scholarly journals Existence and Permanence in a Diffusive KiSS Model with Robust Numerical Simulations

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Kolade M. Owolabi ◽  
Kailash C. Patidar
Keyword(s):  
Patch Size ◽  
Reaction Diffusion ◽  
Mathematical Community ◽  
Diffusion Problem ◽  
One Dimensional ◽  
Critical Patch Size ◽  
The One ◽  
Exponential Time Differencing Method ◽  
Theoretical Results

We have given an extension to the study of Kierstead, Slobodkin, and Skellam (KiSS) model. We present the theoretical results based on the survival and permanence of the species. To guarantee the long-term existence and permanence, the patch size denoted asLmust be greater than the critical patch sizeLc. It was also observed that the reaction-diffusion problem can be split into two parts: the linear and nonlinear terms. Hence, the use of two classical methods in space and time is permitted. We use spectral method in the area of mathematical community to remove the stiffness associated with the linear or diffusive terms. The resulting system is advanced with a modified exponential time-differencing method whose formulation was based on the fourth-order Runge-Kutta scheme. With high-order method, this extends the one-dimensional work and presents experiments for two-dimensional problem. The complexity of the dynamical model is discussed theoretically and graphically simulated to demonstrate and compare the behavior of the time-dependent density function.

Stabilization of Dominant Structures in an Ionic Reaction-Diffusion System

1998 ◽  
Vol 63 (6) ◽  
pp. 761-769 ◽  
Author(s):  
Roland Krämer ◽  
Arno F. Münster
Keyword(s):  
Reaction Diffusion ◽  
Dominant Mode ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Local Perturbation ◽  
Dimensional System ◽  
One Dimensional ◽  
Brusselator Model ◽  
The One ◽  
Dominant Structure

We describe a method of stabilizing the dominant structure in a chaotic reaction-diffusion system, where the underlying nonlinear dynamics needs not to be known. The dominant mode is identified by the Karhunen-Loeve decomposition, also known as orthogonal decomposition. Using a ionic version of the Brusselator model in a spatially one-dimensional system, our control strategy is based on perturbations derived from the amplitude function of the dominant spatial mode. The perturbation is used in two different ways: A global perturbation is realized by forcing an electric current through the one-dimensional system, whereas the local perturbation is performed by modulating concentrations of the autocatalyst at the boundaries. Only the global method enhances the contribution of the dominant mode to the total fluctuation energy. On the other hand, the local method leads to simple bulk oscillation of the entire system.

scholarly journals The trend of the oxidants in boreal forest over 2007–2018: comprehensive modelling study with long-term measurements at SMEAR II, Finland

2020 ◽  
Author(s):  
Dean Chen ◽  
Putian Zhou ◽  
Tuomo Nieminen ◽  
Pontus Roldin ◽  
Ximeng Qi ◽  
...  
Keyword(s):  
Air Pollutants ◽  
Size Range ◽  
Chemical Components ◽  
Detailed Model ◽  
One Dimensional ◽  
The Past ◽  
Main Driver ◽  
The One ◽  
Long Term Trend

Abstract. Major atmospheric oxidants (OH, O3 and NO3) dominate the atmospheric oxidation capacity, while H2SO4 is considered as a main driver for new particle formation events. Although numerous studies have investigated the long-term trend of ozone in Europe, the trend of OH, NO3 and H2SO4 at specific sites are to a large extent unknown. In this study, we investigated how the trends in major atmospheric oxidants (OH, O3 and NO3) and H2SO4 changed in southern Finland during the past 12 years and discuss how these trends relate to decreasing emissions of regulated air pollutants in Europe. The one-dimensional model SOSAA has been applied in several studies at the SMEAR II station, and has been validated by measurements in several projects. Here, we ran the SOSAA model for the years 2007–2018 to simulate the atmospheric chemical components, especially the atmospheric oxidants and H2SO4 at SMEAR II. The simulations were evaluated with observations at SMEAR II for several shorter and longer campaigns. Our results show that OH increased by +1.56 (−0.8; +3.17) % yr−1 during daytime and NO3 decreased by −3.92 (−6.49; −1.79) % yr−1 during nighttime, indicating different trends of the oxidants during day and night. Sulphuric acid decreased during daytime by −5.12 (−11.39; −0.52) % yr−1, which correlated with the observed decreasing concentration of newly formed particles in the size range 3–25 nm by 1.4 % yr−1 at SMEAR II during the years 1997–2012 (Nieminen et al., 2014). Additionally we compared our simulated OH, NO3 and H2SO4 concentrations with proxies, which are commonly applied in case limited amount of parameters are measured and no detailed model simulations are available.

Modeling of Delayed Hydride Crack Initiation

1991 ◽  
Vol 113 (4) ◽  
pp. 443-448 ◽  
Author(s):  
A. F. Shalabi ◽  
D. A. Meneley
Keyword(s):  
Crack Initiation ◽  
Plastic Zone ◽  
Stress Level ◽  
Diffusion Problem ◽  
Transient Condition ◽  
Temperature Dependent ◽  
Mathematical Solution ◽  
One Dimensional ◽  
Percent Niobium ◽  
The One

This paper presents a solution to the one-dimensional time (transient condition) and temperature dependent diffusion problem adjacent to a crack-tip/flaw within the plastic zone region. The solution is used in addressing the problem of delayed hydride crack initiation in zirconium-2.5 wt. percent niobium. The mathematical solution predicts the critical hydride length at a given stress level and temperature for crack initiation.

A Numerical Model for the Radial Flow Through Porous and Deformable Shells

2004 ◽  
Vol 4 (1) ◽  
pp. 34-47 ◽  
Author(s):  
Francisco J. Gaspar ◽  
Francisco J. Lisbona ◽  
Petr N. Vabishchevich
Keyword(s):  
Finite Difference ◽  
Finite Difference Methods ◽  
Energy Estimates ◽  
One Dimensional ◽  
Consolidation Model ◽  
Finite Difference Discretization ◽  
Flow Through ◽  
The One ◽  
Theoretical Results ◽  
Difference Discretization

AbstractEnergy estimates and convergence analysis of finite difference methods for Biot's consolidation model are presented for several types of radial ow. The model is written by a system of partial differential equations which depend on an integer parameter (n = 0; 1; 2) corresponding to the one-dimensional ow through a deformable slab and the radial ow through an elastic cylindrical or spherical shell respectively. The finite difference discretization is performed on staggered grids using separated points for the approximation of pressure and displacements. Numerical results are given to illustrate the obtained theoretical results.

scholarly journals Steady states of the reaction-diffusion equations. Part II: Uniqueness of solutions and some special cases

1983 ◽  
Vol 24 (4) ◽  
pp. 392-416 ◽  
Author(s):  
J. G. Burnell ◽  
A. A. Lacey ◽  
G. C. Wake
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Uniqueness Of Solutions ◽  
One Dimensional ◽  
Nonlinear Elliptic ◽  
Special Cases ◽  
Exothermic Chemical Reaction ◽  
Dimensional Shape ◽  
The One ◽  
Special Case

AbstractIn an earlier paper (Part I) the existence and some related properties of the solution to a coupled pair of nonlinear elliptic partial differential equations was considered. These equations arise when material is undergoing an exothermic chemical reaction which is sustained by the diffusion of a reactant. In this paper we consider the range of parameters for which the uniqueness of solution is assured and we also investigate the converse question of multiple solutions. The special case of the one dimensional shape of the infinite slab is investigated in full as this case admits to solution by integration.

VERTICAL PHYTOPLANKTON DISTRIBUTIONS: PATTERNS AND ANALYTICAL SOLUTIONS

1994 ◽  
Vol 02 (02) ◽  
pp. 137-163
Author(s):  
U. TIMM
Keyword(s):  
Fluid Dynamics ◽  
Vertical Distribution ◽  
Analytical Solutions ◽  
Patch Size ◽  
Reaction Diffusion ◽  
Distribution Patterns ◽  
Marine Plankton ◽  
Shear Dispersion ◽  
Critical Patch Size ◽  
Basic Equations

I apply the basic equations of fluid dynamics to reaction—diffusion—advection models describing vertical distribution patterns of marine plankton. The biological dynamics in these models are growth, death/birth, grazing and interaction. Further, oceanographic phenomena such as shading and shear dispersion are considered. Models for critical patch size and for vertical distribution profiles and analytical solutions are developed.

Theoretical and experimental investigations of the reflexion of normal shock waves with vibrational relaxation

1967 ◽  
Vol 30 (1) ◽  
pp. 51-64 ◽  
Author(s):  
N. H. Johannesen ◽  
G. A. Bird ◽  
H. K. Zienkiewicz
Keyword(s):  
Shock Wave ◽  
Vibrational Relaxation ◽  
Experimental Investigations ◽  
Rayleigh Line ◽  
Dimensional Problem ◽  
Density Measurements ◽  
Wave Characteristic ◽  
One Dimensional ◽  
The One ◽  
Theoretical Results

The one-dimensional problem of shock-wave reflexion with relaxation is treated numerically by combining the shock-wave, characteristic, and Rayleigh-line equations. The theoretical results are compared with pressure and density measurements in CO2, and the agreement is found to be excellent.

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