak falls, a bump emerges on it, and the region of stochastic behavior shrinks in size. As the semiaxes grow, a broadened peak with a stochastic base in the background (a halo-type signal) forms.     

A string-modified four-dimensional gravity theory

The route from string theory to a ten-dimensional supergravity/super-Yang-Mills field theory is briefly illumined. The process of extracting a classical four-dimensional gravity theory from the ten-dimensional theory is discussed and a simple model containing gravity, electromagnetism, a dilaton field, and a Kalb-Ramond field is proposed. The equations of motion of a test particle in a background of gravity, dilation, and Kalb-Ramond fields are displayed. Some static spherically symmetric vacuum solutions are derived, and some astrophysical implications are discussed.     

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。     

Vibrations of double-string complex system under moving forces. Closed solutions

In this paper the dynamic response of a double-string system traversed by a constant or a harmonically oscillating moving force is considered. The force is moving with a constant velocity on the top string. The strings are identical, parallel, one upon the other and continuously coupled by a linear Winkler elastic element. The classical solution of the response of a double-string system subjected to a force moving with a constant velocity has a form of an infinite series. The main goal of this paper is to show that in the considered case a part of the solution can be presented in a closed, analytical form instead of an infinite series. The presented method of finding the solution in a closed, analytical form is based on the observation that the solution of the system of partial differential equations in the form of an infinite series is also a solution of an appropriate system of ordinary differential equations.     

Magnetization of the ferromagnetic-superconductor structures

The magnetization of a structure consisting of a thin superconducting film lying on a thin ferromagnetic substrate with uniaxial anisotropy is considered. It is shown that if a ferromagnet is in a multidomain state, then due to the presence of a superconducting film, the period of its domain structures decreases, which is caused by the increase of the magnetostatic energy of the system owing to Meissner currents. In a certain range of the constant of uniaxial anisotropy, under the action of a superconducting film, a domain structure may transform from a strip structure to the structure with closure domains. It is found that due to the nonuniform magnetic field of a multidomain ferromagnet, Abrikosov vortices may exist in a thin film only at certain parameters of the magnetic field.     

Generalized Lie bialgebroids and Jacobi structures

The notion of a generalized Lie bialgebroid (a generalization of the notion of a Lie bialgebroid) is introduced in such a way that a Jacobi manifold has associated a canonical generalized Lie bialgebroid. As a kind of converse, we prove that a Jacobi structure can be defined on the base space of a generalized Lie bialgebroid. We also show that it is possible to construct a Lie bialgebroid from a generalized Lie bialgebroid and, as a consequence, we deduce a duality theorem. Finally, some special classes of generalized Lie bialgebroids are considered: triangular generalized Lie bialgebroids and generalized Lie bialgebras.     

Experimental demonstration of a technique to generate arbitrary quantum superposition states of a harmonically bound spin-1/2 particle

Using a single, harmonically trapped 9Be(+) ion, we experimentally demonstrate a technique for generation of arbitrary states of a two-level particle confined by a harmonic potential. Rather than engineering a single Hamiltonian that evolves the system to a desired final state, we implement a technique that applies a sequence of simple operations to synthesize the state.     

Quantum spin chains with various defects

Using the density matrix renormalization group (DMRG) method, we study the quantum coherence in one‐dimensional disordered spin chains and Fermi systems. We consider in detail spinless fermions on a ring, and compare the influence of several kinds of impurities in a gapless and a dimerized, gapped system. In the translation‐invariant system a so‐called site‐impurity, which can be realized by a local potential or a modification of one link, increases for repulsive interaction, and decreases for attractive interaction, upon renormalization. The weakening of two neighbouring bonds, which is a realization of a so‐called bond‐impurity, on the other hand, is healed for repulsive interaction, but enhanced for intermediate attractive interactions. This leads to a strong suppression of the quantum coherence measured by the phase sensitivity, but not to localization. Adding a local distortion to a dimerized system, we find that even the presence of a single site‐impurity increases the metallic region found in the dimerized model. For a strong dimerization and a high barrier, an additional sharp maximum, is seen in the phase sensitivity as a function of interaction, already for systems with about 100 sites. A bond‐impurity in the dimerized system also opens a small metallic window in the otherwise isolating regime.     

High-Q exterior whispering-gallery modes in a metal-coated microresonator

We propose a kind of plasmonic whispering-gallery mode highly localized on the exterior surface of a metal-coated microresonator. This exterior (EX) surface mode possesses high quality factors at room temperature, and can be efficiently excited by a tapered fiber. The EX mode can couple to an interior (IN) mode and this coupling produces a strong anticrossing behavior, which not only allows conversion of IN to EX modes, but also forms a long-lived antisymmetric mode. As a potential application, the EX mode could be used for a biosensor with a sensitivity high of up to 500 nm per refraction index unit, a large figure of merit, and a wide detection range.