scholarly journals One-Dimensional Vacuum Steady Seepage Model of Unsaturated Soil and Finite Difference Solution

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Feng Huang ◽  
Jianguo Lyu ◽  
Guihe Wang ◽  
Hongyan Liu
Keyword(s):  
Finite Difference ◽  
Unsaturated Soil ◽  
Vacuum Pressure ◽  
Vacuum Field ◽  
One Dimensional ◽  
Steady Seepage ◽  
Basic Equations ◽  
The One ◽  
Seepage Law ◽  
Relationship Of

Vacuum tube dewatering method and light well point method have been widely used in engineering dewatering and foundation treatment. However, there is little research on the calculation method of unsaturated seepage under the effect of vacuum pressure which is generated by the vacuum well. In view of this, the one-dimensional (1D) steady seepage law of unsaturated soil in vacuum field has been analyzed based on Darcy’s law, basic equations, and finite difference method. First, the gravity drainage ability is analyzed. The analysis presents that much unsaturated water can not be drained off only by gravity effect because of surface tension. Second, the unsaturated vacuum seepage equations are built up in conditions of flux boundary and waterhead boundary. Finally, two examples are analyzed based on the relationship of matric suction and permeability coefficient after boundary conditions are determined. The results show that vacuum pressure will significantly enhance the drainage ability of unsaturated water by improving the hydraulic gradient of unsaturated water.

On the Onset of Breakup in Inviscid and Viscous Jets

1979 ◽  
Vol 46 (2) ◽  
pp. 291-297 ◽  
Author(s):  
D. A. Caulk ◽  
P. M. Naghdi
Keyword(s):  
Linear Equations ◽  
Three Dimensional ◽  
Periodic Wave ◽  
One Dimensional ◽  
Periodic Wave Solutions ◽  
Viscous Jets ◽  
Elliptical Jet ◽  
Basic Equations ◽  
The One ◽  
Small Disturbances

This paper is concerned with the instability of inviscid and viscous jets utilizing the basic equations of the one-dimensional direct theory of a fluid jet based on the concept of a Cosserat (or a directed) curve. First, a system of differential equations is derived for small motions superposed on uniform flow of an inviscid straight circular jet which can twist along its axis. Periodic wave solutions are then obtained for this system of linear equations; and, with reference to a description of growth in the unstable mode, the resulting dispersion relation is found to agree extremely well with the classical (three-dimensional) results of Rayleigh. Next, constitutive equations are obtained for a viscous elliptical jet and these are used to discuss both the symmetric and the antisymmetric small disturbances in the shape of the free surface of a circular jet. Through a comparison with available three-dimensional numerical results, the solution obtained is shown to be an improvement over an existing approximate solution of the problem.

Settlement rate of foundations on unsaturated soils

1999 ◽  
Vol 36 (5) ◽  
pp. 940-946 ◽  
Author(s):  
Ernesto Ausilio ◽  
Enrico Conte
Keyword(s):  
Volume Change ◽  
Unsaturated Soil ◽  
Unsaturated Soils ◽  
Shallow Foundations ◽  
Settlement Rate ◽  
One Dimensional ◽  
Consolidation Rate ◽  
Degree Of Consolidation ◽  
The One ◽  
External Loads

This paper deals with the one-dimensional consolidation of unsaturated soils due to the application of external loads. A simple equation is derived that enables one to predict the rate of settlement of shallow foundations with time. This equation uses the constitutive relationships proposed by Fredlund and Morgenstern to define the volume change of unsaturated soils, and relates the settlement rate to the average degree of consolidation for both the water and air phases. A series of examples is shown to demonstrate the feasibility and usefulness of the derived equation. Key words: one-dimensional consolidation, unsaturated soil, degree of consolidation, rate of settlement.

scholarly journals Non-Standard and Numerov Finite Difference Schemes for Finite Difference Time Domain Method to Solve One- Dimensional Schrödinger Equation

2018 ◽  
Vol 2 (1) ◽  
pp. 27
Author(s):  
Lily Maysari Angraini ◽  
I Wayan Sudiarta
Keyword(s):  
Finite Difference ◽  
Harmonic Oscillator ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Fdtd Method ◽  
Finite Difference Schemes ◽  
Potential Wells ◽  
One Dimensional ◽  
The One ◽  
Difference Time

<span>The purpose of  this paper is to show some improvements of the finite-difference time domain (FDTD) method using Numerov and non-standard finite difference (NSFD) schemes for solving the one-dimensional Schr</span><span>ö</span><span>dinger equation. Starting with results of the unmodified FDTD method, Numerov-FD and NSFD are applied iteratively to produce more accurate results for eigen energies and wavefunctios. Three potential wells, infinite square well, harmonic oscillator and Poschl-Teller, are used to compare results of FDTD calculations. Significant improvements in the results for the infinite square potential and the harmonic oscillator potential are found using Numerov-NSFD scheme, and for Poschl-Teller potential are found using Numerov scheme.</span>

Effect of the Spatial Extent of the Control in a Bilinear Control Problem for the Schroedinger Equation

2009 ◽  
Author(s):  
Katherine A. Kime
Keyword(s):  
Differential Geometry ◽  
Finite Difference ◽  
Lie Algebras ◽  
Grid Point ◽  
Schroedinger Equation ◽  
Time Varying ◽  
One Dimensional ◽  
Bilinear Control ◽  
The One ◽  
Bilinear Control Problem

We consider control of the one-dimensional Schroedinger equation through a time-varying potential. Using a finite difference semi-discretization, we consider increasing the extent of the potential from a single central grid-point in space to two or more gridpoints. With the differential geometry package in Maple 8, we compute and compare the corresponding Control Lie Algebras, identifying a trend in the number of elements which span the Control Lie Algebras.

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