scholarly journals Anti-plane shear Lamb's problem on random mass density fields with fractal and Hurst effects

2019 ◽  
Vol 8 (1) ◽  
pp. 231-246 ◽  
Author(s):  
Xian Zhang ◽  
◽  
Vinesh Nishawala ◽  
Martin Ostoja-Starzewski ◽  
◽  
...  
Keyword(s):  
Mass Density ◽  
Plane Shear ◽  
Lamb’S Problem ◽  
Random Mass

scholarly journals Lamb's problem on random mass density fields with fractal and Hurst effects

2016 ◽  
Vol 472 (2196) ◽  
pp. 20160638 ◽  
Author(s):  
V. V. Nishawala ◽  
M. Ostoja-Starzewski ◽  
M. J. Leamy ◽  
E. Porcu
Keyword(s):  
Coefficient Of Variation ◽  
Mass Density ◽  
Computational Method ◽  
Hurst Parameter ◽  
Imperfection Sensitivity ◽  
Node Density ◽  
Line Load ◽  
Lamb’S Problem ◽  
Random Mass ◽  
Linear Elastic

This paper reports on a generalization of Lamb's problem to a linear elastic, infinite half-space with random fields (RFs) of mass density, subject to a normal line load. Both, uncorrelated and correlated (with fractal and Hurst characteristics) RFs without any weak noise restrictions, are proposed. Cellular automata (CA) is used to simulate the wave propagation. CA is a local computational method which, for rectangular discretization of spatial domain, is equivalent to applying the finite difference method to the governing equations of classical elasticity. We first evaluate the response of CA to an uncorrelated mass density field, more commonly known as white-noise, of varying coarseness as compared to CA's node density. We then evaluate the response of CA to multiscale mass density RFs of Cauchy and Dagum type; these fields are unique in that they are able to model and decouple the field's fractal dimension and Hurst parameter. We focus on stochastic imperfection sensitivity; we determine to what extent the fractal or the Hurst parameter is a significant factor in altering the solution to the planar stochastic Lamb's problem by evaluating the coefficient of variation of the response when compared with the coefficient of variation of the RF.

scholarly journals Anti-plane shear waves in periodic elastic composites: band structure and anomalous wave refraction

2015 ◽  
Vol 471 (2180) ◽  
pp. 20150152 ◽  
Author(s):  
Sia Nemat-Nasser
Keyword(s):  
Band Structure ◽  
Phase Velocity ◽  
Negative Refraction ◽  
Mass Density ◽  
Shear Waves ◽  
Variable Mass ◽  
Three Dimensional ◽  
Positive Energy ◽  
Plane Shear ◽  
Elastic Composites

For anti-plane shear waves in periodic elastic composites, it is shown that negative energy refraction can be accompanied by positive phase-velocity refraction and positive energy refraction can be accompanied by negative phase-velocity refraction , and that this can happen over a broad range of frequencies. Hence, in general, negative refraction does not necessarily require antiparallel group and phase-velocity vectors. Details are given for layered composites and the results are extended to, and illustrated for, two-dimensional periodic composites, revealing a wealth of information about the refractive characteristics of this class of composites. The composite's unit cell may consist of any number of constituents of any variable mass density and elastic modulus, admitting large discontinuities . A powerful variational-based solution method is used that applies to one-, two- and three-dimensional composites, irrespective of their constituents being homogeneous or heterogeneous. The calculations are direct, accurate and efficient, yielding the band structure, group-velocity, energy-flux and phase-velocity vectors as functions of the frequency and wavevector components, over an entire frequency band.

STATISTICAL PROPERTIES OF POTENTIAL FIELDS OVER A RANDOM MEDIUM

Geophysics ◽  
1967 ◽  
Vol 32 (1) ◽  
pp. 88-98 ◽  
Author(s):  
Prabakar S. Naidu
Keyword(s):  
Random Process ◽  
Autocorrelation Function ◽  
Potential Field ◽  
Random Potential ◽  
Mass Density ◽  
Random Medium ◽  
Statistical Properties ◽  
Potential Fields ◽  
Random Mass ◽  
The Relationship

Following a study of the statistical properties of a random potential field, which is often encountered as a background noise in observed geophysical potential fields, and particularly a study of conditions under which the random process is homogeneous and gaussian, an approximate analytical method has been developed to evaluate the correlation functions and the power spectrum of the random process when the mass density is locally uniform but varies randomly over an entire semi‐infinite space. The method is particularly convenient for it gives a unified approach to evaluating the statistical properties of gravity as well as magnetic fields. The relationship between the autocorrelation function of the random potential field and the random mass density is quite involved, but by assuming that the mass density in successive cells is completely uncorrelated the relationship can be simplified. It is a matter of considerable interest to estimate, from the autocorrelation function, the size of cell characteristic of the random medium which reflects the geological characteristics of the rocks.

Frequency and amplitude alterations of sound modes in a space-dependent random mass density field

2004 ◽  
Vol 14 (2) ◽  
pp. 109-117 ◽  
Author(s):  
K Murawski ◽  
L Nocera ◽  
E N Pelinovsky
Keyword(s):  
Mass Density ◽  
Density Field ◽  
Random Mass ◽  
Sound Modes

scholarly journals Impact force and moment problems on random mass density fields with fractal and Hurst effects

2020 ◽  
Vol 378 (2172) ◽  
pp. 20190591 ◽  
Author(s):  
Xian Zhang ◽  
Martin Ostoja-Starzewski
Keyword(s):  
Cellular Automata ◽  
Random Field ◽  
Mass Density ◽  
Point Load ◽  
Dynamic Responses ◽  
Advanced Materials ◽  
Random Mass ◽  
Linear Elastic ◽  
Wide Range ◽  
Elastodynamic Solution

This paper reports the application of cellular automata to study the dynamic responses of Lamb-type problems for a tangential point load and a concentrated moment applied on the free surface of a half-plane. The medium is homogeneous, isotropic and linear elastic while having a random mass density field with fractal and Hurst characteristics. Both Cauchy and Dagum random field models are used to capture these effects. First, the cellular automata approach is tested on progressively finer meshes to verify the code against the continuum elastodynamic solution in a homogeneous continuum. Then, the sensitivity of wave propagation on random fields is assessed for a wide range of fractal and Hurst parameters. Overall, the mean response amplitude is lowered by the mass density field’s randomness, while the Hurst parameter (especially, for β  < 0.2) is found to have a stronger influence than the fractal dimension on the response. The resulting Rayleigh wave is modified more than the pressure wave for the same random field parameters. Additionally, comparisons with previously studied Lamb-type problems under normal in-plane and anti-plane loadings are given. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

Mass Determination by Direct Measurement of Electron Scattering

1975 ◽  
Vol 33 ◽  
pp. 240-241
Author(s):  
M. K. Lamvik ◽  
A. V. Crewe
Keyword(s):  
Cross Section ◽  
Electron Scattering ◽  
Mass Density ◽  
Variable Mass ◽  
Scattering Cross Section ◽  
Mass Determination ◽  
Number Density ◽  
Cross Sectional ◽  
Thin Slice ◽  
Scattering Cross

If a molecule or atom of material has molecular weight A, the number density of such units is given by n=Nρ/A, where N is Avogadro's number and ρ is the mass density of the material. The amount of scattering from each unit can be written by assigning an imaginary cross-sectional area σ to each unit. If the current I0 is incident on a thin slice of material of thickness z and the current I remains unscattered, then the scattering cross-section σ is defined by I=IOnσz. For a specimen that is not thin, the definition must be applied to each imaginary thin slice and the result I/I0 =exp(-nσz) is obtained by integrating over the whole thickness. It is useful to separate the variable mass-thickness w=ρz from the other factors to yield I/I0 =exp(-sw), where s=Nσ/A is the scattering cross-section per unit mass.

Image formation analysis of thick biological specimens using three-dimensional power-spectra of through focus series

1994 ◽  
Vol 52 ◽  
pp. 124-125
Author(s):  
Karen F. Han
Keyword(s):  
Inelastic Scattering ◽  
Imaging Techniques ◽  
Mass Density ◽  
Relative Proportion ◽  
Three Dimensional ◽  
Power Spectra ◽  
Image Formation ◽  
Energy Filtering ◽  
Ewald Sphere ◽  
Nonlinear Imaging

The primary focus in our laboratory is the study of higher order chromatin structure using three dimensional electron microscope tomography. Three dimensional tomography involves the deconstruction of an object by combining multiple projection views of the object at different tilt angles, image intensities are not always accurate representations of the projected object mass density, due to the effects of electron-specimen interactions and microscope lens aberrations. Therefore, an understanding of the mechanism of image formation is important for interpreting the images. The image formation for thick biological specimens has been analyzed by using both energy filtering and Ewald sphere constructions. Surprisingly, there is a significant amount of coherent transfer for our thick specimens. The relative amount of coherent transfer is correlated with the relative proportion of elastically scattered electrons using electron energy loss spectoscopy and imaging techniques.Electron-specimen interactions include single and multiple, elastic and inelastic scattering. Multiple and inelastic scattering events give rise to nonlinear imaging effects which complicates the interpretation of collected images.

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