scholarly journals Analytical Modeling of the Mixed-Mode Growth and Dissolution of Precipitates in a Finite System

Metals ◽  
2019 ◽  
Vol 9 (8) ◽  
pp. 889 ◽  
Author(s):  
Naseri ◽  
Larouche ◽  
Martinez ◽  
Breton ◽  
Massinon
Keyword(s):  
Mixed Mode ◽  
Analytical Modeling ◽  
Mass Conservation ◽  
Time Discretization ◽  
Solute Concentration ◽  
Conservation Equation ◽  
The Matrix ◽  
Numerical Solver ◽  
Interfacial Mobility ◽  
Discretization Procedure

In this paper, a novel analytical modeling of the growth and dissolution of precipitates in substitutional alloys is presented. This model uses an existing solution for the shape-preserved growth of ellipsoidal precipitates in the mixed-mode regime, which takes into account the interfacial mobility of the precipitate. The dissolution model is developed by neglecting the transient term in the mass conservation equation, keeping the convective term. It is shown that such an approach yields the so-called reversed-growth approximation. A time discretization procedure is proposed to take into account the evolution of the solute concentration in the matrix as the phase transformation progresses. The model is applied to calculate the evolution of the radius of spherical -Al2Cu precipitates in an Al rich matrix at two different temperatures, for which growth or dissolution occurs. A comparison of the model is made, with the results obtained using the numerical solver DICTRA. The very good agreement obtained for cases where the interfacial mobility is very high indicates that the time discretization procedure is accurate.

Transport of Microorganisms in the Underground – Processes, Experiments and Simulation Models

1991 ◽  
Vol 24 (2) ◽  
pp. 309-314 ◽  
Author(s):  
G. Teutsch ◽  
K. Herbold-Paschke ◽  
D. Tougianidou ◽  
T. Hahn ◽  
K. Botzenhart
Keyword(s):  
Simulation Models ◽  
Mass Conservation ◽  
Breakthrough Curves ◽  
Conservation Equation ◽  
Retardation Factor ◽  
Natural Systems ◽  
Laboratory Setup ◽  
Preliminary Model ◽  
Sand And Gravel ◽  
Mass Conservation Equation

In this paper the major processes governing the persistence and underground transport of viruses and bacteria are reviewed in respect to their importance under naturally occurring conditions. In general, the simulation of the governing processes is based on the macroscopic mass-conservation equation with the addition of some filter and/or retardation factor and a decay coefficient, representing the natural “die-off” of the microorganisms. More advanced concepts try to incorporate growth and decay coefficients together with deposition and declogging factors. At present, none of the reported concepts has been seriously validated. Due to the complexity of natural systems and the pathogenic properties of some of the microorganisms, experiments under controlled laboratory conditions are required. A laboratory setup is presented in which a great variety of natural conditions can be simulated. This comprises a set of 1 metre columns and an 8 metre stainless-steel flume with 24 sampling ports. The columns are easily filled and conditioned and therefore used to study the effects of different soil-microorganism combinations under various environmental conditions. In the artificial flume natural underground conditions are simulated using sand and gravel aquifer material from the river Neckar alluvium. A first set of results from the laboratory experiments is presented together with preliminary model simulations. The large variety of observed breakthrough curves and recovery for the bacteria and viruses under investigation demonstrates the great uncertainty encountered in microbiological risk assessment.

scholarly journals Quantification of multiple simultaneously occurring nitrogen flows in the euphotic ocean

2016 ◽  
Author(s):  
Min Nina Xu ◽  
Yanhua Wu ◽  
Li Wei Zheng ◽  
Zhenzhen Zheng ◽  
Huade Zhao ◽  
...  
Keyword(s):  
Matrix Equation ◽  
Ammonia Oxidation ◽  
Mass Conservation ◽  
Quantitative Information ◽  
Nitrite Oxidation ◽  
Dissolved Nitrogen ◽  
Total Dissolved Nitrogen ◽  
Transformation Rates ◽  
The Matrix ◽  
Multiple Transformation

Abstract. The general features of the N cycle in the sunlit ocean are known, but quantitative information about multiple transformation rates among nitrogen pools, i.e., ammonium (NH4+), nitrite (NO2−), nitrate (NO3−) and particulate/dissolved organic nitrogen (PN/DON), are limited due to methodological difficulties. By adding a single 15N-labelled NH4+ tracer into incubators, we monitor ed the changes in concentration and isotopic composition of the total dissolved nitrogen (TDN), PN, NH4+, NO2−, and NO3− pools to trace the 15N and 14N flows. Based on mass conservation and isotope mass balance, we formulate d a matrix equation that allow edus to simultaneously derive the rates of multiple transformation processes in the nitrogen reaction web . We abandoned inhibitors and minimized the alteration of the system by adding a limited amount of tracer. In one single incubation, solution of the matrix equation provided the rates of NH4+, NO2−, and NO3− uptake; ammonia oxidation; nitrite oxidation; nitrite excretion; DON release; and potentially, the remineralization rate. To our knowledge, this is the first and most convenient method designed to quantitatively and simultaneously resolve complicated nitrogen transformation rates, albeit with some uncertainties. Field examples are given, and c omparisons with conventional labeling methods are discussed.

Stress Transfer from the Matrix to the Fibre in a Fragmentation Test: Raman Experiments and Analytical Modeling

1999 ◽  
Vol 33 (4) ◽  
pp. 377-399 ◽  
Author(s):  
Alkis Paipetis ◽  
Costas Galiotis ◽  
Yung Ching Liu ◽  
John A. Nairn
Keyword(s):  
Analytical Modeling ◽  
Stress Transfer ◽  
Fragmentation Test ◽  
The Matrix

scholarly journals A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal–icosahedral and cubed-sphere grids

2014 ◽  
Vol 7 (3) ◽  
pp. 909-929 ◽  
Author(s):  
J. Thuburn ◽  
C. J. Cotter ◽  
T. Dubos
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Model Comparison ◽  
Mass Conservation ◽  
Time Discretization ◽  
Water Model ◽  
Tracer Transport ◽  
Exact Mass ◽  
Large Wave ◽  
Cubed Sphere

Abstract. A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank–Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV). The algorithm is implemented and tested on two families of grids: hexagonal–icosahedral Voronoi grids, and modified equiangular cubed-sphere grids. Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed-sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.

Mixed-mode state–time discretization in ODE numerical integration

2020 ◽  
Vol 377 ◽  
pp. 112911 ◽  
Author(s):  
Franco Di Pietro ◽  
Joaquín Fernández ◽  
Gustavo Migoni ◽  
Ernesto Kofman
Keyword(s):  
Numerical Integration ◽  
Mixed Mode ◽  
Time Discretization ◽  
State Time

A New Model for the Simulation of CO2 Absorption in an Industrial-Scale Packed Column

2012 ◽  
Vol 557-559 ◽  
pp. 2208-2216 ◽  
Author(s):  
Wen Bin Li ◽  
Guo Cong Yu ◽  
Bo Tan Liu ◽  
Xi Gang Yuan
Keyword(s):  
Mass Transfer ◽  
Packed Column ◽  
Mass Conservation ◽  
Conservation Equation ◽  
Industrial Scale ◽  
Transfer Model ◽  
Turbulent Heat ◽  
Proposed Model ◽  
Heat Conservation ◽  
Phase Temperature

A new computational mass transfer model is proposed for simulating the chemical absorption process with heat effect by solving the average fluctuating mass flux in turbulent mass conservation equation and the average fluctuating heat flux in turbulent heat conservation equation, so that the concentration profile and the temperature profile of column can be obtained. The feather of the proposed model is to abandon the conventional way of introducing the unknown turbulent mass transfer diffusivity Dtand the turbulent thermal diffusivity αtin the mass and heat conservation equations. By using the proposed model, the simulated results of CO2absorption by aqueous monoethanolamine (MEA) solution in an industrial scale column is presented, including MEA concentration, CO2loading and liquid phase temperature. The simulations are in agreement with the published experiment data.

Mathematical Modelling of Thermo-Hydro-Mechanical Behaviour for Concrete under Elevated Temperature

2014 ◽  
Vol 670-671 ◽  
pp. 355-364
Author(s):  
Shao Bo Zhang ◽  
Xiao Chun Wang ◽  
Xin Pu Shen
Keyword(s):  
Elevated Temperature ◽  
Stokes Equations ◽  
Constitutive Relations ◽  
Gaseous Mixture ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Energy Conservation Equation

A hydro-thermo-mechanical model was presented for concrete at elevated temperature. Three phases of continuum were adopted in this model: gaseous mixture of water vapor and dry air, liquid water, and solid skeleton of concrete. Mass conservation equations, linear momentum conservation equation, and energy conservation equation were derived on the basis of the macroscopic Navier-Stokes equations for a general continuum, along with assumptions made for the purpose of simplification. Mathematical relationships between selected primary variables and secondary variables were given with existing data from references. Specifications of the constitutive relations were made for the kinetic variables and their conjugate forces.

scholarly journals High-Resolution, Rapid-Scan Dual-Doppler Retrievals of Vertical Velocity in a Simulated Supercell

2019 ◽  
Vol 36 (8) ◽  
pp. 1477-1500 ◽  
Author(s):  
Nathan A. Dahl ◽  
Alan Shapiro ◽  
Corey K. Potvin ◽  
Adam Theisen ◽  
Joshua G. Gebauer ◽  
...  
Keyword(s):  
Variational Method ◽  
Vertical Velocity ◽  
Traditional Method ◽  
Mass Conservation ◽  
Conservation Equation ◽  
Observation System ◽  
Near Surface ◽  
Rapid Scan ◽  
Close Range ◽  
The Impact

AbstractObservation system simulation experiments are used to evaluate different dual-Doppler analysis (DDA) methods for retrieving vertical velocity w at grid spacings on the order of 100 m within a simulated tornadic supercell. Variational approaches with and without a vertical vorticity equation constraint are tested, along with a typical (traditional) method involving vertical integration of the mass conservation equation. The analyses employ emulated radar data from dual-Doppler placements 15, 30, and 45 km east of the mesocyclone, with volume scan intervals ranging from 10 to 150 s. The effect of near-surface data loss is examined by denying observations below 1 km in some of the analyses. At the longer radar ranges and when no data denial is imposed, the “traditional” method produces results similar to those of the variational method and is much less expensive to implement. However, at close range and/or with data denial, the variational method is much more accurate, confirming results from previous studies. The vorticity constraint shows the potential to improve the variational analysis substantially, reducing errors in the w retrieval by up to 30% for rapid-scan observations (≤30 s) at close range when the local vorticity tendency is estimated using spatially variable advection correction. However, the vorticity constraint also degrades the analysis for longer scan intervals, and the impact diminishes with increased range. Furthermore, analyses using 30-s data also frequently outperform analyses using 10-s data, suggesting a limit to the benefit of increasing the radar scan rate for variational DDA employing the vorticity constraint.

Macroscopic Modeling of Pedestrian Flow Considering the Herd Behavior

2013 ◽  
Vol 444-445 ◽  
pp. 906-911
Author(s):  
Yan Qun Jiang
Keyword(s):  
Numerical Experiments ◽  
Mass Conservation ◽  
Conservation Equation ◽  
Behavioral Characteristics ◽  
Herd Behavior ◽  
Pedestrian Flow ◽  
Evacuation Time ◽  
Macroscopic Modeling ◽  
Pedestrian Simulation ◽  
Mass Conservation Equation

This paper aims to mimic the herd behavior of pedestrian flow, i.e., the tendency towards majority when a congestion occurs, by macroscopic modeling approach. The macroscopic pedestrian simulation model is composed of a mass-conservation equation and a simple model to reflect behavioral characteristics of pedestrians based on a specific traffic situation. Numerical experiments are designed to show some preliminary results, e.g. the beneficial effect of herding on evacuation time in some situations.

Analytical modeling of mixed-Mode bending behavior of asymmetric adhesively bonded pultruded GFRP joints

2015 ◽  
Vol 147 ◽  
pp. 228-242 ◽  
Author(s):  
Martin Ševčík ◽  
Moslem Shahverdi ◽  
Pavel Hutař ◽  
Anastasios P. Vassilopoulos
Keyword(s):  
Mixed Mode ◽  
Analytical Modeling ◽  
Adhesively Bonded ◽  
Bending Behavior
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