Numerical experiments with a salt dome

Geophysics ◽  
1989 ◽  
Vol 54 (8) ◽  
pp. 1042-1045 ◽  
Author(s):  
Irshad R. Mufti
Keyword(s):  
Numerical Experiments ◽  
Three Dimensional ◽  
Salt Dome ◽  
Model Structure ◽  
Two Dimensional ◽  
Geologic Structure ◽  
Cross Sectional ◽  
Salt Domes ◽  
D Model

A salt dome is a familiar example of a three‐dimensional (3-D) geologic structure. Surprisingly, most of the literature devoted to the investigation of salt domes deals only with cross‐sectional views of the domes. This is particularly true for seismic work. A notable exception is the work of French (1974) which discusses inaccuracies in focusing introduced by performing two‐dimensional (2-D) migration of data obtained over a 3-D model structure.

scholarly journals Three-dimensional Capsular Volume Measurements in Multidirectional Shoulder Instability

2018 ◽  
Vol 21 (3) ◽  
pp. 134-137
Author(s):  
Yong Cheol Jun ◽  
Young Lae Moon ◽  
Moustafa I Elsayed ◽  
Jae Hwan Lim ◽  
Dong Hyuk Cha
Keyword(s):  
Rotator Cuff ◽  
Surface Area ◽  
Three Dimensional ◽  
Volume Measurement ◽  
Control Group ◽  
Two Dimensional ◽  
Cross Sectional ◽  
Volume Measurements ◽  
Glenoid Surface ◽  
3D Software

BACKGROUND: In a previous study undertaken to quantify capsular volume in rotator cuff interval or axillary pouch, significant differences were found between controls and patients with instability. However, the results obtained were derived from two-dimensional cross sectional areas. In our study, we sought correlation between three-dimensional (3D) capsular volumes, as measured by magnetic resonance arthrography (MRA), and multidirectional instability (MDI) of the shoulder.METHODS: The MRAs of 21 patients with MDI of the shoulder and 16 control cases with no instability were retrospectively reviewed. Capsular areas determined by MRA were translated into 3D volumes using 3D software Mimics ver. 16 (Materilise, Leuven, Belgium), and glenoid surface area was measured in axial and coronal MRA views. Then, the ratio between capsular volume and glenoid surface area was calculated, and evaluated with control group.RESULTS: The ratio between 3D capsular volume and glenoid surface area was significantly increased in the MDI group (3.59 ± 0.83 cm³/cm²) compared to the control group (2.53 ± 0.62 cm³/cm²) (p < 0.01).CONCLUSIONS: From these results, we could support that capsular volume enlargement play an important role in MDI of the shoulder using volume measurement.

scholarly journals Three-dimensional molar enamel distribution and thickness in Australopithecus and Paranthropus

2008 ◽  
Vol 4 (4) ◽  
pp. 406-410 ◽  
Author(s):  
A.J Olejniczak ◽  
T.M Smith ◽  
M.M Skinner ◽  
F.E Grine ◽  
R.N.M Feeney ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Cross Sectional ◽  
Enamel Thickness ◽  
Australopithecus Africanus ◽  
Interspecific Differences ◽  
Dimensional Measurements ◽  
Dimensional Distribution ◽  
History Of ◽  
Thickness Measurements

Thick molar enamel is among the few diagnostic characters of hominins which are measurable in fossil specimens. Despite a long history of study and characterization of Paranthropus molars as relatively ‘hyper-thick’, only a few tooth fragments and controlled planes of section (designed to be proxies of whole-crown thickness) have been measured. Here, we measure molar enamel thickness in Australopithecus africanus and Paranthropus robustus using accurate microtomographic methods, recording the whole-crown distribution of enamel. Both taxa have relatively thick enamel, but are thinner than previously characterized based on two-dimensional measurements. Three-dimensional measurements show that P. robustus enamel is not hyper-thick, and A. africanus enamel is relatively thinner than that of recent humans. Interspecific differences in the whole-crown distribution of enamel thickness influence cross-sectional measurements such that enamel thickness is exaggerated in two-dimensional sections of A. africanus and P. robustus molars. As such, two-dimensional enamel thickness measurements in australopiths are not reliable proxies for the three-dimensional data they are meant to represent. The three-dimensional distribution of enamel thickness shows different patterns among species, and is more useful for the interpretation of functional adaptations than single summary measures of enamel thickness.

Cilia Microtubule Deformation: A Preliminary Report

1976 ◽  
Vol 34 ◽  
pp. 80-81
Author(s):  
R. Redding
Keyword(s):  
Dimensional Analysis ◽  
Preliminary Report ◽  
Recent Literature ◽  
Three Dimensional ◽  
Curvilinear Relationship ◽  
Two Dimensional ◽  
Dimensional Approach ◽  
Cross Sectional

Various hypotheses for the mechanism of ciliar motility either purport or oppose the concept of microtubule contraction. Recent literature supporting the Sliding Microtubule Model has established that microtubule doublets move relative to one another during the process of bending. Satir (1968) concluded that there is no change of length in the doublets during bending of cilia. He based his conclusion upon: (1) circular relationships and (2) a two dimensional configuration of the microtubules. Accuracy of the circular relationships is dependent upon how close the approximation is to the true curvilinear relationship expressed by a ciliutn. Cross sectional rotation during bending may limit the validity of two dimensional analysis. This communication is a preliminary report on a new, three dimensional approach for determining the deformational characteristics of elongation or shortening of microtubules as they may be expressed in cilia.

scholarly journals Remote, Volumetric Ultrasonic Imaging of Defects Using Two-Dimensional Laser Induced Phased Arrays

2021 ◽  
Author(s):  
Peter Lukacs ◽  
Geo Davis ◽  
Theodosia Stratoudaki ◽  
Yashar Javadi ◽  
Gareth Pierce ◽  
...  
Keyword(s):  
Phased Arrays ◽  
Extreme Environments ◽  
Three Dimensional ◽  
Fe Model ◽  
Two Dimensional ◽  
Destructive Testing ◽  
Cross Sectional ◽  
Volumetric Images ◽  
Different Depths ◽  
Non Destructive

Abstract Manufacturing processes, such as welding and additive manufacturing, take place at high temperatures and extreme environments that offer significant challenges to conventional non-destructive testing methods. Laser Induced Phased Arrays (LIPAs) have evolved as a promising testing method for the aforesaid applications due to its remote and couplant free operation. Contrary to transducer-based phased arrays, LIPAs are synthesized in post-processing by scanning the generation and detection lasers. The data from one-dimensional (1D) phased arrays are used to produce two-dimensional (2D), cross-sectional images, whereas the data from two-dimensional phased arrays generate three-dimensional (3D) images, thus providing more information on defect characterization. In this work, two-dimensional (2D) LIPAs are synthesized in the non-destructive thermoelastic regime using lasers for ultrasonic generation and detection, in order to image defects at different depths inside an aluminum sample. The acquired data is processed using the Total Focusing Method (TFM) algorithm to obtain volumetric images representing the interior of the sample. A 3D finite element (FE) model is also developed to support the experiments.

New Pseudo Functions To Control Numerical Dispersion

1975 ◽  
Vol 15 (04) ◽  
pp. 269-276 ◽  
Author(s):  
J.R. Kyte ◽  
D.W. Berry
Keyword(s):  
Capillary Pressure ◽  
Cross Section ◽  
Three Dimensional ◽  
Vertical Cross Section ◽  
Numerical Dispersion ◽  
Two Dimensional ◽  
Cross Sectional ◽  
One Dimensional ◽  
Sectional Model ◽  
The Cross

Abstract This paper presents an improved procedure for calculating dynamic pseudo junctions that may be used in two-dimensional, areal reservoir simulations to approximate three-dimensional reservoir behavior. Comparison of one-dimensional areal and two-dimensional vertical cross-sectional results for two example problems shows that the new pseudos accurately transfer problems shows that the new pseudos accurately transfer the effects of vertical variations in reservoir properties, fluid pressures, and saturations from the properties, fluid pressures, and saturations from the cross-sectional model to the areal model. The procedure for calculating dynamic pseudo-relative permeability accounts for differences in computing block lengths between the areal and cross-sectional models. Dynamic pseudo-capillary pressure transfers the effects of pseudo-capillary pressure transfers the effects of different pressure gradients in different layers of the cross-sectional model to the areal model. Introduction Jacks et al. have published procedures for calculating dynamic pseudo-relative permeabilities fro m vertical cross-section model runs. Their procedures for calculating pseudo functions are procedures for calculating pseudo functions are more widely applicable than other published approaches. They demonstrated that, in some cases, the derived pseudo functions could be used to simulate three-dimensional reservoir behavior using two-dimensional areal simulators. For our purposes, an areal simulator is characterized by purposes, an areal simulator is characterized by having only one computing block in the vertical dimension. The objectives of this paper are to present an improved procedure for calculating dynamic pseudo functions, including a dynamic pseudo-capillary pressure, and to demonstrate that the new procedure pressure, and to demonstrate that the new procedure generally is more applicable than any of the previously published approaches. The new pseudos previously published approaches. The new pseudos are similar to those derived by jacks et al. in that they are calculated from two-dimensional, vertical cross-section runs. They differ because (1) they account for differences in computing block lengths between the cross-sectional and areal models, and (2) they transfer the effects of different flow potentials in different layers of the cross-sectional potentials in different layers of the cross-sectional model to the areal model. Differences between cross-sectional and areal model block lengths are sometimes desirable to reduce data handling and computing costs for two-dimensional, areal model runs. For very large reservoirs, even when vertical calculations are eliminated by using pseudo functions, as many as 50,000 computing blocks might be required in the two-dimensional areal model to minimize important errors caused by numerical dispersion. The new pseudos, of course, cannot control numerical pseudos, of course, cannot control numerical dispersion in the cross-sectional runs. This is done by using a sufficiently large number of computing blocks along die length of the cross-section. The new pseudos then insure that no additional dispersion will occur in the areal model, regardless of the areal computing block lengths. Using this approach, the number of computing blocks in the two-dimensional areal model is reduced by a factor equal to the square of the ratio of the block lengths for the cross-sectional and areal models. The new pseudos do not prevent some loss in areal flow-pattern definition when the number of computing blocks in the two-dimensional areal model is reduced. A study of this problem and associated errors is beyond the scope of this paper. Our experience suggests that, for very large reservoirs with flank water injection, 1,000 or 2,000 blocks provide satisfactory definition. Many more blocks provide satisfactory definition. Many more blocks might be required for large reservoirs with much more intricate areal flow patterns. The next section presents comparative results for cross-sectional and one-dimensional areal models. These results demonstrate the reliability of the new pseudo functions and illustrate their advantages pseudo functions and illustrate their advantages over previously derived pseudos for certain situations. The relationship between two-dimensional, vertical cross-sectional and one-dimensional areal reservoir simulators has been published previously and will not be repeated here in any detail. Ideally, the pseudo functions should reproduce two-dimensional, vertical cross-sectional results when they are used in the corresponding one-dimensional areal model. SPEJ P. 269

scholarly journals Simulation of Three-Dimensional, Two-Phase Flow In Oil and Gas Reservoirs

1967 ◽  
Vol 7 (04) ◽  
pp. 377-388 ◽  
Author(s):  
K.H. Coats ◽  
R.L. Nielsen ◽  
Mary H. Terhune ◽  
A.G. Weber
Keyword(s):  
Oil And Gas ◽  
Flow Behavior ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Gas Reservoirs ◽  
Three Dimensional Flow ◽  
Cross Sectional ◽  
Dimensional Flow ◽  
Reservoir Flow ◽  
Fluid Phases

COATS, K.H., THE U. OF TEXAS, AUSTIN, TEX. NIELSEN, R.L., ESSO PRODUCTION RESEARCH CO., HOUSTON, TEX. MEMBERS AIME TERHUNE, MARY H., AMERICAN AIRLINES, TULSA, OKLA., WEBER, A.G., ESSO PRODUCTION RESEARCH CO., HOUSTON, TEX. MEMBER AIME Abstract Two computer-oriented techniques for simulating the three-dimensional flow behavior of two fluid phases in petroleum reservoirs were developed. Under the first technique the flow equations are solved to model three-dimensional flow in a reservoir. The second technique was developed for modeling flow in three-dimensional media that have sufficiently high permeability in the vertical direction so that vertical flow is not seriously restricted. Since this latter technique is a modified two-dimensional areal analysis, suitably structured three-dimensional reservoirs can be simulated at considerably lower computational expenses than is required using the three-dimensional analysis. A quantitative criterion is provided for determining when vertical communication is good enough to permit use of the modified two-dimensional areal analysis. The equations solved by both techniques treat both fluids as compressible, and, for gas-oil applications, provide for the evolution of dissolved gas. Accounted for are the effects of relative permeability, capillary pressure and gravity in addition to reservoir geometry and rock heterogeneity. Calculations are compared with laboratory waterflood data to indicate the validity of the analyses. Other results were calculated with both techniques which show the equivalence of the two solutions for reservoirs satisfying the vertical communication criterion. Introduction Obtaining the maximum profits from oil and gas reservoirs during all stages of depletion is the fundamental charge to the reservoir engineering profession. In recent years much quantitative assistance in evaluating field development programs has been goaded by computerized techniques for predicting reservoir flow behavior. Because of the spatially distributed and dynamic nature of producing operations, automatic optimization procedures, such as those now in use for planning refining operations, are not now available for planning reservoir development. However, present mathematical simulation techniques do furnish powerful means for making case studies to help in planning primary recovery operations and in selecting and timing supplemental recovery operations. A number of methods have been reported which simulate the flow of one, two or three fluid phases within porous media of one or two effective spatial dimensions. However, applying computer analyses to actual reservoirs have been limited mostly to two-dimensional areal or cross-sectional flow studies for two immiscible reservoir fluids. To obtain a three-dimensional picture of reservoir performance using such two-dimensional techniques, it has been necessary to interpret the calculations by combining somehow the results from essentially independent areal and cross-sectional studies. To the author's knowledge, the only other three-dimensional computational procedure, in addition to those presented here, was developed by Peaceman and Rachford to simulate the behavior of a laboratory waterflood. Two computational techniques which may be used to simulate three-dimensional flow of two fluid phases are described in this paper. The first method, called the "three-dimensional analysis", employs a fully three-dimensional mathematical model that treats simultaneously both the areal and cross-sectional aspects of reservoir flow. SPEJ P. 377ˆ

scholarly journals Interaction Potential between Parabolic Rotator and an Outside Particle

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Dan Wang ◽  
Yajun Yin ◽  
Jiye Wu ◽  
Xugui Wang ◽  
Zheng Zhong
Keyword(s):  
Interaction Potential ◽  
Numerical Experiments ◽  
Driving Forces ◽  
Three Dimensional ◽  
Pair Potential ◽  
Essential Elements ◽  
Curved Surfaces ◽  
Two Dimensional ◽  
Negative Exponential

At micro/nanoscale, the interaction potential between parabolic rotator and a particle located outside the rotator is studied on the basis of the negative exponential pair potential1/Rnbetween particles. Similar to two-dimensional curved surfaces, we confirm that the potential of the three-dimensional parabolic rotator and outside particle can also be expressed as a unified form of curvatures; that is, it can be written as the function of curvatures. Furthermore, we verify that the driving forces acting on the particle may be induced by the highly curved micro/nano-parabolic rotator. Curvatures and the gradient of curvatures are the essential elements forming the driving forces. Through the idealized numerical experiments, the accuracy of the curvature-based potential is preliminarily proved.

scholarly journals Orbital Shaped Standing Waves Using Chladni Plates

2019 ◽  
Author(s):  
Eric Janusson ◽  
Johanne Penafiel ◽  
Andrew Macdonald ◽  
Shaun MacLean ◽  
Irina Paci ◽  
...  
Keyword(s):  
Standing Wave ◽  
Atomic Orbital ◽  
Three Dimensional ◽  
Standing Waves ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Cross Sectional ◽  
Atomic Orbitals ◽  
Chemistry Students

Chemistry students are often introduced to the concept of atomic orbitals with a representation of a one-dimensional standing wave. The classic example is the harmonic frequencies which produce standing waves on a guitar string; a concept which is easily replicated in class with a length of rope. From here, students are typically exposed to a more realistic three-dimensional model, which can often be difficult to visualize. Extrapolation from a two-dimensional model, such as the vibrational modes of a drumhead, can be used to convey the standing wave concept to students more easily. We have opted to use Chladni plates which may be tuned to give a two-dimensional standing wave which serves as a cross-sectional representation of atomic orbitals. The demonstration, intended for first year chemistry students, facilitates the examination of nodal and anti-nodal regions of a Chladni figure which students can then connect to the concept of quantum mechanical parameters and their relationship to atomic orbital shape.

scholarly journals A New Dynamical Core of the Global Environmental Multiscale (GEM) Model with a Height-Based Terrain-Following Vertical Coordinate

2019 ◽  
Vol 147 (7) ◽  
pp. 2555-2578 ◽  
Author(s):  
Syed Zahid Husain ◽  
Claude Girard ◽  
Abdessamad Qaddouri ◽  
André Plante
Keyword(s):  
Numerical Experiments ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dynamical Core ◽  
Vertical Coordinate ◽  
Solution Approach ◽  
Global Environmental ◽  
Wide Range ◽  
Terrain Following ◽  
Global Environmental Multiscale

Abstract A new dynamical core of Environment and Climate Change Canada’s Global Environmental Multiscale (GEM) atmospheric model is presented. Unlike the existing log-hydrostatic-pressure-type terrain-following vertical coordinate, the proposed core adopts a height-based approach. The move to a height-based vertical coordinate is motivated by its potential for improving model stability over steep terrain, which is expected to become more prevalent with the increasing demand for very high-resolution forecasting systems. A dynamical core with height-based vertical coordinate generally requires an iterative solution approach. In addition to a three-dimensional iterative solver, a simplified approach has been devised allowing the use of a direct solver for the new dynamical core that separates a three-dimensional elliptic boundary value problem into a set of two-dimensional independent Helmholtz problems. The issue of dynamics–physics coupling has also been studied, and incorporating the physics tendencies within the discretized dynamical equations is found to be the most acceptable approach for the height-based vertical coordinate. The new dynamical core is evaluated using numerical experiments that include two-dimensional nonhydrostatic theoretical cases as well as 25-km resolution global forecasts. For a wide range of horizontal grid resolutions—from a few meters to up to 25 km—the results from the direct solution approach are found to be equivalent to the iterative approach for the new dynamical core. Furthermore, results from the different numerical experiments confirm that the new height-based dynamical core is equivalent to the existing pressure-based core in terms of solution accuracy.

Relationship of Challenge and Hindrance Stressors With Burnout and Its Three Dimensions

2015 ◽  
Vol 14 (4) ◽  
pp. 203-212 ◽  
Author(s):  
Angus Yongheng Yao ◽  
Muhammad Jamal ◽  
Evangelia Demerouti
Keyword(s):  
Emotional Exhaustion ◽  
Positive Relationship ◽  
Life Stage ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Cross Sectional ◽  
Cross Sectional Studies ◽  
Relationship Of

Abstract. The two-dimensional-work-stressor framework suggests that both challenge stressors and hindrance stressors have an undesirable (positive) relationship with burnout for all employees. However, the existing studies testing this framework either treated burnout as a global construct or used one burnout dimension and have not used age as a possible moderator. This paper reports two cross-sectional studies that examined the stressor-burnout relationship while burnout is conceptualized as three-dimensional (i.e., emotional exhaustion, cynicism, and inefficacy). Results indicate that although challenge and hindrance stressors show a similar (positive) relationship with exhaustion, they have differing relationships with cynicism and inefficacy. This study also explored how life stage influences the relationships between the two stressors and emotional exhaustion, cynicism, and inefficacy.

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