Multiple Scattering of Elastic Waves by Cubical Lattices of Spheres

2007 ◽  
Author(s):  
Zunping Liu ◽  
Liang-Wu Cai
Keyword(s):  
Multiple Scattering ◽  
Elastic Waves ◽  
Dimensional Space ◽  
Near Field ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Computational System ◽  
Number Of Layers ◽  
Scattering Of Elastic Waves ◽  
Three Dimensional Space

The band gap for elastic waves propagating in a cubical lattice of spherical scatterers is observed through a series of numerical simulations. Along the direction of the incident wave, scatterer arrangements are viewed as comprising layers of scatterers, within which scatterers form a square grid. Starting from one layer and by increasing the number of layers, near-field forward and backward wave propagation spectra are computed as the number of layers increases. In the computations, scatterer polymerization methodology is used. This methodology is based on an analytically exact solution to a general three-dimensional multiple scattering problem obtained by the authors. It can be used to reduce an assemblage of actual scatterers to a lesser number of abstract scatterers. These simulations also demonstrate that the computational system has the capability to simulate multiple scattering of elastic waves in three-dimensional space.

scholarly journals Three-Dimensional Multiple Scattering of Elastic Waves by Spherical Inclusions

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Zunping Liu ◽  
Liang-Wu Cai
Keyword(s):  
Multiple Scattering ◽  
Elastic Waves ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Antiplane Shear ◽  
Gap Formation ◽  
Computational System ◽  
Cubic Lattice ◽  
Spherical Inclusions ◽  
Scattering Of Elastic Waves

This paper extends the scatterer polymerization methodology to three-dimensional multiple scattering of elastic waves by spherical inclusions. The methodology was originally developed for analyzing multiple scattering of elastic antiplane shear waves in two-dimensional spaces. The analytically exact solution of multiple scattering is reformulated by using this methodology, which is verified by using different ways, with or without scatterer polymerization, to solve physically the same multiple scattering problem. As an application example, the band gap formation for elastic wave propagating in a cubic lattice of spherical scatterers is observed through a series of numerical simulations. These simulations also demonstrate the capability of the present computational system for simulating three-dimensional multiple scattering of elastic waves.

scholarly journals Scattering of Elastic Waves by an Inhomogeneous Boundary in the Acoustic Testing of Permanent Joints

2019 ◽  
Vol 10 (4) ◽  
pp. 360-372
Author(s):  
A. R. Baev ◽  
N. V. Levkovich ◽  
A. L. Mayorov ◽  
M. V. Asadchaya
Keyword(s):  
Elastic Waves ◽  
Dimensional Space ◽  
Ultrasonic Method ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Field Pattern ◽  
Acoustic Beam ◽  
Practical Applications ◽  
Scattering Field ◽  
Scattering Of Elastic Waves

Improving the reliability and testing performance of permanent joints оf different materials made by welding, spraying, gluing, soldering and other methods is an important production task, for which the ultrasonic method is the simplest and most effective. The purpose of this work was to expand the technical possibilities and increase the sensitivity of ultrasonic testing of adhesion defects of materials joints based on the establishment of laws governing the formation of a scattering field of elastic waves from an inhomogeneous boundary in three-dimensional space and issuing recommendations for the development of suggested method.For the first time, in the framework of classical concepts, the scattering fields of elastic waves of an acoustic beam with a circular cross section moving across the boundary of a semi-infinite defect are calculated. It is proposed to use a phase shift between the waves reflected from the indicated surfaces, which varies in the range of π/4–π, as an important parameter of the material joint's defect. It has a significant effect on the field pattern and its angular amplitude extrema — minima and maxima of different orders when the defect boundary is moved relative to the center of the acoustic beam spot.The features of the evolution of the structure of the scattering field are established, which make it possible to identify optimal conditions for the detection of weakly reflective defects in sound. It is shown that it is possible in principle to estimate the defect's area by measuring a change in the amplitude of the primary maximum of the radiation pattern of the scattered waves.Specific examples show the effectiveness of using the proposed method for a number of practical applications.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

A Peptoid with Extended Shape in Water

2019 ◽  
Author(s):  
Jumpei Morimoto ◽  
Yasuhiro Fukuda ◽  
Takumu Watanabe ◽  
Daisuke Kuroda ◽  
Kouhei Tsumoto ◽  
...  
Keyword(s):  
Spectroscopic Analysis ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Biomolecular Recognition ◽  
Biological Application ◽  
New Class ◽  
Proteolytic Resistance ◽  
Pharmacokinetic Properties ◽  
Optically Pure ◽  
Three Dimensional Space

<div> <div> <div> <p>“Peptoids” was proposed, over decades ago, as a term describing analogs of peptides that exhibit better physicochemical and pharmacokinetic properties than peptides. Oligo-(N-substituted glycines) (oligo-NSG) was previously proposed as a peptoid due to its high proteolytic resistance and membrane permeability. However, oligo-NSG is conformationally flexible and is difficult to achieve a defined shape in water. This conformational flexibility is severely limiting biological application of oligo-NSG. Here, we propose oligo-(N-substituted alanines) (oligo-NSA) as a new peptoid that forms a defined shape in water. A synthetic method established in this study enabled the first isolation and conformational study of optically pure oligo-NSA. Computational simulations, crystallographic studies and spectroscopic analysis demonstrated the well-defined extended shape of oligo-NSA realized by backbone steric effects. The new class of peptoid achieves the constrained conformation without any assistance of N-substituents and serves as an ideal scaffold for displaying functional groups in well-defined three-dimensional space, which leads to effective biomolecular recognition. </p> </div> </div> </div>

scholarly journals Quantitative image analysis of microbial communities with BiofilmQ

2021 ◽  
Author(s):  
Raimo Hartmann ◽  
Hannah Jeckel ◽  
Eric Jelli ◽  
Praveen K. Singh ◽  
Sanika Vaidya ◽  
...  
Keyword(s):  
Image Analysis ◽  
Microbial Communities ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Software Tool ◽  
Image Cytometry ◽  
Quantitative Image Analysis ◽  
Space And Time ◽  
Quantitative Image ◽  
Three Dimensional Space

AbstractBiofilms are microbial communities that represent a highly abundant form of microbial life on Earth. Inside biofilms, phenotypic and genotypic variations occur in three-dimensional space and time; microscopy and quantitative image analysis are therefore crucial for elucidating their functions. Here, we present BiofilmQ—a comprehensive image cytometry software tool for the automated and high-throughput quantification, analysis and visualization of numerous biofilm-internal and whole-biofilm properties in three-dimensional space and time.

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