Characterizing the scaling coefficient ω between viscous and inertial permeability of fractures

2021 ◽  
Vol 593 ◽  
pp. 125920
Author(s):  
Kun Xing ◽  
Jiazhong Qian ◽  
Lei Ma ◽  
Haichun Ma ◽  
Weidong Zhao
Keyword(s):  
2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
Wenbao Wang ◽  
Xuanneng Gao ◽  
Lihui Le

The similarity of each scale model is verified based on the theory of similarity, deriving the similarity law of internal explosions in a single-layer spherical lattice shell structure via dimensional theory, calculated based on models with scaling coefficients of 1, 0.8, 0.6, 0.4, 0.2, and 0.1. The results show that the shock wave propagation characteristics, the distribution of the overpressure on the inner surface, the maximum dynamic response position, and the position at which the earliest explosion venting occurs are all similar to those of the original model. With the decrease of scaling coefficients, the overpressure peak value of the shock waves of each scale model, and the specific action time of the positive pressure zone, as well as specific impulse are increasingly deviated from the original model values; when the scaling coefficient is 0.1, the maximum relative error between the overpressure peak value at the measurement point and the specific action time of the positive pressure zone as well as the specific impulse and the original model value is 4.9%. Thus, it is feasible to forecast the internal explosion effect of the original structure size model by using the experiment results of the scale model with scaling coefficient λ≥0.1.


2015 ◽  
Vol 712 ◽  
pp. 43-48
Author(s):  
Rafał Palej ◽  
Artur Krowiak ◽  
Renata Filipowska

The work presents a new approach to the power method serving the purpose of solving the eigenvalue problem of a matrix. Instead of calculating the eigenvector corresponding to the dominant eigenvalue from the formula , the idempotent matrix B associated with the given matrix A is calculated from the formula , where m stands for the method’s rate of convergence. The scaling coefficient ki is determined by the quotient of any norms of matrices Bi and or by the reciprocal of the Frobenius norm of matrix Bi. In the presented approach the condition for completing calculations has the form. Once the calculations are completed, the columns of matrix B are vectors parallel to the eigenvector corresponding to the dominant eigenvalue, which is calculated from the Rayleigh quotient. The new approach eliminates the necessity to use a starting vector, increases the rate of convergence and shortens the calculation time when compared to the classic method.


2013 ◽  
Vol 461 ◽  
pp. 461-468
Author(s):  
Jin Tong ◽  
Mo Li ◽  
Ji Li Wang ◽  
Qing Zhu Zhang

The similarity phenomenon exists widely in nature and similarity theory is of importance in various types of engineering problems, especially in bionic engineering. In this work,a conception of fuzzy similarity was introduced. An effective mathematical method was put forward to identify the extent of morphological similarity between two living things of the homogenous species or the heterogeneous species and quantitative analysis of the similarity degree was carried out. A computer program based on the genetic algorithm was developed to solve and optimize the numerical scaling coefficient between an original profile data and a target one. To seek the maximum fuzzy similarity degree, an object function which is the core idea in this method was built to compute the similarity coefficient according to the corresponding points in these two sample profiles. Moreover, a series of arrays from the profiles of the foreleg of praying mantis (Mantis religiosa Linnaeus) was imported into the program. The results indicated the fuzzy similarity degree of samples was considerably high, which means the shape of the praying mantiss apical claw is quite uniform. Therefore, this computation method of similarity degree is effective.


2019 ◽  
Vol 10 ◽  
Author(s):  
Christopher L. Jerde ◽  
Krista Kraskura ◽  
Erika J. Eliason ◽  
Samantha R. Csik ◽  
Adrian C. Stier ◽  
...  

Fractals ◽  
1999 ◽  
Vol 07 (03) ◽  
pp. 221-234 ◽  
Author(s):  
L. TELESCA ◽  
V. CUOMO ◽  
M. LANFREDI ◽  
V. LAPENNA ◽  
M. MACCHIATO

We reveal the existence of clustering properties in the temporal distribution of the earthquakes observed in a seismic active area of Southern Apennine Chain (Italy) by means of quantitatively fractal tools (Fano Factor and Allan Factor). Data consist in a sequence of seismic events instrumentally recorded during the period 1983–1995 in the Irpinia-Basilicata Region (Southern Italy), in which in past and recent years, many destructive events occurred. The analysis of the Fano and Allan Factors shows that the sequence of the occurrence times of events with magnitude M th ≥2.5 is characterized by a scale-invariant behavior from the time scale τ ~ 5 · 103 s with a scaling coefficient α ~ 0.3. By gradually increasing the threshold magnitude up to M th =3.1, the value of the scaling coefficient monotonically decreases, pointing out a falling-off in the correlation strength. Although the increasing of the threshold magnitude seems to act as a randomizing filter which removes clustered structures, no firm sign of Poissonian, memoryless behavior is detectable in our analysis.


Oecologia ◽  
2021 ◽  
Author(s):  
R. S. K. Barnes

AbstractFor the first time, intraspecific relationships between the macroecological metrics patchiness (P) and both abundance (A) and occupancy (O) were investigated in a faunal assemblage. As a companion study to recent work on interspecific P, A and O patterns at the same localities, intraspecific patterns were documented within each of the more dominant invertebrates forming the seagrass macrobenthos of warm–temperate Knysna estuarine bay (South Africa) and of sub-tropical Moreton Bay (Australia). As displayed interspecifically, individual species showed strong A–O patterns (mean scaling coefficient − 0.76 and mean R2 > 0.8). All P–O relations were negative and most (67%) were statistically significant, although weaker (mean R2 0.5) than A–O ones; most P–A ones were also negative but fewer (43%) achieved significance, and were even weaker (mean R2 0.4); 33% of species showed no significant interrelations of either O or A with P. No species showed only a significant P–A relationship. Compared with interspecific P–A–O data from the same assemblages, power–law scaling exponents were equivalent, but R2 values were larger. Larviparous species comprised 70% of the total studied, but 94% of those displaying significant patchiness interrelationships; 5 of the 9 showing no P–A or P–O relationships, however, were also larviparous. At Knysna, though not in Moreton Bay, larviparous species also showed higher levels of occupancy than non-larviparous ones, whilst non-larviparous species showed higher levels of patchiness. Dominant Moreton Bay species, but not those at Knysna, exhibited homogeneously sloped P–O relationships.


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