Scaling properties of driven interfaces: Symmetries, conservation laws, and the role of constraints

1991 ◽  
Vol 43 (10) ◽  
pp. 5275-5283 ◽  
Author(s):  
Z. Rácz ◽  
M. Siegert ◽  
D. Liu ◽  
M. Plischke
10.29007/c7r5 ◽  
2018 ◽  
Author(s):  
Leonardo Enrico Bertassello ◽  
P. Suresh Rao ◽  
Gianluca Botter ◽  
Antoine Aubeneau

Wetlands are ubiquitous topographic depressions on landscapes and form criticalelements of the mosaic of aquatic habitats. The role of wetlands in the global hydrological and biogeochemical cycles is intimately tied to their geometric characteristics. We used DEM analysis and local search algorithms to identify wetland attributes (maximum stage, surface area and storage volume) in four wetlandscapes across the United States. We then derived the exceedance cumulative density functions (cdfs) of these attributes for the identified wetlands, applied the concept of fractal dimension to investigate the variability in wetland’ shapes. Exponentially tempered Pareto distributions were fitted to DEM derived wetland attributes. In particular, the scaling exponents appear to remain constant through the progressive water-filling of the landscapes, suggesting self-similarity of wetland geometrical attributes. This tendency is also reproduced by the fractal dimension (D) of wetland shorelines, which remains constant across different water-filling levels. In addition, the variability in D is constrained within a narrow range (1 <D < 1.33) in all the four wetlandscapes. Finally, the comparison between wetlands identified by the DEM-based model are consistentwith actual data.


1983 ◽  
Vol 29 (1) ◽  
pp. 111-125 ◽  
Author(s):  
Robert G. Littlejohn

An elementary but rigorous derivation is given for a variational principle for guiding centre motion. The equations of motion resulting from the variational principle (the drift equations) possess exact conservation laws for phase volume, energy (for time-independent systems), and angular momentum (for azimuthally symmetric systems). The results of carrying the variational principle to higher order in the adiabatic parameter are displayed. The behaviour of guiding centre motion in azimuthally symmetric fields is discussed, and the role of angular momentum is clarified. The application of variational principles in the derivation and solution of gyrokinetic equations is discussed.


Fractals ◽  
1993 ◽  
Vol 01 (04) ◽  
pp. 818-826 ◽  
Author(s):  
L.A.N. AMARAL ◽  
A.-L. BARABÁSI ◽  
S.V. BULDYREV ◽  
S. HAVLIN ◽  
H.E. STANLEY

We study the effect on interface roughening of a gradient ∇p in the density of pinning sites p. We identify a new correlation length, ξ, which is a function of ∇p: ξ~(∇p)−γ/α, where α=ν⊥/ν|| is the roughness exponent, and γ=ν⊥/(1+ν⊥). The exponents ν⊥ and ν|| characterize the transverse and longitudinal correlation lengths. To investigate the effect of ∇p on the scaling properties of the interface in (1+1) and (2+1) dimensions, we calculate the critical concentration, pc, and the exponents γ and α from which ν⊥ and ν|| can be determined. Our results are in qualitative agreement with some of the features of imbibition experiments.


1980 ◽  
Vol 58 ◽  
pp. 491-493
Author(s):  
Peter W. Cole ◽  
Robert G. Deupree

AbstractThe role of convection in the core helium flash is simulated by two-dimensional eddies interacting with the thermonuclear runaway. These eddies are followed by the explicit solution of the 2D conservation laws with a 2D finite difference hydrodynamics code. Thus, no phenomenological theory of convection such as the local mixing length theory is required.


1990 ◽  
Vol 05 (17) ◽  
pp. 1339-1344 ◽  
Author(s):  
PRODYOT KUMAR ROY ◽  
ANURADHA LAHIRI ◽  
BIJAN BAGCHI

The role of supersymmetry in the KdV-MKdV hierarchy of conservation laws is examined. Among all the fifth order evolution equations, the Lax equation turns out to be the only one which is mapped onto its modified partner through the pair of supersymmetric transformations.


CALCOLO ◽  
2021 ◽  
Vol 58 (2) ◽  
Author(s):  
Jan Giesselmann ◽  
Fabian Meyer ◽  
Christian Rohde

AbstractStatistical solutions have recently been introduced as an alternative solution framework for hyperbolic systems of conservation laws. In this work, we derive a novel a posteriori error estimate in the Wasserstein distance between dissipative statistical solutions and numerical approximations obtained from the Runge-Kutta Discontinuous Galerkin method in one spatial dimension, which rely on so-called regularized empirical measures. The error estimator can be split into deterministic parts which correspond to spatio-temporal approximation errors and a stochastic part which reflects the stochastic error. We provide numerical experiments which examine the scaling properties of the residuals and verify their splitting.


Author(s):  
Maria Colombo ◽  
Gianluca Crippa ◽  
Marie Graff ◽  
Laura V. Spinolo

We deal with the numerical investigation of the local limit of nonlocal conservation laws. Previous numerical experiments seem to suggest that the solutions of the nonlocal problems converge to the entropy admissible solution of the conservation law in the singular local limit. However, recent analytical results state that (i) in general convergence does not hold because one can exhibit counterexamples; (ii)~convergence can be recovered provided viscosity is added to both the local and the nonlocal equations.  Motivated by these analytical results, we investigate the role of numerical viscosity in the numerical study of the local limit of nonlocal conservation laws. In particular, we show that Lax-Friedrichs type schemes  may provide the wrong intuition and erroneously suggest that the solutions of the nonlocal problems converge to the entropy admissible solution of the conservation law in cases where this is ruled out by analytical results. We also test Godunov type schemes, less affected by numerical viscosity, and show that in some cases they provide an intuition more in accordance with the analytical results.


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