Unknown Geometric Parameters Research Articles

A Two-Parameter Function for Nanoscale Indentation Measurement of Near Surface Properties

A two-parameter function for estimation of projected area in instrumented indentation measurement is obtained to account for indenter tip imperfection. Imperfection near indenter tip is modeled using a spherical function and combined with a linear function describing the edge boundary of the indenter. Through an analytical fusion technique, the spherical and linear functions are combined into a single function with two unknown geometric parameters of tip radius of curvature and edge slope. Data from indentation measurement of force and displacement, using a Berkovich tip and single crystal alumina and silica samples, are implemented in the proposed area function yielding estimated values of Young’s modulus. Results were compared with that obtained from Oliver and Pharr technique for deep as well as shallow indentation regimes. The estimates for Young’s modulus were found to agree quite favorably. More importantly, in contrast to the Oliver–Pharr technique, the use of the two-parameter function resulted in a significantly more accurate estimation of Young’s modulus for shallow indentation depth of 0–50nm. The error in estimation of Young’s modulus was found to be within 10% for indentation depths of 25–50nm and within 20% for indentation depths of 0–25nm.

Optimising flow–sediment transport parameters for rivers

The unsteady flow–sediment transport equations for a real river–reservoir system contain unknown hydraulic, sediment and geometric parameters. Knowledge of these parameters and input data comprising initial and boundary conditions is required to simulate flow–sediment transport, water surface and river bed profiles. The sensitivity analysis and optimisation procedure, which involves determining these parameters by fitting a model with real river field data, is an important tool for finding the best-fit values of each parameter in a river–reservoir sediment transport model. Sensitivity analysis and optimisation methods have been found to be very useful when applied to sediment routeing problems in river–reservoir systems. This technique was employed for optimisation of some of the important parameters involved in graded sediment routeing and bed armouring processes using a non-linear coupled model (NCMG). The particular parameters studied in this investigation are degradation, bed armouring and grain size distribution of bed material in a river bed downstream of a dam. The effects of bed roughness, sediment parameters and thickness of the active layer on bed level changes are studied. A combined Gauss–Newton and modified Newton method are employed to calculate optimised parameters.

Effects of incoherent and coherent source spectral information in geoacoustic inversion.

This paper examines the effect on matched-field geoacoustic inversion of including source spectral information, as can be available in controlled-source acoustic surveys. Source information can consist of relative or absolute knowledge of the source amplitude and/or phase spectra, and can allow frequency-coherent processing of spatial acoustic-field data. A number of multi-frequency acoustic processors, appropriate for specific types of source information, are defined based on the likelihood function for complex acoustic-field data with Gaussian noise. The information content of the various processors is quantified in terms of marginal probability distributions and highest-probability density intervals for the unknown geoacoustic and geometric parameters, which define the accuracy expected in inversion. Marginal distributions are estimated using a fast Gibbs sampler approach to Bayesian inversion, which provides an efficient, unbiased sampling of the multi-dimensional posterior probability density. The analysis is illustrated for incoherent and coherent processors corresponding to several types of source knowledge ranging from complete information to no information, and the results are considered as a function of the spatial and frequency sampling of the acoustic fields.

A comparison of least-squares and Bayesian minimum risk edge parameter estimation

The problem considered here is to compare two methods for finding a common boundary between two objects with two unknown geometric parameters, such as edge position and edge orientation. We compare two model-based approaches: the least squares and the minimum Bayesian risk method. An expression is derived for the expected error as a function of radiometry. This shows that the least squares method emphasises outliers. The outliers increase the error in parameter estimation. In an experiment with edge parameter estimation, the negative aspects of least squares are detectable.

A Direct Closed-Form Solution to General Relative Orientation of Two Stereo Views

Recovering the relative geometry of two perspective stereo images is a classical problem in photogrammetry and also a basic problem in computer vision. General relative orientation refers to recovering five relative orientation parameters and two principal distances from pure image measurements. This paper presents a new direct closed-form solution to this problem. The approach recasts the explicit stereo coplanarity equation into an implicit form whose coefficients are solvable via a direct solution from the image measurements. Two principal distances, the relative baseline vector and rotation of two images are then solved successively in closed-form from these coefficients. This direct closed-form solution is useful not only in real-time implementation of stereo vision, but also for providing the approximate values of unknown geometric parameters to high-precision photogrammetry, as well as for direct functional analysis of error propagation.

On the finite element analysis of inverse problems in fracture mechanics

This paper presents a numerical study of inverse parameter identification problems in fracture mechanics. Inverse methodology is applied to the detection of subsurface cracks and to the study of propagating cracks. The procedure for detecting subsurface cracks combines the finite element method with a sequential quadratic programming algorithm to solve for the unknown geometric parameters associated with the internal flaw. The procedure utilizes finite element substructuring capabilities in order to minimize the processing and solution time for practical problems. The finite element method and non‐linear optimization are also used in determining the direction a crack will propagate in a heterogeneous planar domain. This procedure involves determining the direction that produces the maximum strain energy release for a given increment of crack growth. The procedure is applied to several numerical examples. The results of these numerical studies coincide with theoretical predictions and experimentally observed crack behavior.

Crack paths in three-dimensional elastic solids. ii: three-term expansion of the stress intensity factors—applications and perspectives

This work continues the calculation of the stress intensity factors, as a function of position s along the front of an arbitrary (kinked and curved) infinitesimal extension of some arbitrary crack on some three-dimensional body. More precisely, ε denoting a small parameter which the crack extension length is proportional to, what is studied here is the third term, proportional to ε fn2 fn2 Recall that the values of the various functions defined on the crack front are to be taken at the point s if their argument is not explicitly specified. = ε and noted K (1) ( s) ε, of the expansion of these stress intensity factors at the point s of the crack front in powers of ε. The novelties with respect to previous works due to Gao and Rice on the one hand and Nazarov on the other hand, are that both the original crack and its extension need not necessarily be planar, and that a kink (discontinuity of the tangent plane to the crack) can occur all along the original crack front. Two expressions of K (1) ( s) are obtained; the difference is that the first one is more synthetic whereas the second one makes the influence of the kink angle (which can vary along the original crack front) more explicit. Application of some criterion then allows to obtain the apriori unknown geometric parameters of the small crack extension (length, kink angle, curvature parameters). The small scale segmentation of the crack front which is observed experimentally in the presence of mode III is disregarded here because a large scale point of view is adopted; this phenomenon will be discussed in a separate paper. It is shown how these results can be used to numerically predict crack paths over arbitrary distances in three dimensions. Simple applications to problems of configurational stability and bifurcation of the crack front are finally presented.

Multi-Frequency Inversion of Synthetic Transmission Loss Data Using a Genetic Algorithm

The organizers of the Benchmark Workshop for Geoacoustic Inversion Methods (Vancouver, June 1997) produced in advance several sound propagation scenarios, simulated using the wavenumber integration model SAFARI. The simulated pressure fields were made available to all interested, while several key geoacoustic properties of their environments were kept secret. For a number of these test cases we have applied Matched-Field Inversion to determine the unknown geometric and geoacoustic parameters. A Genetic Algorithm has been used together with the normal-mode model MODELOSS as a forward model. The parameters from the benchmark tests, which the forward model was most sensitive to, were well determined in this way (water depth, source depth and range, the attenuation in the sediment layer and the velocity in the upper part of the layer). The less influential parameters were not found with the same accuracy and were often not reliable. The density in the basement may have been just a random choice.

Structure and properties of dimer, trimer and tetramer aggregates of methyltrioxorhenium (MTO): an ab initio study

We have performed ab initio Hartree-Fock self-consistent field calculations on the electronic and geometric structure of methyltrioxorhenium (MTO) and its dimers, trimer and tetramer. This latter hypothetic compound has many features in common with the recently discovered polymeric form of MTO, poly-MTO, and the present results show that the tetramer provides a model for the interpretation of the IR and Raman spectra. Based on the tetramer, we also predict some unknown geometrical parameters of poly-MTO. The Re atoms in poly-MTO exhibit an electronic structure which closely resembles that of the Re atom in the monomer. The tetramer results suggest that the negatively charged bridging oxygen atoms in the polymeric form are the best candidates for binding the excess protons present in poly-MTO.

Near-field characteristics of periodic surface relief diffraction structures from far-field measurements

Near-field characteristics of periodic surface structures, i.e. their surface relief, may be determined by measuring the diffraction efficiency, i.e. from far-field measurements, if the relief is described by a known periodic function with a few unknown geometric parameters. This method is formulated for one- and two-dimensional periodic structures and demonstrated for some holographic grating structures.

Thermo-viscous Effects in Extrusion of Planar Jets with Solidification

Abstract The present work is a study of the thermo-viscous effects in the extrusion of a “power law” liquid with temperature dependent viscosity by including the effects of solidification. This is achieved by using a novel inverse isotherm finite element method. The method is based on an inversely defined (but not inverted) formulation where the isotherms are characteristic transverse coordinate lines. The method allows the simultaneous evaluation of all the field variables as well as the apriori unknown geometric parameters. It is shown that under certain conditions the extrudate can be significantly affected by the presence of the solidification front. Results are presented for die-swell, pressure, and location of solidification as a function of the material properties.

φ-enhancement and J/ψ suppression in nuclear collisions by rescattering of secondary hadrons

We point out that recent indications from the NA38 Collaboration for an increase of the φ/(ω+ϱ 0) ratio in central 200 A GeV O+U and S+U collisions at CERN give evidence for an approach to chemical equilibrium in these systems. Under the assumption (which is supported by previous theoretical work) that the J/ψ suppression found in the same experiment under similar kinematic conditions is due to final state absorption via rescattering in the dense collision zone, we solve the rate equations for φ-production and -absorption via secondary collisions in the reaction zone. Eliminating unknown geometrical parameters of the collision zone by using the J/ψ suppression data, we obtain a quantitative description of the measured φ enhancement.

An inverse finite element method for directly formulated free boundary problems

AbstractIn free boundary problems, in addition to the primary field variables, velocity, pressure and temperature, unknown geometric parameters need to be evaluated. A characteristic feature of the problems is a demarcation line which separates two domains with different material properties. The problems are highly non‐linear and difficult to handle computationally. Here an accurate and efficient method is presented which can appropriately handle the complexities associated with these problems. The method is based on a tesselation that is constructed by isolines as characteristic co‐ordinate lines. Thus opposite sides of finite elements lie on isolines. The method allows the simultaneous determination of the location of the isolines with the primary unknowns. Its accuracy and efficiency is demonstrated in a number of one and two dimensional steady and unsteady model problems.

Comparative study of some 5- and 6-membered rings of sulfur, nitrogen and carbon or phosphorus. A quantum chemical Hartree—Fock—Slater analysis

Quantum chemical calculations are performed on various 5- and 6-membered rings of sulfur, nitrogen and carbon or phosphorus. Unknown geometrical parameters are obtained with the aid of the MNDO program and the electronic structures are discussed on the basis of the results of a Hartree—Fock—Slater routine. The electronic structures of the N 2S 2C and NSNSC rings are described, the ring N 2S 2P is proposed as a stable species and rationale is provided for the failures of the attempts to synthesize the N 3S 2C ring.

Statistical interpretation of fluorescence energy transfer measurements in macromolecular systems.

A statistical method is presented for the interpretation of intramolecular distance measurements by the fluorescence energy transfer technique in systems for which the detailed geometries of the donor-acceptor pairs are unknown. This method enables calculation of the probability that a specified distance range corresponds to the actual distance to be measured. It makes use of the numerically calculated probability density function for the distance of interest. The two general systems considered are the single donor-acceptor pair and the multi-donor-single-acceptor transfer. In both systems, the statistical method incorporates the uncertainty in the orientation of the donor and acceptor dipoles. In addition, it can take into account the rotational mobility of the donor dipoles determined by time-dependent emission anisotropy measurements. When more than one donor is involved in the transfer process, the uncertainties associated with the number and location of individual donors and the size and shape of the donor distribution are also incorporated in calculating the distance ranges. Application of the method was demonstrated for a wide range of transfer efficiency and Ro values for the single donor-acceptor system. Specific examples are also presented for interpretation of both single donor-acceptor and multi-donor-single-acceptor energy transfer measurements performed in order to reveal the spatial relationship of the sigma subunit and the rifampicin binding site in the Escherichia coli RNA polymerase (see Wu, C.-W., Yarbrough, L. R., Wu, F. Y.-H., and Hillel, Z. (1976), Biochemistry, preceding paper in this issue). Analysis of these energy transfer data by methods which use average values of the unknown geometrical parameters of the system yielded results similar to those obtained by the statistical method. However, the statistical method represents a more realistic approach to the interpretation of energy transfer measurements since it provides information concerning the entire range of possible distances and their relative likelihood.

On a Set of Continuous Wave Electromagnetic Inverse Scattering Boundary Conditions

The inverse problem of continuous wave electromagnetic scattering is considered. The shape and the material constituents of an unknown scatterer need to be determined from bistatic measurement data for a given transmitted field. Although methods have been outlined on how to determine the material constituents of a semi-transparent scatterer, no suitable method has been found which may be employed to simultaneously specify the shape and the material constituents of an unknown smooth, convex-shaped, close, and imperfectly conducting scatterer. Namely, such boundary conditions are sought which do not depend on either the shape or the material constituents of the scattering body and its enclosing surface, but allow one to specify the relevant characteristic parameters uniquely from the recovered near field.The main incentive of this study is to show that the unknown geometrical and material surface parameters can be determined from a set of equations which is derived from the Leontovich impedance boundary condition. The resulting inverse scattering boundary conditions are analyzed in detail and it is shown that in the perfectly conducting case these boundary conditions degenerate to those conditions investigated by Weston and Boerner.The theoretical analysis is verified by computation proving the importance of the result to the inverse theory of electromagnetic scattering.