Closed-Form Expression for the Multi-Modal Unsaturated Conductivity Function

2006 ◽  
Vol 5 (1) ◽  
pp. 121-124 ◽  
Author(s):  
E. Priesack ◽  
W. Durner
Keyword(s):  
Closed Form ◽  
Closed Form Expression ◽  
Form Expression ◽  
Conductivity Function

Physically based closed-form expression for the bimodal unsaturated hydraulic conductivity function

2013 ◽  
Vol 68 (2) ◽  
pp. 328-334
Author(s):  
Shiyu Liu ◽  
Noriyuki Yasufuku ◽  
Qiang Liu ◽  
Hazarika Hemanta
Keyword(s):  
Experimental Data ◽  
Hydraulic Conductivity ◽  
Closed Form ◽  
Characteristic Curve ◽  
Complex Structure ◽  
Closed Form Expression ◽  
Form Expression ◽  
Unsaturated Hydraulic Conductivity ◽  
Physically Based ◽  
Conductivity Function

Simulation of flow and contaminant transport through the vadose zone requires accurate parameterization of the soil hydraulic properties. This requirement is particularly important for soils with a complex structure. In the present study, a physically based closed-form expression for the bimodal unsaturated hydraulic conductivity function is proposed for soils with bimodal pore-size distribution. It combines the bimodal representation of the soil-water characteristic curve (SWCC) function of Liu with the conductivity representation model of Mualem. The proposed equations are defined by parameters that have physical significance, which can be related to the properties of the materials. Experimental data for the representation of bimodal SWCCs and corresponding hydraulic conductivity curves were used to demonstrate the applicability of the proposed functions. The proposed approaches resulted in good agreement with experimental data. These functions can potentially be used as an effective tool for identifying hydraulic porosities in mediums with a complex structure.

scholarly journals Synthesizing of Planar and Conformal Double-Sided Parallel-Cross Dipoles FSS Based on Closed-Form Expression

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Yassine Zouaoui ◽  
Larbi Talbi ◽  
Khelifa Hettak ◽  
Naresh K. Darimireddy
Keyword(s):  
Closed Form ◽  
Closed Form Expression ◽  
Form Expression

Distribution of Consensus in a Broadcasting-based Consensus-forming Algorithm

2021 ◽  
Vol 48 (3) ◽  
pp. 91-96
Author(s):  
Shigeo Shioda
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Closed Form ◽  
Probability Density ◽  
Infinite Number ◽  
Stable Distribution ◽  
Random Variable ◽  
Cauchy Distribution ◽  
Closed Form Expression ◽  
Form Expression

The consensus achieved in the consensus-forming algorithm is not generally a constant but rather a random variable, even if the initial opinions are the same. In the present paper, we investigate the statistical properties of the consensus in a broadcasting-based consensus-forming algorithm. We focus on two extreme cases: consensus forming by two agents and consensus forming by an infinite number of agents. In the two-agent case, we derive several properties of the distribution function of the consensus. In the infinite-numberof- agents case, we show that if the initial opinions follow a stable distribution, then the consensus also follows a stable distribution. In addition, we derive a closed-form expression of the probability density function of the consensus when the initial opinions follow a Gaussian distribution, a Cauchy distribution, or a L´evy distribution.

scholarly journals Colored HOMFLY-PT for hybrid weaving knot $$ {\hat{\mathrm{W}}}_3 $$(m, n)

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Vivek Kumar Singh ◽  
Rama Mishra ◽  
P. Ramadevi
Keyword(s):  
Closed Form ◽  
Topological Strings ◽  
Chebyshev Polynomials ◽  
Fibonacci Numbers ◽  
Infinite Family ◽  
Closed Form Expression ◽  
Two Dimensional ◽  
Laurent Polynomials ◽  
Form Expression ◽  
Torus Knots

Abstract Weaving knots W(p, n) of type (p, n) denote an infinite family of hyperbolic knots which have not been addressed by the knot theorists as yet. Unlike the well known (p, n) torus knots, we do not have a closed-form expression for HOMFLY-PT and the colored HOMFLY-PT for W(p, n). In this paper, we confine to a hybrid generalization of W(3, n) which we denote as $$ {\hat{W}}_3 $$ W ̂ 3 (m, n) and obtain closed form expression for HOMFLY-PT using the Reshitikhin and Turaev method involving $$ \mathrm{\mathcal{R}} $$ ℛ -matrices. Further, we also compute [r]-colored HOMFLY-PT for W(3, n). Surprisingly, we observe that trace of the product of two dimensional $$ \hat{\mathrm{\mathcal{R}}} $$ ℛ ̂ -matrices can be written in terms of infinite family of Laurent polynomials $$ {\mathcal{V}}_{n,t}\left[q\right] $$ V n , t q whose absolute coefficients has interesting relation to the Fibonacci numbers $$ {\mathrm{\mathcal{F}}}_n $$ ℱ n . We also computed reformulated invariants and the BPS integers in the context of topological strings. From our analysis, we propose that certain refined BPS integers for weaving knot W(3, n) can be explicitly derived from the coefficients of Chebyshev polynomials of first kind.

Simple Closed-Form Expression to Estimate the Ring Ratio of 16-APSK to Compensate for Distortion in Nonlinear Systems

2017 ◽  
Author(s):  
M.J. Cañavate-Sánchez ◽  
A. Segneri ◽  
S. Godi ◽  
A. Georgiadis ◽  
S. Kosmopoulos ◽  
...  
Keyword(s):  
Nonlinear Systems ◽  
Closed Form ◽  
Closed Form Expression ◽  
Form Expression ◽  
Ring Ratio

Approximate closed-form expression for the ergodic capacity of polarisation-diversity MIMO systems

2004 ◽  
Vol 40 (19) ◽  
pp. 1192 ◽  
Author(s):  
J. Pérez ◽  
J. Ibáñez ◽  
L. Vielva ◽  
I. Santamaría
Keyword(s):  
Closed Form ◽  
Mimo Systems ◽  
Ergodic Capacity ◽  
Closed Form Expression ◽  
Form Expression
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