Attenuation of Solitary Waves and Localization of Breathers in 1D Granular Crystals Visualized via High Speed Photography

We investigate the propagation, attenuation, and localization of nonlinear elastic waves in a 1D granular crystal using high speed photography. We measure temporal displacement profiles of individual particles with a micrometer-scale resolution, and we reconstruct force profiles of propagating solitary waves and localized breathers by synchronizing and analyzing the acquired data. These investigations provide quantitative evidence for the transmission and attenuation trends of travelling solitary waves in a soft polymeric chain, which are significantly different from those in a hard metallic chain. We additionally study energy localization in a chain of hard particles embedded with a soft polymeric impurity. Specifically, we show that the proposed experimental technique is able to visualize the formation of localized breathers and quantify the energy highly concentrated in the vicinity of the impurity site—a phenomenon which can be exploited for harvesting vibrational energy in engineering applications. Finally, we compare, with good agreement, the experimental results with discrete element numerical simulations that account for dissipative effects due to viscoelasticity. The findings reported in this study imply that high speed photography can be an efficient and effective tool for non-contact measurements of nonlinear wave dynamics in granular lattices, despite their short characteristic times and minute displacements.     

Recent Progress in Digital Image Correlation: Background and Developments since the 2013 W M Murray Lecture

Since presentation of the 2013 Murray Lecture focusing on developments in digital image correlation (DIC), the methods have continued to expand internationally and their use has begun to grow in fields where there was less activity in the past. First, a brief history of digital image correlation methods is presented from the perspective of the first author, followed by a discussion of recent trends associated with the use of digital image correlation methods in academics, governmental laboratories and industrial settings. In the remainder of the article, new results are provided in three areas where DIC methods have seen rapid growth; application of StereoDIC or three-dimensional DIC (3D-DIC) to the study of wall structures in civil engineering; the use of Volumetric DIC or Digital Volume Correlation (DVC) to quantify the internal response of a specially-designed composite material and in the area of model validation for another application in civil engineering; transfer length measurements in pre-stressed concrete beams.     

Development of Patterns for Digital Image Correlation Measurements at Reduced Length Scales

Methods for patterning metal thin films at the microscale and nanoscale by applying the patterns to metallic and polymeric materials for use in shape and deformation measurements in a scanning electron microsope (SEM) or other high magnification imaging system are described. In one approach, thin films of metallic materials (e.g., Au, Ag, Cu, and Cr) are applied to a variety of substrates. The coated samples are then placed into a reaction vessel, where the specimens are heated and exposed to a nitrogen atmosphere saturated with selected volatile chemicals. This process results in nano-scale remodeling of the metallic films, thereby affording high contrast random patterns with different morphologies. In a second approach, thin films of metallic materials, including gold and silver, also have been applied using a simplified UV photolithographic method requiring a minimum amount of laboratory preparation. Using selected substrates, both methods have been used successfully to transfer patterns onto polymeric and metallic materials ranging from 50–500 nanometers with chemical vapor rearrangement and 2 to 20 microns with UV photolithography, providing a pattern that can be used with digital image correlation to quantify both the surface profile and also surface deformations at reduced length scales.     

Determination of elastic-plastic stresses and strains from measured surface strain data

A rigorous approach founded in the fundamental principles of plasticity is used to develop an accurate numerical algorithm for the determination of stresses and elastic and plastic strains from total strain data measured on a structure surface. The approach used to develop the algorithm and its relationship to both the flow theory of plasticity and recent advances in tangent stiffness-based numerical solution procedures for elastic-plastic boundary value problems are presented. Verification of the method for plane stress problems is demonstrated. A discussion of how the method can be used with measured surface displacement data is proved.     

Assessment of High Speed Imaging Systems for 2D and 3D Deformation Measurements: Methodology Development and Validation

Ultra high-speed and moderate speed image acquisition platforms have been characterized, with special emphasis on the variability and accuracy of the measurements obtained when employed in either 2D or 3D computer vision systems for deformation and shape measurements. Specifically, the type of image distortions present in both single channel cameras (HS-CMOS) and multi-channel image intensified cameras (UHS-ICCD) are quantified as part of the overall study, and their effect on the accuracy of experimental measurements obtained using digital image correlation have been determined. Results indicate that established methods for noise suppression and recently developed models for distortion correction can be used effectively in situations where the primary intensity noise components are characterized by minimal cross-talk and stationary spatial distortions. Baseline uniaxial tension experiments demonstrate that image correlation measurements using high speed imaging systems are unbiased and consistent with independent deformation measurements over the same length scale, with point-to-point strain variations that are similar to results obtained from translation experiments. In this study, the point-to-point variability in strain using the image intensified system is on the order of 0.001, whereas the non-intensified system had variability of 0.0001. Results confirm that high speed imaging systems can be utilized for full field two and three-dimensional measurements using digital image correlation methods.

Parton distribution functions at LO,NLO and NNLO with correlated uncertainties between orders

Sets of parton distribution functions (PDFs) of the proton are reported for the leading (LO), next-to-leading (NLO) and next-to-next-to-leading-order (NNLO) QCD calculations. The parton distribution functions are determined with the HERAFitter program using the data from the HERA experiments and preserving correlations between uncertainties for the LO, NLO and NNLO PDF sets. The sets are used to study cross-section ratios and their uncertainties when calculated at different orders in QCD. A reduction of the overall theoretical uncertainty is observed if correlations between the PDF sets are taken into account for the ratio of \(WW\) di-boson to \(Z\) boson production cross sections at the LHC.     

Direct measurement of microstructural avalanches during the martensitic transition of cobalt using coherent x-ray scattering

Heterogeneous microscale dynamics in the martensitic phase transition of cobalt is investigated with real-time x-ray scattering. During the transformation of the high-temperature face-centered cubic phase to the low-temperature hexagonal close-packed phase, the structure factor evolution suggests that an initial rapid local transformation is followed by a slower period during which strain relaxes. Coherent x-ray scattering measurements performed during the latter part of the transformation show that the kinetics is dominated by discontinuous sudden changes-avalanches. The spatial size of observed avalanches varies widely, from 100 nm to 10 μm, the size of the x-ray beam. An empirical avalanche amplitude quantifies this behavior, exhibiting a power-law distribution. The avalanche rate decreases with inverse time since the onset of the transformation.     

Cyclometalated iridium-coumarin ratiometric oxygen sensors: improved signal resolution and tunable dynamic ranges

In this work we introduce a new series of ratiometric oxygen sensors based on phosphorescent cyclometalated iridium centers partnered with organic coumarin fluorophores. Three different cyclometalating ligands and two different pyridyl-containing coumarin types were used to prepare six target complexes with tunable excited-state energies. Three of the complexes display dual emission, with fluorescence arising from the coumarin ligand, and phosphorescence from either the cyclometalated iridium center or the coumarin. These dual-emitting complexes function as ratiometric oxygen sensors, with the phosphorescence quenched under O₂ while fluorescence is unaffected. The use of blue-fluorescent coumarins results in good signal resolution between fluorescence and phosphorescence. Moreover, the sensitivity and dynamic range, measured with Stern–Volmer analysis, can be tuned two orders of magnitude by virtue of our ability to synthetically control the triplet excited-state ordering. The complex with cyclometalated iridium ³MLCT phosphorescence operates under hyperoxic conditions, whereas the two complexes with coumarin-centered phosphorescence are sensitive to very low levels of O₂ and function as hypoxic sensors.

Cyclometalated iridium(iii) coumarin complexes with improved signal resolution for ratiometric oxygen sensing are described. Dynamic ranges are tunable over >2 orders of magnitude.     

Free energies of interfaces from quasi-harmonic theory: A critical appraisal

A critical assessment is given of the quasi-harmonic approximation, and various approximations to the quasi-harmonic approximation, with regard to predicting the free energy and atomic structure of grain boundaries in silicon at elevated temperatures. The quasi-harmonic results are compared with those obtained by molecular dynamics and thermodynamic integration. It is found that the quasi-harmonic approximation yields accurate excess free energies and atomic structures of grain boundaries at 1,000 K. The anharmonic contribution to the free energy that is absent in the quasi-harmonic contribution is virtually the same at a grain boundary in Si and in the perfect crystal. The second-moment and Einstein approximations to the full quasi-harmonic theory yield unreliable free energies, but reasonably accurate atomic structures. However, excess free energies are quite well described by the Einstein model. It is concluded that the quasi-harmonic approximation works remarkably well in silicon. The simplest approximations to the phonon density of states lead to unreliable results for the free energy, but cancellation of errors occurs to a large extent when excess free energies are computed.