scholarly journals On the angular moment operators of attenuated ray transforms of scalar 3D-fields

2020 ◽  
Vol 23 (2) ◽  
pp. 51-62
Author(s):  
E. Yu. Derevtsov
2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Fedor Goncharov

AbstractIn this work we investigate numerically the reconstruction approach proposed in [F. O. Goncharov and R. G. Novikov, An analog of Chang inversion formula for weighted Radon transforms in multidimensions, Eurasian J. Math. Comput. Appl. 4 2016, 2, 23–32] for weighted ray transforms (weighted Radon transforms along oriented straight lines) in 3D. In particular, the approach is based on a geometric reduction of the data modeled by weighted ray transforms to new data modeled by weighted Radon transforms along two-dimensional planes in 3D. Such reduction could be seen as a preprocessing procedure which could be further completed by any preferred reconstruction algorithm. In a series of numerical tests on modelized and real SPECT (single photon emission computed tomography) data we demonstrate that such procedure can significantly reduce the impact of noise on reconstructions.


2021 ◽  
Author(s):  
Mitchell D Clement ◽  
Nikolas Logan ◽  
Mark D Boyer

Abstract GPECnet is a densely connected neural network that has been trained on GPEC data, to predict the plasma stability, neoclassical toroidal viscosity (NTV) torque, and optimized 3D coil current distributions for desired NTV torque profiles. Using NTV torque, driven by non-axisymmetric field perturbations in a tokamak, can be vital in optimizing pedestal performance by controlling the rotation profile in both the core, to ensure tearing stability, and the edge, to avoid edge localized modes (ELMs). The Generalized Perturbed Equilibrium Code (GPEC) software package can be used to calculate the plasma stability to 3D perturbations and the NTV torque profile generated by applied 3D magnetic fields. These calculations, however, involve complex integrations over space and energy distributions, which takes time to compute. Initially, GPECnet has been trained solely on data representative of the quiescent H-mode (QH) scenario, in which neutral beams are often balanced and toroidal rotation is low across the plasma profile. This work provides the foundation for active control of the rotation shear using a combination of beams and 3D fields for robust and high performance QH mode operation.


2018 ◽  
Vol 58 (7) ◽  
pp. 076016 ◽  
Author(s):  
N.C. Logan ◽  
L. Cui ◽  
H. Wang ◽  
Y. Sun ◽  
S. Gu ◽  
...  

2014 ◽  
Vol 54 (4-6) ◽  
pp. 484-492 ◽  
Author(s):  
J. D. Callen
Keyword(s):  

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yu Yufeng

The attenuated X-ray transform arises from the image reconstruction in single-photon emission computed tomography. The theory of attenuated X-ray transforms is so far incomplete, and many questions remain open. This paper is devoted to the inversion of the attenuated X-ray transforms with nonnegative varying attenuation functions μ, integrable on any straight line of the plane. By constructing the symmetric attenuated X-ray transform Aμ on the plane and using the method of Riesz potentials, we obtain the inversion formula of the attenuated X-ray transforms on Lpℝ21≤p<2 space, with nonnegative attenuation functions μ, integrable on any straight line in ℝ2. These results are succinct and may be used in the type of computerized tomography with attenuation.


2011 ◽  
Vol 26 (10n11) ◽  
pp. 1807-1821 ◽  
Author(s):  
K. MAKINO ◽  
M. BERZ ◽  
C. JOHNSTONE

The precise determination of the dynamics in accelerators with complicated field arrangements such as Fixed Field Alternating Gradient accelerators (FFAG) depends critically on the ability to describe the appearing magnetic fields in full 3D. However, frequently measurements or models of FFAG fields postulate their behavior in the midplane only, and rely on the fact that this midplane field and its derivatives determine the field in all of space. The detailed knowledge of the resulting out-of-plane fields is critical for a careful assessment of the vertical dynamics. We describe a method based on the differential algebraic (DA) approach to obtain the resulting out-of-plane expansions to any order in an order-independent, straightforward fashion. In particular, the resulting fields satisfy Maxwell's equations to the order of the expansion up to machine precision errors, and without any inaccuracies that can arise from conventional divided difference or finite element schemes for the computation of out-of-plane fields. The method relies on re-writing the underlying PDE as a fixed point problem involving DA operations, and in particular the differential algebraic integration operator. We illustrate the performance of the method for a variety of practical examples, and obtain estimates for the orders necessary to describe the fields to a prescribed accuracy.


Author(s):  
Martin P.J. Lavery ◽  
David J. Robertson ◽  
Johannes Courtial ◽  
Gregorius C. G. Berkhout ◽  
Gordon D. Love ◽  
...  

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