scholarly journals Simulating chloride penetration in fly ash concrete by a fractal derivative model

2019 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 67-78 ◽  
Author(s):  
Pengfei Qu ◽  
Xiaoting Liu ◽  
Dumitru Baleanu
Keyword(s):  
Fractional Derivative ◽  
Linear Regression Analysis ◽  
Chemical Properties ◽  
Mathematical Expression ◽  
Fractal Model ◽  
Chloride Ions ◽  
Diffusion Behavior ◽  
Fractional Derivative Model ◽  
Fractal Derivative ◽  
Diffusion Phenomena

In the real engineering field, the chloride ions behave abnormal diffusion phenomena in concrete caused by different compositions of the concrete which lead to the complex physical and chemical properties. This paper utilizes a fractal derivative model and a fractional derivative model to describe the diffusion phenomena. Furthermore, according to actual experimental data in the field, the fractional and fractal model can simulate the diffusion behavior of chloride ions in concrete. In comparison to the fractional derivative model, the fractal derivative model gives a simpler mathematical expression and lower calculation costs. In addition, the linear regression analysis method is used to establish an effective relationship between the internal composition of concrete and the parameters of fractal model such as fractal order, ?, and diffusion coefficient, D. As a result, the fractal model with the parameters estimated by previous relationship can predict the diffusion behavior of chloride ions.

A variable-order time-fractional derivative model for chloride ions sub-diffusion in concrete structures

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Wen Chen ◽  
Jianjun Zhang ◽  
Jinyang Zhang
Keyword(s):  
Fractional Derivative ◽  
Measurement Data ◽  
Chloride Ions ◽  
Chloride Diffusion ◽  
Influence Coefficient ◽  
Variable Order ◽  
Binding Behavior ◽  
Fractional Derivative Model ◽  
Proposed Model ◽  
Variable Function

AbstractThis study proposes a new variable-order fractional diffusion equation model to describe the coupled chloride diffusion-binding processes in reinforced concrete, in which the order of fractional derivative term is a variable function instead of a constant in the standard fractional model. The concentration influence coefficient k is introduced to capture the effect of concentration dependency on chloride transport due to the chloride binding behavior. The two parameters in the proposed model can be determined directly by a statistical analysis of measurement data. Four test cases illustrate that the proposed variable-order fractional derivative model agrees significantly better with experimental data than the most commonly used traditional model governed by the classical Fick’s second law, especially when a large concentration coefficient k is involved. That proposed model is also verified by accurately predicting chloride concentration profiles in a period of 200 days.

scholarly journals A variable-order fractal derivative model for anomalous diffusion

2017 ◽  
Vol 21 (1 Part A) ◽  
pp. 51-59 ◽  
Author(s):  
Xiaoting Liu ◽  
Hong-Guang Sun ◽  
Mihailo Lazarevic ◽  
Zhuojia Fu
Keyword(s):  
Anomalous Diffusion ◽  
Transport Processes ◽  
Variable Order ◽  
Physical Explanation ◽  
Diffusion Behavior ◽  
New Model ◽  
Fractal Derivative ◽  
Diffusion Phenomena ◽  
Temporal Moment ◽  
Variable Order Fractional Derivative

This paper pays attention to develop a variable-order fractal derivative model for anomalous diffusion. Previous investigations have indicated that the medium structure, fractal dimension or porosity may change with time or space during solute transport processes, results in time or spatial dependent anomalous diffusion phenomena. Hereby, this study makes an attempt to introduce a variable-order fractal derivative diffusion model, in which the index of fractal derivative depends on temporal moment or spatial position, to characterize the above mentioned anomalous diffusion (or transport) processes. Compared with other models, the main advantages in description and the physical explanation of new model are explored by numerical simulation. Further discussions on the dissimilitude such as computational efficiency, diffusion behavior and heavy tail phenomena of the new model and variable-order fractional derivative model are also offered.

Decomposition of hydrogen peroxide on nickel-silver two-component catalyst

1984 ◽  
Vol 49 (10) ◽  
pp. 2222-2230 ◽  
Author(s):  
Viliam Múčka ◽  
Rostislav Silber
Keyword(s):  
Hydrogen Peroxide ◽  
Chemical Properties ◽  
Silver Ions ◽  
Surface Concentration ◽  
Chloride Ions ◽  
Nickel Silver ◽  
Silver Catalysts ◽  
Physico Chemical ◽  
Low Degree ◽  
Defective Crystal

The catalytic and physico-chemical properties of low-temperature nickel-silver catalysts with nickel oxide concentrations up to 43.8% (m/m) are examined via decomposition of hydrogen peroxide in aqueous solution. The mixed catalysts prepared at 250°C are composed of partly decomposed silver carbonate or oxide and nickel carbonate or hydroxide decomposed to a low degree only and exhibiting a very defective crystal structure. The activity of these catalysts is determined by the surface concentration of silver ions, which is affected by the nickel component present. The latter also contributes to the thermal stability of the catalytic centres of the silver component, viz. the Ag+ ions. The concentration of these ions varies with the temperature of the catalyst treatment, the activity varies qualitatively in the same manner, and the system approaches the Ag-NiO composition. The catalytic centres are very susceptible to poisoning by chloride ions. A previous exposition of the catalyst to a gamma dose of 10 kGy from a 60Co source has no measurable effect on the physico-chemical properties of the system.

A fractal micro-electromechanical system and its pull-in stability

2021 ◽  
pp. 146134842098404
Author(s):  
Dan Tian ◽  
Chun-Hui He
Keyword(s):  
Fractal Model ◽  
Electromechanical System ◽  
Normal Operation ◽  
Fractal Derivative ◽  
Operation Period ◽  
Micro Electromechanical System

Pull-in instability occurs in a micro-electromechanical system, and it greatly hinders its normal operation. A fractal modification is suggested to make the system stable in all operation period. A fractal model is established using a fractal derivative, and the results show that by suitable fabrication of the micro-electromechanical system device, the pull-in instability can be converted into a novel state of pull-in stability.

scholarly journals Modeling ramp-hold indentation measurements based on Kelvin–Voigt fractional derivative model

2018 ◽  
Vol 29 (3) ◽  
pp. 035701 ◽  
Author(s):  
Hongmei Zhang ◽  
Qing zhe Zhang ◽  
Litao Ruan ◽  
Junbo Duan ◽  
Mingxi Wan ◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Fractional Derivative Model

Can a Time Fractional-Derivative Model Capture Scale-Dependent Dispersion in Saturated Soils?

Ground Water ◽  
2017 ◽  
Vol 55 (6) ◽  
pp. 857-870 ◽  
Author(s):  
Rhiannon M. Garrard ◽  
Yong Zhang ◽  
Song Wei ◽  
HongGuang Sun ◽  
Jiazhong Qian
Keyword(s):  
Fractional Derivative ◽  
Saturated Soils ◽  
Fractional Derivative Model ◽  
Time Fractional Derivative

Kelvin-Voigt versus fractional derivative model as constitutive relations for viscoelastic materials

AIAA Journal ◽  
1995 ◽  
Vol 33 (3) ◽  
pp. 547-550 ◽  
Author(s):  
Lloyd B. Eldred ◽  
William P. Baker ◽  
Anthony N. Palazotto
Keyword(s):  
Fractional Derivative ◽  
Constitutive Relations ◽  
Viscoelastic Materials ◽  
Fractional Derivative Model
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