Inverse scattering of Hz waves using local shape-function imaging: A T-matrix formulation

Inverse scattering algorithms for H_z polarized waves are scarce, due to the added difficulties of polarization charges. Nevertheless, the polarization charges cannot be ignored for 3D problems as well as for 2D H_z problems. This work aims to reconstruct arbitrary inhomogeneous dielectric objects from H_z scattering data using a new formulation that abandons the standard integral equation model for a T-matrix model. This new algorithm, called local shape-function (LSF) imaging, is modified for dielectric objects with H_z incident fields, where previously the LSF algorithm was applied to metallic objects with E_z incident fields. The advantage of the LSF algorithm is a more accurate modeling of the induced interfacial polarization charges. For comparison, the H_z distorted Born iterative method using integral equations is shown to be valid only for small contrasts, while the LSF algorithm converges for much larger dielectric contrasts.©1994 John Wiley & Sons Inc     

Modeling of dispersion and nonlinear characteristics of tapered photonic crystal fibers for applications in nonlinear optics

In this article, we investigate for the first time the dispersion and the nonlinear characteristics of the tapered photonic crystal fibers (PCFs) as a function of length z, via solving the eigenvalue equation of the guided mode using the finite-difference frequency-domain method. Since the structural parameters such as the air-hole diameter and the pitch of the microstructured cladding change along the tapered PCFs, dispersion and nonlinear properties change with the length as well. Therefore, it is important to know the exact behavior of such fiber parameters along z which is necessary for nonlinear optics applications. We simulate the z dependency of the zero-dispersion wavelength, dispersion slope, effective mode area, nonlinear parameter, and the confinement loss along the tapered PCFs and propose useful relations for describing dispersion and nonlinear parameters. The results of this article, which are in a very good agreement with the available experimental data, are important for simulating pulse propagation as well as investigating nonlinear effects such as supercontinuum generation and parametric amplification in tapered PCFs.     

Multifrequency backscattering tomography for constant and vertically varying backgrounds

To improve the resolution and image quality of the SFDT (Sigle-Frequency Diffraction Tomography), a special fast multi-frequency imaging method: Multi-Frequency Backscattering Tomography (MFBT) is introduced in this paper. The method uses only the backscattered waves (after plane wave decomposition) while maintaining the merit of multi-frequency method. The method is formulated for both the constant and vertically varying backgrounds. For the latter case the WKBJ approximation is used for the background Green's function. Formulas are derived both for volume scattering using the Born approximation and for boundary scattering using the physical optics approximation. Two reconstruction methods are presented. The backpropagation method can be used and has the same computation speed for both the constant and vertically varying backgrounds. Meanwhile the direct FT method is only formulated for the constant background, in which the backpropagation in z-direction is implemented by FFT and therefore the computation speed is significantly increased. Compared with the SFDT using backpropagation reconstruction, the MFBT is nearly N_z/log₂N_z faster, where N_z is the number of grid points in z-direction, and at the same time has a much better resolution and image quality. When N_z is big, the time saving is remarkable. Compared with other multi-frequency methods such as the multi-frequency holography (prestack migration), the speeding factor becomes N_fN_z/log₂N_z, where N_f, is the number of frequencies used. Numerical simulations for both constant and vertically varying backgrounds are performed to demonstrate the feasibility of the method and the quality of reconstructed images for different situations. Examples are also given to show that when the reconstruction procedure of constant background is applied to the case of vertically varying background, the image quality will be greatly deteriorated.©1994 John Wiley & Sons Inc     

Rank-based ant colony optimization applied to dynamic traveling salesman problems

This study proposes a rank-based ant colony optimization (ACO) method with a rank-based nonlinear selective pressure function and a modified Q-learning method to enhance the convergence characteristics of original ACO Dorigo et al., which defines the probability of exploring a city to be visited by ants with a random proportional rule. This probability distribution of the random proportional rule, which is similar to that of the stochastic universal sampling method generally applied to the selection operation in genetic algorithms, is good for exploring favorable paths in small traveling salesman problems (TSPs), but inefficient at exploring such paths in large TSPs. Therefore, this study presents the rank-based nonlinear selection pressure function, based on ranking of [τ (r, z)][η (r, z)]^β, to improve the performance of the state transition rule of the original ACO, as well as a modified Q-learning method to solve reinforcement learning problems efficiently. The modified Q-learning method, which incorporates a constant pheromone trail distribution with standard Q-learning, can yield a solution effectively when applied in the local-updating rule of an ACO. In this article, the optimal settings for the control parameters (q) used in the rank-based selective pressure function and the discounted factor (γ) associated with modified Q-learning were investigated numerically using a benchmark St70 case of the static TSP. Furthermore, the improved ACO was applied to the static TSP of the KroA100 case and a route programing with 532 nodes. This study also applied the rank-based ACO to solve dynamic TSPs. By introducing the rank-based nonlinear selective pressure function and the modified Q-learning model into the original ACO, the presented rank-based ACO algorithm effectively explores paths affected by a change in the environment. In this work, the environment changes are traffic jams and road closures between cities, which sometimes force the salesman to change his route.     

Criterion for the onset of ostwald ripening stage with allowance for the particle number fluctuations in a nucleus

A theory of condensation is proposed for an open system in which the growth rate varies with the number of particles and the total particle concentration (supersaturation flux) varies with the time as described by power laws with arbitrary exponents (indices). It is established that the distribution of nuclei with respect to their sizes z, which is formed at the nucleation stage, is subject to fluctuational blurring. The dependence of the distribution width on the average size z is related in a nontrivial manner to the values of the growth and flux indices. Conditions for the onset of the Ostwald ripening (OR) stage in the system are analyzed with allowance for fluctuations in the number of particles. It is shown that the Kukushkin-Osipov criterion remains valid, since the transition curve occurs in a region where the distribution width grows slower than z. At the same time, the form of the initial condition and the character of evolution of the distribution at the OR stage significantly vary under the action of fluctuations.     

Root neighborhoods, generalized lemniscates, and robust stability of dynamic systems

A root neighborhood (or pseudozero set) of a degree-n polynomial p(z) is the set of all complex numbers that are the roots of polynomials whose coefficients differ from those of p(z), under a specified norm in , by no more than a fixed amount . Root neighborhoods corresponding to commonly used norms are bounded by higher-order algebraic curves called generalized lemniscates. Although it may be neither convenient nor useful to derive their implicit equations, such curves are amenable to graphical analysis by means of simple contouring algorithms. Root neighborhood methods offer advantages over alternative approaches (the Kharitonov theorems and their generalizations) for investigating the robust stability of dynamic systems with uncertain parameters, since they offer valuable insight concerning which roots of the characteristic polynomial will become unstable first, and the relative importance of parameter variations on the root locations—and hence speed and damping of the system response. We derive a generalization of root neighborhoods to the case of polynomial coefficients having an affine linear dependence on a set of complex uncertainty parameters, bounded under a general weighted norm, and we discuss their applications to robust stability problems. The methods are illustrated by several computed examples.     

Taylor vortices between almost cylindrical boundaries

Summary We consider a modified Taylor problem, with the fluid flowing between a rotating inner circular cylinder and an outer stationary surface whose radius is a constant plus a small and slowly varying function of the axial co-ordinate z. This variation is chosen in such a way that the flow is locally more unstable near z=0 than near z=±, so that Taylor vortices appear more readily near z=0. The theory is developed to show how vortices of strength varying with z develop as the speed of rotation is increased through a critical value which is a perturbation of the classical value. Wave number changes in the axial direction are also calculated.     

A relationship between diffusion and charge transfer parameters in a binary melt formed during contact melting

Theoretical and experimental data on the mass and charge transfer, charge transfer during contact melting, and hydrodynamic mixing of inert labels introduced into a contact between two dissimilar metals are analyzed and an integral criterion for the charge and mass transfer direction in this system is formulated. According to this criterion, which is valid in all the known binary systems of this type, (Ω₁–Ω₂)(D ₁–D ₂)]=−z ₁*–z ₂*, where Ω_i, D _i , and z _i * are the atomic volumes, partial diffusion coefficients, and effective charges of light (i=1) and heavy (i=2) components.     

Anisotropic superconductivity in the two-dimensional Hubbard model

We address the problem of anisotropic superconductivity in the two-dimensional Hubbard model. The Eliashberg equations have been generalized to the case which accounts for the anisotropy of the order parameter. Strong local correlations are treated within the mean field slave boson approximation. The superconducting transition temperatureT _c is evaluated as a function of the occupation number. Our results indicate that thed-wave state is the most likely channel for superconductivity for small concentration of holes. We have also derived an approximate analytical formula forT _c valid for any value of the occupation number. In addition, the influence of strong correlations on the electron-phonon coupling function is also discussed.     

A Simple Method for Calculating the Stress Intensity Factor of a One-Sided Reinforced Crack

A simple method is suggested to calculate the stress intensity factor for a one-sided reinforced crack using the spring constant as a function of the through-thickness coordinate z. The present results coincide very well with three-dimensional finite element results( Wang, et al., 1998).     

Torsion by a circular die of a nonhomogeneous elastic layer bonded to a nonhomogeneous half-space

The title problem is equivalent to a torsional mixed boundary value problem in the theory of elasticity in which the only non-zero displacement component is specified inside the circular area r ? l and the shearing stress σ_θz, is zero in the area r > 1 on the face z = 0; the continuity of the displacement and the shearing stress σ_θz is assumed at the interface z = h between the layer and the half-space having different modulii of rigidity. The modulii of rigidity are assumed to be continuous functions of 2. The problem is reduced to the solution of a Fredholm integral equation of the second kind whose iterative solution has been obtained valid for values of h >l, for a few particular cases. Expression for the torque T required to rotate the die through an angle ω has been obtained for the general as well as particular cases.     

A NEW FINITE ELEMENT FORMULATION FOR PLANAR ELASTIC DEFORMATION

For the stress analysis of planar deformable bodies, we usually refer to either plane stress or plane strain hypothesis. Three-dimensional analysis is required when neither hypothesis is applicable, e.g. bodies with finite thickness. In this paper, we derive an ‘exact’ solution for the plane stress problem based on a less restrictive hypothesis than σ_z=0. By requiring the out-plane stress σ_z to be a harmonic function, the three-dimensional solution is obtained. In addition, we present a two-dimensional finite element for planar analysis of problems where the thickness of the body 2h is comparable to other characteristic dimensions. This element is presented as a substitute for classical plane stress and plane strain finite elements. The typical plane stress and plane strain state are recovered in the case where h→0 and the case h→∞, respectively. As an example for the application of such formulation, the behaviour of a concrete gravity dam is investigated. It is shown that this structure, typically analysed by using plane strain hypothesis, has its out-plane stress underestimated. © 1997 John Wiley & Sons, Ltd.     

The numerical solution of two generalizations of the neumann moving interface problem into two dimensions

We present numerical solutions for the following Stefan problems. The half-space z > 0 is initially filled with liquid at its fusion temperature. The boundary z = 0, taken to be the x axis, is maintained at a constant temperature, less than the fusion temperature, for x < 0. For x > 0, the first problem considers the case of an insulated boundary, and the second problem considers the case of the boundary maintained at the fusion temperature. This gives rise to a solid-liquid interface curved in the (x , z ) plane.     

The exact form of caustics in mixed-mode fracture: A comparison with approximate solutions

Summary The form of caustics created by stress singularities in elastic problems was up-to-now derived from the Sneddon expressions for the components of stresses at the point of singularity, which are based on the first and singular term of the series expansion of the Muskhelishvili complex stress function. In this paper the closed from expression for the Muskhelishvili complex stress function (z) was used to define the exact form of the caustic. Moreover, the forms of the caustics were constructed for several terms, besides the first one, in the Taylor expansion of (z).The approximate forms with the singular term of (z) and several terms of the Taylor expansion of (z) were compared with the form derived from the exact solution. The discrepancies between exact and approximate solutions were evaluated for the case of a slant crack in an infinite plate under in-plane biaxial loading where theK _I andK _II -mode stress intensity factors were compared as derived from the various solutions. It was concluded that, although the method of caustics yields superior results than any other experimental method, it is possible to improve these results by using either the exact solution for the particular problem, or higher order approximations.With 11 Figures     

Geodesic Gaussian Processes for the Parametric Reconstruction of a Free-Form Surface

Reconstructing a free-form surface from 3-dimensional (3D) noisy measurements is a central problem in inspection, statistical quality control, and reverse engineering. We present a new method for the statistical reconstruction of a free-form surface patch based on 3D point cloud data. The surface is represented parametrically, with each of the three Cartesian coordinates (x, y, z) a function of surface coordinates (u, v), a model form compatible with computer-aided-design (CAD) models. This model form also avoids having to choose one Euclidean coordinate (say, z) as a “response” function of the other two coordinate “locations” (say, x and y), as commonly used in previous Euclidean kriging models of manufacturing data. The (u, v) surface coordinates are computed using parameterization algorithms from the manifold learning and computer graphics literature. These are then used as locations in a spatial Gaussian process model that considers correlations between two points on the surface a function of their geodesic distance on the surface, rather than a function of their Euclidean distances over the xy plane. We show how the proposed geodesic Gaussian process (GGP) approach better reconstructs the true surface, filtering the measurement noise, than when using a standard Euclidean kriging model of the “heights”, that is, z(x, y). The methodology is applied to simulated surface data and to a real dataset obtained with a noncontact laser scanner. Supplementary materials are available online.     

A new method of accurate polarization measurement on isobaric analog resonance to detect parity non-conservation effect

For the study of parity mixing in the compound states, a method to measure the longitudinal analyzing power A_z of the isobaric analog resonance (IAR) as a function of energy in the proton elastic scattering is discussed. A thick target is used and energy loss of the protons in the target is utilized to measure the energy dependence. The energy resolution is presented and the sources of the systematic errors in A_z are discussed together with the way of their elimination. The method has been shown to be quite efficient for deriving both the transverse and the longitudinal analyzing powers. The measurement of A_z for the s-wave IAR at E_cm=5.86 MeV in ⁹⁰Zr(p,p) and the analysis to derive PNC matrix elements are described.     

Impulse Modeling of the Rayleigh Wave Propagation Generated by a Spherical Focused Transducer

In order to characterize materials locally by means of the Rayleight wave analysis, a new modeling of acoustic microscopy in the case of an impulse excitation is presented. The usualV(z) representation established for a given frequency component, is extended to the case of a broadband excitation of the transducer. Therefore, the time-dependant acoustic response of the material,s(z,t), is mainly composed of two echoes: the specular and the Rayleigh contributions which are resolved in time. In the first part, we demonstrate that the acoustic response can be represented by the time convolution product between the acoustic signal detected at the focus on an ideal reflector, and a function depending onz andt variables. This last function is connected to the tranducer emission profile, which includes the diffraction effects, and the reflectance of the material. In the second part, the modeling is discussed with regard to experimental data on several materials and takes into account the attenuation phenomena. Experimental results and computations are shown to be in a good agreement.     

A SINGLE EXPRESSION FORMULA FOR INVERTING STRAIN-LIFE AND STRESS-STRAIN RELATIONSHIPS

Starting with the basic fatigue life formula Δε/Δε_T= (N_f/N_T)^b+ (N_f/N_T)^c an inversion formula is derived in the form N _f/N_T= [(Δε/Δε_T)^z/b+ (Δε/Δε_T)^z/c]^1/z where z is a function of strain range and the ratio c/b. The inversion formula is valid over the entire life range of engineering interest for all materials examined. Conformity between the two equations is extremely close, suitable for all engineering problems. The approach used to invert the life relation is also suitable for the inversion of other formulas involving the sum of two power-law terms.     

Stress-intensity factors of r-cracks in fiber-reinforced composites under thermal and mechanical loading

This paper is concerned with the problem of the calculation of stress-intensity factors at the tips of radial matrix cracks (r-cracks) in fiber-reinforced composites under thermal and/or transverse uniaxial or biaxial mechanical loading. The crack is either located in the immediate vicinity of a single fiber or it terminates at the interface between the fiber and the matrix. The problem is stated and solved numerically within the framework of linear elasticity using Erdogan's integral equation technique. It is shown that the solutions for purely thermal and purely mechanical loading can simply be superimposed in order to obtain the results of the combined loading case. Stress-intensity factors (SIFs) are calculated for various lengths and distances of the crack from the interface for each of these loading conditions. The behavior of the SIFs for cracks growing towards or away from the interface is examined. The role of the elastic mismatch between the fibers and the matrix is emphasized and studied extensively using the so-called Dundurs' parameters. It is shown that an r-crack, which is remotely located from the fiber, can either be stabilized or destabilized depending on both the elastic as well as the thermal mismatch of the fibrous composite. Furthermore, Dundurs' parameters are used to predict the exponent of the singularity of the crack tip elastic field and the behavior of the corresponding SIFs for cracks which terminate at the interface. An analytical solution for the SIFs is derived for all three loading conditions under the assumption that the elastic constants of the matrix and the fiber are equal. It is shown that the analytical solution is in good agreement with the corresponding numerical results. Moreover, another analytical solution from the literature [15], which is based upon Paris' equation for the calculation of stress-intensity factors, is compared with the numerical results and it is shown to be valid only for extremely short r-cracks touching the interface. The numerical results presented are valid for practical fiber composites with r-cracks close to or terminating at the interface provided the matrix material is brittle and the crack does not interact with other neighboring fibers. They may be applied to predict the transverse mechanical behavior of high strength fiber composites.     

Fast matrix exponent for deterministic or random excitations

The solution of ż=Az is z(t)=exp(At)z₀=E_tz₀, z₀=z(0). Since z(2t)=E_2tz₀=Ez₀, z(4t)=E_4tz₀=Ez₀, etc., one function evaluation can double the time step. For an n‐degree‐of‐freedoms system, A is a 2n matrix of the nth‐order mass, damping and stiffness matrices M, C and K. If the forcing term is given as piecewise combinations of the elementary functions, the force response can be obtained analytically. The mean‐square response P to a white noise random force with intensity W(t) is governed by the Lyapunov differential equation: Ṗ=AP+PA^T+W. The solution of the homogeneous Lyapunov equation is P(t)=exp(At) P₀ exp(A^Tt), P₀=P(0). One function evaluation can also double the time step. If W(t) is given as piecewise polynomials, the mean‐square response can also be obtained analytically. In fact, exp(At) consists of the impulsive‐ and step‐response functions and requires no special treatment. The method is extended further to coloured noise. In particular, for a linear system initially at rest under white noise excitation, the classical non‐stationary response is resulted immediately without integration. The method is further extended to modulated noise excitations. The method gives analytical mean‐square response matrices for lightly damped or heavily damped systems without using modal expansion. No integration over the frequency is required for the mean‐square response. Four examples are given. The first one shows that the method include the result of Caughy and Stumpf as a particular case. The second one deals with non‐white excitation. The third finds the transient stress intensity factor of a gun barrel and the fourth finds the means‐square response matrix of a simply supported beam by finite element method. Copyright © 2001 John Wiley & Sons, Ltd.