Study of Slow Beam Extraction through the Third Order Resonance with Transverse Phase Space Manipulation by a Mono-Frequency RFKO

2006 ◽  
Author(s):  
A. Miyamoto ◽  
F. Hinode ◽  
M. Kawai ◽  
K. Shinto ◽  
T. Tanaka ◽  
...  
Keyword(s):  
Phase Space ◽  
Beam Extraction ◽  
Third Order ◽  
Order Resonance ◽  
The Third

A Pulse Stretcher by Slow Extraction Utilizing the Third-Order Resonance with the RF Knockout Method

2002 ◽  
Vol 41 (Part 1, No. 4A) ◽  
pp. 2276-2284
Author(s):  
Takashi Sugimura ◽  
Akio Morita ◽  
Hiromu Tongu ◽  
Toshiyuki Shirai ◽  
Yoshihisa Iwashita ◽  
...  
Keyword(s):  
Third Order ◽  
Order Resonance ◽  
The Third ◽  
Slow Extraction

scholarly journals THE ROOT CONDITION FOR THE THIRD ORDER POLYNOMIALS

1999 ◽  
Vol 4 (1) ◽  
pp. 163-173
Author(s):  
A. Štikonas
Keyword(s):  
Phase Space ◽  
Third Order ◽  
The Third ◽  
Complex Coefficients

This paper deals with a root condition for polynomial of the second and third order. We prove the root criterion for such polynomial with complex coefficients and find regions for the root condition in the special coefficients’ phase space.

Negative Refractive Index at the Third-Order Resonance of Flower-Shaped Metamaterial

2012 ◽  
Vol 30 (22) ◽  
pp. 3451-3455 ◽  
Author(s):  
Pham Van Tuong ◽  
J. W. Park ◽  
V. D. Lam ◽  
W. H. Jang ◽  
E. H. Choi ◽  
...  
Keyword(s):  
Refractive Index ◽  
Negative Refractive Index ◽  
Third Order ◽  
Order Resonance ◽  
The Third

scholarly journals Nonlinear Stability of Oblate Infinitesimal in Elliptic Restricted Three-Body Problem Influenced by the Oblate and Radiating Primaries

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
A. Narayan ◽  
A. Chakraborty ◽  
A. Dewangan
Keyword(s):  
Nonlinear Stability ◽  
Binary Systems ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Third Order ◽  
Order Resonance ◽  
The Third ◽  
The Stability ◽  
Three Body

This work deals with the nonlinear stability of the elliptical restricted three-body problem with oblate and radiating primaries and the oblate infinitesimal. The stability has been analyzed for the resonance cases around ω1=2ω2 and ω1=3ω2 and also the nonresonance cases. It was observed that the motion of the infinitesimal in this system shows instable behavior when considered in the third order resonance. However, for the fourth order resonance the stability is shown for some mass parameters. The motion in the case of nonresonance was found to be unstable. The problem has been numerically applied to study the movement of the infinitesimal around two binary systems, Luyten-726 and Sirius.

Injection method using the third order resonance at TARN II

2002 ◽  
Author(s):  
M. Tomizawa ◽  
Y. Arakaki ◽  
K. Chida ◽  
S. Watanabe ◽  
T. Watanabe ◽  
...  
Keyword(s):  
Third Order ◽  
Injection Method ◽  
Order Resonance ◽  
The Third

scholarly journals Towards Overcoming the Curse of Dimensionality: The Third-Order Adjoint Method for Sensitivity Analysis of Response-Coupled Linear Forward/Adjoint Systems, with Applications to Uncertainty Quantification and Predictive Modeling

Energies ◽  
2019 ◽  
Vol 12 (21) ◽  
pp. 4216 ◽  
Author(s):  
Cacuci
Keyword(s):  
Sensitivity Analysis ◽  
Phase Space ◽  
Uncertainty Quantification ◽  
Predictive Modeling ◽  
Curse Of Dimensionality ◽  
System Response ◽  
Model Parameters ◽  
Third Order ◽  
Adjoint Systems ◽  
The Third

This work presents the Third-Order Adjoint Sensitivity Analysis Methodology (3rd-ASAM) for response-coupled forward and adjoint linear systems. The 3rd-ASAM enables the efficient computation of the exact expressions of the 3rd-order functional derivatives (“sensitivities”) of a general system response, which depends on both the forward and adjoint state functions, with respect to all of the parameters underlying the respective forward and adjoint systems. Such responses are often encountered when representing mathematically detector responses and reaction rates in reactor physics problems. The 3rd-ASAM extends the 2nd-ASAM in the quest to overcome the “curse of dimensionality” in sensitivity analysis, uncertainty quantification and predictive modeling. This work also presents new formulas that incorporate the contributions of the 3rd-order sensitivities into the expressions of the first four cumulants of the response distribution in the phase-space of model parameters. Using these newly developed formulas, this work also presents a new mathematical formalism, called the 2nd/3rd-BERRU-PM “Second/Third-Order Best-Estimated Results with Reduced Uncertainties Predictive Modeling”) formalism, which combines experimental and computational information in the joint phase-space of responses and model parameters, including not only the 1st-order response sensitivities, but also the complete hessian matrix of 2nd-order second-sensitivities and also the 3rd-order sensitivities, all computed using the 3rd-ASAM. The 2nd/3rd-BERRU-PM uses the maximum entropy principle to eliminate the need for introducing and “minimizing” a user-chosen “cost functional quantifying the discrepancies between measurements and computations,” thus yielding results that are free of subjective user-interferences while generalizing and significantly extending the 4D-VAR data assimilation procedures. Incorporating correlations, including those between the imprecisely known model parameters and computed model responses, the 2nd/3rd-BERRU-PM also provides a quantitative metric, constructed from sensitivity and covariance matrices, for determining the degree of agreement among the various computational and experimental data while eliminating discrepant information. The mathematical framework of the 2nd/3rd-BERRU-PM formalism requires the inversion of a single matrix of size Nr Nr, where Nr denotes the number of considered responses. In the overwhelming majority of practical situations, the number of responses is much less than the number of model parameters. Thus, the 2nd-BERRU-PM methodology overcomes the curse of dimensionality which affects the inversion of hessian matrices in the parameter space.

Design Study of the Third Order Resonance Extraction System at TARN II

1985 ◽  
Vol 32 (5) ◽  
pp. 2436-2438 ◽  
Author(s):  
M. Takanaka ◽  
Y. Hattori ◽  
A. Noda ◽  
T. Tanabe ◽  
H. Tsujikawa
Keyword(s):  
Extraction System ◽  
Design Study ◽  
Third Order ◽  
Order Resonance ◽  
The Third
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