scholarly journals High-Order Interpolation Algorithms for Charge Conservation in Particle-in-Cell Simulations

2013 ◽  
Vol 13 (4) ◽  
pp. 1134-1150 ◽  
Author(s):  
Jinqing Yu ◽  
Xiaolin Jin ◽  
Weimin Zhou ◽  
Bin Li ◽  
Yuqiu Gu
Keyword(s):  
Particle Trajectory ◽  
High Order ◽  
Third Order ◽  
Charge Conservation ◽  
Particle In Cell ◽  
Interpolation Algorithms ◽  
Odd Order ◽  
Even Order ◽  
Pic Code ◽  
High Order Interpolation

AbstractHigh-order interpolation algorithms for charge conservation in Particle-in-Cell (PIC) simulations are presented. The methods are valid for the case that a particle trajectory is a zigzag line. The second-order and third-order algorithms which can be applied to any even-order and odd-order are discussed in this paper, respectively. Several test simulations are performed to demonstrate their validity in two-dimensional PIC code. Compared with the simulation results of one-order, high-order algorithms have advantages in computation precision and enlarging the grid scales which reduces the CPU time.

scholarly journals Cusp-artifacts in high order Superresolution Optical Fluctuation Imaging

2019 ◽  
Author(s):  
Xiyu Yi ◽  
Shimon Weiss
Keyword(s):  
Dynamic Range ◽  
Imaging Techniques ◽  
Photophysical Properties ◽  
Super Resolution ◽  
High Order ◽  
Fluorescence Probes ◽  
Structured Illumination ◽  
Odd Order ◽  
Even Order ◽  
High Order Cumulants

AbstractSuperresolution Optical Fluctuation Imaging (SOFI) offers a simple and affordable alternative to the more sophisticated (and expensive) super-resolution imaging techniques such as STED, PALM, STORM, structured illumination, and other derivative methods. In SOFI, the calculation of high order cumulants provides higher resolution but drastically expands the dynamic range of the resulting image. In this study, we have identified another type of artifact for high order SOFI cumulants, dubbed as ‘cusp artifacts.’ A series of realistic simulations are performed to study the cusp artifacts under the influences of various factors, including the blinking statistics, the spatial distribution of photophysical properties of the sample, the total number of frames processed per dataset, photobleaching, and noise. Experiments, simulations, and theory all show that high order cumulants and odd-order moments could suffer from cusp artifacts. These cusp artifacts also degrade the fidelity of bSOFI that has been proposed to solve the dynamic range expansion of image pixel intensities. Alternatively, cusp-artifacts could be altogether eliminated by utilizing even-order moments constructed directly or from cumulants for image reconstruction. Together with dynamic range compression, these approaches yield improved SOFI images. Our study provides new insight into the nature of high order SOFI images, outlines guidelines for developing and screening SOFI-optimized fluorescence probes, and suggests improved strategies for SOFI data acquisition.

scholarly journals Numerical Aspects of Particle-in-Cell Simulations for Plasma-Motion Modeling of Electric Thrusters

Aerospace ◽  
2021 ◽  
Vol 8 (5) ◽  
pp. 138
Author(s):  
Giuseppe Gallo ◽  
Adriano Isoldi ◽  
Dario Del Gatto ◽  
Raffaele Savino ◽  
Amedeo Capozzoli ◽  
...  
Keyword(s):  
Numerical Model ◽  
Computing Time ◽  
Computational Time ◽  
Electric Motors ◽  
Motion Modeling ◽  
Particle In Cell ◽  
Computing Platform ◽  
Hall Effect Thruster ◽  
Set Up ◽  
Pic Code

The present work is focused on a detailed description of an in-house, particle-in-cell code developed by the authors, whose main aim is to perform highly accurate plasma simulations on an off-the-shelf computing platform in a relatively short computational time, despite the large number of macro-particles employed in the computation. A smart strategy to set up the code is proposed, and in particular, the parallel calculation in GPU is explored as a possible solution for the reduction in computing time. An application on a Hall-effect thruster is shown to validate the PIC numerical model and to highlight the strengths of introducing highly accurate schemes for the electric field interpolation and the macroparticle trajectory integration in the time. A further application on a helicon double-layer thruster is presented, in which the particle-in-cell (PIC) code is used as a fast tool to analyze the performance of these specific electric motors.

scholarly journals Mutual information for low-rank even-order symmetric tensor estimation

2020 ◽  
Author(s):  
Clément Luneau ◽  
Jean Barbier ◽  
Nicolas Macris
Keyword(s):  
Mutual Information ◽  
Finite Rank ◽  
Interpolation Method ◽  
Symmetric Tensor ◽  
Low Rank ◽  
Tensor Factorization ◽  
Adaptive Interpolation ◽  
Odd Order ◽  
Rank One ◽  
Even Order

Abstract We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its asymptotic mutual information when the tensor is of even order. The proof applies the adaptive interpolation method originally invented for rank-one factorization. Here we show how to extend the adaptive interpolation to finite-rank and even-order tensors. This requires new non-trivial ideas with respect to the current analysis in the literature. We also underline where the proof falls short when dealing with odd-order tensors.

Time dispersion correction for arbitrarily even-order Lax-Wendroff methods and the application on full waveform inversion

Geophysics ◽  
2021 ◽  
pp. 1-89
Author(s):  
Zhiming Ren ◽  
Qianzong Bao ◽  
Bingluo Gu
Keyword(s):  
Waveform Inversion ◽  
Second Order ◽  
High Order ◽  
Full Waveform Inversion ◽  
Dispersion Correction ◽  
Equal Time ◽  
Full Waveform ◽  
Time Dispersion ◽  
Correction Scheme ◽  
Even Order

A second-order accurate finite-difference (FD) approximation is commonly used to approximate the second-order time derivative of wave equation. The second-order accurate FD scheme may introduce time dispersion in wavefield extrapolation. Lax-Wendroff methods can suppress such dispersion by replacing the high-order time FD error-terms with space FD error correcting terms. However, the time dispersion cannot be completely eliminated and the computation cost dramatically increases with increasing order of (temporal) accuracy. To mitigate the problem, we extend the existing time dispersion correction scheme for second- or fourth-order Lax-Wendroff method to a scheme for arbitrary even-order methods, which uses the forward and inverse time dispersion transform (FTDT and ITDT) to add and remove the time dispersion from synthetic data. We test the correction scheme using a homogeneous model and the Sigsbee2A model. Modeling examples suggest that the use of derived FTDT and ITDT pairs on high-order Lax-Wendroff methods can effectively remove time dispersion errors from high-frequency waves while using longer time steps than allowed in low-order Lax-Wendroff methods. We investigate the influence of the time dispersion on full waveform inversion (FWI) and show an anti-dispersion workflow. We apply the FTDT to source terms and recorded traces before inversion, resulting in that the source and adjoint wavefields contain equal time dispersion from source-side wave propagation, and the modeled and observed traces accumulate equal time dispersion from source- and receiver-side wave propagation. Inversion results reveal that the anti-dispersion workflow is capable of increasing the accuracy of FWI for arbitrary even-order Lax-Wendroff methods. Additionally, the high-order method can obtain better inversion results compared to the second-order method with the same anti-dispersion workflow.

Downstream Transport Beam Spill with Particle In Cell (PIC) code Lsp

2021 ◽  
Author(s):  
Derek Neben ◽  
Michael Weller ◽  
Evan Scott
Keyword(s):  
Particle In Cell ◽  
Pic Code

scholarly journals Simulation of gyrotrons using the high-order particle-in-cell code PICLas

2017 ◽  
Vol 149 ◽  
pp. 04019 ◽  
Author(s):  
S. M. Copplestone ◽  
P. Ortwein ◽  
C.-D. Munz ◽  
K. A. Avramidis ◽  
J. Jelonnek
Keyword(s):  
High Order ◽  
Particle In Cell

scholarly journals Bipartite Consensus of High-Order Edge Dynamics on Coopetition Multiagent Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Yilong Yang ◽  
Zhijian Ji ◽  
Lei Tian ◽  
Huizi Ma ◽  
Qingyuan Qi
Keyword(s):  
Multiagent Systems ◽  
Line Graph ◽  
Sufficient Conditions ◽  
High Order ◽  
Third Order ◽  
Positive Weight ◽  
The Third ◽  
Initial Graph ◽  
Strongly Connected ◽  
Bipartite Consensus

The bipartite consensus of high-order edge dynamics is investigated for coopetition multiagent systems, in which the cooperative and competitive relationships among agents are characterized by positive weight and negative weight, respectively. By mapping the initial graph to a line graph, the distributed control protocol is proposed for the strongly connected, digon sign-symmetric structurally balanced line graph; and then we give sufficient conditions for the third-order multi-gent system to achieve both the bipartite consensus of edge dynamics and the final value of bipartite consensus. By transforming the coefficients of characteristic polynomial from complex domain to real number domain, the sufficient conditions for the bipartite consensus of high-order edge dynamics are also proposed, and the final values of the high-order edge dynamics on multiagent systems are obtained.

scholarly journals Probing the Locally Generated Even and Odd Order Nonlinearity in Y–Ba–Cu–O and Tl–Ba–Ca–Cu–O (2212) Microwave Resonators Around <img src="/images/tex/19586.gif" alt="T_{\rm C}">

2013 ◽  
Vol 23 (3) ◽  
pp. 9000105-9000105 ◽  
Author(s):  
Brooke Jeries ◽  
Sean Cratty ◽  
S Remillard
Keyword(s):  
Meissner Effect ◽  
Second Order ◽  
Intermodulation Distortion ◽  
Coaxial Cable ◽  
Superconducting Resonators ◽  
Third Order ◽  
Odd Order ◽  
Similar Temperature Dependence ◽  
Similar Temperature ◽  
Lower Temperature

Spatial scanning of the synchronously generated second- and third-order intermodulation distortion in superconducting resonators uncovers local nonlinearity hot spots, and possible time reversal symmetry breaking, using a simple probe fashioned from coaxial cable. It is clear that even and odd order nonlinearity in these samples do not share the same physical origins, because their temperature and static magnetic field dependences are quite different. 2nd order intermodulation distortion remains strong in these measurements as the temperature continues to drop belowTCto 77 K even though the 3rd order peaks nearTCand becomes smaller at lower temperature as predicted by the nonlinear Meissner effect. Both YBa2Cu3O7and Tl2Ba2CaCu2O8resonators of the same structure exhibit similar temperature dependence in the second order with second order remaining high at lower temperature. The YBa2Cu3O7sample has lower third-order intermodulation distortion with a pronounced peak atTC.

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