scholarly journals Scaling theory of few-particle delocalization

2021 ◽  
Vol 104 (21) ◽  
Author(s):  
Louk Rademaker
Keyword(s):  
Scaling Theory

Tree growth as affected by stem and crown structure

Trees ◽  
2021 ◽  
Author(s):  
Hans Pretzsch
Keyword(s):  
Tree Growth ◽  
Scaling Theory ◽  
Tree Age ◽  
Stem Volume ◽  
Projection Area ◽  
Metabolic Scaling ◽  
Crown Structure ◽  
The Future ◽  
Metabolic Scaling Theory ◽  
Crown Characteristics

Abstract Key message Prediction of tree growth based on size or mass as proposed by the Metabolic Scaling Theory is an over-simplification and can be significantly improved by consideration of stem and crown morphology. Tree growth and metabolic scaling theory, as well as corresponding growth equations, use tree volume or mass as predictors for growth. However, this may be an over-simplification, as the future growth of a tree may, in addition to volume or mass, also depend on its past development and aspects of the current inner structure and outer morphology. The objective of this evaluation was to analyse the effect of selected structural and morphological tree characteristics on the growth of common tree species in Europe. Here, we used eight long-term experiments with a total of 24 plots and extensive individual measurements of 1596 trees in monospecific stands of European beech (Fagus sylvatica L.), Norway spruce (Picea abies (L.) Karst.), Scots pine (Pinus sylvestris L.) and sessile oak (Quercus petraea (Matt.) Liebl.). Some of the experiments have been systematically surveyed since 1870. The selected plots represent a broad range of stand density, from fully to thinly stocked stands. We applied linear mixed models with random effects for analysing and modelling how tree growth and productivity are affected by stem and crown structure. We used the species-overarching relationship $$\mathrm{iv}={{a}_{0}\times v}$$ iv = a 0 × v between stem volume growth, $$\mathrm{iv}$$ iv and stem volume, $$v,$$ v , as the baseline model. In this model $${a}_{0}$$ a 0 represents the allometric factor and α the allometric exponent. Then we included tree age, mean stem volume of the stand and structural and morphological tree variables in the model. This significantly reduced the AIC; RMSE was reduced by up to 43%. Interestingly, the full model estimating $$\mathrm{iv}$$ iv as a function of $$v$$ v and mean tree volume, crown projection area, crown ratio and mean tree ring width, revealed a $$\alpha \cong 3/4$$ α ≅ 3 / 4 scaling for the relationship between $$\mathrm{iv}\propto {v}^{\alpha }$$ iv ∝ v α . This scaling corresponded with Kleiber’s rule and the West-Brown-Enquist model of the metabolic scaling theory. Simplified approaches based on stem diameter or tree mass as predictors may be useful for a rough estimation of stem growth in uniform stands and in cases where more detailed predictors are not available. However, they neglect other stem and crown characteristics that can have a strong additional effect on the growth behaviour. This becomes of considerable importance in the heterogeneous mixed-species stands that in many countries of the world are designed for forest restoration. Heterogeneous stand structures increase the structural variability of the individual trees and thereby cause a stronger variation of growth compared with monocultures. Stem and crown characteristics, which may improve the analysis and projection of tree and stand dynamics in the future forest, are becoming more easily accessible by Terrestrial laser scanning.

Adaptive differences in plant physiology and ecosystem paradoxes: insights from metabolic scaling theory

2007 ◽  
Vol 13 (3) ◽  
pp. 591-609 ◽  
Author(s):  
BRIAN J. ENQUIST ◽  
ANDREW J. KERKHOFF ◽  
TRAVIS E. HUXMAN ◽  
EVAN P. ECONOMO
Keyword(s):  
Plant Physiology ◽  
Scaling Theory ◽  
Metabolic Scaling ◽  
Metabolic Scaling Theory

Scaling theory and the nature of measurement

Synthese ◽  
1966 ◽  
Vol 16 (2) ◽  
pp. 170-233 ◽  
Author(s):  
William W. Rozeboom
Keyword(s):  
Scaling Theory

On the validity of scaling theory for the anisotropic ising model

1972 ◽  
Vol 38 (2) ◽  
pp. 107-108 ◽  
Author(s):  
I.G Enting ◽  
J Oitmaa
Keyword(s):  
Ising Model ◽  
Scaling Theory

scholarly journals Scaling theory and numerical simulations of aerogel sintering

1995 ◽  
Vol 188 (1-2) ◽  
pp. 1-10 ◽  
Author(s):  
Rémi Jullien ◽  
Nathalie Olivi-Train ◽  
Anwar Hasmy ◽  
Thierry Woignier ◽  
Jean Phalippou ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Scaling Theory

scholarly journals EXACTLY SOLVABLE SCALING THEORY OF CONDUCTION IN DISORDERED WIRES

1994 ◽  
Vol 08 (08n09) ◽  
pp. 469-478 ◽  
Author(s):  
C. W. J. Beenakker
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Scaling Theory ◽  
Transmission Eigenvalues ◽  
Conductance Fluctuations ◽  
Recent Developments ◽  
Log Normal ◽  
Universal Conductance ◽  
Conductance Distribution

Recent developments in the scaling theory of phase-coherent conduction through a disordered wire are reviewed. The Dorokhov–Mello–Pereyra–Kumar equation for the distribution of transmission eigenvalues has been solved exactly, in the absence of time-reversal symmetry. Comparison with the previous prediction of random-matrix theory shows that this prediction was highly accurate but not exact: the repulsion of the smallest eigenvalues was overestimated by a factor of two. This factor of two resolves several disturbing discrepancies between random-matrix theory and microscopic calculations, notably in the magnitude of the universal conductance fluctuations in the metallic regime, and in the width of the log-normal conductance distribution in the insulating regime.

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