Current Issue : January - March Volume : 2021 Issue Number : 1 Articles : 5 Articles
Cavitation in plants is caused by development of air bubbles, which is related\nto their equilibrium and development. There is a univariate cubic equation\nfor bubble balance. New root formula of this kind of equation was proposed\nby Shenjin Fan, which is simpler than the Caldanâ??s. Using Shenjin formulas\nand taking water pressure l P as an independent variable, this paper gives the\nexact solution of the equation under certain conditions. The stability of the\nequilibrium of an air bubble in its different radius ranges is obtained by the\nway different from the previous. This kind of cavitation includes two types:\nFirst type may be caused by the growth of pre-existent air bubbles; Second\ntype is air seeding, here defined as the sucking of air bubbles from already\ngas-filled conduits. For air seeding three ways of cavitation have been proposed....
Motivated by the special theory of gradient elasticity (GradEla), a proposal is\nadvanced for extending it to construct gradient models for interatomic potentials,\ncommonly used in atomistic simulations. Our focus is on Londonâ??s\nquantum mechanical potential which is an analytical expression valid until a\ncertain characteristic distance where â??attractiveâ? molecular interactions change\ncharacter and become â??repulsiveâ? and cannot be described by the classical\nform of Londonâ??s potential. It turns out that the suggested internal length\ngradient (ILG) generalization of Londonâ??s potential generates both an â??attractiveâ?\nand a â??repulsiveâ? branch, and by adjusting the corresponding gradient\nparameters, the behavior of the empirical Lennard-Jones potentials is\ntheoretically captured....
Exponentiated power Lindley distribution is proposed as a generalization of some widely well-known distributions such as\nLindley, power Lindley, and generalized Lindley distributions. In this paper, the exact explicit expressions for moments of order\nstatistics from the exponentiated power Lindley distribution are derived. By using these relations, the best linear unbiased\nestimates of the location and scale parameters, based on type-II right-censored sample, are obtained. Next, the mean, variance, and\ncoefficients of skewness and kurtosis of some certain linear functions of order statistics are calculated and then used to derive the\napproximate confidence interval for the location and scale parameters using the Edgeworth approximation. Finally, some\nnumerical illustrations and two real data applications are presented....
Indefinite equation is an unsolved problem in number theory. Through exploration,\nthe author has been able to use a simple elementary algebraic method\nto solve the solutions of all three variable indefinite equations. In this\npaper, we will introduce and prove the solutions of Pythagorean equation,\nFermatâ??s theorem, Bill equation and so on....
In this paper, we propose a combination of discrete elements for the soil and\nfinite elements for the fluid flow field inside the pore space to simulate the\ntriggering of landslides. We give the details for the implementation of third\norder finite elements (â??P2 with bubbleâ?) together with polygonal discrete elements,\nwhich allows the formulation with a minimal number of degrees of\nfreedom to save computer time and memory. We verify the implementation\nwith several standard problems from computational fluid dynamics, as well as\nthe decay of a granular step in a fluid as test case for complex flow....
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