Forward model of Cerenkov luminescence tomography with the third-order simplified spherical harmonics approximation

2011 ◽  
Author(s):  
Jianghong Zhong ◽  
Jie Tian ◽  
Xin Yang ◽  
Chenghu Qin
Keyword(s):  
Spherical Harmonics ◽  
Forward Model ◽  
Third Order ◽  
The Third

scholarly journals Spectrally resolved bioluminescence tomography with the third-order simplified spherical harmonics approximation

2009 ◽  
Vol 54 (21) ◽  
pp. 6477-6493 ◽  
Author(s):  
Yujie Lu ◽  
Ali Douraghy ◽  
Hidevaldo B Machado ◽  
David Stout ◽  
Jie Tian ◽  
...  
Keyword(s):  
Spherical Harmonics ◽  
Third Order ◽  
Bioluminescence Tomography ◽  
The Third ◽  
Spectrally Resolved

The Differences Between the Two Forms of Semi-Analytical Nodal Methods on Solving the Third-Order Simplified Spherical Harmonics Method Equations1

2018 ◽  
Vol 4 (2) ◽  
Author(s):  
Pan Qingquan ◽  
Lu Haoliang ◽  
Li Dongsheng ◽  
Wang Kan
Keyword(s):  
Spherical Harmonics ◽  
High Accuracy ◽  
Calculation Methods ◽  
Expansion Process ◽  
Third Order ◽  
The Third ◽  
Nodal Method ◽  
Key Points ◽  
Reactor Calculation ◽  
The Difference

Solving the third-order simplified spherical harmonics method (SP3) equations is one of the key points in the development of advanced reactor calculation methods and has been widely concerned. The semi-analytical nodal method (SANM), based on transverse-integrated diffusion equation, has the advantages of high accuracy and convenience for multigroup calculation. Due to its advantages, the method is expected to be used in solving the SP3 equations. However, the traditional SANM is not rigorous since the expansion process does not take the special modality of the SP3 equations and their analytical solutions into consideration. There are two modalities of the SP3 equations, so there are two traditional SANM forms on solving the SP3 equations, and the differences between the two forms will be very important in further research on the SANM. A code is developed to solve the SP3 equations under the two different forms. After the calculation of the same benchmark, the difference between the two forms on solving the SP3 equations is found. According to the results, and in view of the special modality of the SP3 equations, points on a more rigorous SANM for solving the SP3 equations are discussed.

Probe size and 5th-order aberration

1987 ◽  
Vol 45 ◽  
pp. 134-135 ◽  
Author(s):  
Zhifeng Shao
Keyword(s):  
Electron Probe ◽  
Spherical Aberration ◽  
Wave Length ◽  
Cylindrical Symmetry ◽  
Electron Wave ◽  
Third Order ◽  
The Third ◽  
Probe Radius ◽  
Small Probe ◽  
Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

Children’s Recall of Approximations to English

1973 ◽  
Vol 16 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Elizabeth Carrow ◽  
Michael Mauldin
Keyword(s):  
Language Development ◽  
Fourth Order ◽  
Third Order ◽  
Memory Processes ◽  
The Third ◽  
General Index ◽  
General Linguistic

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.

scholarly journals Ultrafast Third-Order Nonlinear Optical Response Excited by fs Laser Pulses at 1550 nm in GaN Crystals

Materials ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3194
Author(s):  
Adrian Petris ◽  
Petronela Gheorghe ◽  
Tudor Braniste ◽  
Ion Tiginyanu
Keyword(s):  
Harmonic Generation ◽  
Nonlinear Optical ◽  
Laser Pulses ◽  
Third Harmonic Generation ◽  
High Repetition Rate ◽  
Third Order ◽  
Third Harmonic ◽  
The Third ◽  
High Repetition ◽  
Gan Crystal

The ultrafast third-order optical nonlinearity of c-plane GaN crystal, excited by ultrashort (fs) high-repetition-rate laser pulses at 1550 nm, wavelength important for optical communications, is investigated for the first time by optical third-harmonic generation in non-phase-matching conditions. As the thermo-optic effect that can arise in the sample by cumulative thermal effects induced by high-repetition-rate laser pulses cannot be responsible for the third-harmonic generation, the ultrafast nonlinear optical effect of solely electronic origin is the only one involved in this process. The third-order nonlinear optical susceptibility of GaN crystal responsible for the third-harmonic generation process, an important indicative parameter for the potential use of this material in ultrafast photonic functionalities, is determined.

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

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