Isospectral surfaces with distinct covering spectra via Cayley graphs

The covering spectrum is a geometric invariant of a Riemannian manifold, more generally of a metric space, that measures the size of its one-dimensional holes by isolating a portion of the length spectrum. In a previous paper we demonstrated that the covering spectrum is not a spectral invariant of a manifold in dimensions three and higher. In this article we give an example of two isospectral Cayley graphs that admit length space structures with distinct covering spectra. From this we deduce the existence of infinitely many pairs of Sunada-isospectral surfaces with unequal covering spectra.     

A simple tool for speckle-shearing interferometry

A common glass plate has been shown to be an adaptable and effective tool for use in speckle-shearing interferometry. Analyses of both the imaging system and the optical-filtering arrangement have been developed. Experiments were performed successfully. The results of these experiments have shown that visible speckle correlation fringes related to the derivatives of surface displacement are obtained when a common glass plate is used as a shearing component.     

Strain-field analysis acquired through correlation of X-ray radiographs of a fiber-reinforced composite laminate

The strain fields can be determined on the surface of fiber-reinforced composites by correlation analysis of X-ray radiographs of the specimen. One radiograph is taken of the specimen in an unloaded state and another radiograph of the same specimen is taken in a deformed state. Each radiograph is then imaged by a video camera and digitized using a Matrox digitization board. The displacement map is obtained from the two radiographs by dividing one image into subsets of 20 pixels by 20 pixels and using a correlation algorithm to identify the corresponding subsets in the second image. The correlation is completed between patterns of the grey-level intensities for each subset. The appropriate discrete derivatives can then be evaluated by first difference taken to form the in-plane strains. The X-ray radiographs correlation analysis strain-field method outlined above was applied to a uniaxially loaded [90, 0] _s Gl-Ep coupon. Simultaneously, an extensometer measured the average longitudinal strain over a 2.54-cm (1-in.) gage length. The error between the two methods was less than three percent of the applied strain of 1.3 percent. The same specimen was impacted and re-examined. A radical shift in the strain field was observed when the specimen was reloaded. Further investigation showed the method reliable down to 0.5-percent strain. Paper was presented at the 1986 SEM Spring Conference on Experimental Mechanics held in New Orleans, LA on June 8–13.     

Full-field speckle pattern image correlation with B-Spline deformation function

A full-field speckle pattern image correlation method is presented that will determine directly the complete, two-dimensional deformation field during the image correlation process on digital images obtained using computer vision systems. In this work, a B-Spline function is used to represent the object deformation field throughout the entire image area. This is an improvement over subset-based image correlation methods by implicitly maintaining position and derivative continuity constraints among subsets up to a specified order. The control point variables within the B-Spline deformation function are optimized iteratively with the Levenberg-Marquardt method to achieve minimum disparity between the predicted and actual deformed images. Results have shown that the proposed method is computationally efficient, accurate and robust. The general framework of this method can be applied ton-dimensional image correlation systems that solve for multi-dimension vector fields.     

Identification of Interaction Pressure Between Structure and Explosive with Inverse Approach

An inverse approach for the identification of the time-dependent localized interaction pressure between a structure and an explosive has been proposed and developed. In this approach, surface measurements of structural response (displacement and velocity) are integrated with numerical simulations to identify the spatial and time-dependent interaction pressure (i.e. the normal traction) on a structure surface. For verification and validation purposes, numerical simulations are used to (a) generate the time-dependent displacement and velocity fields on the free surface of the specimen at specified time intervals, (b) form a blast wave and compute the resulting interaction traction field between the structure and blast wave on the interaction interface for comparison to inverse predictions. In particular, validation of the proposed approach was performed using numerical simulation results for an underwater explosion, with excellent agreement between the identified interaction traction and the simulation generated interaction traction up to and including the maximum traction condition. To demonstrate the potential of the method, the proposed inverse procedure was employed to estimate the interaction traction field on a thin aluminum specimen subjected to transient pressure loading through detonation of explosive buried in sand.     

Drone-Based StereoDIC: System Development,Experimental Validation and Infrastructure Application

Background

Digital Image Correlation (DIC) is widely used for remote and non-destructive structural health evaluation of infrastructure. Current DIC applications are limited to relatively small areas of structures and require the use of stationary stereo vision camera systems that are not easy to transfer and deploy in remote areas.

Objective

The enclosed work describes the development and validation of an Unmanned Aircraft System (UAS, commonly known as drone) with an onboard stereo-vision system capable of acquiring, storing and transmitting images for analysis to obtain full-field, three-dimensional displacement and strain measurements.

Methods

The UAS equipped with a StereoDIC system has been developed and tested in the lab. The drone system, named DroneDIC, autonomously hovers in front of a prestressed railroad tie under pressure and DIC data are collected. A stationary DIC system is used in parallel to collect data for the railroad tie. We compare the data to validate the readings from the DroneDIC system.

Results

We present the analysis of the results obtained by both systems. Our study shows that the results we obtain from the DroneDIC system are similar to the ones gathered from the stationary DIC system.

Conclusions

This work serves as a proof of concept for the successful integration of DIC and drone technologies into the DroneDIC system. DroneDIC combines the high accuracy inspection capabilities of traditional stationary DIC systems with the mobility offered by drone platforms. This is a major step towards autonomous DIC inspection in portions of a structure where access is difficult via conventional methods.

     

X‐ray speckle visibility spectroscopy in the single‐photon limit

The technique of speckle visibility spectroscopy has been employed for the measurement of dynamics using coherent X‐ray scattering. It is shown that the X‐ray contrast within a single exposure can be related to the relaxation time of the intermediate scattering function, and this methodology is applied to the diffusion of 72 nm‐radius latex spheres in glycerol. Data were collected with exposure times as short as 2 ms by employing a resonant shutter. The weak scattering present for short exposures necessitated an analysis formalism based on the spatial correlation function of individual photon charge droplets on an area detector, rather than the usual methods employed for intensity correlations. It is demonstrated that this method gives good agreement between theory and experiment and thus holds promise for extending area‐detector‐based coherent scattering methods to the study of faster dynamics than previously obtainable.     

Vibrational temperature measurements in a shock layer using laser induced predissociation fluorescence

Single shot spatially and spectrally resolved laser induced predissociation fluorescence measurements in a shock layer around a cylinder in a pulsed supersonic free stream are presented. Fluoresence signals were produced using the tuned output of an argon fluoride excimer laser to excite a mixture of rovibrational transitions in molecular oxygen. The signals produced along a line inside the shock layer were focussed onto a two dimensional detector coupled to a spectrometer, thus allowing spectral and spatial resolution of the fluoresence. In this way, it was possible to detect two fluoresence signals from two different transitions simultaneously, allowing the determination of vibrational temperatures without the need for calibration. To minimize problems associated with low signal to noise ratios, background subtraction and spatial averaging was required.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.