scholarly journals Form factor of rounded objects: the sections method

2018 ◽  
Vol 51 (4) ◽  
pp. 1005-1012
Author(s):  
Bernard Croset
Keyword(s):  
Form Factor ◽  
Asymptotic Behaviour ◽  
Analytical Method ◽  
Numerical Study ◽  
Rapid Decrease ◽  
Close Link ◽  
Surface Singularities

An analytical method, the sections method, is developed to build a close link between the singularities of the surface of a body and the asymptotic behaviour of its amplitude form factor at large scattering vector, q. In contrast with a sphere, for which the asymptotic behaviour is in q −2, surface singularities lead to both narrow regions, for which the amplitude form factor exhibits trailing behaviour, and extended regions, for which it exhibits a rapid decrease. A numerical study of a simple example, the fourfold truncated sphere, illustrates the usefulness of these analytical predictions.

Information Loss in Riffle Shuffling

2002 ◽  
Vol 11 (1) ◽  
pp. 79-95 ◽  
Author(s):  
DUDLEY STARK ◽  
A. GANESH ◽  
NEIL O’CONNELL
Keyword(s):  
Asymptotic Behaviour ◽  
Relative Entropy ◽  
Numerical Study ◽  
Information Loss ◽  
Information Theoretic

We study the asymptotic behaviour of the relative entropy (to stationarity) for a commonly used model for riffle shuffling a deck of n cards m times. Our results establish and were motivated by a prediction in a recent numerical study of Trefethen and Trefethen. Loosely speaking, the relative entropy decays approximately linearly (in m) for m < log2n, and approximately exponentially for m > log2n. The deck becomes random in this information-theoretic sense after m = 3/2 log2n shuffles.

Factorization and asymptotic behaviour of pion form factor in QCD

1980 ◽  
Vol 94 (2) ◽  
pp. 245-250 ◽  
Author(s):  
A.V. Efremov ◽  
A.V. Radyushkin
Keyword(s):  
Form Factor ◽  
Asymptotic Behaviour ◽  
Pion Form Factor

Pion form factor and its asymptotic behaviour

1979 ◽  
Vol 29 (2) ◽  
pp. 142-154 ◽  
Author(s):  
S. Dubnička ◽  
A. Z. Dubničková ◽  
V. A. Meshcheryakov
Keyword(s):  
Form Factor ◽  
Asymptotic Behaviour ◽  
Pion Form Factor

scholarly journals Tests for the asymptotic behaviour of the form factor

1998 ◽  
Vol 425 (3-4) ◽  
pp. 365-368 ◽  
Author(s):  
J.-M Gérard ◽  
G López Castro
Keyword(s):  
Form Factor ◽  
Asymptotic Behaviour

scholarly journals Numerical study of the lattice meson form factor

1986 ◽  
Vol 33 (1) ◽  
pp. 222-226 ◽  
Author(s):  
R. M. Woloshyn ◽  
A. M. Kobos
Keyword(s):  
Form Factor ◽  
Numerical Study

Asymptotic behaviour of the form factor for non-relativistic many-body systems

1975 ◽  
Vol 58 (2) ◽  
pp. 125-128 ◽  
Author(s):  
I.M. Narodetsky ◽  
Yu.A. Simonov ◽  
F. Palumbo
Keyword(s):  
Form Factor ◽  
Asymptotic Behaviour ◽  
Many Body ◽  
Many Body Systems

Vibration of Flexible Structures Under Nonlinear Boundary Conditions

2017 ◽  
Vol 84 (11) ◽  
Author(s):  
Xiao-Ye Mao ◽  
Hu Ding ◽  
Li-Qun Chen
Keyword(s):  
Boundary Conditions ◽  
Analytical Method ◽  
Nonlinear Boundary ◽  
Numerical Study ◽  
Flexible Structures ◽  
Nonlinear Boundary Conditions ◽  
Simulation Technique ◽  
Flexible Structure ◽  
Modal Shape ◽  
Differential Quadrature Element Method

The nonlinear response of a flexible structure, subjected to generally supported conditions with nonlinearities, is investigated for the first time. An analytical procedure is proposed first. Moreover, a simulation technique usually employed in static analysis is developed for confirmation. Generally, ordinary perturbation methods could analyze dynamics of flexible structures with linear boundary conditions. As nonlinear boundaries are taken into account, they are out of operation for the modal shape that is hardly to be obtained, which is the key to the analysis. In order to overcome this, nonlinear boundary conditions are rescaled and the technique of modal revision is employed. Consequently, each governing equation with different time-scales could be analyzed exactly according to corresponding rescaled boundary conditions. The total response of any point at the flexible structure will be composed by harmonic responses yielded by the analytical method. Furthermore, the differential quadrature element method (DQEM), a numerical simulation technique could satisfy boundary conditions strictly, is introduced to certify analytical results. The comparison shows a reasonable agreement between these two methods. In fact, the accuracy of the analytical method for nonlinear boundaries could be explained in theory. Based on the certification, boundary nonlinearities are discussed in detail analytically and found to play an important role in responses. Because of the important role played by the nonlinear factors in the vibration and control of the flexible structure, this paper will open the vibration analysis and numerical study of the flexible structure with nonlinear constraints.

scholarly journals Rounded leaf end effect of multileaf collimator on penumbra width and radiation field offset: an analytical and numerical study

2015 ◽  
Vol 49 (3) ◽  
pp. 299-306 ◽  
Author(s):  
Dong Zhou ◽  
Hui Zhang ◽  
Peiqing Ye
Keyword(s):  
Monte Carlo ◽  
Radiation Field ◽  
Analytical Method ◽  
Numerical Study ◽  
Intensity Modulated Radiotherapy ◽  
Source Size ◽  
Multileaf Collimator ◽  
Large Radius ◽  
End Effect ◽  
End Effects

AbstractBackground.Penumbra characteristics play a significant role in dose delivery accuracy for radiation therapy. For treatment planning, penumbra width and radiation field offset strongly influence target dose conformity and organ at risk sparing.Methods.In this study, we present an analytical and numerical approach for evaluation of the rounded leaf end effect on penumbra characteristics. Based on the rule of half-value layer, algorithms for leaf position calculation and radiation field offset correction were developed, which were advantageous particularly in dealing with large radius leaf end. Computer simulation was performed based on the Monte Carlo codes of EGSnrc/BEAMnrc, with groups of leaf end radii and source sizes. Data processing technique of curve fitting was employed for deriving penumbra width and radiation field offset.Results.Results showed that penumbra width increased with source size. Penumbra width curves for large radius leaf end were U-shaped. This observation was probably related to the fact that radiation beams penetrated through the proximal and distal leaf sides. In contrast, source size had negligible impact on radiation field offset. Radiation field offsets were found to be constant both for analytical method and numerical simulation. However, the overall resulting values of radiation field offset obtained by analytical method were slightly smaller compared with Monte Carlo simulation.Conclusions.The method we proposed could provide insight into the investigation of rounded leaf end effects on penumbra characteristics. Penumbra width and radiation field offset calibration should be carefully performed to commission multileaf collimator for intensity modulated radiotherapy.

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