scholarly journals Estimating the degree of preferential flow to drainage in an agricultural clay till field for a 10-year period

2020 ◽  
Author(s):  
David Nagy ◽  
Annette E. Rosenbom ◽  
Bo V. Iversen ◽  
Mohamed Jabloun ◽  
Finn Plauborg
Keyword(s):  
Conceptual Understanding ◽  
Preferential Flow ◽  
Lower Boundary ◽  
Saturated Zone ◽  
Model Concept ◽  
One Dimensional ◽  
Model Study ◽  
The Matrix ◽  
The One ◽  
Preferential Water

Abstract. The conceptual understanding of the preferential water flow is crucial and hence understanding the degree of water percolating rapidly through vertical macropores, or slowly through the low-permeable matrix, is vital in order to assess the risk of contaminants like nitrate and pesticides being transported through a variably-saturated macroporous clay till to drainage. This study compared six different model concepts, using the dual-permeability module of the one-dimensional model DAISY, incorporating three different macropore settings and two different groundwater tables set as lower boundary conditions. The three macropore settings included vertical macropores supplying water directly to (a) drainage, (b) drainage and matrix and (c) drainage and matrix including fractures supplying water to the matrix in the saturated zone. The model study was based on ten years of coherent climate, drainage, and groundwater data from an agricultural clay till field. The estimated drainage obtained with the six model concepts was compared to the measured drainage. No significant discrepancies between the estimated and measured drainage were identified. The model concept with the macropore setting (b) exposed to groundwater fluctuations measured in the southern part of the field, gave the best description of the drainage. Bromide leaching tests were used to evaluate the mass balance of the model concepts. The estimated water balance of all six concepts revealed that 70 % of the precipitation input to drainage was transported via macropores. According to the results of bromide leaching simulation, 54 % of the drainage was estimated to be transported via vertical macropores being initiated in the plow layer.

One-Dimensional Harmonic Oscillator in Quantum Phase Space

2011 ◽  
Vol 110-116 ◽  
pp. 3750-3754
Author(s):  
Jun Lu ◽  
Xue Mei Wang ◽  
Ping Wu
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Quantum Phase ◽  
Space Representation ◽  
Wave Mechanics ◽  
One Dimensional ◽  
Matrix Mechanics ◽  
The Matrix ◽  
Quantum Wave ◽  
The One

Within the framework of the quantum phase space representation established by Torres-Vega and Frederick, we solve the rigorous solutions of the stationary Schrödinger equations for the one-dimensional harmonic oscillator by means of the quantum wave-mechanics method. The result shows that the wave mechanics and the matrix mechanics are equivalent in phase space, just as in position or momentum space.

scholarly journals Comparative application and optimization of different single-borehole dilution test techniques

2020 ◽  
Author(s):  
Nikolai Fahrmeier ◽  
Nadine Goeppert ◽  
Nico Goldscheider
Keyword(s):  
Groundwater Monitoring ◽  
Saturated Zone ◽  
One Dimensional ◽  
Monitoring Wells ◽  
Advantages And Disadvantages ◽  
Advection Dispersion ◽  
Fractured Aquifers ◽  
Tracer Distribution ◽  
Deep Boreholes ◽  
The One

AbstractSingle-borehole dilution tests (SBDTs) are a method for characterizing groundwater monitoring wells and boreholes, and are based on the injection of a tracer into the saturated zone and the observation of concentration over depth and time. SBDTs are applicable in all aquifer types, but especially interesting in heterogeneous karst or fractured aquifers. Uniform injections aim at a homogeneous tracer concentration throughout the entire saturated length and provide information about inflow and outflow horizons. Also, in the absence of vertical flow, horizontal filtration velocities can be calculated. The most common method for uniform injections uses a hosepipe to inject the tracer. This report introduces a simplified method that uses a permeable injection bag (PIB) to achieve a close-to-uniform tracer distribution within the saturated zone. To evaluate the new method and to identify advantages and disadvantages, several tests have been carried out, in the laboratory and in multiple groundwater monitoring wells in the field. Reproducibility of the PIB method was assessed through repeated tests, on the basis of the temporal development of salt amount and calculated apparent filtration velocities. Apparent filtration velocities were calculated using linear regression as well as by inverting the one-dimensional (1D) advection-dispersion equation using CXTFIT. The results show that uniform-injection SBDTs with the PIB method produce valuable and reproducible outcomes and contribute to the understanding of groundwater monitoring wells and the respective aquifer. Also, compared to the hosepipe method, the new injection method requires less equipment and less effort, and is especially useful for deep boreholes.

scholarly journals Analysis of the Discrete Theory of Radiative Transfer in the Coupled “Ocean–Atmosphere” System: Current Status, Problems and Development Prospects

2020 ◽  
Vol 8 (3) ◽  
pp. 202 ◽  
Author(s):  
Viktor P. Afanas’ev ◽  
Alexander Yu. Basov ◽  
Vladimir P. Budak ◽  
Dmitry S. Efremenko ◽  
Alexander A. Kokhanovsky
Keyword(s):  
Radiative Transfer ◽  
Three Dimensional ◽  
Operator Method ◽  
Current Status ◽  
One Dimensional ◽  
Current State ◽  
The Matrix ◽  
The One ◽  
Discrete Theory ◽  
Development Prospects

In this paper, we analyze the current state of the discrete theory of radiative transfer. One-dimensional, three-dimensional and stochastic radiative transfer models are considered. It is shown that the discrete theory provides a unique solution to the one-dimensional radiative transfer equation. All approximate solution techniques based on the discrete ordinate formalism can be derived based on the synthetic iterations, the small-angle approximation, and the matrix operator method. The possible directions for the perspective development of radiative transfer are outlined.

scholarly journals Linearization of a Matrix Riccati Equation Associated to an Optimal Control Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Foued Zitouni ◽  
Mario Lefebvre
Keyword(s):  
Optimal Control ◽  
Riccati Equation ◽  
Stochastic Optimal Control ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Dimensional Problem ◽  
Matrix Riccati Equation ◽  
One Dimensional ◽  
The Matrix ◽  
The One

The matrix Riccati equation that must be solved to obtain the solution to stochastic optimal control problems known as LQG homing is linearized for a class of processes. The results generalize a theorem proved by Whittle and the one-dimensional case already considered by the authors. A particular two-dimensional problem is solved explicitly.

scholarly journals The topological line of ABJ(M) theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Nicola Gorini ◽  
Luca Griguolo ◽  
Luigi Guerrini ◽  
Silvia Penati ◽  
Domenico Seminara ◽  
...  
Keyword(s):  
Partition Function ◽  
Central Charge ◽  
Exact Representation ◽  
One Dimensional ◽  
Topological Sector ◽  
The Matrix ◽  
The One ◽  
The Masses ◽  
Dimension One ◽  
M Theory

Abstract We construct the one-dimensional topological sector of $$ \mathcal{N} $$ N = 6 ABJ(M) theory and study its relation with the mass-deformed partition function on S3. Supersymmetric localization provides an exact representation of this partition function as a matrix integral, which interpolates between weak and strong coupling regimes. It has been proposed that correlation functions of dimension-one topological operators should be computed through suitable derivatives with respect to the masses, but a precise proof is still lacking. We present non-trivial evidence for this relation by computing the two-point function at two-loop, successfully matching the matrix model expansion at weak coupling and finite ranks. As a by-product we obtain the two-loop explicit expression for the central charge cT of ABJ(M) theory. Three- and four-point functions up to one-loop confirm the relation as well. Our result points towards the possibility to localize the one-dimensional topological sector of ABJ(M) and may also be useful in the bootstrap program for 3d SCFTs.

Heat-Transfer for Fins with Two-Port Theory

1996 ◽  
Vol 24 (1) ◽  
pp. 61-72 ◽  
Author(s):  
C. Lombard
Keyword(s):  
Heat Transfer ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Flow Structures ◽  
One Dimensional ◽  
Various Boundary Conditions ◽  
The Matrix ◽  
The Subject ◽  
Complicated Geometry ◽  
The One

Fin heat transfer is an essential part of the education of mechanical engineers. It represents the simplest application of the heat conduction equation: the one-dimensional, steady, case. The usual presentation of the subject involves solving the conduction equation for various boundary conditions. In this paper, two-port techniques are applied to fin heat transfer. This concept is more suitable for the training of engineers because it emphasizes the importance of the boundaries rather than the internal conduction. Besides this important conceptual aid, the matrix is a powerful aid in computations; making it much easier to solve arrangements with complicated geometry. In fact, the two-port representation makes it possible to use graph theory for the automatic solution of complicated heat-flow structures.

scholarly journals Quantum mechanics of electrons in crystal lattices

1931 ◽  
Vol 130 (814) ◽  
pp. 499-513 ◽  
Keyword(s):  
Three Dimensional ◽  
Matrix Elements ◽  
Periodic Field ◽  
Crystal Lattices ◽  
One Dimensional ◽  
Physical Problems ◽  
Radiative Transitions ◽  
First Approximation ◽  
The Matrix ◽  
The One

Introduction .–Through the work of Bloch our understanding of the behaviour of electrons in crystal lattices has been much advanced. The principal idea of Bloch’s theory is the assumption that the interaction of a given electron with the other particles of the lattice may be replaced in first approximation by a periodic field of potential. With this model an interpretation of the specific heat, the electrical and thermal conductivity, the magnetic susceptibility, the Hall effect, and the optical properties of metals could be obtained. The advantages and limitations inherent in the assumption of Bloch will be much the same as those encountered when replacing the interaction of the electrons in an atom by a suitable central shielding of the unclear field, as in the work of Thomas and Hartree. In the papers quoted a number of general results were given regarding the behaviour of electrons in any periodic field of potential. To obtain a clearer idea of the details of this behaviour with a view to the application in special problems, however, it appeared worth while to investigate the mechanics of electrons in periodic fields of potential somewhat similar to those met with in practice and of such nature that the energy values W and eigenfunctions Ψ of the wave-equation can actually be computed. It is the purpose of this article to discuss a case where the integration is possible. In Section 1 the energy values and in Section 2 the wave-functions in their dependence on the binding introduced by the potential field are discussed for the one dimensional problem. In Section 3 the matrix elements of the linear momentum, which furnish the electric current associated with the various stationary states, are well as the probability of radiative transitions between these states, are evaluated. In Section 4 the results are extended to the three dimensional case and those features considered which one may expect to find in the case of more general periodic fields of potential. Section 5 deals with some applications to physical problems.

scholarly journals The Numerical Approximation of the Bioheat Equation of Space-Fractional Type Using Shifted Fractional Legendre Polynomials

2020 ◽  
pp. 875-889
Author(s):  
Firas A. Al-Saadawi ◽  
Hameeda Oda Al-Humedi
Keyword(s):  
Legendre Polynomials ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Dimensional Space ◽  
Bioheat Equation ◽  
One Dimensional ◽  
Good Convergence ◽  
The Matrix ◽  
The One ◽  
Fractional Type

The aim of this paper is to employ the fractional shifted Legendre polynomials (FSLPs) in the matrix form to approximate the fractional derivatives and find the numerical solutions of the one-dimensional space-fractional bioheat equation (SFBHE). The Caputo formula was utilized to approximate the fractional derivative. The proposed methodology applied for two examples showed its usefulness and efficiency. The numerical results showed that the utilized technique is very efficacious with high accuracy and good convergence.

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