Comparison of two numerical methods for the integration of the Takagi–Taupin equations

1981 ◽  
Vol 14 (6) ◽  
pp. 432-436 ◽  
Author(s):  
C. Nourtier ◽  
D. Taupin
Keyword(s):  
Numerical Calculation ◽  
Numerical Methods ◽  
Two Dimensions ◽  
Integration Step ◽  
Order Method ◽  
Third Order ◽  
Acta Cryst ◽  
One Dimensional ◽  
Numerical Resolution ◽  
The One

Two methods for the numerical resolution of the Takagi-Taupin equations are compared. It is shown that for a small integration step Taupin's [Acta Cryst. (1967), 23, 25–35] extension to two dimensions of the one-dimensional Runge–Kutta third-order method is more accurate than the algorithm of Authier, Malgrange & Tournarie [Acta Cryst. (1968), A24, 126–136] but, for a given precision, Authier, Malgrange & Tournarie's method is faster than Taupin's so the former will usually be preferred for numerical calculation.

scholarly journals Assessing a Linear Nanosystem's Limiting Reliability from its Components

2008 ◽  
Vol 45 (03) ◽  
pp. 879-887 ◽  
Author(s):  
Nader Ebrahimi
Keyword(s):  
Present State ◽  
Size Range ◽  
Two Dimensions ◽  
The Other ◽  
One Dimension ◽  
Present Moment ◽  
One Dimensional ◽  
The One ◽  
Fixed Moment ◽  
Nanosized Systems

Nanosystems are devices that are in the size range of a billionth of a meter (1 x 10-9) and therefore are built necessarily from individual atoms. The one-dimensional nanosystems or linear nanosystems cover all the nanosized systems which possess one dimension that exceeds the other two dimensions, i.e. extension over one dimension is predominant over the other two dimensions. Here only two of the dimensions have to be on the nanoscale (less than 100 nanometers). In this paper we consider the structural relationship between a linear nanosystem and its atoms acting as components of the nanosystem. Using such information, we then assess the nanosystem's limiting reliability which is, of course, probabilistic in nature. We consider the linear nanosystem at a fixed moment of time, say the present moment, and we assume that the present state of the linear nanosystem depends only on the present states of its atoms.

scholarly journals Fractional Heat Conduction Models and Thermal Diffusivity Determination

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Monika Žecová ◽  
Ján Terpák
Keyword(s):  
Heat Conduction ◽  
Thermal Diffusivity ◽  
Numerical Methods ◽  
Fractional Order ◽  
Experimental Verification ◽  
Heat Conduction Equation ◽  
Historical Overview ◽  
One Dimensional ◽  
The One ◽  
Fractional Heat Conduction

The contribution deals with the fractional heat conduction models and their use for determining thermal diffusivity. A brief historical overview of the authors who have dealt with the heat conduction equation is described in the introduction of the paper. The one-dimensional heat conduction models with using integer- and fractional-order derivatives are listed. Analytical and numerical methods of solution of the heat conduction models with using integer- and fractional-order derivatives are described. Individual methods have been implemented in MATLAB and the examples of simulations are listed. The proposal and experimental verification of the methods for determining thermal diffusivity using half-order derivative of temperature by time are listed at the conclusion of the paper.

scholarly journals Impact of Energy Slope Averaging Methods on Numerical Solution of 1D Steady Gradually Varied Flow

2015 ◽  
Vol 62 (3-4) ◽  
pp. 101-119 ◽  
Author(s):  
Wojciech Artichowicz ◽  
Dzmitry Prybytak
Keyword(s):  
Numerical Methods ◽  
Numerical Solution ◽  
Numerical Integration ◽  
Cross Sections ◽  
Flow Model ◽  
One Dimensional ◽  
Averaging Methods ◽  
Integration Formulas ◽  
Different Types ◽  
The One

AbstractIn this paper, energy slope averaging in the one-dimensional steady gradually varied flow model is considered. For this purpose, different methods of averaging the energy slope between cross-sections are used. The most popular are arithmetic, geometric, harmonic and hydraulic means. However, from the formal viewpoint, the application of different averaging formulas results in different numerical integration formulas. This study examines the basic properties of numerical methods resulting from different types of averaging.

SOLVING THE TWO-DIMENSIONAL INVERSE FRACTAL PROBLEM WITH THE WAVELET TRANSFORM

Fractals ◽  
1996 ◽  
Vol 04 (04) ◽  
pp. 469-475 ◽  
Author(s):  
ZBIGNIEW R. STRUZIK
Keyword(s):  
Wavelet Transform ◽  
Scale Invariance ◽  
Wavelet Decomposition ◽  
Two Dimensions ◽  
The Self ◽  
Continuous Wavelet ◽  
Two Dimensional ◽  
One Dimensional ◽  
Affine Functions ◽  
The One

The methodology of the solution to the inverse fractal problem with the wavelet transform1,2 is extended to two-dimensional self-affine functions. Similar to the one-dimensional case, the two-dimensional wavelet maxima bifurcation representation used is derived from the continuous wavelet decomposition. It possesses translational and scale invariance necessary to reveal the invariance of the self-affine fractal. As many fractals are naturally defined on two-dimensions, this extension constitutes an important step towards solving the related inverse fractal problem for a variety of fractal types.

A new efficient implicit four-step method with vanished phase-lag and some of its derivatives for the numerical solution of the radial Schr¨odinger equation

2017 ◽  
Vol 8 (1-2) ◽  
pp. 77 ◽  
Author(s):  
Ali Shokri ◽  
Morteza Tahmourasi
Keyword(s):  
Approximate Solution ◽  
Stability Analysis ◽  
Multistep Method ◽  
Phase Lag ◽  
Order Method ◽  
Step Method ◽  
One Dimensional ◽  
First Derivative ◽  
Algebraic Order ◽  
The One

A new four-step implicit linear sixth algebraic order method with vanished phase-lag and its first derivative is constructed in this paper. The purpose of this paper is to develop an efficient algorithm for the approximate solution of the one-dimensional radial Schr¨odinger equation and related problems. In order to produce an efficient multistep method the phase-lag property and its derivatives are used. An error analysis and a stability analysis is also investigated and a comparison with other methods is also studied. The efficiency of the new methodology is proved via theoretical analysis and numerical applications.

The True Proportions of Gay's Acis and Galatea

PMLA ◽  
1965 ◽  
Vol 80 (4-Part1) ◽  
pp. 325-331
Author(s):  
Bertrand H. Bronson
Keyword(s):  
Eighteenth Century ◽  
Two Dimensions ◽  
One Dimensional ◽  
John Gay ◽  
The Arts ◽  
The One ◽  
The Mind ◽  
Theatrical Criticism

The Masque, or serenata, or pastoral opera, Acis and Galatea—in eighteenth-century printings it was indifferently categorized—has been not so much neglected as quite ignored by the biographers and critics of John Gay. In its entirety, words and music, it is a masterpiece, and the reasons for its lying unregarded, except by historians of music, deserve to be scrutinized because they signalize a recurrent failing on the part of those who write on the arts, when a work exists simultaneously in more than one medium. Only lately, in truth, has criticism begun to cope with Shakespeare himself as drama existent in and for living embodiment on a physical stage and nowhere else, not even in the mind of Coleridge. (Theatrical criticism is by habit only piecemeal commentary on separate productions.) Similarly, to set small matters beside great ones, only of late has the ballad of tradition begun to be considered as song and not as a literary or pseudo-literary genre, sufficient and self-sustaining in its text alone. And the bardic tradition of the Ugo-Slavs is teaching us much about the Homeric epics of which former generations were unaware. Signs, in fact, are here and there beginning to appear of an unwillingness to rest content with the one-dimensional conception of arts which are only half-fulfilled until they are realized in two dimensions or more. A drawing of a sculpture is not enough; a sculpture of an action is not enough; pantomime does not suffice the spoken scene; the verbal text of a musical scena will not satisfy. Nor can any of these be adequately criticized on a basis of missing dimensions.

scholarly journals Neutron flux simulation of a one-dimensional reactor zone taking into account xenon generation

Energetika ◽  
2020 ◽  
Vol 65 (4) ◽  
Author(s):  
Zsófia Tóth ◽  
Dániel Péter Kis
Keyword(s):  
Numerical Methods ◽  
Neutron Flux ◽  
Nuclear Power ◽  
Power Plants ◽  
Research Work ◽  
Reactor Core ◽  
Time And Space ◽  
One Dimensional ◽  
Safety And Reliability ◽  
The One

The energy in nuclear power plants is produced by thermal fission. It is extremely important to be able to monitor the processes in the reactor to ensure the safety and reliability of the power plant. One of the main traits of the reactor core is neutron flux. It changes in time and space therefore it is crucial to be able to simulate its changes with computer codes. In the research work a program code was established in the Matlab software with which the neutron flux of a one-dimensional zone can be simulated with homogenous and heterogenic zone parameters as well. The code is written using the one-group one-dimensional time- and space-dependent diffusion equation. The equation of an average delayed neutron group and xenon and iodine distributions was also included in the system to give a more precise look on the problem. The main innovation in the code is that numerical methods were used to solve the problem: the finite difference approach was applied for the place-dependent and for the time-dependent solution. The advantage of this code compared to other ones is that one-dimensional zones can be simulated in a really short time and it still gives a precise solution because of the complex numerical methods used.

scholarly journals One- and Multi-dimensional CWENOZ Reconstructions for Implementing Boundary Conditions Without Ghost Cells

2021 ◽  
Author(s):  
M. Semplice ◽  
E. Travaglia ◽  
G. Puppo
Keyword(s):  
Boundary Conditions ◽  
The Novel ◽  
Two Dimensional ◽  
Finite Volume Schemes ◽  
Third Order ◽  
One Dimensional ◽  
Numerical Tests ◽  
Ghost Cells ◽  
The One ◽  
Appl Math

AbstractWe address the issue of point value reconstructions from cell averages in the context of third-order finite volume schemes, focusing in particular on the cells close to the boundaries of the domain. In fact, most techniques in the literature rely on the creation of ghost cells outside the boundary and on some form of extrapolation from the inside that, taking into account the boundary conditions, fills the ghost cells with appropriate values, so that a standard reconstruction can be applied also in the boundary cells. In Naumann et al. (Appl. Math. Comput. 325: 252–270. 10.1016/j.amc.2017.12.041, 2018), motivated by the difficulty of choosing appropriate boundary conditions at the internal nodes of a network, a different technique was explored that avoids the use of ghost cells, but instead employs for the boundary cells a different stencil, biased towards the interior of the domain. In this paper, extending that approach, which does not make use of ghost cells, we propose a more accurate reconstruction for the one-dimensional case and a two-dimensional one for Cartesian grids. In several numerical tests, we compare the novel reconstruction with the standard approach using ghost cells.

A Comparison of Diffusion Flame Stability in One and Two Spatial Dimensions Near Cold, Inert Surfaces

2001 ◽  
Author(s):  
Robert Vance ◽  
Indrek S. Wichman
Keyword(s):  
Two Dimensions ◽  
Low Flow ◽  
Dimensional System ◽  
Flame Stability ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
One Dimensional ◽  
Cellular Flames ◽  
The One ◽  
Inert Surfaces

Abstract A linear stability analysis is performed on two simplified models representing a one-dimensional flame between oxidizer and fuel reservoirs and a two-dimensional “edge-flame” between the same reservoirs but above a cold, inert wall. Comparison of the eigenvalue spectra for both models is performed to discern the validity of extending the results from the one-dimensional problem to the two-dimensional problem. Of primary interest is the influence on flame stability of thermal-diffusive imbalances, i.e. non-unity Lewis numbers. Flame oscillations are observed when Le > 1, and cellular flames are witnessed when Le < 1. It is found that when Le > 1 the characteristics of flame behavior are consistent between the two models. Furthermore, when Le < 1, the models are found to be in good agreement with respect to the magnitude of the critical wave numbers. Results from the coarse mesh analysis of the two-dimensional system are presented and compared to the one-dimensional eigenvalue spectra. Additionally, an examination of low reactant convection is undertaken. It is concluded that for low flow rates the behavior in one and two dimensions are similar qualitatively and quantitatively.

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