Two-dimensional Index Research Articles

Nondestructive damage evaluation of plates using the multi-resolution analysis of two-dimensional Haar wavelet

A wavelet application to the vibration-based damage evaluation technique is introduced. The proposed method requires only a few of the lower mode shapes before and after a small damage event in order to detect, locate, and size damage on plate-like structures. The proposed method takes account for uncertainty in mass density, surrounding forces, foundation stiffness, etc. Based on a small damage assumption of a thin plate, the two-dimensional damage index (DI) equation is revealed within the context of elasticity. The singularity problem, which occurs in the resulting DI equation, is solved in the two-dimensional multi-resolution wavelet domain with the aid of the singular value decomposition technique. Finally, the desired damage measures are reconstructed from the one in the wavelet space by inverse wavelet transformation. The performance of the proposed method is compared with an existing damage detection method. Finally, an uncertainty analysis of the proposed method is provided.

Flow Visualization and Modeling of Convection During Growth of KDP Crystals

Buoyancy-driven convection is an important limiting factor during the growth of KDP crystals from their aqueous solution. Convection patterns have been visualised using a shadowgraph technique, and numerically analyzed. A numerical model is developed to obtain two-dimensional refractive index distribution averaged along the length of the growth chamber, followed by the tracing of light rays through the region of interest. The refractive index gradients around the crystal become sharper as the growth progresses, and manifest itself as high contrast plumes in the shadowgraph image. Estimates of the physical displacement of the light rays as they pass through the KDP solution have been found to be insignificant in comparison to the extent of disturbance, indicating that the higher order effects such as interference and scattering are negligible during shadowgraphic imaging of convection around a growing crystal. The experimental and numerical results show the utility of optical imaging of the convective field for monitoring crystal growth.

Two-dimensional refractive index patterns with crystalline symmetry

Photosensitive samples of poly-methylmethacrylate containing about 10% residual monomer and the photo-initiator Cp2TiCl2 have been prepared. In a two-beam configuration the formation of a volume phase grating was photo-initiated, and, while the first grating was still growing, a second one was recorded after turning the sample by an arbitrary angle γ. As a result, two-dimensional gratings with the symmetry of a monoclinic crystal (a1 ≠ a2, γ ≠ 90°) were obtained and stabilized by a simple heat treatment.In a diffraction experiment the lattice constants and the amplitudes ΔnI and ΔnII of the overlapping gratings forming the crystal pattern could be deduced from its diffraction pattern and all the diffracted beams were assigned to their Miller indices (h, k).

Numerical Method of Determining the Cutoff Frequency and Mode Speckle Pattern of Optical Waveguides

Based on a numerical solution of the nonstationary wave equation, an algorithm for determining the eigenfunctions and eigenvalues of the LPim modes of axially symmetric optical waveguides is suggested. The cutoff frequency of the LP11 mode of different waveguides is determined using the algorithm constructed. The results obtained are compared with the well-known analytical formulas and results of numerical calculations for the equivalent step-index waveguide model. Based on the analytical results obtained, an eigenfunction and eigenvalue search algorithm is suggested for a waveguide with a two-dimensional refractive index profile (in particular, for an axially nonsymmetric waveguide).

Developing an operational reference framework for fisheries management on the basis of a two-dimensional index of ecosystem impact

Abstract A composite quantitative index for the percentage of primary production required to sustain fisheries and the average trophic level of catch (%PPR–TLc) was employed to develop ecosystem-based reference functions suitable for fisheries management. Established ecosystem models, characterized by pairs of %PPR–TLc, were classified as either sustainably exploited or ecosystem overfished, on the basis of the results of factorial correspondence analysis applied to selected ecological indices, and on information from various sources. Canonical discriminant analysis of these pairs was applied to establish the discriminant function to separate the two exploitation classes. Next, reference functions related to different probabilities of ecosystem overfishing were developed to obtain an operational framework for ecosystem-based fisheries management. Values of ecosystem-based maximum sustainable catches associated with different probabilities of belonging to a sustainable situation were calculated. Overall, results show that most current fishing scenarios entail high risks of ecosystem overfishing.

Two-dimensional fatty acid retention indices

A two-dimensional retention index system for fatty acid methyl esters (2D-FARI) is proposed. The system is based on the application of different temperature and pressure programs on a single capillary column. A calibration sample is analysed and the retention data is calibrated against a set of reference 2D-FARI values. The calibration models are then applied to predict the 2D-FARI values for compounds that are not present in the calibration sample. The two dimensions in the retention index system lead to increased selectivity and a reduced risk of retention index overlap between different compounds. The 2D-FARI system is also more robust towards differences in stationary phase properties than ordinary retention indices and is therefore convenient for comparison of retention data acquired on different columns, or at different times at the same column.

Fabrication and analysis of 2 × 2 thermo-optic SOI waveguide switch with low power consumption and fast response by anisotropy chemical etching

A low power consumption 2×2 thermo-optic switch with fast response was fabricated on silicon-on-insulator by anisotropy chemical etching. Blocking trenches were etched on both sides of the phase-shifting arms to shorten device length and reduce power consumption. Thin top cladding layer was grown to reduce power consumption and switching time. The device showed good characteristics, including a low switching power of 145 mW and a fast switching speed of 8±1 μs, respectively. Two-dimensional finite element method was applied to simulate temperature field in the phase-shifting arm instead of conventional one-dimensional method. According to the simulated result, a new two-dimensional index distribution of phase-shifting arm was determined. Consequently finite-difference beam propagation method was employed to simulate the light propagation in the switch, and calculate the power consumption as well as the switching speed. The experimental results were in good agreement with the theoretical estimations.

Microreflectivity characterization of the two-dimensional refractive index distribution of electron-beam-written optical waveguides in germanium-doped flame-hydrolysis silica

In this letter, we report on the detailed refractive index distribution of optical waveguides induced by electron-beam irradiation of Ge-doped flame hydrolysis silica and its variation with dose. The characterization was performed using microreflectivity measurements.

Fast convergence and higher-order mode calculation of optical waveguides: perturbation method with finite difference algorithm

We present an efficient algorithm for determining mode eigenvalues as well as field distributions of optical waveguides with two-dimensional transverse refractive index profile. The algorithm is devised with the analytical perturbation correction method combined with the finite difference approximation of Helmoltz's equation. The technique is simple and does not involve solving any eigenvalue equation or matrix formalism. The algorithm reduces abruptly the computation time required for the field convergence to mode, and can calculate any higher-order modes without the need of any pre-conditioning the field w.r.t. waveguide geometry, or calculation of previous order modes and/orthogonalization. The analysis can yield precisely both scalar and polarized modes. By applying it to waveguide problems whose solutions are otherwise known, the efficacy of the method has been established.

Fluorescence-based array biosensors for detection of biohazards.

Total internal reflection fluorescence (TIRF) is a process whereby fluorophores that are either attached to or are in close proximity with the surface of a waveguide are selectively excited via an evanescent wave. Planar waveguides provide the possibility of immobilizing multiple capture biomolecules onto a single surface and therefore, offer the exciting prospect of multi-analyte detection. The production of arrays and the results of various groups which use TIRF to interrogate such surfaces is reviewed, along with a look at how far the field has advanced toward the production of an automated, portable, multi-analyte array biosensor for real-time biohazard detection. In particular, a miniaturized, fully automated, stand-alone array biosensor developed at the Naval Research Laboratory is reported that monitors interactions between binding partners either as the final image or in real-time. A variety of analytes including toxins, bacteria and viruses have been detected both in buffer and complex matrices, such as blood and soil suspensions, with comparable detection limits. A number of developments have led to a TIRF array biosensor weighing only 5.5 kg which is automated for environmental, clinical and food monitoring or for detection of bioterrorist agents.

Repetitive dobutamine stress echocardiography for the prediction of anthracycline cardiotoxicity.

To evaluate whether repetitive assessment of systolic and diastolic cardiac function by dobutamine stress echocardiography (DSE) can predict anthracycline cardiotoxicity. Thirty-one patients (age, 57+/-13 years, 22 male) were studied before chemotherapy, with follow-ups during, at the end, and 6 months after chemotherapy. Left ventricular (LV) function was assessed by two-dimensional (2D) echocardiographic wall motion score index (WMSI) and by Doppler echocardiography of mitral valve inflow at rest and during DSE. Radionuclide ventriculography was used as an independent reference for ejection fraction (EF). A reduction of EF >/=5% occurred in 17 patients (group A) at the last follow-up. Patients without decreased EF comprised group B. Early/late diastolic velocity of mitral inflow (E/A ratio) at rest was lower in group A (0.91+/-0.2 vs 1.28+/-0.3, P<0.001), and it was an independent predictor of cardiotoxicity (adjusted for baseline patient characteristics and parameters of systolic and diastolic function). At follow-up, WMSI at rest paralleled radionuclide EF. Contractile reserve at low-dose DSE was preserved in group A. WMSI measured by 2D echocardiography parallels radionuclide EF at follow-up. Assessment of contractile reserve has no incremental value for the early detection of cardiotoxicity. A baseline abnormal E/A ratio is an independent predictor of anthracycline cardiotoxicity.

Two-dimensional soliton-induced refractive index change in photorefractive crystals

An analysis of light-induced space-charge field, valid for the propagation of two-dimensional solitons in photorefractive (PR) crystals, is carried out. Under conditions appropriate to the formation of self-trapped beams, the equation for the electrostatic potential is simplified and solved, to obtain an analytical expression for the space-charge field, and thus the refractive index change. The expression exhibits an excellent agreement with the numerical calculation for a variety of localized two-dimensional light beams, in particular for the bright fundamental and higher-order vortex spatial screening solitary waves. Based on analytical results, a class of models for the local isotropic two-dimensional space-charge field is proposed. They are compared to the general nonlocal anisotropic model, using the propagation and breakup of vortex beams as an example.

Periodic analysis of a 2-D negative refractive index transmission line structure

The propagation characteristics of a two-dimensional (2-D) negative refractive index (NRI) transmission line (TL) structure are explained using Bloch theory. Bloch analysis of a generalized 2-D periodic electrical network is performed and the results are applied to the NRI TL structure. A 2-D Brillouin diagram of the NRI TL metamaterial is presented and its band structure is intuitively explained. Voltage and current relationships, Bloch impedance expressions and dispersion equations which aid in the design, proper excitation and termination of such structures are derived. Effective material parameters for regions of isotropic and homogeneous operation are also derived, providing a simplified understanding of the NRI TL metamaterial's 2-D band structure. Finally, simulations of negative refraction for a relative refractive index of n=-1 are shown. The simulation results verify the analytic expressions presented in this paper and demonstrate the proper termination and excitation of finite size structures.

Scalar BPM analyses of TE and TM polarized fields in bent waveguides

We have applied the effective index method to reduce the two-dimensional (2-D) refractive index profile into the 1-D refractive index structure and modified the wave equations to obtain the paraxial wave equations. Then, transverse electric (TE) and transverse magnetic (TM) polarized fields in the curved single-mode planar waveguides are analyzed by using the scalar beam-propagation method (BPM) employing the finite-difference method with a slab structure. The bending loss in bent waveguides is analyzed for optical fields obtained from the BPM and comparisons are made between the loss for the waveguides with various radius of curvature and refractive index difference. The outward shift of the optical field, which is generated at the connection between a straight and a bent waveguide, is obtained from the results of calculation of location of the maximum optical intensity. The transition loss can be reduced by introducing an optimized inward offset at a straight-to-bend junction. The birefringence for TE and TM polarized fields in bent waveguides is calculated from the phase difference of the optical fields. The wavelength shift due to the birefringence of TE and TM polarized fields in bent waveguides is also calculated.

Generalizations of suffix arrays to multi-dimensional matrices

We propose multi-dimensional index data structures that generalize suffix arrays to square matrices and cubic matrices. Giancarlo proposed a two-dimensional index data structure, the Lsuffix tree, that generalizes suffix trees to square matrices. However, the construction algorithm for Lsuffix trees maintains complicated data structures and uses a large amount of space. We present simple construction algorithms for multi-dimensional suffix arrays by applying a new partitioning technique to lexicographic sorting. Our contributions are the first efficient algorithms for constructing two-dimensional and three-dimensional suffix arrays directly.

Generalizations of suffix arrays to multi-dimensional matrices

We propose multi-dimensional index data structures that generalize suffix arrays to square matrices and cubic matrices. Giancarlo proposed a two-dimensional index data structure, the Lsuffix tree, that generalizes suffix trees to square matrices. However, the construction algorithm for Lsuffix trees maintains complicated data structures and uses a large amount of space. We present simple construction algorithms for multi-dimensional suffix arrays by applying a new partitioning technique to lexicographic sorting. Our contributions are the first efficient algorithms for constructing two-dimensional and three-dimensional suffix arrays directly.

Two-dimensional Hurst Index of Joint Surfaces

The three-dimensional roughness morphology of joint surfaces affects their mechanical behavior. The one-dimensional joint profiles provide an incomplete and biased characterization of joint surface morphology. A two-dimensional quantitative description of surface roughness is thus needed. This paper extends the Hurst index applied on the one-dimensional profile to the two-dimensional joint surfaces. The two-variable fractal Brownian motion theory is employed successfully to describe the whole degree of roughness on the joint surface. To find this two-dimensional roughness index, two base dimensions and asperity height of the joint surface are enlarged by different ratios to achieve the requirement of statistical self-affinity properties. The Hurst index and thus fractal dimension of two joint surfaces cored from sandstone and schist is examined using the triangular-prism-surface-area method as well as this new method. It is shown that for distinguishing the whole roughness difference between these joint surfaces the new method is better. The asperity height distribution of the joint surface is Gaussian and behaves like a self-affine fractal, while the sampling points are enough. For practical application, a two-dimensional Hurst index H 2D ; that is directly expressed in the form of Fourier series represented by the profiles in two properly orthogonal directions is proposed to describe the anisotropy of a whole joint surface.

A tunable class hierarchy index for object-oriented databases using a multidimensional index structure

This paper presents a tunable two-dimensional class hierarchy indexing technique (2D-CHI) for object-oriented databases. We use a two-dimensional file organization as the index structure. 2D-CHI deals with the problem of clustering objects in a two-dimensional domain space consisting of the key attribute domain and the class identifier domain. In conventional class indexing techniques using one-dimensional index structures such as the B +-tree, the clustering property is owned exclusively by one attribute. These indexing techniques do not handle the queries that address both the attribute keys and the class identifiers efficiently. 2D-CHI enhances query performance by adjusting the degree of clustering between the key value domain and the class identifier domain based on the precollected usage pattern. For performance evaluation, we first compare 2D-CHI with the conventional class indexing techniques using an analytic cost model based on the assumption of uniform object distribution, and then, verify the cost model through experiments using the multilevel grid file as the two-dimensional index. We further perform experiments with nonuniform object distributions. The experiments show that our proposed method builds optimal class index structures in terms of the total number of page accesses for given the precollected usage pattern regardless of query types and object distributions.

Density measurements in a DC arcjet using scanned beam deflection tomography

We have demonstrated a scanned beam deflection technique, and applied this technique to imaging the free stream of a dc arcjet plasma plume. An acousto-optic deflector sweeps a HeNe beam transverse to the jet flow direction. A transform lens and split photodiode measure angular beam deflections produced by refractive index gradients in the arcjet plume. Line scans of beam deflection angle are collected at a 1 kHz sweep rate. Assuming axial symmetry, tomographic reconstruction is used convert the beam deflection data to refractive index. Multiple one-dimensional scans are stacked to produce two-dimensional refractive index images. Index of refraction is directly related to density for measurements in pure argon. Good images are obtained at chamber pressures as low as 4 Torr. Measurements were performed using both pure argon and argon / hydrogen / methane mixtures in the arcjet reactor at a variety of reactor chamber pressures including conditions for diamond deposition. We found significant differences in the radial transport with chamber pressure and with feedstock composition. Comparison of index of refraction data with photographs of arcjet optical emission shows that the emission is not a good representation of the jet density. The simplicity and sensitivity of the scanned beam deflection technique may allow its use for process control when using arcjets for plasma deposition of material.

Porous Silicon Refractive Index Lattices

Refractive index lattices with large contrast were fabricated by combining porous silicon with lateral patterning. The anodization of a p-substrate with periodically spaced n-doped regions produced a two-dimensional refractive index lattice comprised of low refractive index porous and high refractive index crystalline silicon regions. Under the lattice, the anodization proceeded not only downward but also sideways, extending a porous layer under the lattice. This porous layer acts as a bottom cladding layer to confine optical waves vertically. A higher refractive index contrast air–silicon lattice was fabricated by applying a selective etching or polishing mode anodization.