Elastic wave propagation in composite media

Geophysics ◽  
1992 ◽  
Vol 57 (9) ◽  
pp. 1155-1165 ◽  
Author(s):  
William J. Lamb ◽  
Xianhuai Zhu ◽  
George A. McMechan ◽  
Matt L. Greenberg ◽  
John P. Castagna
Keyword(s):  
Material Properties ◽  
Single Scattering ◽  
Two Dimensional ◽  
Composite Media ◽  
Constructive Interference ◽  
Coherent Wave ◽  
Solid Media ◽  
The Matrix ◽  
Cylindrical Inclusions ◽  
Composite Moduli

Numerical simulation can be a useful tool for studying composite media. It is not limited by weak or single scattering assumptions, and it requires only constituent properties and an arrangement of constituents as input. For solid/solid media with octagonal cylindrical inclusions and for typical values of constituent moduli, composite moduli are accurately predicted by two‐dimensional (2-D) analogs of Kuster‐Toksöz formulas. For solid/solid media there is a small but discernable difference between responses of square and those of octagonal inclusions. Coherent reflections are produced by a coherent wave incident at a change in concentration of inclusions, if the contrast between material properties of the matrix and those of the inclusions is sufficient to produce significant scattering, and if the size of scatterers is sufficiently small and their concentration sufficiently large so there is constructive interference between waves originating at adjacent scatterers.

Comparison of Calculated and Recorded Electron Energy-Loss Spectra of Aluminium and Carbon

1990 ◽  
Vol 48 (2) ◽  
pp. 64-65
Author(s):  
L. Reimer ◽  
R. Oelgeklaus
Keyword(s):  
Fourier Transform ◽  
Energy Loss ◽  
Electron Energy ◽  
Rotational Symmetry ◽  
Mean Free Path ◽  
Single Scattering ◽  
Specimen Thickness ◽  
Two Dimensional ◽  
Image Position ◽  
Electron Energy Loss

Quantitative electron energy-loss spectroscopy (EELS) needs a correction for the limited collection aperture α and a deconvolution of recorded spectra for eliminating the influence of multiple inelastic scattering. Reversely, it is of interest to calculate the influence of multiple scattering on EELS. The distribution f(w,θ,z) of scattered electrons as a function of energy loss w, scattering angle θ and reduced specimen thickness z=t/Λ (Λ=total mean-free-path) can either be recorded by angular-resolved EELS or calculated by a convolution of a normalized single-scattering function ϕ(w,θ). For rotational symmetry in angle (amorphous or polycrystalline specimens) this can be realised by the following sequence of operations :(1)where the two-dimensional distribution in angle is reduced to a one-dimensional function by a projection P, T is a two-dimensional Fourier transform in angle θ and energy loss w and the exponent -1 indicates a deprojection and inverse Fourier transform, respectively.

scholarly journals Tunable characteristics of low-frequency bandgaps in two-dimensional multivibrator phononic crystal plates under prestrain

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hai-Fei Zhu ◽  
Xiao-Wei Sun ◽  
Ting Song ◽  
Xiao-Dong Wen ◽  
Xi-Xuan Liu ◽  
...  
Keyword(s):  
Phononic Crystal ◽  
Real Life ◽  
Low Frequency ◽  
Acoustic Vibration ◽  
Crystal Plate ◽  
Frequency Noise ◽  
Two Dimensional ◽  
The Matrix ◽  
Noise Frequency ◽  
Realtime Control

AbstractIn view of the influence of variability of low-frequency noise frequency on noise prevention in real life, we present a novel two-dimensional tunable phononic crystal plate which is consisted of lead columns deposited in a silicone rubber plate with periodic holes and calculate its bandgap characteristics by finite element method. The low-frequency bandgap mechanism of the designed model is discussed simultaneously. Accordingly, the influence of geometric parameters of the phononic crystal plate on the bandgap characteristics is analyzed and the bandgap adjustability under prestretch strain is further studied. Results show that the new designed phononic crystal plate has lower bandgap starting frequency and wider bandwidth than the traditional single-sided structure, which is due to the coupling between the resonance mode of the scatterer and the long traveling wave in the matrix with the introduction of periodic holes. Applying prestretch strain to the matrix can realize active realtime control of low-frequency bandgap under slight deformation and broaden the low-frequency bandgap, which can be explained as the multiple bands tend to be flattened due to the localization degree of unit cell vibration increases with the rise of prestrain. The presented structure improves the realtime adjustability of sound isolation and vibration reduction frequency for phononic crystal in complex acoustic vibration environments.

scholarly journals A methodology for hygrothermal modelling of imperfect masonry interfaces

2021 ◽  
pp. 174425912198938
Author(s):  
Michael Gutland ◽  
Scott Bucking ◽  
Mario Santana Quintero
Keyword(s):  
Boundary Conditions ◽  
Material Properties ◽  
Structural Integrity ◽  
Bulk Material ◽  
Weather Conditions ◽  
Masonry Wall ◽  
Two Dimensional ◽  
Liquid Transport ◽  
Imperfect Contact ◽  
Moisture Contents

Hygrothermal models are important tools for assessing the risk of moisture-related decay mechanisms which can compromise structural integrity, loss of architectural features and material. There are several sources of uncertainty when modelling masonry, related to material properties, boundary conditions, quality of construction and two-dimensional interactions between mortar and unit. This paper examines the uncertainty at the mortar-unit interface with imperfections such as hairline cracks or imperfect contact conditions. These imperfections will alter the rate of liquid transport into and out of the wall and impede the liquid transport between mortar and masonry unit. This means that the effective liquid transport of the wall system will be different then if only properties of the bulk material were modelled. A detailed methodology for modelling this interface as a fracture is presented including definition of material properties for the fracture. The modelling methodology considers the combined effect of both the interface resistance across the mortar-unit interface and increase liquid transport in parallel to the interface, and is generalisable to various combinations of materials, geometries and fracture apertures. Two-dimensional DELPHIN models of a clay brick/cement-mortar masonry wall were created to simulate this interaction. The models were exposed to different boundary conditions to simulate wetting, drying and natural cyclic weather conditions. The results of these simulations were compared to a baseline model where the fracture model was not included. The presence of fractures increased the rate of absorption in the wetting phase and an increased rate of desorption in the drying phase. Under cyclic conditions, the result was higher peak moisture contents after rain events compared to baseline and lower moisture contents after long periods of drying. This demonstrated that detailed modelling of imperfections at the mortar-unit interface can have a definitive influence on results and conclusions from hygrothermal simulations.

scholarly journals Divergent ⇒ complex amplitudes in two dimensional string theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Ashoke Sen
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Matrix Model ◽  
Two Dimensional ◽  
Full Matrix ◽  
Instanton Contribution ◽  
The Matrix ◽  
Theory Result ◽  
The One ◽  
Remarkable Agreement

Abstract In a recent paper, Balthazar, Rodriguez and Yin found remarkable agreement between the one instanton contribution to the scattering amplitudes of two dimensional string theory and those in the matrix model to the first subleading order. The comparison was carried out numerically by analytically continuing the external energies to imaginary values, since for real energies the string theory result diverges. We use insights from string field theory to give finite expressions for the string theory amplitudes for real energies. We also show analytically that the imaginary parts of the string theory amplitudes computed this way reproduce the full matrix model results for general scattering amplitudes involving multiple closed strings.

scholarly journals A new fourth-order explicit group method in the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Muhammad Asim Khan ◽  
Norhashidah Hj. Mohd Ali ◽  
Nur Nadiah Abd Hamid
Keyword(s):  
Finite Difference ◽  
Stokes Problem ◽  
Stability And Convergence ◽  
Second Grade ◽  
Group Method ◽  
Two Dimensional ◽  
Second Grade Fluid ◽  
The Matrix ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid

Abstract In this article, a new explicit group iterative scheme is developed for the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid. The proposed scheme is based on the high-order compact Crank–Nicolson finite difference method. The resulting scheme consists of three-level finite difference approximations. The stability and convergence of the proposed method are studied using the matrix energy method. Finally, some numerical examples are provided to show the accuracy of the proposed method.

scholarly journals Lymphocyte locomotion and attachment on two-dimensional surfaces and in three-dimensional matrices

1982 ◽  
Vol 92 (3) ◽  
pp. 747-752 ◽  
Author(s):  
WS Haston ◽  
JM Shields ◽  
PC Wilkinson
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Collagen Gels ◽  
Peripheral Lymph Node ◽  
Cellulose Esters ◽  
Peripheral Lymph ◽  
The Matrix ◽  
Identical Material ◽  
Variable Morphology ◽  
Collagen Lattices

The adhesion and locomotion of mouse peripheral lymph node lymphocytes on 2-D protein- coated substrata and in 3-D matrices were compared. Lymphocytes did not adhere to, or migrate on, 2-D substrata suck as serum- or fibronectin-coated glass. They did attach to and migrate in hydrated 3-D collagen lattices. When the collagen was dehydrated to form a 2-D surface, lymphocyte attachment to it was reduced. We propose that lymphocytes, which are poorly adhesive, are able to attach to and migrate in 3-D matrices by a nonadhesive mechanism such as the extension and expansion of pseudopodia through gaps in the matrix, which could provide purchase for movement in the absence of discrete intermolecular adhesions. This was supported by studies using serum-coated micropore filters, since lymphocytes attached to and migrated into filters with pore sizes large enough (3 or 8 mum) to allow pseudopod penetration but did not attach to filters made of an identical material (cellulose esters) but of narrow pore size (0.22 or 0.45 mum). Cinematographic studies of lymphocyte locomotion in collagen gels were also consistent with the above hypothesis, since lymphocytes showed a more variable morphology than is typically seen on plane surfaces, with formation of many small pseudopodia expanded to give a marked constriction between the cell and the pseudopod. These extensions often remained fixed with respect to the environment as the lymphocyte moved away from or past them. This suggests that the pseudopodia were inserted into gaps in the gel matrix and acted as anchorage points for locomotion.

Investigation of Contact Conditions During Stamping of a Thin Plate

2020 ◽  
Author(s):  
Harshal Y. Shahare ◽  
Rohan Rajput ◽  
Puneet Tandon
Keyword(s):  
Wave Propagation ◽  
Material Properties ◽  
High Speed ◽  
Fdtd Method ◽  
Propagation Model ◽  
Transmitted Wave ◽  
Two Dimensional ◽  
Contact Conditions ◽  
Simulation Based ◽  
Difference Time

Abstract Stamping is one of the most used manufacturing processes, where real-time monitoring is quite difficult due to high speed of the mechanical press, which leads to deterioration of the accuracy of the products In the present work, a method is developed to model elastic waves propagation in solids to measure contact conditions between die and workpiece during stamping. A two-dimensional model is developed that reduces the wave propagation equations to two-dimensional equations. To simulate the wave propagation inside the die-workpiece model, the finite difference time domain (FDTD) method and modified Yee algorithm has been employed. The numerical stability of the wave propagation model is achieved through courant stability condition, i.e., Courant-Friedrichs-Lewy (CFL) number. Two cases, i.e., flat die-workpiece interface and inclined die-workpiece interface, are investigated in the present work. The elastic wave propagation is simulated with a two-dimension (2D) model of the die and workpiece using reflecting boundary conditions for different material properties. The experimental and simulation-based results of reflected and transmitted wave characteristics are compared for different materials in terms of reflected and transmitted wave height ratio and material properties such as acoustic impedance. It is found that the numerical simulation results are in good agreement with the experimental results.

Finite Element Study of Oxygen Diffusion in the Intervertebral Disc

2000 ◽  
Author(s):  
E. Sélard ◽  
A. Shirazi-Adl ◽  
J. P. G. Urban
Keyword(s):  
Intervertebral Disc ◽  
Blood Supply ◽  
Oxygen Diffusion ◽  
Consumption Rate ◽  
The Body ◽  
Cellular Viability ◽  
Two Dimensional ◽  
Concentration Gradients ◽  
Exchange Area ◽  
The Matrix

Abstract The intervertebral disc consists of a water-rich extra-cellular matrix which is synthesized and maintained by its cells. The disc is the largest avascular tissue in the body with its cells lying as much as 8mm away from the blood supply. Nutrients, essential for maintaining cellular viability, diffuse through the matrix from blood supply under a concentration gradient arising from cellular demand. The oxygen concentration gradients in the intervertebral disc are investigated to examine the effects of exchange area and disc thickness on oxygen flux in the disc. The concentration gradients are computed using the two-dimensional Poisson’s equation and measured values for oxygen consumption rate and oxygen diffusion.

Service quality function deployment by the C-shaped QFD 3D matrix

2018 ◽  
Vol 25 (9) ◽  
pp. 3386-3405 ◽  
Author(s):  
Maryam Hassani ◽  
Arash Shahin ◽  
Manouchehr Kheradmandnia
Keyword(s):  
Quality Function Deployment ◽  
Design Methodology ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Customer Requirements ◽  
Content Type ◽  
Process Characteristics ◽  
The Matrix ◽  
3D Matrix ◽  
Simultaneous Comparison

Purpose The purpose of this paper is to examine the application of C-shaped QFD 3D Matrix in comparing process characteristics (PC), performance aspects (PA) and customer requirements, simultaneously and to prioritize the first two sets, respectively. Design/methodology/approach A three dimensional matrix has been developed with three sets of PC, PA and customers’ requirements and C-shaped matrix has been applied for simultaneous comparison of the dimensions and prioritization of the subsets of PC and PA. The proposed approach has been examined in a post bank. Findings Findings confirm the possibility of simultaneous comparison and prioritization of the three sets of dimensions of this study in post bank services. In addition, “growth and learning” and “bilateral relationship with suppliers” had the first priorities among PA and PC, respectively. Research limitations/implications While the proposed approach has many advantages, filling the matrixes is time-consuming. Since illustrating the 3D matrix was not possible, the matrix was separated into five two-dimensional matrixes. Originality/value Compared to the studied literature, the proposed approach is practically new in the post bank services.

scholarly journals Higher-order Darboux transformations for two-dimensional Dirac systems with diagonal matrix potential

2021 ◽  
Vol 2090 (1) ◽  
pp. 012038
Author(s):  
A Schulze-Halberg
Keyword(s):  
Dirac Equation ◽  
Explicit Form ◽  
Higher Order ◽  
Diagonal Matrix ◽  
Two Dimensional ◽  
Darboux Transformations ◽  
Dirac Systems ◽  
Matrix Potential ◽  
De Vries ◽  
The Matrix

Abstract We construct the explicit form of higher-order Darboux transformations for the two-dimensional Dirac equation with diagonal matrix potential. The matrix potential entries can depend arbitrarily on the two variables. Our construction is based on results for coupled Korteweg-de Vries equations [27].

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