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.

THE INTERACTION POTENTIAL BETWEEN MICRO/NANO CURVED SURFACE BODY WITH NEGATIVE GAUSS CURVATURE AND AN OUTSIDE PARTICLE

2015 ◽  
Vol 15 (06) ◽  
pp. 1540055
Author(s):  
DAN WANG ◽  
YAJUN YIN ◽  
JIYE WU ◽  
ZHENG ZHONG
Keyword(s):  
Interaction Potential ◽  
Numerical Experiments ◽  
Driving Forces ◽  
Pair Potential ◽  
Gauss Curvature ◽  
Curved Surface ◽  
Negative Exponential

Based on the negative exponential pair potential ([Formula: see text]), the interaction potential between curved surface body with negative Gauss curvature and an outside particle is proved to be of curvature-based form, i.e., it can be written as a function of curvatures. Idealized numerical experiments are designed to test the accuracy of the curvature-based potential. Compared with the previous results, it is confirmed that the interaction potential between curved surface body and an outside particle has a unified expression of curvatures regardless of the sign of Gauss curvature. Further, propositions below are confirmed: Highly curved surface body may induce driving forces, curvatures and the gradient of curvatures are the essential factors forming the driving forces.

scholarly journals Computer-Aided Sketching: Incorporating the Locus to Improve the Three-Dimensional Geometric Design

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1181 ◽  
Author(s):  
José Ignacio Rojas-Sola ◽  
David Hernández-Díaz ◽  
Ricardo Villar-Ribera ◽  
Vicente Hernández-Abad ◽  
Francisco Hernández-Abad
Keyword(s):  
Computational Geometry ◽  
Computer Aided Design ◽  
Three Dimensional ◽  
Geometric Design ◽  
Curved Surfaces ◽  
Two Dimensional ◽  
Technical Design ◽  
Computer Aided ◽  
Aided Design

This article presents evidence of the convenience of implementing the geometric places of the plane into commercial computer-aided design (CAD) software as auxiliary tools in the computer-aided sketching process. Additionally, the research considers the possibility of adding several intuitive spatial geometric places to improve the efficiency of the three-dimensional geometric design. For demonstrative purposes, four examples are presented. A two-dimensional figure positioned on the flat face of an object shows the significant improvement over tools currently available in commercial CAD software, both vector and parametric: it is more intuitive and does not require the designer to execute as many operations. Two more complex three-dimensional examples are presented to show how the use of spatial geometric places, implemented as CAD software functions, would be an effective and highly intuitive tool. Using these functions produces auxiliary curved surfaces with points whose notable features are a significant innovation. A final example provided solves a geometric place problem using own software designed for this purpose. The proposal to incorporate geometric places into CAD software would lead to a significant improvement in the field of computational geometry. Consequently, the incorporation of geometric places into CAD software could increase technical-design productivity by eliminating some intermediate operations, such as symmetry, among others, and improving the geometry training of less skilled users.

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 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.

A Solver for Helmholtz System Generated by the Discretization of Wave Shape Functions

2013 ◽  
Vol 5 (06) ◽  
pp. 791-808 ◽  
Author(s):  
Long Yuan ◽  
Qiya Hu
Keyword(s):  
Variational Formulation ◽  
Numerical Experiments ◽  
Three Dimensional ◽  
Discretization Method ◽  
Two Dimensional ◽  
Shape Functions ◽  
Wave Shape ◽  
Helmholtz Equations ◽  
Fast Solver ◽  
Block Diagonal

AbstractAn interesting discretization method for Helmholtz equations was introduced in B. Després [1]. This method is based on the ultra weak variational formulation (UWVF) and the wave shape functions, which are exact solutions of the governing Helmholtz equation. In this paper we are concerned with fast solver for the system generated by the method in [1]. We propose a new preconditioner for such system, which can be viewed as a combination between a coarse solver and the block diagonal preconditioner introduced in [13]. In our numerical experiments, this preconditioner is applied to solve both two-dimensional and three-dimensional Helmholtz equations, and the numerical results illustrate that the new preconditioner is much more efficient than the original block diagonal preconditioner.

Tension of organizing filaments of scroll waves

1994 ◽  
Vol 347 (1685) ◽  
pp. 611-630 ◽  
Keyword(s):  
Evolution Equation ◽  
Numerical Experiments ◽  
Asymptotic Theory ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Filament Length ◽  
Monotonic Change ◽  
Scroll Wave ◽  
Scroll Waves

We consider the asymptotic theory for the dynamics of organizing filaments of three-dimensional scroll waves. For a generic autowave medium where two dimensional vortices do not meander, we show that some of the coefficients of the evolution equation are always zero. This simpler evolution equation predicts a monotonic change of the total filament length with time, independently of initial conditions. Whether the filament will shrink or expand is determined by a single coefficient, the filament tension, that depends on the medium parameters. We illustrate the behaviour of scroll wave filaments with positive and negative tension by numerical experiments. In particular, we show that in the case of negative filament tension, the straight filament is unstable, and its evolution may lead to a multiplication of vortices.

scholarly journals RDTS-Based Two-Dimensional Temperature Monitoring with High Positioning Accuracy Using Grid Distribution

Sensors ◽  
2019 ◽  
Vol 19 (22) ◽  
pp. 4993
Author(s):  
Can Zhang ◽  
ZhongXie Jin
Keyword(s):  
Heat Source ◽  
Three Dimensional ◽  
Temperature Sensing ◽  
Curved Surfaces ◽  
Two Dimensional ◽  
Distributed Temperature Sensing ◽  
Positioning Accuracy ◽  
Flat Surfaces ◽  
Routing Design ◽  
Positioning Method

A novel two-dimensional (2D) positioning method based on Raman distributed temperature sensing (RDTS) has been reported to dramatically improve positioning accuracy. Using a well-designed 2D distribution of optical fiber and corresponding algorithms, the heat source can be accurately located without crosstalk; however, there is a tradeoff between sensing distance and positioning accuracy. In our experiments, an RDTS system with a spatial resolution of 0.8 m along a 3 km multimode fiber (MMF) is used with specific 2D routing rules and corresponding algorithms. A positioning accuracy of about 0.1 m is obtained without hardware modification, which could be improved through the dense arrangement of fiber; however, this would sacrifice the sensing length. This solution can be used for both flat surfaces and curved surfaces such as pipes or tank surfaces. This scheme can also be extended to three-dimensional positioning using a delicate routing design of sensing fiber.

High Resolution Microscopy of Multi-Layered Biological Crystals

1982 ◽  
Vol 40 ◽  
pp. 80-83
Author(s):  
H.A. Cohen ◽  
T.W. Jeng ◽  
W. Chiu
Keyword(s):  
High Resolution ◽  
Low Dose ◽  
Three Dimensional ◽  
Data Interpretation ◽  
Two Dimensional ◽  
Biological Objects ◽  
Density Maps ◽  
Density Map ◽  
Complex Crystal ◽  
High Resolution Microscopy

This tutorial will discuss the methodology of low dose electron diffraction and imaging of crystalline biological objects, the problems of data interpretation for two-dimensional projected density maps of glucose embedded protein crystals, the factors to be considered in combining tilt data from three-dimensional crystals, and finally, the prospects of achieving a high resolution three-dimensional density map of a biological crystal. This methodology will be illustrated using two proteins under investigation in our laboratory, the T4 DNA helix destabilizing protein gp32*I and the crotoxin complex crystal.

Instrumentation For Quantitative Microscopy

1977 ◽  
Vol 35 ◽  
pp. 206-209
Author(s):  
B. Ralph ◽  
A.R. Jones
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Automatic Data ◽  
Phase Volume Fraction ◽  
Statistical Confidence ◽  
Resultant Data ◽  
Automatic Data Collection ◽  
Third Dimension ◽  
Evolution Of Microstructure

In all fields of microscopy there is an increasing interest in the quantification of microstructure. This interest may stem from a desire to establish quality control parameters or may have a more fundamental requirement involving the derivation of parameters which partially or completely define the three dimensional nature of the microstructure. This latter categorey of study may arise from an interest in the evolution of microstructure or from a desire to generate detailed property/microstructure relationships. In the more fundamental studies some convolution of two-dimensional data into the third dimension (stereological analysis) will be necessary.In some cases the two-dimensional data may be acquired relatively easily without recourse to automatic data collection and further, it may prove possible to perform the data reduction and analysis relatively easily. In such cases the only recourse to machines may well be in establishing the statistical confidence of the resultant data. Such relatively straightforward studies tend to result from acquiring data on the whole assemblage of features making up the microstructure. In this field data mode, when parameters such as phase volume fraction, mean size etc. are sought, the main case for resorting to automation is in order to perform repetitive analyses since each analysis is relatively easily performed.

A linearity test for thick specimens imaged by HVEM over a 180° angular range

1991 ◽  
Vol 49 ◽  
pp. 552-553
Author(s):  
Yu Liu
Keyword(s):  
Phase Contrast ◽  
Three Dimensional ◽  
Angular Range ◽  
Two Dimensional ◽  
Back Projection ◽  
Line Integral ◽  
Exponential Law ◽  
Transmission Electron ◽  
Absorption Law ◽  
Linearity Test

The image obtained in a transmission electron microscope is the two-dimensional projection of a three-dimensional (3D) object. The 3D reconstruction of the object can be calculated from a series of projections by back-projection, but this algorithm assumes that the image is linearly related to a line integral of the object function. However, there are two kinds of contrast in electron microscopy, scattering and phase contrast, of which only the latter is linear with the optical density (OD) in the micrograph. Therefore the OD can be used as a measure of the projection only for thin specimens where phase contrast dominates the image. For thick specimens, where scattering contrast predominates, an exponential absorption law holds, and a logarithm of OD must be used. However, for large thicknesses, the simple exponential law might break down due to multiple and inelastic scattering.

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