scholarly journals Jacobian Free Methods for Coupling Transport with Chemistry in Heterogenous Porous Media

Water ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 370
Author(s):  
Laila Amir ◽  
Michel Kern
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Reactive Transport ◽  
Chemical Species ◽  
Nuclear Waste Storage ◽  
Krylov Method ◽  
Waste Storage ◽  
Solution Methods ◽  
The Individual ◽  
Fully Coupled

Reactive transport plays an important role in various subsurface applications, including carbon dioxide sequestration, nuclear waste storage, biogeochemistry and the simulation of hydro–thermal reservoirs. The model couples a set of partial differential equations, describing the transport of chemical species, to nonlinear algebraic or differential equations, describing the chemical reactions. Solution methods for the resulting large nonlinear system can be either fully coupled or can iterate between transport and chemistry. This paper extends previous work by the authors where an approach based on the Newton–Krylov method applied to a reduced system has been developed. The main feature of the approach is to solve the nonlinear system in a fully coupled manner while keeping transport and chemistry modules separate. Here we extend the method in two directions. First, we take into account mineral precipitation and dissolution reactions by using an interior point Newton method, so as to avoid the usual combinatorial approach. Second, we study two-dimensional heterogeneous geometries. We show how the method can make use of an existing transport solver, used as a black box. We detail the methods and algorithms for the individual modules, and for the coupling step. We show the performance of the method on synthetic examples.

Radiation Damage in Ceramics

1982 ◽  
Vol 40 ◽  
pp. 600-603
Author(s):  
T. E. Mitchell ◽  
M. R. Pascucci ◽  
R. A. Youngman
Keyword(s):  
Radiation Damage ◽  
Outer Space ◽  
Point Of View ◽  
Nuclear Waste Storage ◽  
Waste Storage ◽  
Storage Media ◽  
Transmission Electron ◽  
Fundamental Point ◽  
Small Defect ◽  
Present Understanding

1. Introduction. Studies of radiation damage in ceramics are of interest not only from a fundamental point of view but also because it is important to understand the behavior of ceramics in various practical radiation enyironments- fission and fusion reactors, nuclear waste storage media, ion-implantation devices, outer space, etc. A great deal of work has been done on the spectroscopy of point defects and small defect clusters in ceramics, but relatively little has been performed on defect agglomeration using transmission electron microscopy (TEM) in the same kind of detail that has been so successful in metals. This article will assess our present understanding of radiation damage in ceramics with illustrations using results obtained from the authors' work.

scholarly journals On a nonlinear system of Riemann-Liouville fractional differential equations with semi-coupled integro-multipoint boundary conditions

2021 ◽  
Vol 19 (1) ◽  
pp. 760-772
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Badrah Alghamdi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Numerical Examples ◽  
Multipoint Boundary ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential

Abstract We study a nonlinear system of Riemann-Liouville fractional differential equations equipped with nonseparated semi-coupled integro-multipoint boundary conditions. We make use of the tools of the fixed-point theory to obtain the desired results, which are well-supported with numerical examples.

scholarly journals (Hydroxy)apatite on cement: insights into a new surface treatment

2021 ◽  
Author(s):  
Ronald Joseph Turner ◽  
Pieter Bots ◽  
Alan Richardson ◽  
Paul Bingham ◽  
Alex Scrimshire ◽  
...  
Keyword(s):  
Low Temperature ◽  
Surface Treatment ◽  
Nuclear Waste ◽  
Environmental Remediation ◽  
Coating Material ◽  
Hydroxy Apatite ◽  
Nuclear Waste Storage ◽  
Waste Storage ◽  
Architectural Preservation

(Hydroxy)apatite [Ca10(PO4)6(OH)2], has emerging potential as a cement coating material, with applications in environmental remediation, nuclear waste storage and architectural preservation. In these low temperature environments and when precipitating from...

scholarly journals Management of the Energy and Economic Potential of Nuclear Waste Use

Energies ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3709
Author(s):  
Bader Alshuraiaan ◽  
Sergey Pushkin ◽  
Anastasia Kurilova ◽  
Magdalena Mazur
Keyword(s):  
Nuclear Fuel ◽  
Nuclear Waste ◽  
Spent Nuclear Fuel ◽  
Integrated Approach ◽  
Economic Potential ◽  
Nuclear Waste Storage ◽  
Scientific Discussion ◽  
Management Algorithm ◽  
Waste Storage ◽  
The Eu

Recently, issues related to the effects (benefit or harm) of processing nuclear waste and its further use as fuel have been increasingly often raised in the scientific discussion. In this regard, the research aims to investigate issues related to the assessment of the economic potential of nuclear waste use, as well as the cooperation between states in the context of the reduction of risks associated with nuclear waste storage and processing. The research methodology is based on an integrated approach, including statistical, factor analysis, and the proposed system of performance indicators for managing spent nuclear fuel use. The research was carried out on the basis of materials from Russia and the EU countries. In the course of the study, a model of cooperation between states has been developed (based on the example of technologies and methods of processing nuclear waste used in the EU and Russia) according to the nuclear waste (spent nuclear fuel) management algorithm. The model considers the risks and threats associated with ecology and safety. The developments and other results described in the study should be used in further research devoted to the use of nuclear waste as heat-producing elements.

Strongly Nonlinear Vibrations of a Hyperelastic Thin-walled Cylindrical Shell Based on the Modified Lindstedt–Poincaré Method

2019 ◽  
Vol 19 (12) ◽  
pp. 1950160 ◽  
Author(s):  
Jing Zhang ◽  
Jie Xu ◽  
Xuegang Yuan ◽  
Wenzheng Zhang ◽  
Datian Niu
Keyword(s):  
Cylindrical Shell ◽  
Nonlinear System ◽  
Differential Equations ◽  
Nonlinear Vibrations ◽  
Harmonic Excitation ◽  
System Of Differential Equations ◽  
Response Curves ◽  
Strongly Nonlinear ◽  
Hardening Behavior ◽  
Thin Walled

Some significant behaviors on strongly nonlinear vibrations are examined for a thin-walled cylindrical shell composed of the classical incompressible Mooney–Rivlin material and subjected to a single radial harmonic excitation at the inner surface. First, with the aid of Donnell’s nonlinear shallow-shell theory, Lagrange’s equations and the assumption of small strains, a nonlinear system of differential equations for the large deflection vibration of a thin-walled shell is obtained. Second, based on the condensation method, the nonlinear system of differential equations is reduced to a strongly nonlinear Duffing equation with a large parameter. Finally, by the appropriate parameter transformation and modified Lindstedt–Poincar[Formula: see text] method, the response curves for the amplitude-frequency and phase-frequency relations are presented. Numerical results demonstrate that the geometrically nonlinear characteristic of the shell undergoing large vibrations shows a hardening behavior, while the nonlinearity of the hyperelastic material should weak the hardening behavior to some extent.

A Full-System Approach of the Elastohydrodynamic Line/Point Contact Problem

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
W. Habchi ◽  
D. Eyheramendy ◽  
P. Vergne ◽  
G. Morales-Espejel
Keyword(s):  
Finite Element ◽  
Nonlinear System ◽  
System Approach ◽  
Jacobian Matrix ◽  
Point Contact ◽  
System Of Equations ◽  
Nonlinear System Of Equations ◽  
Full System ◽  
Element Discretization ◽  
Fully Coupled

The solution of the elastohydrodynamic lubrication (EHL) problem involves the simultaneous resolution of the hydrodynamic (Reynolds equation) and elastic problems (elastic deformation of the contacting surfaces). Up to now, most of the numerical works dealing with the modeling of the isothermal EHL problem were based on a weak coupling resolution of the Reynolds and elasticity equations (semi-system approach). The latter were solved separately using iterative schemes and a finite difference discretization. Very few authors attempted to solve the problem in a fully coupled way, thus solving both equations simultaneously (full-system approach). These attempts suffered from a major drawback which is the almost full Jacobian matrix of the nonlinear system of equations. This work presents a new approach for solving the fully coupled isothermal elastohydrodynamic problem using a finite element discretization of the corresponding equations. The use of the finite element method allows the use of variable unstructured meshing and different types of elements within the same model which leads to a reduced size of the problem. The nonlinear system of equations is solved using a Newton procedure which provides faster convergence rates. Suitable stabilization techniques are used to extend the solution to the case of highly loaded contacts. The complexity is the same as for classical algorithms, but an improved convergence rate, a reduced size of the problem and a sparse Jacobian matrix are obtained. Thus, the computational effort, time and memory usage are considerably reduced.

scholarly journals Ensemble bootstrap methodology for forecasting dynamic growth processes using differential equations: application to epidemic outbreaks

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Gerardo Chowell ◽  
Ruiyan Luo
Keyword(s):  
Differential Equations ◽  
Ensemble Method ◽  
Transmission Model ◽  
Logistic Growth ◽  
Ensemble Modeling ◽  
Growth Processes ◽  
Probabilistic Forecasts ◽  
Forecasting Performance ◽  
Dynamic Growth ◽  
The Individual

AbstractBackgroundEnsemble modeling aims to boost the forecasting performance by systematically integrating the predictive accuracy across individual models. Here we introduce a simple-yet-powerful ensemble methodology for forecasting the trajectory of dynamic growth processes that are defined by a system of non-linear differential equations with applications to infectious disease spread.MethodsWe propose and assess the performance of two ensemble modeling schemes with different parametric bootstrapping procedures for trajectory forecasting and uncertainty quantification. Specifically, we conduct sequential probabilistic forecasts to evaluate their forecasting performance using simple dynamical growth models with good track records including the Richards model, the generalized-logistic growth model, and the Gompertz model. We first test and verify the functionality of the method using simulated data from phenomenological models and a mechanistic transmission model. Next, the performance of the method is demonstrated using a diversity of epidemic datasets including scenario outbreak data of theEbola Forecasting Challengeand real-world epidemic data outbreaks of including influenza, plague, Zika, and COVID-19.ResultsWe found that the ensemble method that randomly selects a model from the set of individual models for each time point of the trajectory of the epidemic frequently outcompeted the individual models as well as an alternative ensemble method based on the weighted combination of the individual models and yields broader and more realistic uncertainty bounds for the trajectory envelope, achieving not only better coverage rate of the 95% prediction interval but also improved mean interval scores across a diversity of epidemic datasets.ConclusionOur new methodology for ensemble forecasting outcompete component models and an alternative ensemble model that differ in how the variance is evaluated for the generation of the prediction intervals of the forecasts.

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