scholarly journals A MATHEMATICAL MODEL FOR SALINITY INTRUSION

1972 ◽  
Vol 1 (13) ◽  
pp. 126
Author(s):  
A.Y. Kuo ◽  
C.S. Fang
Keyword(s):  
Mathematical Model ◽  
Dispersion Coefficient ◽  
River System ◽  
Computer Time ◽  
Longitudinal Dispersion Coefficient ◽  
York River ◽  
Implicit Finite Difference Scheme ◽  
Reasonable Solution ◽  
Implicit Finite Difference

A long term time-dependent mathematical model has been developed for predicting the salinity distributions in the upper York River System, including the tidal portions of the Mattaponi and Pamunkey Rivers. The method of calculating the longitudinal dispersion coefficient is discussed in detail. The study area and field project are described. The downstream boundary condition was found from a scheme combining a semi-explicit technique and linear extrapolation. The mass-balance equation, averaged over a tidal cycle and solved numerically by the implicit finite difference scheme, provided a reasonable solution and afforded economy in computer time. Field data were compared with the corresponding model results, indicating the general accuracy of the methodology.

Mathematical tidal model of the Tay Estuary

1980 ◽  
Vol 78 (3-4) ◽  
pp. s171-s182
Author(s):  
D. J. A. Williams ◽  
V. Nassehi
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Tidal Range ◽  
Level Curve ◽  
Tidal Level ◽  
Tidal Model ◽  
One Dimensional ◽  
Implicit Finite Difference Scheme ◽  
Implicit Finite Difference ◽  
Tay Estuary

SynopsisA one-dimensional mathematical model based on an implicit finite difference scheme is used to predict tidal levels and discharges throughout the Tay Estuary. The model accounts for the transformation of the tidal level curve along the estuary and predicts a maximum tidal range near Flisk. There is a measure of agreement between computed velocities and observed data in the upper reaches of the estuary.

scholarly journals Pulsatile blood flow in constricted tapered artery using a variable-order fractional Oldroyd-B model

2017 ◽  
Vol 21 (1 Part A) ◽  
pp. 29-40 ◽  
Author(s):  
Hamzah Bakhti ◽  
Lahcen Azrar ◽  
Baleanu Dumitru
Keyword(s):  
Mathematical Model ◽  
Numerical Approximation ◽  
Constitutive Models ◽  
Variable Order ◽  
Pulsatile Blood Flow ◽  
Medical Practitioners ◽  
Tapered Artery ◽  
Implicit Finite Difference Scheme ◽  
Implicit Finite Difference ◽  
Variable Order Fractional Derivative

The aim of this paper is to deal with the pulsatile flow of blood in stenosed arteries using one of the known constitutive models that describe the viscoelasticity of blood witch is the generalized Oldroyd-B model with a variable-order fractional derivative. Numerical approximation for the axial velocity and wall shear stress were obtained by use of the implicit finite-difference scheme. The velocity profile is analyzed by graphical illustrations. This mathematical model gives more realistic results that will help medical practitioners and it has direct applications in the treatment of cardiovascular diseases.

Buoyancy effects upon longitudinal dispersion in wide well-mixed estuaries

1980 ◽  
Vol 296 (1421) ◽  
pp. 467-496 ◽  
Keyword(s):  
Dispersion Coefficient ◽  
Longitudinal Dispersion ◽  
Vertical Shear ◽  
Transport Mechanisms ◽  
Salinity Distribution ◽  
Longitudinal Dispersion Coefficient ◽  
A Value ◽  
Horizontal Circulation ◽  
Mass Transport Mechanisms

As the width of a vertically well-mixed estuary increases, the longitudinal dispersion coefficient eventually reduces from a value associated with the transverse shear of the tidal current to a much smaller value associated with the oscillatory vertical shear. In this paper the final stages of this transition are investigated, with particular emphasis on buoyancy effects due to the salinity distribution. The central mathematical result relates the long-term longitudinal dispersion coefficient to the local unsteady horizontal dispersion coefficients and to the residual horizontal circulation. A useful consequence of this result is a demarcation of the parameter regimes in which the various mass transport mechanisms are dominant. The Thames downstream of London Bridge is revealed to be buoyancy dominated.

Basic principles for assessing the safety of fish products from the ponds exposed to the influence of nuclear fuel cycle enterprises

2019 ◽  
pp. 106-114
Author(s):  
A. V. Trapeznikov ◽  
V. N. Trapeznikova ◽  
A. V. Korzhavin ◽  
V. N. Nikolkin ◽  
A. P. Plataev
Keyword(s):  
Fuel Cycle ◽  
Specific Activity ◽  
River System ◽  
Food Product ◽  
Human Consumption ◽  
Basic Principles ◽  
Fish Products ◽  
Permissible Levels ◽  
Irtysh River

Relevance. In connection with the development of nuclear energy, many aquatic ecosystems have been exposed to radioactive substances. Fish, as an element of biota, is capable to accumulate radionuclides. However, fish is a traditional food. The control of the technogenic radionuclides accumulation level in the ichthyofauna is an important link in ensuring human security.Intention. To analyze the long-term data on the content of long-lived technogenic radionuclides 90Sr and 137Cs in the ichthyofauna of the Ob-Irtysh river system for the period from 2004 to 2016 and Beloyarsky pond for the period from 1977 to 2018.Methodology. Fish as a food product was assessed according to two criteria: a) permissible levels of specific activity of radionuclides (SanPiN 2.3.2.1078-01); b) using the indicator of conformity B and the uncertainty of its definition В (GOST 32161-2013 and GOST 32163-2013).Results and Discussion. Fish of all species that live in the river Tetcha, is not suitable for food use according to the criteria of SanPiN 2.3.2.1078-01, GOST 32161-2013 and GOST 32163-2013. The fish of the Ob-Irtysh river system, the habitat of which is located outside the Tetcha, meets the requirements for fish products. In the period from 1977 to 1989 in the Beloyarsk pond the accumulations of technogenic radionuclides in fish in quantities exceeding sanitary and hygienic standards were possible. Currently, the fish of the Beloyarsky pond fully complies with the sanitary and hygienic requirements for the radiation factor and is safe for human consumption.Conclusion. In the ponds exposed to the atomic energy enterprises, it is necessary to continuously monitor the content of long-lived technogenic radionuclides in fish and assess their amount in accordance with the requirements of SanPiN 2.3.2.1078-01 and using the conformity indicator В and the uncertainty of its determination В. 

Application of the method of mathematical modeling for forecasting channel deformations at the underwater crossing of the main pipeline

2020 ◽  
Vol 10 (6) ◽  
pp. 599-609
Author(s):  
Valery А. Gruzdev ◽  
◽  
Georgy V. Mosolov ◽  
Ekaterina A. Sabayda ◽  
◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Roughness Coefficient ◽  
Computational Domain ◽  
Channel Deformations ◽  
Geological Surveys ◽  
Kuban River ◽  
The Stability ◽  
Protective Structures

In order to determine the possibility of using the method of mathematical modeling for making long-term forecasts of channel deformations of trunk line underwater crossing (TLUC) through water obstacles, a methodology for performing and analyzing the results of mathematical modeling of channel deformations in the TLUC zone across the Kuban River is considered. Within the framework of the work, the following tasks were solved: 1) the format and composition of the initial data necessary for mathematical modeling were determined; 2) the procedure for assigning the boundaries of the computational domain of the model was considered, the computational domain was broken down into the computational grid, the zoning of the computational domain was performed by the value of the roughness coefficient; 3) the analysis of the results of modeling the water flow was carried out without taking the bottom deformations into account, as well as modeling the bottom deformations, the specifics of the verification and calibration calculations were determined to build a reliable mathematical model; 4) considered the possibility of using the method of mathematical modeling to check the stability of the bottom in the area of TLUC in the presence of man-made dumping or protective structure. It has been established that modeling the flow hydraulics and structure of currents, making short-term forecasts of local high-altitude reshaping of the bottom, determining the tendencies of erosion and accumulation of sediments upstream and downstream of protective structures are applicable for predicting channel deformations in the zone of the TLUC. In all these cases, it is mandatory to have materials from engineering-hydro-meteorological and engineering-geological surveys in an amount sufficient to compile a reliable mathematical model.

River Quality Models for Consent Setting in England and Wales

1989 ◽  
Vol 21 (8-9) ◽  
pp. 1015-1024 ◽  
Author(s):  
C. P. Crockett ◽  
R. W. Crabtree ◽  
I. D. Cluckie
Keyword(s):  
River System ◽  
Quality Model ◽  
Catchment Scale ◽  
Quality Models ◽  
England And Wales ◽  
Future Developments ◽  
Statistical Framework ◽  
River Quality ◽  
National Approach

In England and Wales the placing of effluent discharge consents within a statistical framework has led to the development of a new hybrid type of river quality model. Such catchment scale consent models have a stochastic component for the generation of model inputs and a deterministic component to route them through the river system. This paper reviews and compares the existing approaches for consent modelling used by various Water Authorities. A number of possible future developments are suggested including the potential need for a national approach to the review and setting of long term consents.

scholarly journals Numerical Investigation into Emission, Depletion, and Thermal Decomposition in a Reacting Slab

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
O. D. Makinde ◽  
T. Chinyoka ◽  
R. S. Lebelo
Keyword(s):  
Thermal Decomposition ◽  
Fossil Fuels ◽  
Mitigation Strategies ◽  
Assessment Tools ◽  
Nonlinear Mathematical Model ◽  
Heat And Mass Exchange ◽  
Implicit Finite Difference Scheme ◽  
Oil And Natural Gas ◽  
Implicit Finite Difference ◽  
Thermal Stability Of

The emission of carbon dioxide (CO2) is closely associated with oxygen (O2) depletion, and thermal decomposition in a reacting stockpile of combustible materials like fossil fuels (e.g., coal, oil, and natural gas). Moreover, it is understood that proper assessment of the emission levels provides a crucial reference point for other assessment tools like climate change indicators and mitigation strategies. In this paper, a nonlinear mathematical model for estimating the CO2emission, O2depletion, and thermal stability of a reacting slab is presented and tackled numerically using a semi-implicit finite-difference scheme. It is assumed that the slab surface is subjected to a symmetrical convective heat and mass exchange with the ambient. Both numerical and graphical results are presented and discussed quantitatively with respect to various parameters embedded in the problem.

scholarly journals On the effect of antiresorptive drugs on the bone remodeling of the mandible after dental implantation: a mathematical model

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Mehran Ashrafi ◽  
Farzan Ghalichi ◽  
Behnam Mirzakouchaki ◽  
Manuel Doblare
Keyword(s):  
Mathematical Model ◽  
Bone Density ◽  
Bone Remodeling ◽  
Dental Implants ◽  
Implant Design ◽  
Patient Specific ◽  
Dental Implantation ◽  
Antiresorptive Agents ◽  
Antiresorptive Drugs

AbstractBone remodeling identifies the process of permanent bone change with new bone formation and old bone resorption. Understanding this process is essential in many applications, such as optimizing the treatment of diseases like osteoporosis, maintaining bone density in long-term periods of disuse, or assessing the long-term evolution of the bone surrounding prostheses after implantation. A particular case of study is the bone remodeling process after dental implantation. Despite the overall success of this type of implants, the increasing life expectancy in developed countries has boosted the demand for dental implants in patients with osteoporosis. Although several studies demonstrate a high success rate of dental implants in osteoporotic patients, it is also known that the healing time and the failure rate increase, necessitating the adoption of pharmacological measures to improve bone quality in those patients. However, the general efficacy of these antiresorptive drugs for osteoporotic patients is still controversial, requiring more experimental and clinical studies. In this work, we investigate the effect of different doses of several drugs, used nowadays in osteoporotic patients, on the evolution of bone density after dental implantation. With this aim, we use a pharmacokinetic–pharmacodynamic (PK/PD) mathematical model that includes the effect of antiresorptive drugs on the RANK/RANK-L/OPG pathway, as well as the mechano-chemical coupling with external mechanical loads. This mechano-PK/PD model is then used to analyze the evolution of bone in normal and osteoporotic mandibles after dental implantation with different drug dosages. We show that using antiresorptive agents such as bisphosphonates or denosumab increases bone density and the associated mechanical properties, but at the same time, it also increases bone brittleness. We conclude that, despite the many limitations of these very complex models, the one presented here is capable of predicting qualitatively the evolution of some of the main biological and chemical variables associated with the process of bone remodeling in patients receiving drugs for osteoporosis, so it could be used to optimize dental implant design and coating for osteoporotic patients, as well as the drug dosage protocol for patient-specific treatments.

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