Electromagnetic Sensor Arrays— Experimental Studies

The objectives of this research program are to develop the theoretical models, design methodology, and technology needed for the optimum application of near-field electromagnetic sensor arrays in NDE and robot control. A basic requirement for this work is to be able to analyze and control the spatial-frequency content in the field configuration generated by the array. To aid in understanding how best to satisfy this requirement, initial efforts at SRI have focused on obtaining experimental measurements of the relative spatial distributions associated with the responses of eddy-current reflection probes to surface steps and surface-breaking rectangular slots in aluminum plates. This paper presents the results obtained using a commercial reflection probe (Nortec SPO-2065) and an SRI-constructed five-coil, air-core reflection probe to interrogate such surface discontinuities. The data obtained with the five-coil probe are then compared with the results of a theory for the spatial response of such a probe that has been developed at Stanford University [1]

Microwave NDE of Ceramics

The objective of this work is to evaluate the potential of microwave techniques for detecting, classifying, and determining the dimensions of inclusions and surface cracks in structural ceramics such as Si3N4. Experimental results that show the feasibility of detecting various types of inclusions and voids in Si3N4 have been obtained, and these results are reviewed. In addition, the question of the quantitative capability of microwave NDE for this application is discussed

Microwave Eddy-Current Techniques for Quantitative NDE

The objectives of this work are to develop an electromagnetic scattering model that can be used to predict the scattering from a crack in a conducting surface and to evaluate the feasibility of using this model in conjunction with microwave-measurement techniques to determine the dimensions of such a crack. Such a theory has been developed, and its derivation is presented. Theory and experiment are compared for rectangular slots measured at 100 GHz, and the agreement is found to be good. The necessary measurement protocol for determining the dimensions of a crack is discussed, and an example of inverting the measured data to determine the dimensions of a rectangular slot is presented

Microwave Techniques for NDE of Ceramics

In recent years, the technology for generating and controlling electromagnetic energy at frequencies of 100 GHz and above has improved considerably, and such components are now readily available. In view of this fact, we have undertaken a program to assess the applicability of this technology to the NDE of ceramic materials and components. We have found that Si3N4 is nearly transparent at these high frequencies, which permits the interior of components made from this material to be inspected using microwave energy. The dielectric constant of hot-pressed Si3N4 is about 7.5, so the wavelength in this material at 100 GHz is about 1mm. This electromagnetic wavelength is comparable to the acoustic wavelength of 10 MHz ultrasound in this material. Thus, microwave C-scan images will have resolutions roughly comparable to those produced by commercial ultrasonic equipment, but do not require the use of a water bath or other coupling medium in order to achieve rapid scanning. In addition, electromagnetic and ultrasonic scattering will differ for a given flaw, and thus microwave imaging may provide better flaw discrimination in some cases

Quantitative Measurement of Crack Parameters Using Microwave Eddy-Current Techniques

The objectives of this work were to develop an electromagnetic scattering model that can be used to predict the microwave scattering from a crack in a metallic surface, and to evaluate the potential of using microwave scattering measurements to determine the dimensions of the crack. The initial approach to this problem has been to model the surface crack as a section of rectangular waveguide shorted at one end. Theoretical and experimental results are presented for this case, and the potential for obtaining a quantitative evaluation of the crack dimensions is discussed

From covariant to canonical formulations of discrete gravity

Starting from an action for discretized gravity we derive a canonical formalism that exactly reproduces the dynamics and (broken) symmetries of the covariant formalism. For linearized Regge calculus on a flat background -- which exhibits exact gauge symmetries -- we derive local and first class constraints for arbitrary triangulated Cauchy surfaces. These constraints have a clear geometric interpretation and are a first step towards obtaining anomaly--free constraint algebras for canonical lattice gravity. Taking higher order dynamics into account the symmetries of the action are broken. This results in consistency conditions on the background gauge parameters arising from the lowest non--linear equations of motion. In the canonical framework the constraints to quadratic order turn out to depend on the background gauge parameters and are therefore pseudo constraints. These considerations are important for connecting path integral and canonical quantizations of gravity, in particular if one attempts a perturbative expansion.Comment: 37 pages, 5 figures (minor modifications, matches published version + updated references

From the discrete to the continuous - towards a cylindrically consistent dynamics

Discrete models usually represent approximations to continuum physics. Cylindrical consistency provides a framework in which discretizations mirror exactly the continuum limit. Being a standard tool for the kinematics of loop quantum gravity we propose a coarse graining procedure that aims at constructing a cylindrically consistent dynamics in the form of transition amplitudes and Hamilton's principal functions. The coarse graining procedure, which is motivated by tensor network renormalization methods, provides a systematic approximation scheme towards this end. A crucial role in this coarse graining scheme is played by embedding maps that allow the interpretation of discrete boundary data as continuum configurations. These embedding maps should be selected according to the dynamics of the system, as a choice of embedding maps will determine a truncation of the renormalization flow.Comment: 22 page