MINIMUM ENERGY DISSIPATION AND FRACTAL STRUCTURES OF VASCULAR SYSTEMS

Fractals ◽  
1995 ◽  
Vol 03 (01) ◽  
pp. 123-153 ◽  
Author(s):  
TAO SUN ◽  
PAUL MEAKIN ◽  
TORSTEIN JØSSANG

A two dimensional minimum energy dissipation rate model has been used to study the structure of vascular networks. The geometry of the resulting minimum energy dissipation rate vascular system (MEDVS) has been studied. The structures of MEDVS networks are self-similar and have a fractal dimension of 2 on long length scales with a crossover to a fractal dimension of 1 on short length scales. A power-law distribution of link energy dissipation rates was found. The MEDVS networks have also been studied in terms of their transport properties.

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Wei Gao ◽  
Xu Wang ◽  
Shuang Dai ◽  
Dongliang Chen

To solve the main shortcoming of numerical method for analysis of the stability of rock slope, such as the selection the convergence condition for the strength reduction method, one method based on the minimum energy dissipation rate is proposed. In the new method, the basic principle of fractured rock slope failure, that is, the process of the propagation and coalescence for cracks in rock slope, is considered. Through analysis of one mining rock slope in western China, this new method is verified and compared with the generally used strength reduction method. The results show that the new method based on the minimum energy dissipation rate can be used to analyze the stability of the fractured rock slope and its result is very good. Moreover, the new method can obtain less safety factor for the rock slope than those by other methods. Therefore, the new method based on the minimum energy dissipation rate is a good method to analyze the stability of the fractured rock slope and should be superior to other generally used methods.


2020 ◽  
Vol 27 (2) ◽  
pp. 175-185 ◽  
Author(s):  
Macarena Domínguez ◽  
Giuseppina Nigro ◽  
Víctor Muñoz ◽  
Vincenzo Carbone ◽  
Mario Riquelme

Abstract. The description of the relationship between interplanetary plasma and geomagnetic activity requires complex models. Drastically reducing the ambition of describing this detailed complex interaction and, if we are interested only in the fractality properties of the time series of its characteristic parameters, a magnetohydrodynamic (MHD) shell model forced using solar wind data might provide a possible novel approach. In this paper we study the relation between the activity of the magnetic energy dissipation rate obtained in one such model, which may describe geomagnetic activity, and the fractal dimension of the forcing. In different shell model simulations, the forcing is provided by the solution of a Langevin equation where a white noise is implemented. This forcing, however, has been shown to be unsuitable for describing the solar wind action on the model. Thus, we propose to consider the fluctuations of the product between the velocity and the magnetic field solar wind data as the noise in the Langevin equation, the solution of which provides the forcing in the magnetic field equation. We compare the fractal dimension of the magnetic energy dissipation rate obtained, of the magnetic forcing term, and of the fluctuations of v⋅bz, with the activity of the magnetic energy dissipation rate. We examine the dependence of these fractal dimensions on the solar cycle. We show that all measures of activity have a peak near solar maximum. Moreover, both the fractal dimension computed for the fluctuations of v⋅bz time series and the fractal dimension of the magnetic forcing have a minimum near solar maximum. This suggests that the complexity of the noise term in the Langevin equation may have a strong effect on the activity of the magnetic energy dissipation rate.


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