Physically based closed-form expression for the bimodal unsaturated hydraulic 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.

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A study on the geotechnical characterization and water retention characteristic curve of pond ash

Water Science & Technology ◽

10.2166/wst.2019.334 ◽

2019 ◽

Vol 80 (5) ◽

pp. 929-938

Author(s):

Janmeet Singh ◽

Sanjay Kumar Singh ◽

M. A. Alam

Keyword(s):

Hydraulic Conductivity ◽

Water Retention ◽

Characteristic Curve ◽

Input Parameter ◽

Wetting And Drying ◽

Pond Ash ◽

Retention Characteristic ◽

Unsaturated Hydraulic Conductivity ◽

Conductivity Function ◽

Engineering Practices

Abstract The understanding of the engineering behaviour of unsaturated soil is totally dependent on the water retention characteristic curve (WRCC). In this paper, a comprehensive study of the WRCCs of pond ash along with the ash's geotechnical behaviour has been made. The WRCC has been drawn experimentally using a Fredlund device based upon the pressure plate technique for both wetting and drying cycles. Further, an investigation was carried out to study WRCC hysteresis of pond ash. There exists a considerable hysteresis in drying and wetting curves of pond ash sample. The different WRCC models were used to fit the experimental WRCC data. The effect of compaction on WRCC was also studied. The air entry value in the case of a loose sample is low and the sample gets nearly desaturated at low soil suction as compared to a dense sample. Also, the wetting WRCC is predicted using the Feng and Fredlund model as it is difficult and time consuming to measure the whole hysteresis. The predicted results are compared with the measured wetting WRCC. Since the direct measurement of unsaturated hydraulic conductivity is difficult to obtain in engineering practices, the unsaturated hydraulic conductivity function is predicted using the measured WRCC as the input parameter using SEEP/W software.

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

Vadose Zone Journal ◽

10.2136/vzj2005.0066 ◽

2006 ◽

Vol 5 (1) ◽

pp. 121-124 ◽

Cited By ~ 76

Author(s):

E. Priesack ◽

W. Durner

Keyword(s):

Closed Form ◽

Closed Form Expression ◽

Form Expression ◽

Conductivity Function

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

IEEE Access ◽

10.1109/access.2021.3096419 ◽

2021 ◽

pp. 1-1

Author(s):

Yassine Zouaoui ◽

Larbi Talbi ◽

Khelifa Hettak ◽

Naresh K. Darimireddy

Keyword(s):

Closed Form ◽

Closed Form Expression ◽

Form Expression

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

ACM SIGMETRICS Performance Evaluation Review ◽

10.1145/3453953.3453974 ◽

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.

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

Journal of High Energy Physics ◽

10.1007/jhep06(2021)063 ◽

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.

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