Cellular Automaton Simulations of Surface Mass Transport Due to Curvature Gradients: Simulations of Sintering in 3-D.

1991 ◽  
Vol 249 ◽  
Author(s):  
D.P. Bentz ◽  
P.J.P. Pimienta ◽  
E.J. Garboczi ◽  
W.C. Carter
Keyword(s):  
Cellular Automaton ◽  
Scaling Laws ◽  
Chemical Potential ◽  
Pore Space ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Computation Method ◽  
Surface Mass ◽  
Digital Version ◽  
The Continuum

ABSTRACTA cellular automaton algorithm is described that simulates the evolution of a surface driven by the reduction of chemical potential differences on the surface. When the surface tension is isotropic, the chemical potential is proportional to the curvature at the surface. This process is important in the development of microstructure during the sintering of powders. The algorithm is implemented in two and three dimensions in a digital image mode, using discrete pixels to represent continuum objects. The heart of the algorithm is a pixel-counting-based method for computing the potential at a pixel located in a digital surface. This method gives an approximate measure of the curvature at the given surface pixel. The continuum version of this method is analytically shown to give the true curvature at a point on a continuum surface. The digital version of the curvature computation method is shown to obey the scaling laws derived for the continuum version. The evolution of the surface of a three dimensional loosely packed powder, along with the percolation characteristics of its pore space, are computed as an example of the algorithm.

scholarly journals Analytical procedures for 3D mapping at the Photogeological Laboratory of the Geological Survey of Denmark and Greenland

2018 ◽  
pp. 99-104 ◽  
Author(s):  
Erik Vest Sørensen ◽  
Mads Dueholm
Keyword(s):  
Three Dimensional ◽  
Three Dimensions ◽  
Geological Survey ◽  
Aerial Photographs ◽  
3D Mapping ◽  
Digital Version ◽  
Remote Sensing Technique ◽  
Small Frame ◽  
Analytical Procedures ◽  
Steep Terrain

Photogrammetry is a classical remote sensing technique dating back to the 19th century that allows geologists to make three-dimensional observations in two-dimensional images using human stereopsis. Pioneering work in the 1980s and 1990s (Dueholm 1992) combined the use of vertical (nadirlooking) aerial photographs with oblique stereo images from handheld small-frame cameras into so-called multi-model photogrammetry. This was a huge technological step forward that made it possible to map, in three dimensions, steep terrain that would otherwise be inaccessible or poorly resolved in conventional nadir-looking imagery. The development was fundamental to the mapping and investigation of e.g. the Nuussuaq basin (Pedersen et al. 2006). Digital photogrammetry, the all-digital version of multi-model photogrammetry, is nowadays an efficient and powerful geological tool that is used by the Photogeological Laboratory at the Geological Survey of Denmark and Greenland (GEUS) to address geological problems in a range of projects from 3D mapping to image-based surface reconstruction and orthophoto production. Here we present an updated description (complementary to Dueholm 1992) of the analytical procedures in the typical digital workflow used in current 3Dmapping projects at GEUS.

Improving Turbine Component Efficiency

1979 ◽  
Author(s):  
K. D. Mach
Keyword(s):  
Structural Integrity ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Computation Method ◽  
Test Procedures ◽  
Aerodynamic Efficiency ◽  
Turbine Engine ◽  
Careful Control ◽  
Component Efficiency

The thermal efficiency of a gas turbine engine depends on the cycle pressure and temperature ratio and on the aerodynamic efficiencies of the gas path components. Maintaining and/or improving structural integrity and aerodynamic efficiency in this high pressure, high temperature environment is the preeminent problem of the turbine designer. High gas temperatures require at least some of the metal structures to be cooled, yet cooling air is a loss to the cycle and its consumption must be kept to a minimum. Research into cooling techniques and boundary layer behavior on airfoils and endwalls and into test procedures for obtaining heat transfer data are providing some of the answers the designer needs. Increased operating pressures generate increased mechanical stresses. Finite element analyses and automated design procedures are proving to be powerful aids to the designer. Improving aerodynamic efficiency requires careful control of the flow in three dimensions, particularly in low aspect ratio machines. The first practical computation method for three-dimensional, viscous, transonic flows became available in late 1977 and has made this one of the most exciting areas of turbine technology. Additional gains in aerodynamic efficiency can be realized by controlling leakages, especially those over the rotor tip, by accounting for the transient interactions between rotor and stator and by careful control of discharged coolant flow. This paper briefly describes the turbine cooling research conducted by the Air Force Aero Propulsion Laboratory and describes mor extensively the AFAPL programs in turbine aerodynamics, including applications of three-dimensional flow analysis.

Velocity distribution function for a dilute granular material in shear flow

1997 ◽  
Vol 340 ◽  
pp. 319-341 ◽  
Author(s):  
V. KUMARAN
Keyword(s):  
Distribution Function ◽  
Shear Flow ◽  
Velocity Distribution ◽  
Scaling Laws ◽  
Three Dimensional ◽  
Particle Diameter ◽  
Velocity Distribution Function ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Binary Collisions

The velocity distribution function for the steady shear flow of disks (in two dimensions) and spheres (in three dimensions) in a channel is determined in the limit where the frequency of particle–wall collisions is large compared to particle–particle collisions. An asymptotic analysis is used in the small parameter ε, which is naL in two dimensions and n2L in three dimensions, where n is the number density of particles (per unit area in two dimensions and per unit volume in three dimensions), L is the separation of the walls of the channel and a is the particle diameter. The particle–wall collisions are inelastic, and are described by simple relations which involve coefficients of restitution et and en in the tangential and normal directions, and both elastic and inelastic binary collisions between particles are considered. In the absence of binary collisions between particles, it is found that the particle velocities converge to two constant values (ux, uy) =(±V, 0) after repeated collisions with the wall, where ux and uy are the velocities tangential and normal to the wall, V=(1−et) Vw/(1+et), and Vw and −Vw are the tangential velocities of the walls of the channel. The effect of binary collisions is included using a self-consistent calculation, and the distribution function is determined using the condition that the net collisional flux of particles at any point in velocity space is zero at steady state. Certain approximations are made regarding the velocities of particles undergoing binary collisions in order to obtain analytical results for the distribution function, and these approximations are justified analytically by showing that the error incurred decreases proportional to ε1/2 in the limit ε→0. A numerical calculation of the mean square of the difference between the exact flux and the approximate flux confirms that the error decreases proportional to ε1/2 in the limit ε→0. The moments of the velocity distribution function are evaluated, and it is found that 〈u2x〉→V2, 〈u2y〉 ∼V2ε and − 〈uxuy〉 ∼ V2εlog(ε−1) in the limit ε→0. It is found that the distribution function and the scaling laws for the velocity moments are similar for both two- and three-dimensional systems.

Spatial dispersion of interstellar civilizations: a probabilistic site percolation model in three dimensions

2012 ◽  
Vol 12 (1) ◽  
pp. 45-52 ◽  
Author(s):  
Thomas W. Hair ◽  
Andrew D. Hedman
Keyword(s):  
Cellular Automaton ◽  
Uniform Distribution ◽  
Spatial Dispersion ◽  
Three Dimensional ◽  
Percolation Model ◽  
Three Dimensions ◽  
Site Percolation ◽  
Original Seed ◽  
Probabilistic Cellular Automaton

AbstractA model of the spatial emergence of an interstellar civilization into a uniform distribution of habitable systems is presented. The process of emigration is modelled as a three-dimensional probabilistic cellular automaton. An algorithm is presented which defines both the daughter colonies of the original seed vertex and all subsequent connected vertices, and the probability of a connection between any two vertices. The automaton is analysed over a wide set of parameters for iterations that represent up to 250 000 years within the model's assumptions. Emigration patterns are characterized and used to evaluate two hypotheses that aim to explain the Fermi Paradox. The first hypothesis states that interstellar emigration takes too long for any civilization to have yet come within a detectable distance, and the second states that large volumes of habitable space may be left uninhabited by an interstellar civilization and Earth is located in one of these voids.

scholarly journals Bound states in the continuum in open acoustic resonators

2015 ◽  
Vol 780 ◽  
pp. 370-387 ◽  
Author(s):  
A. A. Lyapina ◽  
D. N. Maksimov ◽  
A. S. Pilipchuk ◽  
A. F. Sadreev
Keyword(s):  
Bound States ◽  
Three Dimensional ◽  
Life Time ◽  
Three Dimensions ◽  
Destructive Interference ◽  
Acoustic Resonators ◽  
Coupled Mode ◽  
Resonant Modes ◽  
Axisymmetric Duct ◽  
The Continuum

We consider bound states in the continuum (BSCs) or embedded trapped modes in two- and three-dimensional acoustic axisymmetric duct–cavity structures. We demonstrate numerically that, under variation of the length of the cavity, multiple BSCs occur due to the Friedrich–Wintgen two-mode full destructive interference mechanism. The BSCs are detected by tracing the resonant widths to the points of the collapse of Fano resonances where one of the two resonant modes acquires infinite life-time. It is shown that the approach of the acoustic coupled mode theory cast in the truncated form of a two-mode approximation allows us to analytically predict the BSC frequencies and shape functions to a good accuracy in both two and three dimensions.

scholarly journals MODELING OF MULTISCALE POROUS MEDIA

2011 ◽  
Vol 27 (1) ◽  
pp. 23 ◽  
Author(s):  
Bibhu Biswal ◽  
Pål-Eric Øren ◽  
Rudolf J Held ◽  
Stig Bakke ◽  
Rudolf Hilfer
Keyword(s):  
Porous Media ◽  
Pore Space ◽  
Three Dimensional ◽  
Flow Simulation ◽  
Pore Scale ◽  
Matrix Space ◽  
Spatially Correlated ◽  
Wide Variability ◽  
Fully Connected ◽  
The Continuum

A stochastic geometrical modeling method for reconstructing three dimensional pore scale microstructures of multiscale porous media is presented. In this method the porous medium is represented by a random but spatially correlated structure of objects placed in the continuum. The model exhibits correlations with the sedimentary textures, scale dependent intergranular porosity over many decades, vuggy or dissolution porosity, a percolating pore space, a fully connected matrix space, strong resolution dependence and wide variability in the permeabilities and other properties. The continuum representation allows discretization at arbitrary resolutions providing synthetic micro-computertomographic images for resolution dependent fluid flow simulation. Model implementations for two different carbonate rocks are presented. The method can be used to generate pore scale models of a wide class of multiscale porous media.

Pore Structures in the Biomineralized Byssus of Anomia simplex

2016 ◽  
Vol 672 ◽  
pp. 71-79 ◽  
Author(s):  
Simon Frølich ◽  
Hanna Leemreize ◽  
Jesper Skovhus Thomsen ◽  
Henrik Birkedal
Keyword(s):  
Computed Tomography ◽  
Pore Space ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Marine Bivalve ◽  
Micro Computed Tomography ◽  
Significant Challenge ◽  
Pore Structures ◽  
Dimensional Distribution ◽  
Biological Organisms

Underwater attachment is a significant challenge, for which we have no good general solutions in our technology. Yet, a number of biological organisms have evolved solutions to this problem. One intriguing approach to underwater attachment is that of the marine bivalve mussel Anomia simplex that uses a biomineralized byssus to permanently anchor itself to substrates. The byssus has a highly complex hierarchical structure and contains over 90 wt% CaCO3. The byssus features a complex set of porosities, presumed to be highly important for the function of the attachment system. The pore space is the main focus of the present work. We characterize the three dimensional distribution of pore spaces in the byssus using micro-computed tomography (µCT) through a combination of in house mCT and high resolution synchrotron µCT. The pore structures are observed to fall into distinct categories in various parts of the byssus. We discuss the branching of one set of pores that reach the byssus substrate interface in particular. They form a network reaching the byssus surface that we now visualize in three dimensions.

LOW DENSITY HUBBARD MODEL IN TWO AND THREE DIMENSIONS

1992 ◽  
Vol 06 (12) ◽  
pp. 753-760
Author(s):  
S. YU. KHLEBNIKOV
Keyword(s):  
Scattering Length ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Low Density ◽  
Two Dimensional ◽  
Three Dimensional Model ◽  
Hubbard Models ◽  
Short Range Repulsion ◽  
Upper Half Plane ◽  
The Continuum

We consider two- and three-dimensional repulsive Hubbard models at low density, using the gas approximation. The large-U three-dimensional model is shown to behave as a Fermi liquid and the corresponding two-particle scattering length is found. In the two-dimensional case we find that the gas approximation is inconsistent, as indicated by an isolated pole of the two-particle Green function below the occupied states in the upper half-plane. This behaviour is specific to the lattice system as opposed to the continuum two-dimensional Fermi gas with short-range repulsion.

Improving Turbine Component Efficiency

1980 ◽  
Vol 102 (2) ◽  
pp. 434-436
Author(s):  
K. D. Mach
Keyword(s):  
Structural Integrity ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Metal Structure ◽  
Three Dimensions ◽  
Computation Method ◽  
Test Procedures ◽  
Aerodynamic Efficiency ◽  
Careful Control ◽  
Component Efficiency

The thermal efficiency of a gas turbine engine depends on the cycle pressure and temperature ratio and on the aerodynamic efficiencies of the gas path components. Maintaining and/or improving structural integrity and aerodynamic efficiency in this high pressure, high temperature environment is the preeminent problem of the turbine designer. High gas temperatures require at least some of the metal structure to be cooled, yet cooling air is a loss to the cycle and its consumption must be kept to a minimum. Research into cooling techniques and boundary layer behavior on airfoils and endwalls and into test procedures for obtaining heat transfer data are providing some of the answers the designer needs. Increased operating-pressures generate increased mechanical stresses. Finite element analyses and automated design procedures are proving to be powerful aids to the designer. Improving aerodynamic efficiency requires careful control of the flow in three dimensions, particularly in low aspect ratio machines. The first practical computation method for three-dimensional, viscous, transonic flows became available in late 1977 and has made this one of the most exciting areas of turbine technology. Additional gains in aerodynamic efficiency can be realized by controlling leakages, especially those over the rotor tip, by accounting for the transient interactions between rotor and stator; and by careful control of discharged coolant flow. This paper briefly describes the turbine cooling research conducted by the Air Force Aero Propulsion Laboratory and describes more extensively the AFAPL programs in turbine aerodynamics, including applications of three-dimensional flow analysis.

convergent-beam diffraction from surfaces

1987 ◽  
Vol 45 ◽  
pp. 30-33
Author(s):  
J. A. Eades ◽  
A. E. Smith ◽  
D. F. Lynch
Keyword(s):  
Reciprocal Lattice ◽  
Three Dimensional ◽  
Grazing Incidence ◽  
Three Dimensions ◽  
Plane Figure ◽  
Transmission Electron ◽  
Convergent Beam ◽  
Beam Patterns ◽  
Beam Diffraction

It is quite simple (in the transmission electron microscope) to obtain convergent-beam patterns from the surface of a bulk crystal. The beam is focussed onto the surface at near grazing incidence (figure 1) and if the surface is flat the appropriate pattern is obtained in the diffraction plane (figure 2). Such patterns are potentially valuable for the characterization of surfaces just as normal convergent-beam patterns are valuable for the characterization of crystals.There are, however, several important ways in which reflection diffraction from surfaces differs from the more familiar electron diffraction in transmission.GeometryIn reflection diffraction, because of the surface, it is not possible to describe the specimen as periodic in three dimensions, nor is it possible to associate diffraction with a conventional three-dimensional reciprocal lattice.

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