RETARDATION EFFECTS IN A FINITE DIFFUSION-REACTION SYSTEM

2008 ◽  
Vol 22 (12) ◽  
pp. 1947-1959 ◽  
Author(s):  
KNUD ZABROCKI ◽  
STEFFEN TRIMPER ◽  
MICHAEL SCHULZ
Keyword(s):  
Reaction System ◽  
Reaction Diffusion ◽  
Diffusion Reaction ◽  
One Dimension ◽  
Anisotropic Behavior ◽  
Production Term ◽  
Spatial Point ◽  
Delay Effects ◽  
Spatiotemporal Delay ◽  
Reaction Processes

The reaction-diffusion process is generalized by including spatiotemporal delay effects. As a first example, we study the influence of a constant production term which is switched off after a finite time. In a second case, all diffusion-reaction processes within a distance R(t) = κtα around a certain spatial point are assumed to contribute to the instantaneous dynamics of the system. There occurs a competition between reaction-diffusion and the accumulation process which leads to a non-trivial stationary state. The evolving concentration profiles are calculated analytically for both a ballistic behavior with α = 1 and a diffusion-like transport with α = 1/2. Because the spatiotemporal delay breaks the reflection symmetry, the profiles reveal an anisotropic behavior. The exact solution in one dimension is supported by numerical simulations.

scholarly journals A Reaction–Diffusion–Reaction System for Forming Periodic Precipitation Bands of Cu-Fe-Based Prussian Blue Analogues

2021 ◽  
Vol 11 (11) ◽  
pp. 5000
Author(s):  
Hisashi Hayashi ◽  
Tomoko Suzuki
Keyword(s):  
Prussian Blue ◽  
Reaction System ◽  
Reaction Diffusion ◽  
Diffusion Reaction ◽  
Ion Diffusion ◽  
Periodic Precipitation ◽  
Precipitation Patterns ◽  
Prussian Blue Analogues ◽  
Potential Applications ◽  
Alternating Voltage

We propose a simple and novel system to form precipitation patterns of Cu-Fe-based Prussian blue analogues (Cu-Fe PBA) in agarose gel through coupled electrochemical reactions, reactant ion diffusion influenced by electric field, and precipitation reactions. The spatiotemporal evolution, spatial distribution, and crystallite morphologies of the precipitates were investigated by visual inspection, Fe Kα intensity distribution measurements, and optical and scanning electron microscope observations. The observed precipitation patterns and their evolution depended on the applied voltage. Multicolored periodic precipitation bands were stochastically formed under cyclic alternating voltage (4 V for 1 h and then 1 V for 4 h per cycle). The distances between adjacent bands were randomly distributed (0.30 ± 0.25 mm). The sizes and shapes of the crystallites generated in the gel were position-dependent. Cubic but fairly irregular crystallites (0.1–0.8 μm) were formed in the periodic bands, whereas definitely cube-shaped crystallites (1–3 μm) appeared close to the anode. These cube-like reddish–brown crystallites were assigned to Cu-FeII PBA. In some periodic bands, plate-like blue crystallites (assigned to Cu(OH)2) were also present. Future issues for potential applications of the observed periodic banding for selective preparation of Cu-Fe PBA crystallites were discussed.

scholarly journals Highly scalable numerical simulation of coupled reaction–Diffusion systems with moving interfaces

2021 ◽  
pp. 109434202110459
Author(s):  
Mojtaba Barzegari ◽  
Liesbet Geris
Keyword(s):  
High Performance ◽  
Moving Boundary ◽  
Reaction Diffusion ◽  
Diffusion Reaction ◽  
Boundary Problems ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Wide Range ◽  
Strong Scaling ◽  
Reaction Processes

A combination of reaction–diffusion models with moving-boundary problems yields a system in which the diffusion (spreading and penetration) and reaction (transformation) evolve the system’s state and geometry over time. These systems can be used in a wide range of engineering applications. In this study, as an example of such a system, the degradation of metallic materials is investigated. A mathematical model is constructed of the diffusion-reaction processes and the movement of corrosion front of a magnesium block floating in a chemical solution. The corresponding parallelized computational model is implemented using the finite element method, and the weak and strong-scaling behaviors of the model are evaluated to analyze the performance and efficiency of the employed high-performance computing techniques.

scholarly journals A structural approach to control of transitional waves of nonlinear diffusion-reaction systems: Theory and possible applications to bio-medicine

2002 ◽  
Vol 7 (1) ◽  
pp. 27-40 ◽  
Author(s):  
Victor Kardashov ◽  
Shmuel Einav
Keyword(s):  
Nonlinear Diffusion ◽  
Structural Parameters ◽  
Deterministic Chaos ◽  
Reaction Diffusion ◽  
Diffusion Reaction ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Novel Approach ◽  
Dynamics Models ◽  
And Control

This paper has considered a novel approach to structural recognition and control of nonlinear reaction-diffusion systems (systems with density dependent diffusion). The main consistence of the approach is interactive variation of the nonlinear diffusion and sources structural parameters that allows to implement a qualitative control and recognition of transitional system conditions (transients). The method of inverse solutions construction allows formulating the new analytic conditions of compactness and periodicity of the transients that is also available for nonintegrated systems. On the other hand, using of energy conservations laws, allows transfer to nonlinear dynamics models that gives the possiblity to apply the modern deterministic chaos theory (particularly the Feigenboum's universal constants and scenario of chaotic transitions).

scholarly journals Allee dynamics: growth, extinction and range expansion

2017 ◽  
Author(s):  
I Bose ◽  
M Pal ◽  
C Karmakar
Keyword(s):  
Population Density ◽  
Range Expansion ◽  
Population Biology ◽  
Allee Effect ◽  
Additive Noise ◽  
Finite Population ◽  
Reaction Diffusion ◽  
Travelling Wave ◽  
One Dimension ◽  
Negative Growth

AbstractIn population biology, the Allee dynamics refer to negative growth rates below a critical population density. In this Letter, we study a reaction-diffusion (RD) model of population growth and dispersion in one dimension, which incorporates the Allee effect in both the growth and mortality rates. In the absence of diffusion, the bifurcation diagram displays regions of both finite population density and zero population density, i.e., extinction. The early signatures of the transition to extinction at a bifurcation point are computed in the presence of additive noise. For the full RD model, the existence of travelling wave solutions of the population density is demonstrated. The parameter regimes in which the travelling wave advances (range expansion) and retreats are identified. In the weak Allee regime, the transition from the pushed to the pulled wave is shown as a function of the mortality rate constant. The results obtained are in agreement with the recent experimental observations on budding yeast populations.

A New Mechanical Algorithm for Calculating the Amplitude Equation of the Reaction-Diffusion Systems

2011 ◽  
pp. 205-213
Author(s):  
Houye Liu ◽  
Weiming Wang
Keyword(s):  
Hopf Bifurcation ◽  
Pattern Formation ◽  
Normal Form ◽  
Reaction Diffusion ◽  
Amplitude Equation ◽  
Diffusion Reaction ◽  
Future Studies ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Form Approach

Amplitude equation may be used to study pattern formatio. In this chapter, we establish a new mechanical algorithm AE_Hopf for calculating the amplitude equation near Hopf bifurcation based on the method of normal form approach in Maple. The normal form approach needs a large number of variables and intricate calculations. As a result, deriving the amplitude equation from diffusion-reaction is a difficult task. Making use of our mechanical algorithm, we derived the amplitude equations from several biology and physics models. The results indicate that the algorithm is easy to apply and effective. This algorithm may be useful for learning the dynamics of pattern formation of reaction-diffusion systems in future studies.

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