Computationally efficient method to calculate the Coulomb interactions in three-dimensional systems with two-dimensional periodicity

2002 ◽  
Vol 116 (8) ◽  
pp. 3430-3448 ◽  
Author(s):  
Masaaki Kawata ◽  
Masuhiro Mikami ◽  
Umpei Nagashima
Keyword(s):  
Efficient Method ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Coulomb Interactions ◽  
Computationally Efficient

Direct simulation of evolution and control of three-dimensional instabilities in attachment-line boundary layers

1995 ◽  
Vol 291 ◽  
pp. 369-392 ◽  
Author(s):  
Ronald D. Joslin
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Plate Boundary ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Computationally Efficient ◽  
Simulation Results ◽  
Dimensional Simulation ◽  
Attachment Line

The spatial evolution of three-dimensional disturbances in an attachment-line boundary layer is computed by direct numerical simulation of the unsteady, incompressible Navier–Stokes equations. Disturbances are introduced into the boundary layer by harmonic sources that involve unsteady suction and blowing through the wall. Various harmonic-source generators are implemented on or near the attachment line, and the disturbance evolutions are compared. Previous two-dimensional simulation results and nonparallel theory are compared with the present results. The three-dimensional simulation results for disturbances with quasi-two-dimensional features indicate growth rates of only a few percent larger than pure two-dimensional results; however, the results are close enough to enable the use of the more computationally efficient, two-dimensional approach. However, true three-dimensional disturbances are more likely in practice and are more stable than two-dimensional disturbances. Disturbances generated off (but near) the attachment line spread both away from and toward the attachment line as they evolve. The evolution pattern is comparable to wave packets in flat-plate boundary-layer flows. Suction stabilizes the quasi-two-dimensional attachment-line instabilities, and blowing destabilizes these instabilities; these results qualitatively agree with the theory. Furthermore, suction stabilizes the disturbances that develop off the attachment line. Clearly, disturbances that are generated near the attachment line can supply energy to attachment-line instabilities, but suction can be used to stabilize these instabilities.

Computationally Efficient Model for 2D Ion Implantation Simulation

1997 ◽  
Vol 490 ◽  
Author(s):  
Misha Temkin ◽  
Ivan Chakarov
Keyword(s):  
Ion Implantation ◽  
Efficient Method ◽  
Two Dimensional ◽  
Computationally Efficient ◽  
Crystalline Materials ◽  
One Dimensional ◽  
The One

ABSTRACTA computationally efficient method for ion implantation simulation is presented. The method allows two-dimensional ion implantation profiles in arbitrary shaped structures to be calculated and is valid for both amorphous and crystalline materials. It uses an extension of the one-dimensional dual Pearson approximation into the second dimension.

The generation of possible crystal structures of primary amides

1983 ◽  
Vol 388 (1794) ◽  
pp. 133-175 ◽  
Keyword(s):  
Crystal Structures ◽  
Van Der Waals ◽  
Three Dimensional ◽  
Close Packing ◽  
Two Dimensional ◽  
Coulomb Interactions ◽  
Primary Amide ◽  
Size And Shape ◽  
Dimensional Crystal ◽  
Hydrogen Bonded

Procedures are outlined for generation of crystal structures of primary amide molecules by constructing the possible ways in which the molecules may pack. For each given one- or two-dimensional hydrogen-bonded array, ensembles of three-dimensional crystal structures are generated by considering the possible ways in which the arrays may be juxtaposed. Observed and generated hypothetical molecular arrangements are analysed to highlight both favourable and unfavourable features, par­ticularly in terms of close packing principles, the size and shape of the molecule, van der Waals and Coulomb interactions and N-H ∙ ∙ ∙ O bonding geometry.

scholarly journals Smoothness correction for better SOFI imaging

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Siewert Hugelier ◽  
Wim Vandenberg ◽  
Tomáš Lukeš ◽  
Kristin S. Grußmayer ◽  
Paul H. C. Eilers ◽  
...  
Keyword(s):  
Statistical Analysis ◽  
Fluorescence Imaging ◽  
Spatial Resolution ◽  
Three Dimensional ◽  
Super Resolution ◽  
Cellular Structures ◽  
Stationary Processes ◽  
Two Dimensional ◽  
Computationally Efficient ◽  
Statistical Analysis Methods

AbstractSub-diffraction or super-resolution fluorescence imaging allows the visualization of the cellular morphology and interactions at the nanoscale. Statistical analysis methods such as super-resolution optical fluctuation imaging (SOFI) obtain an improved spatial resolution by analyzing fluorophore blinking but can be perturbed by the presence of non-stationary processes such as photodestruction or fluctuations in the illumination. In this work, we propose to use Whittaker smoothing to remove these smooth signal trends and retain only the information associated to independent blinking of the emitters, thus enhancing the SOFI signals. We find that our method works well to correct photodestruction, especially when it occurs quickly. The resulting images show a much higher contrast, strongly suppressed background and a more detailed visualization of cellular structures. Our method is parameter-free and computationally efficient, and can be readily applied on both two-dimensional and three-dimensional data.

A PRECISE METHOD FOR DETERMINING CONTOURED SURFACES

1982 ◽  
Vol 22 (1) ◽  
pp. 205 ◽  
Author(s):  
G. M. Philip ◽  
D. F. Watson
Keyword(s):  
Cross Sections ◽  
Control Point ◽  
Three Dimensional ◽  
Control Points ◽  
Two Dimensional ◽  
Computationally Efficient ◽  
Precise Method ◽  
Contour Maps ◽  
Delaunay Tessellations ◽  
Rapid Calculation

Although the petroleum geologist is concerned with analysing three-dimensional data, he relies entirely on two-dimensional portrayals - cross-sections and particularly contour maps of all types. With the advent of digital computers, machine contouring has become increasingly common, but little attention has been directed to the limitations of the various algorithms that can be employed to generate contour maps from a set of control points. For example, it is not widely appreciated that contouring procedures which faithfully honour the value of original control points produce poor predictions at locations where no control is available. Contouring a published set of topographic data shows how this and other limitations lead to approximations and errors in machine-generated contours.A new method based on triangulation interpolation using Delaunay tessellations (deltri analysis) is superior to existing methods. Not only does the method give the most accurate and objective measurement and display of the contoured surface, but it is also computationally efficient. Rapid calculation of volume of closure over contoured structures is possible. The method also allows estimation of the adequacy of the data on which the contouring is based by introducing a measure of 'roughness' of the surface. This is achieved by analysing the directions of normals to triangles surrounding each control point.

Simple but Efficient Method for Integrating 1/r Singularities

2013 ◽  
Vol 444-445 ◽  
pp. 615-620
Author(s):  
Feng Liu ◽  
Hong Zheng ◽  
Chun Guang Li
Keyword(s):  
Efficient Method ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Numerical Examples ◽  
Integration Schemes ◽  
Integration Techniques ◽  
Elastic Fracture ◽  
Duffy Transformation

New integration schemes are presented for integrands with singularity of 1/r. We partition the element with a singular center into several triangles sharing the center. Then, a transformation between a standard square and each of the triangles is conducted. We prove such a transformation itself brings about the Jacobian with the factor r, leading to no need to introduce any other transformation. Both two-dimensional and three-dimensional cases are considered. Compared to the Duffy transformation, the proposed methods enjoy more excellent numerical properties. Numerical examples in elastic fracture are also presented to illustrate the performance of the new integration techniques.

scholarly journals 3-D depth migration via McClellan transformations

Geophysics ◽  
1991 ◽  
Vol 56 (11) ◽  
pp. 1778-1785 ◽  
Author(s):  
Dave Hale
Keyword(s):  
Computational Efficiency ◽  
Digital Filters ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Computationally Efficient ◽  
One Dimensional ◽  
Depth Migration ◽  
Large N ◽  
The Cost ◽  
Accurate Imaging

Three‐dimensional seismic wavefields may be extrapolated in depth, one frequency at a time, by two‐dimensional convolution with a circularly symmetric, frequency‐ and velocity‐dependent filter. This depth extrapolation, performed for each frequency independently, lies at the heart of 3-D finite‐difference depth migration. The computational efficiency of 3-D depth migration depends directly on the efficiency of this depth extrapolation. McClellan transformations provide an efficient method for both designing and implementing two‐dimensional digital filters that have a particular form of symmetry, such as the circularly symmetric depth extrapolation filters used in 3-D depth migration. Given the coefficients of one‐dimensional, frequency‐ and velocity‐dependent filters used to accomplish 2-D depth migration, McClellan transformations lead to a simple and efficient algorithm for 3-D depth migration. 3-D depth migration via McClellan transformations is simple because the coefficients of two‐dimensional depth extrapolation filters are never explicitly computed or stored; only the coefficients of the corresponding one‐dimensional filter are required. The algorithm is computationally efficient because the cost of applying the two‐dimensional extrapolation filter via McClellan transformations increases only linearly with the number of coefficients N in the corresponding one‐dimensional filter. This efficiency is not intuitively obvious, because the cost of convolution with a two‐dimensional filter is generally proportional to [Formula: see text]. Computational efficiency is particularly important for 3-D depth migration, for which long extrapolation filters (large N) may be required for accurate imaging of steep reflectors.

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