scholarly journals The sixth moment of automorphic L-functions

2017 ◽  
Vol 11 (3) ◽  
pp. 583-633 ◽  
Author(s):  
Vorrapan Chandee ◽  
Xiannan Li
Keyword(s):  
Sixth Moment

On the sixth moment of Rayleigh spectra of fluid N2

1985 ◽  
Vol 114 (3) ◽  
pp. 297-300 ◽  
Author(s):  
A. De Santis ◽  
R. Frattini ◽  
M. Sampoli
Keyword(s):  
Sixth Moment

scholarly journals A Bayesian Approach for Statistical–Physical Bulk Parameterization of Rain Microphysics. Part II: Idealized Markov Chain Monte Carlo Experiments

2019 ◽  
Vol 77 (3) ◽  
pp. 1043-1064 ◽  
Author(s):  
Marcus van Lier-Walqui ◽  
Hugh Morrison ◽  
Matthew R. Kumjian ◽  
Karly J. Reimel ◽  
Olivier P. Prat ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Sampling ◽  
Microphysics Scheme ◽  
True Parameter ◽  
Microphysical Process ◽  
Monte Carlo Experiments ◽  
Sixth Moment ◽  
Parameter Values

Abstract Observationally informed development of a new framework for bulk rain microphysics, the Bayesian Observationally Constrained Statistical–Physical Scheme (BOSS; described in Part I of this study), is demonstrated. This scheme’s development is motivated by large uncertainties in cloud and weather simulations associated with approximations and assumptions in existing microphysics schemes. Here, a proof-of-concept study is presented using a Markov chain Monte Carlo sampling algorithm with BOSS to probabilistically estimate microphysical process rates and parameters directly from a set of synthetically generated rain observations. The framework utilized is an idealized steady-state one-dimensional column rainshaft model with specified column-top rain properties and a fixed thermodynamical profile. Different configurations of BOSS—flexibility being a key feature of this approach—are constrained via synthetic observations generated from a traditional three-moment bulk microphysics scheme. The ability to retrieve correct parameter values when the true parameter values are known is illustrated. For cases when there is no set of true parameter values, the accuracy of configurations of BOSS that have different levels of complexity is compared. It is found that addition of the sixth moment as a prognostic variable improves prediction of the third moment (proportional to bulk rain mass) and rain rate. In contrast, increasing process rate formulation complexity by adding more power terms has little benefit—a result that is explained using further-idealized experiments. BOSS rainshaft simulations are shown to well estimate the true process rates from constraint by bulk rain observations, with the additional benefit of rigorously quantified uncertainty of these estimates.

Sixth-moment method for multi-channel Bragg filter optimization

2010 ◽  
Author(s):  
Oleg V. Belai ◽  
Anton V. Nemykin ◽  
David A. Shapiro
Keyword(s):  
Moment Method ◽  
Sixth Moment

Sixth moment optimization of multi-channel Bragg filters

2011 ◽  
Vol 284 (6) ◽  
pp. 1565-1568 ◽  
Author(s):  
D.A. Shapiro ◽  
A.I. Latkin
Keyword(s):  
Sixth Moment

Sixth Moment of the Magnetic-Resonance Line Shape

1972 ◽  
Vol 6 (5) ◽  
pp. 1724-1728 ◽  
Author(s):  
William F. Wurzbach ◽  
S. Gade
Keyword(s):  
Magnetic Resonance ◽  
Line Shape ◽  
Resonance Line ◽  
Sixth Moment
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