scholarly journals Combination Technique Based Second Moment Analysis for Elliptic PDEs on Random Domains

2016 ◽  
pp. 51-77 ◽  
Author(s):  
Helmut Harbrecht ◽  
Michael Peters
Keyword(s):  
Moment Analysis ◽  
Elliptic Pdes ◽  
Second Moment ◽  
Combination Technique ◽  
Random Domains

scholarly journals Sparse second moment analysis for elliptic problems in stochastic domains

2008 ◽  
Vol 109 (3) ◽  
pp. 385-414 ◽  
Author(s):  
Helmut Harbrecht ◽  
Reinhold Schneider ◽  
Christoph Schwab
Keyword(s):  
Elliptic Problems ◽  
Moment Analysis ◽  
Second Moment ◽  
Stochastic Domains

scholarly journals First-order second-moment analysis of the buckling of shells with random imperfections

AIAA Journal ◽  
1987 ◽  
Vol 25 (8) ◽  
pp. 1113-1117 ◽  
Author(s):  
I. Elishakoff ◽  
S. van Manen ◽  
P. G. Vermeulen ◽  
J. Arbocz
Keyword(s):  
Moment Analysis ◽  
Second Moment ◽  
First Order ◽  
First Order Second Moment

scholarly journals Evaluating height structure in Scots pine forests using marked point processes

2008 ◽  
Vol 38 (7) ◽  
pp. 1924-1934 ◽  
Author(s):  
Fernando Montes ◽  
Ignacio Barbeito ◽  
Agustín Rubio ◽  
Isabel Cañellas
Keyword(s):  
Scots Pine ◽  
Point Processes ◽  
Marked Point ◽  
Null Model ◽  
Tree Height ◽  
Moment Analysis ◽  
Marked Point Processes ◽  
Height Distribution ◽  
Second Moment ◽  
Point Patterns

In this study, the second-moment analysis of marked spatial point processes is applied to the characterization of the tree height distribution in two Scots pine ( Pinus sylvestris L.) forests in the Central Mountain Range of Spain. The cumulative function Lm(d) weighted by the normalized mark variance is proposed to analyse the second-order properties of marked point patterns. The empirical Lm(d) was compared with two null models to assess the relationship between the spatial distribution of the trees and the tree height correlations: the first null model was used to characterize the spatial clustering of the trees and was derived from the complete spatial randomness model used with Ripley’s K(d) function. The second null model, which is derived from the random labelling model used with the intertype second-moment measure K12(d) (type 1 intensity conditioned to the type 2 intensity and vice versa), allows us to identify the mark correlations. The performance of the technique was assessed through simulated marked point patterns. The second-moment analysis showed that most of the analysed Scots pine stands have a uniform height distribution at small scale and greater heterogeneity at large scales, with the exception of an upper altitudinal stand, which exhibited heterogeneity at short distances. These results demonstrate the utility of second-moment analysis of marked point processes for characterizing height structure in forest stands and the interaction between the height and the spatial pattern of the trees.

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