scholarly journals THE EFFECT OF THE THIRD DIMENSION ON ROUGH SURFACES FORMED BY SEDIMENTING PARTICLES IN QUASI-TWO-DIMENSIONS

2002 ◽  
Vol 16 (08) ◽  
pp. 1217-1223 ◽  
Author(s):  
K. V. MCCLOUD ◽  
M. L. KURNAZ
Keyword(s):  
Two Dimensions ◽  
Scaling Analysis ◽  
Silica Spheres ◽  
Two Dimensional ◽  
One Dimensional ◽  
The Third ◽  
Roughness Exponent ◽  
Third Dimension ◽  
Dimensional Cell ◽  
Roughness Exponents

The roughness exponent of surfaces obtained by dispersing silica spheres into a quasi-two-dimensional cell is examined. The cell consists of two glass plates separated by a gap, which is comparable in size to the diameter of the beads. Previous work has shown that the quasi-one-dimensional surfaces formed have two roughness exponents in two length scales, which have a crossover length about 1 cm. We have studied the effect of changing the gap between the plates to a limit of about twice the diameter of the beads. If the conventional scaling analysis is performed, the roughness exponent is found to be robust against changes in the gap between the plates; however, the possibility that scaling does not hold should be taken seriously.

Optical Characterization of Silica Aerogel

1988 ◽  
Vol 121 ◽  
Author(s):  
Lawrence W. Hrubesh ◽  
Cynthia T. Alviso
Keyword(s):  
Silica Aerogel ◽  
Porous Silica ◽  
Optical Characterization ◽  
Optical Methods ◽  
Gradient Index ◽  
Two Dimensional ◽  
Two Dimensional Image ◽  
The Third ◽  
Third Dimension

ABSTRACTTwo optical methods are described for mapping the local variations of refractive index within monoliths of porous silica aerogel. One is an interferometrie measurement that produces “iso-index” fringes in a two dimensional image; an orthogonal view gives the third dimension information. The other method uses the deflection of a He-Ne laser beam to map the gradient index within a sample. The quantification of the measurements is described and the accuracy of the results is discussed.

Theory of Electron Diffraction by Crystals

1967 ◽  
Vol 22 (4) ◽  
pp. 422-431 ◽  
Author(s):  
Kyozaburo Kambe
Keyword(s):  
Integral Equation ◽  
Electron Diffraction ◽  
General Theory ◽  
Green’S Function ◽  
Green's Function ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Two Dimensions ◽  
The Third ◽  
Third Dimension

A general theory of electron diffraction by crystals is developed. The crystals are assumed to be infinitely extended in two dimensions and finite in the third dimension. For the scattering problem by this structure two-dimensionally expanded forms of GREEN’S function and integral equation are at first derived, and combined in single three-dimensional forms. EWALD’S method is applied to sum up the series for GREEN’S function.

A faster method for erosion and dilation of reservoir pore-complex images

1988 ◽  
Vol 25 (7) ◽  
pp. 1128-1131 ◽  
Author(s):  
J. R. Parker
Keyword(s):  
Flow Behavior ◽  
Reservoir Rock ◽  
Two Dimensional ◽  
Thin Sections ◽  
Reservoir Rocks ◽  
Image Processing Techniques ◽  
The Third ◽  
Computer Image Processing ◽  
Third Dimension ◽  
Processing Techniques

Studies of thin sections of reservoir rock have been conducted for some time with the goal of understanding flow behavior and estimating physical properties. These sections are essentially two dimensional, but it has always been assumed that the results obtained can be extrapolated to the third dimension. Computer image-processing techniques are often used in this sort of analysis because of the large amounts of data contained in a single digitized section image. One of the methods used to process these images is erosion–dilation, wherein layers of each pore are stripped off (erosion) and then replaced (dilation). This results in a smoothing of the pore perimeters and can be used to estimate pore radii, volume, and roughness. Because of the size of each image, erosion–dilation of images of the pore complex of reservoir rocks is a time-consuming process. A new method called global erosion is much faster, with no increase in memory requirement or decrease in accuracy. This should permit the processing of larger images or a greater number of small images than does the standard method.

4. Gelification and soapiness

2020 ◽  
pp. 63-90
Author(s):  
Tom McLeish
Keyword(s):  
Brownian Motion ◽  
Self Assembly ◽  
Soft Matter ◽  
Intermolecular Forces ◽  
Two Dimensional ◽  
Important Distinction ◽  
One Dimensional ◽  
The Third ◽  
Self Assembled ◽  
Weak Intermolecular Forces

‘Gelification and soapiness’ looks at the third class of soft matter: ‘self-assembly’. Like the colloids of inks and clays, and the polymers of plastics and rubbers, ‘self-assembled’ soft matter also emerges as a surprising consequence of Brownian motion combined with weak intermolecular forces. Like them, it also leads to explanations of a very rich world of materials and phenomena, such as gels, foams, soaps, and ultimately to many of the structures of biological life. There is an important distinction that needs to be made between one-dimensional and two-dimensional self-assembly.

scholarly journals New insights into the suitability of the third dimension for visualizing multivariate/multidimensional data: A study based on loss of quality quantification

2014 ◽  
Vol 15 (1) ◽  
pp. 3-30 ◽  
Author(s):  
Antonio Gracia ◽  
Santiago González ◽  
Víctor Robles ◽  
Ernestina Menasalvas ◽  
Tatiana von Landesberger
Keyword(s):  
Analytical Approach ◽  
Distance Perception ◽  
Statistical Tests ◽  
Three Dimensional ◽  
Multidimensional Data ◽  
Two Dimensional ◽  
Dimensional Representation ◽  
The Third ◽  
Quality Degradation ◽  
Third Dimension

Most visualization techniques have traditionally used two-dimensional, instead of three-dimensional representations to visualize multidimensional and multivariate data. In this article, a way to demonstrate the underlying superiority of three-dimensional, with respect to two-dimensional, representation is proposed. Specifically, it is based on the inevitable quality degradation produced when reducing the data dimensionality. The problem is tackled from two different approaches: a visual and an analytical approach. First, a set of statistical tests (point classification, distance perception, and outlier identification) using the two-dimensional and three-dimensional visualization are carried out on a group of 40 users. The results indicate that there is an improvement in the accuracy introduced by the inclusion of a third dimension; however, these results do not allow to obtain definitive conclusions on the superiority of three-dimensional representation. Therefore, in order to draw further conclusions, a deeper study based on an analytical approach is proposed. The aim is to quantify the real loss of quality produced when the data are visualized in two-dimensional and three-dimensional spaces, in relation to the original data dimensionality, to analyze the difference between them. To achieve this, a recently proposed methodology is used. The results obtained by the analytical approach reported that the loss of quality reaches significantly high values only when switching from three-dimensional to two-dimensional representation. The considerable quality degradation suffered in the two-dimensional visualization strongly suggests the suitability of the third dimension to visualize data.

An Instrument for One- or Two-Dimensional Tracking

1965 ◽  
Vol 21 (1) ◽  
pp. 307-312
Author(s):  
William C. Roehrig
Keyword(s):  
Low Cost ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Error Signal ◽  
One Dimensional ◽  
Constant Torque ◽  
Sinusoidal Motion ◽  
The Cross ◽  
Target Path

A rugged electro-mechanical tracking apparatus of simple, low-cost construction is described. The apparatus can be used for one-dimensional tracking by connecting only the longitudinal motor, thus forcing the target to move back and forth in either simple sinusoidal motion or according to the sum of two or three sinusoids. The relative phases of the three sinusoids can be rapidly altered, as can the amplitudes (within limits) of each of the sinusoids. The frequency of the sinusoids can be changed either independently or conjointly. By also connecting the cross-feed motor, an essentially unpredictable target path in two dimensions is obtained, and this path can be rapidly altered by changing cams, and/or frequency, amplitude, and phase of the sinusoids. Movement of the cursor is by low, constant torque lathe-type controls. The distance the cursor moves per each rotation of the controls, can be altered for either or both of the controls. A continuous error signal is generated which is directly proportional to the distance the cursor is off target in any direction.

A Hybrid Unstructured/Spectral Method for the Resolution of Navier-Stokes Equations

2009 ◽  
Author(s):  
Roque Corral ◽  
Javier Crespo
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Stokes Equations ◽  
High Order ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
The Third ◽  
Third Dimension ◽  
Volume Method

A novel high-order finite volume method for the resolution of the Navier-Stokes equations is presented. The approach combines a third order finite volume method in an unstructured two-dimensional grid, with a spectral approximation in the third dimension. The method is suitable for the resolution of complex two-dimensional geometries that require the third dimension to capture three-dimensional non-linear unsteady effects, such as those for instance present in linear cascades with separated bubbles. Its main advantage is the reduction in the computational cost, for a given accuracy, with respect standard finite volume methods due to the inexpensive high-order discretization that may be obtained in the third direction using fast Fourier transforms. The method has been applied to the resolution of transitional bubbles in flat plates with adverse pressure gradients and realistic two-dimensional airfoils.

scholarly journals Flow Of Ice Sheets In The Vicinity Of Subglacial Peaks

1982 ◽  
Vol 3 ◽  
pp. 290-294 ◽  
Author(s):  
G. de Q. Robin ◽  
D. H. M. Millar
Keyword(s):  
Flow Line ◽  
Ice Sheets ◽  
Sharp Peak ◽  
Shear Stresses ◽  
Two Dimensional ◽  
Surface Slope ◽  
Antarctic Ice Sheet ◽  
The Third ◽  
Third Dimension ◽  
The Antarctic

Although changes of surface slope across a subglacial peak can be explained at least semi-quantitatively on a two-dimensional basis in terms of gradients of longitudinal and shear stresses along a flow line, we lack appreciation of flow in the third dimension which may tend to cause lower layers to flow around rather than over a sharp peak. This paper collects and surveys evidence relevant to flow in the third dimension and discusses the processes involved, particularly the evidence from radio-echo layering, and also discusses possible reasons for the lack of radio-echo layers near the base of the Antarctic ice sheet.

scholarly journals Flow Of Ice Sheets In The Vicinity Of Subglacial Peaks

1982 ◽  
Vol 3 ◽  
pp. 290-294 ◽  
Author(s):  
G. de Q. Robin ◽  
D. H. M. Millar
Keyword(s):  
Flow Line ◽  
Ice Sheets ◽  
Sharp Peak ◽  
Shear Stresses ◽  
Two Dimensional ◽  
Surface Slope ◽  
Antarctic Ice Sheet ◽  
The Third ◽  
Third Dimension ◽  
The Antarctic

Although changes of surface slope across a subglacial peak can be explained at least semi-quantitatively on a two-dimensional basis in terms of gradients of longitudinal and shear stresses along a flow line, we lack appreciation of flow in the third dimension which may tend to cause lower layers to flow around rather than over a sharp peak. This paper collects and surveys evidence relevant to flow in the third dimension and discusses the processes involved, particularly the evidence from radio-echo layering, and also discusses possible reasons for the lack of radio-echo layers near the base of the Antarctic ice sheet.

SOLVING THE TWO-DIMENSIONAL INVERSE FRACTAL PROBLEM WITH THE WAVELET TRANSFORM

Fractals ◽  
1996 ◽  
Vol 04 (04) ◽  
pp. 469-475 ◽  
Author(s):  
ZBIGNIEW R. STRUZIK
Keyword(s):  
Wavelet Transform ◽  
Scale Invariance ◽  
Wavelet Decomposition ◽  
Two Dimensions ◽  
The Self ◽  
Continuous Wavelet ◽  
Two Dimensional ◽  
One Dimensional ◽  
Affine Functions ◽  
The One

The methodology of the solution to the inverse fractal problem with the wavelet transform1,2 is extended to two-dimensional self-affine functions. Similar to the one-dimensional case, the two-dimensional wavelet maxima bifurcation representation used is derived from the continuous wavelet decomposition. It possesses translational and scale invariance necessary to reveal the invariance of the self-affine fractal. As many fractals are naturally defined on two-dimensions, this extension constitutes an important step towards solving the related inverse fractal problem for a variety of fractal types.

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