The propagation of elastic waves in a certain class of inhomogeneous anisotropic materials. I. The refraction of a horizontally polarized shear wave source

1992 ◽  
Vol 436 (1898) ◽  
pp. 449-478 ◽  
Keyword(s):  
Shear Wave ◽  
Isotropic Material ◽  
Displacement Vector ◽  
Transversely Isotropic ◽  
Constitutive Law ◽  
Coarse Grained ◽  
Wave Source ◽  
Uniform Asymptotic Expansion ◽  
Wide Range ◽  
Steel Welds

This paper is the first in a series of articles describing the refraction and propagation of infinitesimal disturbances in a 'coarse grained’ inhomogeneous anisotropic material which is fused to an isotropic substrate. Here, the basic constitutive law for the material is motivated by applications to the non-destructive evaluation of austenitic steel welds, although it is clear that the phenomena described and the mathematical analysis used is also of interest in geophysics, the study of composite materials and several other areas of continuum mechanics. This work is concerned with the refraction of a horizontally polarized shear wave source at the fusion interface between a homogeneous isotropic material and transversely isotropic material. The latter is inhomogeneous by virtue of the fact that the zonal axis or axis of symmetry of the crystals varies in direction with the distance from the interface. The mathematical boundary-value problem is solved exactly, and, in the highfrequency limit, a uniform asymptotic expansion for the displacement vector is found. It is shown that in this limit, and for a wide range of material constants, the refracted energy which penetrates certain regions of the ‘weld material’ is totally internally reflected. This conclusion is highly significant in the design of inspection procedures for structurally important welds.

A Constitutive Law for Mitral Valve Tissue

1998 ◽  
Vol 120 (1) ◽  
pp. 38-47 ◽  
Author(s):  
K. May-Newman ◽  
F. C. P. Yin
Keyword(s):  
Mitral Valve ◽  
Transversely Isotropic ◽  
Quantitative Information ◽  
Substantial Improvement ◽  
Material Behavior ◽  
Constitutive Law ◽  
Highly Nonlinear ◽  
Wide Range ◽  
Mechanical Models ◽  
Biaxial Mechanical Testing

Biaxial mechanical testing and theoretical continuum mechanics analysis are employed to formulate a constitutive law for cardiac mitral valve anterior and posterior leaflets. A strain energy description is formulated based on the fibrous architecture of the tissue, accurately describing the large deformation, highly nonlinear transversely isotropic material behavior. The results show that a simple three-coefficient exponential constitutive law provides an accurate prediction of stress–stretch behavior over a wide range of deformations. Regional heterogeneity may be accommodated by spatially varying a single coefficient and incorporating collagen fiber angle. The application of this quantitative information to mechanical models and bioprosthetic development could provide substantial improvement in the evaluation and treatment of valvular disease, surgery, and replacement.

scholarly journals Three-dimensional Shear Wave Elastography Using a 2D Row Column Addressing (RCA) Array

2021 ◽  
Author(s):  
Zhijie Dong ◽  
Jihun Kim ◽  
Chengwu Huang ◽  
Matthew R. Lowerison ◽  
Shigao Chen ◽  
...  
Keyword(s):  
Shear Wave ◽  
3D Imaging ◽  
Shear Wave Elastography ◽  
High Volume ◽  
Clinical Translation ◽  
Wave Source ◽  
Shear Wave Speed ◽  
External Vibration ◽  
Volume Rate ◽  
Wide Range

Objective: To develop a 3D shear wave elastography (SWE) technique using a 2D row column addressing (RCA) array, with either external vibration or acoustic radiation force (ARF) as the shear wave source. Impact Statement: The proposed method paves the way for clinical translation of 3D-SWE based on the 2D RCA, providing a low-cost and high volume-rate solution that is compatible with existing clinical systems. Introduction: SWE is an established ultrasound imaging modality that provides a direct and quantitative assessment of tissue stiffness, which is significant for a wide range of clinical applications including cancer and liver fibrosis. SWE requires high frame-rate imaging for robust shear wave tracking. Due to the technical challenges associated with high volume-rate imaging in 3D, current SWE techniques are typically confined to 2D. Advancing SWE from 2D to 3D is significant because of the heterogeneous nature of tissue, which demands 3D imaging for accurate and comprehensive evaluation. Methods: A 3D SWE method using a 2D RCA array was developed with a volume-rate up to 2000 Hz. The performance of the proposed method was systematically evaluated on tissue-mimicking elasticity phantoms. Results: 3D shear wave motion induced by either external vibration or ARF was successfully detected with the proposed method. Robust 3D shear wave speed maps were reconstructed for both homogeneous and heterogeneous phantoms with inclusions. Conclusion: The high volume-rate 3D imaging provided by the 2D RCA array provides a robust and practical solution for 3D SWE with a clear pathway for future clinical translation.

Patterns in diversity and composition of the microbenthos of subarctic intertidal beaches with different morphodynamics

2020 ◽  
Vol 648 ◽  
pp. 19-38
Author(s):  
AI Azovsky ◽  
YA Mazei ◽  
MA Saburova ◽  
PV Sapozhnikov
Keyword(s):  
Species Abundance ◽  
Abundance Ratio ◽  
Wave Action ◽  
Coarse Grained ◽  
Sediment Properties ◽  
Β Diversity ◽  
Α Diversity ◽  
Wide Range ◽  
Similar Mode ◽  
Abundance And Diversity

Diversity and composition of benthic diatom algae and ciliates were studied at several beaches along the White and Barents seas: from highly exposed, reflective beaches with coarse-grained sands to sheltered, dissipative silty-sandy flats. For diatoms, the epipelic to epipsammic species abundance ratio was significantly correlated with the beach index and mean particle size, while neither α-diversity measures nor mean cell length were related to beach properties. In contrast, most of the characteristics of ciliate assemblages (diversity, total abundance and biomass, mean individual weight and percentage of karyorelictids) demonstrated a strong correlation to beach properties, remaining low at exposed beaches but increasing sharply in more sheltered conditions. β-diversity did not correlate with beach properties for either diatoms or ciliates. We suggest that wave action and sediment properties are the main drivers controlling the diversity and composition of the intertidal microbenthos. Diatoms and ciliates, however, demonstrated divergent response to these factors. Epipelic and epipsammic diatoms exhibited 2 different strategies to adapt to their environments and therefore were complementarily distributed along the environmental gradient and compensated for each other in diversity. Most ciliates demonstrated a similar mode of habitat selection but differed in their degree of tolerance. Euryporal (including mesoporal) species were relatively tolerant to wave action and therefore occurred under a wide range of beach conditions, though their abundance and diversity were highest in fine, relatively stable sediments on sheltered beaches, whereas the specific interstitial (i.e. genuine microporal) species were mostly restricted to only these habitats.

scholarly journals Predictive modelling of soils’ hydraulic conductivity using artificial neural network and multiple linear regression

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
Charles Gbenga Williams ◽  
Oluwapelumi O. Ojuri
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Hydraulic Conductivity ◽  
Linear Regression ◽  
Multiple Linear Regression ◽  
Coarse Grained ◽  
Soil Types ◽  
Wide Range ◽  
Artificial Neural ◽  
Input Variables

AbstractAs a result of heterogeneity nature of soils and variation in its hydraulic conductivity over several orders of magnitude for various soil types from fine-grained to coarse-grained soils, predictive methods to estimate hydraulic conductivity of soils from properties considered more easily obtainable have now been given an appropriate consideration. This study evaluates the performance of artificial neural network (ANN) being one of the popular computational intelligence techniques in predicting hydraulic conductivity of wide range of soil types and compared with the traditional multiple linear regression (MLR). ANN and MLR models were developed using six input variables. Results revealed that only three input variables were statistically significant in MLR model development. Performance evaluations of the developed models using determination coefficient and mean square error show that the prediction capability of ANN is far better than MLR. In addition, comparative study with available existing models shows that the developed ANN and MLR in this study performed relatively better.

scholarly journals Quantum information probes of charge fractionalization in large-N gauge theories

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Brandon S. DiNunno ◽  
Niko Jokela ◽  
Juan F. Pedraza ◽  
Arttu Pönni
Keyword(s):  
Degrees Of Freedom ◽  
Gauge Theories ◽  
Entanglement Entropy ◽  
Coarse Grained ◽  
Strongly Coupled ◽  
Information Theoretic ◽  
Large N ◽  
Wide Range ◽  
Charge Fractionalization ◽  
Electric Flux

Abstract We study in detail various information theoretic quantities with the intent of distinguishing between different charged sectors in fractionalized states of large-N gauge theories. For concreteness, we focus on a simple holographic (2 + 1)-dimensional strongly coupled electron fluid whose charged states organize themselves into fractionalized and coherent patterns at sufficiently low temperatures. However, we expect that our results are quite generic and applicable to a wide range of systems, including non-holographic. The probes we consider include the entanglement entropy, mutual information, entanglement of purification and the butterfly velocity. The latter turns out to be particularly useful, given the universal connection between momentum and charge diffusion in the vicinity of a black hole horizon. The RT surfaces used to compute the above quantities, though, are largely insensitive to the electric flux in the bulk. To address this deficiency, we propose a generalized entanglement functional that is motivated through the Iyer-Wald formalism, applied to a gravity theory coupled to a U(1) gauge field. We argue that this functional gives rise to a coarse grained measure of entanglement in the boundary theory which is obtained by tracing over (part) of the fractionalized and cohesive charge degrees of freedom. Based on the above, we construct a candidate for an entropic c-function that accounts for the existence of bulk charges. We explore some of its general properties and their significance, and discuss how it can be used to efficiently account for charged degrees of freedom across different energy scales.

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