scholarly journals Multigrain indexing of unknown multiphase materials

2016 ◽  
Vol 49 (2) ◽  
pp. 616-621 ◽  
Author(s):  
Christian Wejdemann ◽  
Henning Friis Poulsen
Keyword(s):  
A Priori ◽  
Computing Time ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Complex Samples ◽  
Multiphase Materials ◽  
Mineral Phases ◽  
Dirac Comb ◽  
Crystallographic Planes ◽  
The Right

A multigrain indexing algorithm for use with samples comprising an arbitrary number of known or unknown phases is presented. No a priori crystallographic knowledge is required. The algorithm applies to data acquired with a monochromatic beam and a conventional two-dimensional detector for diffraction. Initially, candidate grains are found by searching for crystallographic planes, using a Dirac comb convoluted with a box function as a filter. Next, candidate grains are validated and the unit cell is optimized. The algorithm is validated by simulations. Simulations of 500 cementite grains and ∼100 reflections per grain resulted in 99.2% of all grains being indexed correctly and 99.5% of the reflections becoming associated with the right grain. Simulations with 200 grains associated with four mineral phases and 50–700 reflections per grain resulted in 99.9% of all grains being indexed correctly and 99.9% of the reflections becoming associated with the right grain. The main limitation is in terms of overlap of diffraction spots and computing time. Potential areas of use include three-dimensional grain mapping, structural solution and refinement studies of complex samples, and studies of dilute phases.

Separation of the 3D stress state of a loaded plate into two-dimensional tasks: bending and symmetric compression of the plate

2021 ◽  
Vol 103 (3) ◽  
pp. 53-62
Author(s):  
Victor Revenko ◽  
Andrian Revenko
Keyword(s):  
Boundary Conditions ◽  
Harmonic Functions ◽  
Three Dimensional ◽  
Partial Solution ◽  
Theory Of Elasticity ◽  
Two Dimensional ◽  
Normal Stresses ◽  
Equilibrium Equations ◽  
Dimensional Boundary ◽  
The Right

The three-dimensional stress-strain state of an isotropic plate loaded on all its surfaces is considered in the article. The initial problem is divided into two ones: symmetrical bending of the plate and a symmetrical compression of the plate, by specified loads. It is shown that the plane problem of the theory of elasticity is a special case of the second task. To solve the second task, the symmetry of normal stresses is used. Boundary conditions on plane surfaces are satisfied and harmonic conditions are obtained for some functions. Expressions of effort were found after integrating three-dimensional stresses that satisfy three equilibrium equations. For a thin plate, a closed system of equations was obtained to determine the harmonic functions. Displacements and stresses in the plate were expressed in two two-dimensional harmonic functions and a partial solution of the Laplace equation with the right-hand side, which is determined by the end loads. Three-dimensional boundary conditions were reduced to two-dimensional ones. The formula was found for experimental determination of the sum of normal stresses via the displacements of the surface of the plate.

scholarly journals Making Anaglyphs in Photoshop

2005 ◽  
Vol 13 (3) ◽  
pp. 36-39 ◽  
Author(s):  
Jerry Sedgewick
Keyword(s):  
Imaging System ◽  
Three Dimensional ◽  
Ct Scans ◽  
Two Dimensional ◽  
The Right ◽  
Two Dimensional Images

In order to achieve a three dimensional appearance to a pair of two dimensional images, two off-axis images can be produced and colorized. These can be overlayed slightly apart and then viewed through glasses with two differently colored sides, one color for the left eye and another for the right eye in combinations containing red, green or blue colors. These off-axis and colorized images are referred to as anaglyphs.Off-axis images can be achieved through the use of a tilting stage on a microscope, by physically changing the position of a camera in relation to a still object, or through changing the axis of an optical stack of sections, such as what is created by confocal/CT scans. Some images lend themselves more to a 3D look both by virtue of inherent three dimensionality limited by the resolution of the imaging system.

Application of an Implicit Relaxation Method Solving the Euler Equations for Time-Accurate Unsteady Problems

1990 ◽  
Vol 112 (4) ◽  
pp. 510-520 ◽  
Author(s):  
A. Brenneis ◽  
A. Eberle
Keyword(s):  
Euler Equations ◽  
Computing Time ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Relaxation Method ◽  
Coefficient Matrix ◽  
Viscous Effects ◽  
Left Hand ◽  
Implicit Equations ◽  
The Right

A numerical procedure is presented for computing time-accurate solutions of flows about two and three-dimensional configurations using the Euler equations in conservative form. A nonlinear Newton method is applied to solve the unfactored implicit equations. Relaxation is performed with a point Gauss-Seidel algorithm ensuring a high degree of vectorization by employing the so-called checkerboard scheme. The fundamental feature of the Euler solver is a characteristic variable splitting scheme (Godunov-type averaging procedure, linear locally one-dimensional Riemann solver) based on an eigenvalue analysis for the calculation of the fluxes. The true Jacobians of the fluxes on the right-hand side are used on the left-hand side of the first order in time-discretized Euler equations. A simple matrix conditioning needing only few operations is employed to evade singular behavior of the coefficient matrix. Numerical results are presented for transonic flows about harmonically pitching airfoils and wings. Comparisons with experiments show good agreement except in regions where viscous effects are evident.

scholarly journals The interaction of atoms and molecules with solid surfaces XII—Critical phenomena in a two-dimensional gas

1937 ◽  
Vol 163 (912) ◽  
pp. 132-138 ◽  
Keyword(s):  
Critical Temperature ◽  
Equation Of State ◽  
Critical Phenomena ◽  
Three Dimensional ◽  
Inert Gases ◽  
Two Dimensional ◽  
Lennard Jones ◽  
Low Concentrations ◽  
High Concentrations ◽  
The Right

In a paper recently published by Professor Lennard-Jones and the author (Lennard-Jones and Devonshire 1937) the equation of state of a gas at high concentrations has been calculated in terms of the interatomic fields. The equation found had the right kind of properties and, in particular, using the interatomic fields previously determined from the observed equation of state at low concentrations (Lennard-Jones 1931), the critical temperature was given correctly to within a few degrees for the inert gases. In this paper we shall apply the same method to determine the equation of state of a two-dimensional gas. Although such a gas cannot strictly be obtained in practice, an inert gas adsorbed on a surface (or in fact any gas held by van der Waals’ forces only) would probably behave very much like one, the fluctuations of the potential field over the surface not being of much importance. In confirmation of this it may be noted that the specific heat of argon adsorbed on charcoal was found by Simon (Simon 1935) to be equal to that of a perfect two-dimensional gas down to 60° K. A gas adsorbed on a liquid would be an even better representation of a two-dimensional one. Some measurements on the adsorption of krypton and xenon on liquid mercury have been made by Cassel and Neugebauer (Cassel and Neugebauer 1936), and they found no trace of any critical phenomena though they worked at temperatures considerably below the critical temperature of xenon. Our results are in agreement with this, for they show that the critical temperature of a two-dimensional gas should be about half that of the corresponding three-dimensional one.

Action potential morphology heterogeneity in the atrium and its effect on atrial reentry: a two-dimensional and quasi-three-dimensional study

2006 ◽  
Vol 364 (1843) ◽  
pp. 1349-1366 ◽  
Author(s):  
Samuel R Kuo ◽  
Natalia A Trayanova
Keyword(s):  
Action Potential ◽  
Action Potentials ◽  
Three Dimensional ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Two Dimensional ◽  
Crista Terminalis ◽  
Wave Dynamics ◽  
Continuous Surface ◽  
The Right

Atrial fibrillation (AF) is believed to be perpetuated by recirculating spiral waves. Atrial structures are often characterized with action potentials of varying morphologies; however, the role of the structure-dependent atrial electrophysiological heterogeneity in spiral wave behaviour is not well understood. The purpose of this study is to determine the effect of action potential morphology heterogeneity associated with the major atrial structures in spiral wave maintenance. The present study also focuses on how this effect is further modulated by the presence of the inherent periodicity in atrial structure. The goals of the study are achieved through the simulation of electrical behaviour in a two-dimensional atrial tissue model that incorporates the representation of action potentials in various structurally distinct regions in the right atrium. Periodic boundary conditions are then imposed to form a cylinder (quasi three-dimensional), thus allowing exploration of the additional effect of structure periodicity on spiral wave behaviour. Transmembrane potential maps and phase singularity traces are analysed to determine effects on spiral wave behaviour. Results demonstrate that the prolonged refractoriness of the crista terminalis (CT) affects the pattern of spiral wave reentry, while the variation in action potential morphology of the other structures does not. The CT anchors the spiral waves, preventing them from drifting away. Spiral wave dynamics is altered when the ends of the sheet are spliced together to form a cylinder. The main effect of the continuous surface is the generation of secondary spiral waves which influences the primary rotors. The interaction of the primary and secondary spiral waves decreased as cylinder diameter increased.

Field validation of a three-dimensional dynamic track-subgrade interaction model

2016 ◽  
Vol 232 (1) ◽  
pp. 130-143 ◽  
Author(s):  
Yin Gao ◽  
Hai Huang ◽  
Carlton L Ho ◽  
Aaron Judge
Keyword(s):  
Finite Element ◽  
Rhode Island ◽  
Computing Time ◽  
Three Dimensional ◽  
Interaction Model ◽  
Longitudinal Direction ◽  
The United States ◽  
Rigid Bodies ◽  
Accelerometer Data ◽  
Two Dimensional

An efficient three-dimensional dynamic track-subgrade interaction model has been formulated and then validated by field investigations at various field and traffic conditions including the effect of different train speeds and types of trains. The model contains a two-dimensional discrete support track model and three-dimensional computation-efficient finite element soil subgrade model. In the two-dimensional track model, the rail beam is modelled as an Euler-Bernoulli beam. The two-dimensional track model discretizes the tie and ballast as rigid bodies with designated spacing. The three-dimensional finite element subgrade model is simulated by plane-stress quadrilateral finite elements. The longitudinal direction of the subgrade model is expanded in the frequency domain and is assumed to be homogeneous. Therefore, the computing time could be largely reduced. A moving dynamic loading is applied on top of the rail. The model is capable of taking train speed variations and the profile change of the cross section into consideration. Multiple field instrumentation tests covering the two train types and different train speeds at the test site were then conducted to verify the accuracy of the dynamic track-subgrade interaction model. Testing site is located on the Amtrak's highest speed line (Northeast Corridor: 250 km/h) near Kingston, Rhode Island in the United States. A method to obtain the tie deflection from accelerometer data at Kingston was proposed and then validated at another site on the Northeast Corridor. Tie deflections measured in the field were compared with those predicted by the three-dimensional dynamic track-subgrade interaction model. It is concluded that this model can predict track performance accurately for the Kingston site.

An obstacle problem for Koiter’s shells

2019 ◽  
Vol 24 (10) ◽  
pp. 3061-3079 ◽  
Author(s):  
Philippe G Ciarlet ◽  
Paolo Piersanti
Keyword(s):  
Asymptotic Analysis ◽  
A Priori ◽  
Elastic Shell ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Three Dimensional Model ◽  
Limit Model ◽  
Membrane Shells ◽  
Point Of Departure ◽  
Confinement Condition

In this paper, we define, a priori, a natural two-dimensional Koiter’s model of a ‘general’ linearly elastic shell subject to a confinement condition. As expected, this model takes the form of variational inequalities posed over a non-empty closed convex subset of the function space used for the ‘unconstrained’ Koiter’s model. We then perform a rigorous asymptotic analysis as the thickness of the shell, considered a ‘small’ parameter, approaches zero, when the shell belongs to one of the three main classes of linearly elastic shells, namely elliptic membrane shells, generalized membrane shells and flexural shells. To illustrate the soundness of this model, we consider elliptic membrane shells to fix ideas. We then show that, in this case, the ‘limit’ model obtained in this fashion coincides with the two-dimensional ‘limit’ model obtained by means of another rigorous asymptotic analysis, but this time with the three-dimensional model of a ‘general’ linearly elastic shell subject to a confinement condition as a point of departure. In this fashion, our proposed Koiter’s model of a linearly elastic shell subject to a confinement condition is fully justified in this case, even though it is not itself a ‘limit’ model.

Sign in / Sign up

Export Citation Format

Share Document