Analytical solution for nonlinear hydrologic routing with general power-law storage function

2021 ◽  
pp. 126203
Author(s):  
Behzad Nazari ◽  
Dong-Jun Seo
Keyword(s):  
Analytical Solution ◽  
Power Law ◽  
Storage Function ◽  
General Power

scholarly journals The Similarity Hypothesis and New Analytical Support on the Estimation of Horizontal Infiltration into Sand

2010 ◽  
Vol 2010 ◽  
pp. 1-7 ◽  
Author(s):  
Celso L. Prevedello ◽  
Jocely M. T. Loyola
Keyword(s):  
Analytical Solution ◽  
Soil Water ◽  
Power Law ◽  
Specific Power ◽  
Water Density ◽  
Diverse Range ◽  
Similarity Hypothesis ◽  
Initial Soil ◽  
Water Contents ◽  
Soil Water Contents

A method based on a specific power-law relationship between the hydraulic head and the Boltzmann variable, presented using a similarity hypothesis, was recently generalized to a range of powers to satisfy the Bruce and Klute equation exactly. Here, considerations are presented on the proposed similarity assumption, and new analytical support is given to estimate the water density flux into and inside the soil, based on the concept of sorptivity and on Buckingham-Darcy's law. Results show that the new analytical solution satisfies both theories in the calculation of water density fluxes and is in agreement with experimental results of water infiltrating horizontally into sand. However, the utility of this analysis still needs to be verified for a variety of different textured soils having a diverse range of initial soil water contents.

Convergence and approximate calculation of average degree under different network sizes for decreasing random birth-and-death networks

2018 ◽  
Vol 32 (15) ◽  
pp. 1850159
Author(s):  
Yin Long ◽  
Xiao-Jun Zhang ◽  
Kui Wang
Keyword(s):  
Analytical Solution ◽  
Numerical Method ◽  
Power Law ◽  
Approximate Calculation ◽  
Approximate Expression ◽  
Network Size ◽  
Average Degree ◽  
Large Network ◽  
Network Link ◽  
Theoretical Results

In this paper, convergence and approximate calculation of average degree under different network sizes for decreasing random birth-and-death networks (RBDNs) are studied. First, we find and demonstrate that the average degree is convergent in the form of power law. Meanwhile, we discover that the ratios of the back items to front items of convergent reminder are independent of network link number for large network size, and we theoretically prove that the limit of the ratio is a constant. Moreover, since it is difficult to calculate the analytical solution of the average degree for large network sizes, we adopt numerical method to obtain approximate expression of the average degree to approximate its analytical solution. Finally, simulations are presented to verify our theoretical results.

Time scale of dynamic heterogeneity in model ionic liquids and its relation to static length scale and charge distribution

2015 ◽  
Vol 17 (43) ◽  
pp. 29281-29292 ◽  
Author(s):  
Sang-Won Park ◽  
Soree Kim ◽  
YounJoon Jung
Keyword(s):  
Ionic Liquid ◽  
Ionic Liquids ◽  
Charge Distribution ◽  
Power Law ◽  
Structural Relaxation ◽  
Time Scale ◽  
Length Scale ◽  
Dynamic Heterogeneity ◽  
General Power

We find a general power-law behavior: , where ζdh ≈ 1.2 for all the ionic liquid models, regardless of charges and the length scale of structural relaxation.

Implementing General Power Law to Interconvert Linear Viscoelastic Functions of Modified Asphalt Binders

2018 ◽  
Vol 144 (2) ◽  
pp. 04018010 ◽  
Author(s):  
Pouria Hajikarimi ◽  
Fereidoon Moghadas Nejad ◽  
Mohammad Mohammadi Aghdam
Keyword(s):  
Power Law ◽  
Asphalt Binders ◽  
Modified Asphalt ◽  
Linear Viscoelastic ◽  
General Power

scholarly journals Dynamic Euler-Bernoulli Beam Equation: Classification and Reductions

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
R. Naz ◽  
F. M. Mahomed
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Partial Differential Equation ◽  
Power Law ◽  
Fourth Order ◽  
Applied Load ◽  
Mass Density ◽  
Load Case ◽  
Order Ordinary Differential Equation ◽  
General Power

We study a dynamic fourth-order Euler-Bernoulli partial differential equation having a constant elastic modulus and area moment of inertia, a variable lineal mass densityg(x), and the applied load denoted byf(u), a function of transverse displacementu(t,x). The complete Lie group classification is obtained for different forms of the variable lineal mass densityg(x)and applied loadf(u). The equivalence transformations are constructed to simplify the determining equations for the symmetries. The principal algebra is one-dimensional and it extends to two- and three-dimensional algebras for an arbitrary applied load, general power-law, exponential, and log type of applied loads for different forms ofg(x). For the linear applied load case, we obtain an infinite-dimensional Lie algebra. We recover the Lie symmetry classification results discussed in the literature wheng(x)is constant with variable applied loadf(u). For the general power-law and exponential case the group invariant solutions are derived. The similarity transformations reduce the fourth-order partial differential equation to a fourth-order ordinary differential equation. For the power-law applied load case a compatible initial-boundary value problem for the clamped and free end beam cases is formulated. We deduce the fourth-order ordinary differential equation with appropriate initial and boundary conditions.

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