Fluctuation spectra of free and supported membrane pairs

Fluctuation spectra of fluid compound membrane systems are calculated. The systems addressed contain two (or more) almost parallel membranes that are connected by harmonic tethers or by a continuous, harmonic confining potential. Additionally, such a compound system can be attached to a supporting substrate. We compare quasi-analytical results for tethers with analytical results for corresponding continuous models and investigate under what circumstances the discrete nature of the tethers actually influences the fluctuations. A tethered, supported membrane pair with similar bending rigidities and stiff tethers can possess a nonmonotonic fluctuation spectrum with a maximum. A nonmonotonic spectrum with a maximum and a minimum can occur for an either free or supported membrane pair of rather different bending rigidities and for stiff tethers. Typical membrane displacements are calculated for supported membrane pairs with discrete or continuous interacting potentials. Thereby an estimate of how close the constituent two membranes and the substrate typically approach each other is given. For a supported membrane pair with discrete or continuous interactions, the typical displacements of each membrane are altered with respect to a single supported membrane, where those of the membrane near the substrate are diminished and those of the membrane further away are enhanced.     

Vector Diffraction Integrals for Solving Inverse Problems of Radio-Holographic Sensing of the Earth's Surface and Atmosphere

Vector relationships between the fields on a certain surface confining an inhomogeneous three-dimensional volume and the fields inside this volume are obtained by the Stratton–Chu method developed for the case of homogeneous media. The vector relationships allow us to solve the direct and inverse problems of determining the fields inside an inhomogeneous medium given the field on its boundary. The vector equations take into acount the polarization changes of direct and inverse waves propagated in an inhomogeneous medium. In the case of a two-dimensional homogeneous medium, the vector equations reduce to the previously obtained scalar equations used in the approximation of spherical symmetry to describe the process of backward wave propagation during the atmospheric and ionospheric radio-occultation monitoring. It is shown that the Green's function of the scalar wave equation in an inhomogeneous medium should be used as the reference signal for solving the inverse problem of radio-occultation monitoring. This validates the method of focused synthetic aperture previously used for high-accuracy retrieval of the vertical refractive-index profiles in the ionosphere and atmosphere. In this method, the reference-signal phase was determined from a model which describes with sufficient accuracy the radiophysical parameters of a refracting medium in the region of radio-occultation sensing. The obtained equations can be used for the high-accuracy solving of inverse problems of radio-holographic sensing of the Earth's atmosphere and surface by precision signals from radio-navigation satellites.     

杆的离散系统的某些混合型振动反问题

研究杆的离散系统的混合型振动反问题,即由给定的部分频谱数据和部分模态数据构造一个杆的离散系统的刚度矩阵和质量矩阵.提出3个此类反问题,给出反问题的解法,讨论反问题的解的存在条件,给出相应的计算实例,并分析这类反问题的潜在价值.     

Stationary response of combined linear dynamic systems to stationary excitation

The stationary response of a broad class of combined linear systems to stationary random excitation is determined by the normal mode method. The systems are characterized by a viscously damped simple beam (or string, membrane, thin plate or shell, etc.) connected at discrete points to a multiplicity of viscously damped linear oscillators and/or masses. The solution of the free vibration problem by way of Green functions and the deterministic forced vibration problem by modal analysis for both proportional and non-proportional damping is reviewed. The orthogonality relation for the natural modes of vibration is used to derive a unique relationship between the cross-spectral density functions of the applied forces and the cross-spectral density functions of the generalized forces. Finally, the response spectral density functions and the mean square responses of the beam and oscillators are derived in closed form, exact for the proportionally damped system and approximate for the non-proportionally damped system.     

空气开关等离子体干涉条纹图像的处理

利用Mach-Zehnder干涉仪测量了空气开关中等离子体电子密度分布,使用高速分幅相机拍摄记录不同时延下的干涉条纹图像。针对实验获得的干涉条纹图像的特点,提出了一种首先进行频域FFT滤波去噪,然后进行空域二值化、细化的处理方法。该方法能够很好的消除图像噪声的影响,提取出单像素的亮条纹中心线,从而能够准确读取条纹坐标信息,再通过对干涉条纹偏移量进行Abel逆变换,得到等离子体电子密度分布。     

HYDROELASTIC COUPLED VIBRATIONS IN A CYLINDRICAL CONTAINER WITH A MEMBRANE BOTTOM, CONTAINING LIQUID WITH SURFACE TENSION

A linear free hydroelastic vibration analysis of a frictionless liquid with a free surface contained in a cylindrical tank with a flexible bottom has been performed. The side-wall has been treated as rigid and the effect of surface tension taken into consideration. The container bottom was treated as a membrane, while for the free liquid surface the effect of two contact line conditions has been investigated. One edge condition was that of a slipping contact line, while the other one treated the contact line as fixed, ie., an anchored edge. The vibration characteristics of a membrane-liquid coupled system have been investigated for various system parameters, i.e., membrane tension parameter T, liquid surface tension parameter σ, material density parameter ρ, liquid height ratio ?₀ and vibration mode numbers m and n. The degree of coupling between a membrane and a liquid was represented with vibration mode diagrams as well as with frequency diagrams. For axisymmetric coupled vibrations with anchored edge condition, vibration mode exchanging of both a membrane and liquid free surface with membrane bottom tension parameter T has been investigated. An interesting phenomenon which is only observed for a flexible bottom container and an anchored edge free surface condition is presented.     

On interfacial free energy versus interfacial stress of fluids adsorbed on chemically patterned surfaces: lessons from the special case of striped substrates

The statistical mechanics of fluids adsorbed on chemically patterned surfaces is far from straightforward when attempting to develop virial theorems for the interfacial free energy. This is because in general one would have to devise new procedures to distinguish surface tension from surface stress, even for wall-fluid models where the substrate atoms are replaced by an effective external field. However, the distinction may be made explicit for the special case of striped walls. This paper makes use of striped wall-fluid models to discuss the significance of fluid interfacial stress to patterned inhomogeneous fluids. In particular, it considers the adsorption of hemicylindrical drops on an array of high energy stripes. For the planar stripe geometry it is also possible to make effective use of the pressure tensor formalism. Beyond the special case of striped patterns it is not possible to use standard procedures based on virial theorems to directly evaluate interfacial free energy. The lessons learnt from these exercises apply especially to computer simulation studies of patterned inhomogeneous fluids.     

A computational approach to calculating frequency-dependent structural operators using the spectral finite element method and a wavenumber-based gridding technique

Spectral finite element methods are used to compute exact vibration solutions of structural models at specific frequencies. The applicability of these methods to certain areas of structural dynamics is limited by two major factors: the lack of separate structural operators (mass, damping, and stiffness matrices), and the subsequent difficulty in computing mode shapes via eigenvalue decomposition. In the work presented in this article, a method is investigated to accurately calculate spectral finite elements while overcoming these limitations. The approach incorporates a two-dimensional, discrete solution utilizing a wavenumber-based gridding technique to compute frequency-dependent local mass, damping, and stiffness matrices which can be assembled into the global structural operators. Computed models are able to be used for precise vibration analysis as well as modal analysis via eigenvalue decomposition of the structural operators.     

Measurement of decoherence of electron waves and visualization of the quantum-classical transition

Controlled decoherence of free electrons due to Coulomb interaction with a truly macroscopic environment, the electron (and phonon) gas inside a semiconducting plate, is studied experimentally. The quantitative results are compared with different theoretical models. The experiment confirms the main features of the theory of decoherence and can be interpreted in terms of which-path information. In contrast to previous model experiments on decoherence, the obtained interferograms directly visualize the transition from quantum to classical.     

3D measurement of micromechanical devices vibration mode shapes with a stroboscopic interferometric microscope

Microscopic interferometry is a powerful technique for the static and dynamic characterization of micromechanical devices. In this paper we emphasize its capabilities for 3D vibration mode shapes profiling of Al cantilever microbeams and Cr micromachined membranes. It is demonstrated that time-resolved measurements up to 800 kHz can be performed with a lateral resolution in the micrometer range and a vibration amplitude detection limit of 3–5 nm. In addition, with reduced image sizes (256×256), quasi-real time (150–500 ms) visualization of the vibration mode 3D profiles becomes possible. These performances were obtained by using stroboscopic illumination with an array of superluminescent LED and an optimized automatic fast Fourier transform phase demodulation of the interferograms. The results are compared with theoretical shapes of the vibration modes and with point measurements of the vibration spectra.     

Hydrogen isotope permeability of membranes with inhomogeneous properties along the thickness of material

The problem of hydrogen permeation through membranes with inhomogeneous properties along the thickness has been considered as the limiting case of permeation through a multilayered membrane when the layer thicknesses tend to zero. The steady-state permeability equation for multilayer membranes and membranes with inhomogeneous properties along the thickness has been derived. The diffusion equation for the case of inhomogeneous solubility in a membrane has been obtained.     

Non-acoustical and acoustical properties of reticulated and partially reticulated polyurethane foams

A series of measurements on four polyurethane foam samples with pore membranes and a polyurethane foam sample without pore membranes have been made. Tortuosity has been deduced using the ultrasonic slope method. It has been found that the deduced value of tortuosity depends on the measurement temperature and for two of the polyurethane foam samples with many pore membranes physically meaningful values of tortuosity cannot be obtained at a temperature of around 25 °C. However more realistic values of tortuosity have been obtained by from measurements at or around the glass transition temperature of polyurethane foam (i.e. at ?20 °C) when using the ultrasonic slope method.Flow resistivity, Young’s moduli and loss factors have been measured also.Vibration of the pore membranes has been observed to influence the effective density and characteristic impedance derived from the surface impedance measured in an impedance tube. This paper discusses relationships between membrane vibration and the slow and fast compressional waves. The relative merits of predictions based on rigid-porous models and the Biot–Johnson–Champoux–Allard model are discussed also.     

Vibration of a flexible plate in contact with the free surface of a heavy liquid

Free vibration of a flexible plate floating on the free surface of a perfect incompressible finite-depth heavy liquid are studied. The problem is solved in the shallow water approximation. Conditions for the existence of discrete frequencies below the waveguide cutoff frequency and associated localized (nonpropagating) liquid vibration modes in the plate-liquid system are determined.     

Nonlinear oscillations of circular membranes of a low-frequency acoustic radiator

We study the features of oscillations of an acoustic radiator in the form of a rigid cylinder with elastic circular membranes fixed at the cylinder ends. For different membrane models and different vibration modes, the spectra of linear and nonlinear free and forced oscillations are found. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 3, pp. 199–215, March 2008.     

On the sound field of a resilient disk in free space

Radiation characteristics are calculated for a circular planar sound source in free space with a uniform surface pressure distribution, which can be regarded as a freely suspended membrane with zero mass and stiffness. This idealized dipole source is shown to have closed form solutions for its far-field pressure response and radiation admittance. The latter is found to have a simple mathematical relationship with the radiation impedance of a rigid piston in an infinite baffle. Also, a single expansion is derived for the near-field pressure field, which degenerates to a closed form solution on the axis of symmetry. From the normal gradient of the surface pressure, the surface velocity is calculated. The near-field expression is then generalized to an arbitrary surface pressure distribution. It is shown how this can be used as a simplified solution for a rigid disk in free space or a more realistic sound source such as pre-tensioned membrane in free space with non-zero mass and a clamped rim.     

Spherically symmetric anisotropic and inhomogeneous cosmological models

Spherically symmetric cosmological models filled with dust (pressure-free fluid) content are analyzed. It has been pointed out that these models are anisotropic (of non-vanishing shear) and inhomogeneous (∂p/ρr ≠ 0), the characteristics related directly to the presence of the free gravitational field. It is demonstrated that when the free gravitational field vanishes these models degenerate to the corresponding Friedmann-Robertson-Walker (FRW) models. It is further shown that the energy density of the free gravitational field can be introduced into observational cosmology as a new parameter since it enters into the expansion and deceleration equations, as well as conservation law for total energy, implying that the present Hubble velocity can be reached in a shorter time from the big bang. Finally, the effect of shear on the redshift is also discussed. This paper is dedicated to my teacher Professor V V Narlikar on the occasion of his 81st birthday.     

Detection and localization of inclusions in plates using inversion of point actuated surface displacements

A numerical simulation is carried out demonstrating the use of plate surface vibration measurements for detecting and locating inclusions within the structure. A finite element code is used to calculate normal surface displacement for both steel and mortar plates subjected to a monochromatic point force. The data is generated for the homogeneous plate and the identical plate within which exists a small rectangular inclusion. It is observed that when the elastic modulus of the inclusion is orders of magnitude lower than the base material, resonances of the inclusion produce large local displacements that are readily observed in the raw displacement data. For more modest moduli differences, there are no such directly observable effects. In this case, three inverse algorithms are used to process the displacement data. The first two are local inversion techniques that each yield a spatial map of the elastic modulus normalized by density. These algorithms successfully detect and localize the inclusion based on its modulus difference from that of the base plate. The third technique uses a form of the inhomogeneous equation of motion to obtain the induced force distribution connected with the inclusion. The spatial mapping of this force also successfully detects and localizes the inclusion.     

Nonlocal discrete and continuous modeling of free vibration of stocky ensembles of vertically aligned single-walled carbon nanotubes

Free dynamic analysis of transverse motion of vertically aligned stocky ensembles of single-walled carbon nanotubes is of particular interest. A linear model is developed to take into account the van der Waals forces between adjacent SWCNTs because of their bidirectional transverse displacements. Using Hamilton's principle, the discrete equations of motion of free vibration of the nanostructure are obtained based on the nonlocal Rayleigh, Timoshenko, and higher-order beam theories. The application of such discrete models for frequency analysis of highly populated ensembles would be associated with so much computational effort. To overcome such a problem, some useful nonlocal continuous models are established. The obtained results reveal that the newly developed models can successfully capture the predicted fundamental frequencies of the discrete models. Through various numerical studies, the roles of slenderness ratio, radius of the SWCNT, small-scale parameter, population of the ensemble, and intertube distance on the fundamental flexural frequency of the nanostructure are examined and discussed. The capabilities of the proposed nonlocal continuous models in predicting flexural frequencies of the nanostructure are also addressed.     

Study on the algorithm of computational ghost imaging based on discrete fourier transform measurement matrix

We have developed a model and realized an algorithm for the calculation of the coefficient of coherent (direct) transmission of light through a layer of liquid crystal (LC) droplets in a polymer matrix. The model is based on the Hulst anomalous diffraction approximation for describing the scattering by an individual particle and the Foldy-Twersky approximation for a coherent field. It allows one to investigate polymer dispersed LC (PDLC) materials with homogeneous and inhomogeneous interphase surface anchoring on the droplet surface. In order to calculate the configuration of the field of the local director in the droplet, the relaxation method of solving the problem of minimization of the free energy volume density has been used. We have verified the model by comparison with experiment under the inverse regime of the ionic modification of the LC-polymer interphase boundary. The model makes it possible to solve problems of optimization of the optical response of PDLC films in relation to their thickness and optical characteristics of the polymer matrix, sizes, polydispersity, concentration, and anisometry parameters of droplets. Based on this model, we have proposed a technique for estimating the size of LC droplets from the data on the dependence of the transmission coefficient on the applied voltage.     

Multiple-image encryption by two-step phase-shifting interferometry and spatial multiplexing of smooth compressed signal

A multiple-image encryption method based on two-step phase-shifting interferometry(PSI) and spatial multiplexing of a smooth compressed signal is proposed. In the encoding and encryption process, with the help of four index matrices to store original pixel positions, all the pixels of four secret images are firstly reordered in an ascending order; then, the four reordered images are transformed by five-order Haar wavelet transform and performed sparseness operation. After Arnold transform and pixels sampling operation, one combined image can be grouped with the aid of compressive sensing(CS)and spatial multiplexing techniques. Finally, putting the combined image at the input plane of the PSI encryption scheme,only two interferograms ciphertexts can be obtained. During the decoding and decryption, utilizing all the secret key groups and index matrices keys, all the original secret images can be successfully decrypted by a wave-front retrieval algorithm of two-step PSI, spatial de-multiplexing, inverse Arnold transform, inverse discrete wavelet transform, and pixels reordering operation.