scholarly journals Technical Note: Approximate solution of transient drawdown for constant-flux pumping at a partially penetrating well in a radial two-zone confined aquifer

2015 ◽  
Vol 19 (6) ◽  
pp. 2639-2647 ◽  
Author(s):  
C.-S. Huang ◽  
S.-Y. Yang ◽  
H.-D. Yeh
Keyword(s):  
Approximate Solution ◽  
Steady State ◽  
Early Stage ◽  
Vertical Component ◽  
Technical Note ◽  
Neumann Condition ◽  
Dimensionless Time ◽  
Confined Aquifer ◽  
Constant Flux ◽  
Partially Penetrating Well

Abstract. An aquifer consisting of a skin zone and a formation zone is considered as a two-zone aquifer. Existing solutions for the problem of constant-flux pumping in a two-zone confined aquifer involve laborious calculation. This study develops a new approximate solution for the problem based on a mathematical model describing steady-state radial and vertical flows in a two-zone aquifer. Hydraulic parameters in these two zones can be different but are assumed homogeneous in each zone. A partially penetrating well may be treated as the Neumann condition with a known flux along the screened part and zero flux along the unscreened part. The aquifer domain is finite with an outer circle boundary treated as the Dirichlet condition. The steady-state drawdown solution of the model is derived by the finite Fourier cosine transform. Then, an approximate transient solution is developed by replacing the radius of the aquifer domain in the steady-state solution with an analytical expression for a dimensionless time-dependent radius of influence. The approximate solution is capable of predicting good temporal drawdown distributions over the whole pumping period except at the early stage. A quantitative criterion for the validity of neglecting the vertical flow due to a partially penetrating well is also provided. Conventional models considering radial flow without the vertical component for the constant-flux pumping have good accuracy if satisfying the criterion.

scholarly journals Technical Note: Approximate solution of transient drawdown for constant-flux pumping at a partially penetrating well in a radial two-zone confined aquifer

2015 ◽  
Vol 12 (3) ◽  
pp. 2741-2760
Author(s):  
C.-S. Huang ◽  
S.-Y. Yang ◽  
H.-D. Yeh
Keyword(s):  
Approximate Solution ◽  
Steady State ◽  
Early Stage ◽  
Vertical Component ◽  
Technical Note ◽  
Neumann Condition ◽  
Dimensionless Time ◽  
Confined Aquifer ◽  
Constant Flux ◽  
Partially Penetrating Well

Abstract. An aquifer consisting of a skin zone and a formation zone is considered as a two-zone aquifer. Existing solutions for the problem of constant-flux pumping (CFP) in a two-zone confined aquifer involve laborious calculation. This study develops a new approximate solution for the problem based on a mathematical model including two steady-state flow equations with different hydraulic parameters for the skin and formation zones. A partially penetrating well may be treated as the Neumann condition with a known flux along the screened part and zero flux along the unscreened part. The aquifer domain is finite with an outer circle boundary treated as the Dirichlet condition. The steady-state drawdown solution of the model is derived by the finite Fourier cosine transform. Then, an approximate transient solution is developed by replacing the radius of the boundary in the steady-state solution with an analytical expression for a dimensionless time-dependent radius of influence. The approximate solution is capable of predicting good temporal drawdown distributions over the whole pumping period except at the early stage. A quantitative criterion for the validity of neglecting the vertical flow component due to a partially penetrating well is also provided. Conventional models considering radial flow without the vertical component for the CFP have good accuracy if satisfying the criterion.

Analytical Method of Response of Piping System With Nonlinear Support

2000 ◽  
Vol 122 (4) ◽  
pp. 437-442
Author(s):  
Shigeru Aoki ◽  
Takeshi Watanabe
Keyword(s):  
Approximate Solution ◽  
Steady State ◽  
Analytical Method ◽  
Mode Shapes ◽  
Piping System ◽  
Steady State Response ◽  
Response Curves ◽  
State Response ◽  
Damping Characteristics ◽  
Nonlinear Support

This paper deals with steady-state response of the piping system with nonlinear support having hysteresis damping characteristics. Considering the energy loss for contact with a support, an analytical method of approximate solution for the beam, a one-span model of the piping system, with quadrilateral hysteresis loop characteristics is presented. Some numerical results of the approximate solution for the response curves and the mode shapes are shown. [S0094-9930(00)00204-3]

scholarly journals An Analytical Approximate Solution for the Quasi-Steady State Michaelis-Menten Problem

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
U. Filobello-Nino ◽  
H. Vazquez-Leal ◽  
R. Castaneda-Sheissa ◽  
V. M. Jimenez-Fernandez ◽  
A. L. Herrera-May ◽  
...  
Keyword(s):  
Approximate Solution ◽  
Steady State ◽  
Perturbation Method ◽  
Numerical Solutions ◽  
Absolute Error ◽  
Quasi Steady State ◽  
General Behaviour ◽  
Analytical Approximate Solution

This article utilizes perturbation method (PM) to find an analytical approximate solution for the Quasi-Steady-State Michaelis-Menten problem. From the comparison of Figures and absolute error values, between approximate and numerical solutions, it is shown that the obtained solutions are accurate, and therefore, they explain the general behaviour of the Michaelis-Menten mechanism.

scholarly journals Technical Note: Simple formulations and solutions of the dual-phase diffusive transport for biogeochemical modeling

2014 ◽  
Vol 11 (14) ◽  
pp. 3721-3728 ◽  
Author(s):  
J. Y. Tang ◽  
W. J. Riley
Keyword(s):  
Steady State ◽  
Tracer Diffusion ◽  
Technical Note ◽  
Analytical Models ◽  
Dual Phase ◽  
Near Surface ◽  
Solution Algorithms ◽  
Biogeochemical Models ◽  
Volume Approximation ◽  
Multi Phase

Abstract. Representation of gaseous diffusion in variably saturated near-surface soils is becoming more common in land biogeochemical models, yet the formulations and numerical solution algorithms applied vary widely. We present three different but equivalent formulations of the dual-phase (gaseous and aqueous) tracer diffusion transport problem that is relevant to a wide class of volatile tracers in land biogeochemical models. Of these three formulations (i.e., the gas-primary, aqueous-primary, and bulk-tracer-based formulations), we contend that the gas-primary formulation is the most convenient for modeling tracer dynamics in biogeochemical models. We then provide finite volume approximation to the gas-primary equation and evaluate its accuracy against three analytical models: one for steady-state soil CO2 dynamics, one for steady-state soil CH4 dynamics, and one for transient tracer diffusion from a constant point source into two different sequentially aligned medias. All evaluations demonstrated good accuracy of the numerical approximation. We expect our result will standardize an efficient mechanistic numerical method for solving relatively simple, multi-phase, one-dimensional diffusion problems in land models.

Steady-State and Transient Dynamical Systems Analysis of Uncoupled and Coupled Very Large Amplitude Roll Response of a Vessel in Regular and Random Waves

2006 ◽  
Author(s):  
Jeffrey M. Falzarano ◽  
Srinivas Vishnubhotla ◽  
Sarah E. Juckett
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Dynamical Systems ◽  
Large Amplitude ◽  
Early Stage ◽  
Static Stability ◽  
Random Waves ◽  
The Us ◽  
Us Navy ◽  
Regular And Random Waves

This paper contains the most recent results of our analysis of the DTMB 5415 model hull. This hull is an early stage version of the US Navy’s DDG-51 and approximately represents the last traditional destroyer hull form designed, built and operated by the US Navy. Moreover, the US Navy has recently proposed an alternative simulation based approach to traditional static stability analysis for advanced hull forms. Static stability analysis has been in use by the US Navy for at least 50 years. This paper proposes an alternative analysis technique which uses modern techniques of dynamical systems to analyze the large amplitude (nonlinear) roll response of a vessel in waves. The technique considers the steady state (local) roll response, the transient (global) roll response in both regular and random waves. Moreover, the effects of coupling, damping and reduced GM are all investigated.

Forced Response of Continuous System With Hysteresis Loop Characteristics: System With Quadrilateral Hysteresis Loop Characteristics

2005 ◽  
Author(s):  
Shigeru Aoki ◽  
Takeshi Watanabe
Keyword(s):  
Approximate Solution ◽  
Steady State ◽  
Energy Loss ◽  
Hysteresis Loop ◽  
Nonlinear Response ◽  
Continuous System ◽  
Forced Response ◽  
Steady State Response ◽  
State Response ◽  
Discontinuous Line

This paper deals with steady-state response of a continuous system with collision characteristics. Considering the energy loss in a collision, an analytical method of approximate solution for the continuous system with symmetrical hysteresis loop characteristics is presented. The resonance curves of nonlinear response obtained from approximate solution are shown as discontinuous line, and are discussed the phenomenon.

Changes in the incidence of cervical tumours by disease stage in a cytology-based screening programme

2019 ◽  
Vol 27 (2) ◽  
pp. 96-104
Author(s):  
Lauro Bucchi ◽  
Silvia Mancini ◽  
Flavia Baldacchini ◽  
Orietta Giuliani ◽  
Alessandra Ravaioli ◽  
...  
Keyword(s):  
Steady State ◽  
Incidence Rate ◽  
Screening Programme ◽  
Early Stage ◽  
Squamous Carcinoma ◽  
Disease Stage ◽  
Adenocarcinoma In Situ ◽  
Advanced Stage ◽  
Tumour Stage

Objectives To report changes in incidence of cervical tumours by disease stage, following the introduction of an organized cytology-based screening programme. Methods An intention-to-screen study of a cytology-based screening programme targeting 1,219,000 women aged 25–64 in northern Italy was carried out. Based on the previously reported trend in total incidence of cervical cancer, the study period 1995–2014 was divided into 1995–1996 (pre-screening, or reference, years), 1997–1998 (screening implementation phase), 1999–2006 (transition phase, when incidence decreased), and 2007–2014 (steady-state phase, when incidence stabilized again). Tumour stage was categorized as preinvasive (cervical intraepithelial neoplasia grade 3 (CIN3) and adenocarcinoma in situ), early (pT1a), advanced (pT1b or greater, ypT), and unknown (pT1 not otherwise specified, pTx, missing information). Average annual incidence rates observed in each phase were compared with the expected (reference) rates, using the incidence rate ratio, calculated with a Poisson regression model. Results In the steady-state phase, incidence rate ratios were: CIN3, 1.55 (95% confidence interval, 1.41–1.70); early-stage squamous carcinoma, 0.49 (0.36–0.67); advanced-stage squamous carcinoma, 0.44 (0.33–0.57); unknown-stage squamous carcinoma, 0.69 (0.48–0.99); adenocarcinoma in situ, 1.44 (0.72–2.88); early-stage adenocarcinoma, 2.65 (0.82–8.53); advanced-stage adenocarcinoma, 1.03 (0.56–1.91); and unknown-stage adenocarcinoma, 0.46 (0.23–0.92). Conclusions After stabilization, changes in incidence by tumour stage included a 55% increase for CIN3 and a 50–55% decrease both for early- and advanced-stage squamous carcinoma, but no significant changes for glandular tumours. These data will serve to quantify the incremental impact of the implementation of human papillomavirus-based screening, introduced in 2015.

The Approximate Calculation of Eigenvalues for Certain Second-Order Linear Differential Equations

1961 ◽  
Vol 65 (605) ◽  
pp. 360-360 ◽  
Author(s):  
W. J. Goodey
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Simple Formula ◽  
Approximate Calculation ◽  
Technical Note ◽  
Second Order ◽  
Numerical Results ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Linear Differential

In a recent technical note, Squire discussed the approximate solution of certain second-order linear differential equations by the method attributed variously to Riccati, Madelung, Wentzel, Kramers and Brillouin (the W.K.B. method), and others. The problem of eigenvalues, frequently met with in this type of equation, does not, however, appear to have received much attention by this method, and in this note a simple formula is developed which appears to give excellent numerical results in many cases.

Comparative analyses of alternative breakthrough curves from cumulative mass column testing of soil–bentonite backfills

2020 ◽  
Vol 57 (8) ◽  
pp. 1197-1214 ◽  
Author(s):  
Charles D. Shackelford ◽  
Catherine S. Hong
Keyword(s):  
Steady State ◽  
Solute Transport ◽  
Breakthrough Curves ◽  
Retardation Factor ◽  
Dimensionless Time ◽  
Mass Ratio ◽  
Column Tests ◽  
Cutoff Walls ◽  
Cumulative Mass ◽  
Linear Regressions

The results of eight cumulative mass column tests were analyzed via several different methods to evaluate the dispersion coefficient, D, and the retardation factor, Rd, governing the migration of chloride (Cl−), potassium (K), and zinc (Zn) through soil–bentonite backfills for vertical cutoff walls. Regression of the measured relative (effluent) concentration (RC) breakthrough curves (BTCs) resulted in relatively accurate determinations of Rd, but relatively inaccurate determinations of D for all three solutes. Values of Rd based on dimensionless time, T, corresponding to an RC of 0.5 were underestimated for all three solutes due to the significance of diffusion on solute transport. With a few exceptions, Rd for K and Zn based on analyses of the steady-state portions of measured cumulative mass ratio (CMR) BTCs and T – CMR BTCs were relatively accurate, whereas analysis of measured T – CMR BTCs was more accurate for determining Rd of Cl−. Overall, there is no advantage to analyzing the results of cumulative mass column tests in the form of RC BTCs, whereas the CMR and T – CMR BTCs offer the advantage of determining Rd based on simple linear regressions of the steady-state portions of the BTCs, i.e., provided steady-state solute transport has been established.

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