A self-similar problem dealing with the one-dimensional collision of two half spaces of a nonlinear-elastic material

1990 ◽  
Vol 30 (6) ◽  
pp. 976-980 ◽  
Author(s):  
I. E. Agapov ◽  
A. M. Belogortsev ◽  
A. A. Burenin ◽  
A. V. Rezunov
Keyword(s):  
Elastic Material ◽  
Nonlinear Elastic Material ◽  
One Dimensional ◽  
Self Similar ◽  
The One ◽  
Nonlinear Elastic

A self-similar solution for expansion into a vacuum of a collisionless plasma bunch

1998 ◽  
Vol 59 (1) ◽  
pp. 83-90 ◽  
Author(s):  
A. V. BAITIN ◽  
K. M. KUZANYAN
Keyword(s):  
Electron Distribution Function ◽  
Collisionless Plasma ◽  
Electron Component ◽  
One Dimensional ◽  
Ultrarelativistic Electron ◽  
Plasma Bunch ◽  
Self Similar Solution ◽  
Self Similar ◽  
The One ◽  
Similar Solutions

The process of expansion into a vacuum of a collisionless plasma bunch with relativistic electron temperature is investigated for the one-dimensional case. Self-similar solutions for the evolution of the electron distribution function and ion acceleration are obtained, taking account of cooling of the electron component of plasma for the cases of non-relativistic and ultrarelativistic electron energies.

scholarly journals Sharp upper bounds on the maximum $M$-eigenvalue of fourth-order partially symmetric nonnegative tensors

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yuyan Yao ◽  
Gang Wang
Keyword(s):  
Fourth Order ◽  
Elastic Material ◽  
Quantum Physics ◽  
Upper Bounds ◽  
Nonlinear Elastic Material ◽  
Numerical Examples ◽  
Nonnegative Tensors ◽  
Material Analysis ◽  
Nonlinear Elastic ◽  
Partially Symmetric

<p style='text-indent:20px;'><inline-formula><tex-math id="M1">\begin{document}$ M $\end{document}</tex-math></inline-formula>-eigenvalues of partially symmetric nonnegative tensors play important roles in the nonlinear elastic material analysis and the entanglement problem of quantum physics. In this paper, we establish two upper bounds for the maximum <inline-formula><tex-math id="M2">\begin{document}$ M $\end{document}</tex-math></inline-formula>-eigenvalue of partially symmetric nonnegative tensors, which improve some existing results. Numerical examples are proposed to verify the efficiency of the obtained results.</p>

Theoretical modeling of the carbon dioxide injection into the porous medium saturated with methane and water taking into account the CO2 hydrate formation

2018 ◽  
Author(s):  
Gubaidullin A. A. ◽  
Musakaev N. G. ◽  
Duong Ngoc Hai ◽  
Borodin S. L. ◽  
Nguyen Quang Thai ◽  
...  
Keyword(s):  
Carbon Dioxide ◽  
Hydrate Formation ◽  
Carbon Dioxide Injection ◽  
Reservoir Temperature ◽  
One Dimensional ◽  
Porous Reservoir ◽  
Self Similar ◽  
The One ◽  
Similar Solutions ◽  
The Mathematical Model

In this work the mathematical model is constructed and the features of the injection of warm carbon dioxide (with the temperature higher than the initial reservoir temperature) into the porous reservoir initially saturated with methane gas and water are investigated. Self-similar solutions of the one-dimensional problem describing the distributions of the main parameters in the reservoir are constructed. The effect of the parameters of the injected carbon dioxide and the reservoir on the intensity of the CO2 hydrate formation is analyzed

scholarly journals A NEW DISTRIBUTION-BASED TEST OF SELF-SIMILARITY

Fractals ◽  
2004 ◽  
Vol 12 (03) ◽  
pp. 331-346 ◽  
Author(s):  
SERGIO BIANCHI
Keyword(s):  
Necessary Conditions ◽  
Statistical Significance ◽  
Distribution Functions ◽  
Self Similarity ◽  
Similarity Parameter ◽  
One Dimensional ◽  
Probability Distribution Functions ◽  
Self Similar ◽  
The One ◽  
New Distribution

In studying the scale invariance of an empirical time series a twofold problem arises: it is necessary to test the series for self-similarity and, once passed such a test, the goal becomes to estimate the parameter H0 of self-similarity. The estimation is therefore correct only if the sequence is truly self-similar but in general this is just assumed and not tested in advance. In this paper we suggest a solution for this problem. Given the process {X(t),t∈T}, we propose a new test based on the diameter δ of the space of the rescaled probability distribution functions of X(t). Two necessary conditions are deduced which contribute to discriminate self-similar processes and a closed formula is provided for the diameter of the fractional Brownian motion (fBm). Furthermore, by properly choosing the distance function, we reduce the measure of self-similarity to the Smirnov statistics when the one-dimensional distributions of X(t) are considered. This permits the application of the well-known two-sided test due to Kolmogorov and Smirnov in order to evaluate the statistical significance of the diameter δ, even in the case of strongly dependent sequences. As a consequence, our approach both tests the series for self-similarity and provides an estimate of the self-similarity parameter.

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