An efficient meshless computational technique to simulate nonlinear anomalous reaction–diffusion process in two-dimensional space

2019 ◽  
Vol 96 (2) ◽  
pp. 1191-1211 ◽  
Author(s):  
Hadi Roohani Ghehsareh ◽  
Ali Zaghian ◽  
Sayyed Mahmood Zabetzadeh
Keyword(s):  
Diffusion Process ◽  
Dimensional Space ◽  
Reaction Diffusion ◽  
Computational Technique ◽  
Two Dimensional ◽  
Anomalous Reaction

The boundary knot method for the solution of two-dimensional advection reaction-diffusion and Brusselator equations

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mehdi Dehghan ◽  
Vahid Mohammadi
Keyword(s):  
Mathematical Models ◽  
Dimensional Space ◽  
Reaction Diffusion ◽  
Implicit Scheme ◽  
Coupled Systems ◽  
Reaction Diffusion Equations ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Time Step ◽  
Content Type

Purpose This study aims to apply a numerical meshless method, namely, the boundary knot method (BKM) combined with the meshless analog equation method (MAEM) in space and use a semi-implicit scheme in time for finding a new numerical solution of the advection–reaction–diffusion and reaction–diffusion systems in two-dimensional spaces, which arise in biology. Design/methodology/approach First, the BKM is applied to approximate the spatial variables of the studied mathematical models. Then, this study derives fully discrete scheme of the studied models using a semi-implicit scheme based on Crank–Nicolson idea, which gives a linear system of algebraic equations with a non-square matrix per time step that is solved by the singular value decomposition. The proposed approach approximates the solution of a given partial differential equation using particular and homogeneous solutions and without considering the fundamental solutions of the proposed equations. Findings This study reports some numerical simulations for showing the ability of the presented technique in solving the studied mathematical models arising in biology. The obtained results by the developed numerical scheme are in good agreement with the results reported in the literature. Besides, a simulation of the proposed model is done on buttery shape domain in two-dimensional space. Originality/value This study develops the BKM combined with MAEM for solving the coupled systems of (advection) reaction–diffusion equations in two-dimensional spaces. Besides, it does not need the fundamental solution of the mathematical models studied here, which omits any difficulties.

TRANSIENT DYNAMICS AND SCALING PHENOMENA IN URBAN GROWTH

Fractals ◽  
1999 ◽  
Vol 07 (01) ◽  
pp. 1-8 ◽  
Author(s):  
SUSANNA C. MANRUBIA ◽  
DAMIÁN H. ZANETTE ◽  
RICARD V. SOLÉ
Keyword(s):  
Diffusion Process ◽  
Urban Growth ◽  
Reaction Diffusion ◽  
Real Data ◽  
Transient Dynamics ◽  
Two Dimensional ◽  
Urban Centers ◽  
Cellular Automata Model ◽  
The World ◽  
Empty Area

Urban centers present all over the world striking similarities which translate into universal laws describing their growth and morphology. In this paper, we study a simple two-dimensional cellular automata model containing what we identify as essential ingredients in the demographic change. The slow addition of population to an initially empty area (mimicking migration) added with a reaction diffusion process (representing reorganization of the population) allow us to recover many real data and provide us with a better understanding of the main processes forming and shaping the modern metropolis.

scholarly journals Curved fronts of bistable reaction–diffusion equations with nonlinear convection

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hui-Ling Niu ◽  
Jiayin Liu
Keyword(s):  
Dimensional Space ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Asymptotically Stable ◽  
Two Dimensional ◽  
Nonlinear Convection ◽  
Globally Asymptotically Stable

Abstract This paper is concerned with traveling curved fronts of bistable reaction–diffusion equations with nonlinear convection in a two-dimensional space. By constructing super- and subsolutions, we establish the existence of traveling curved fronts. Furthermore, we show that the traveling curved front is globally asymptotically stable.

On the Classification of Fractal and Non-Fractal Objects in Two-Dimensional Space

2020 ◽  
Vol 14 (6) ◽  
pp. 1232-1239
Author(s):  
P. M. Pustovoit ◽  
E. G. Yashina ◽  
K. A. Pshenichnyi ◽  
S. V. Grigoriev
Keyword(s):  
Dimensional Space ◽  
Two Dimensional

Political Cleavages and Political Parties

2018 ◽  
Author(s):  
Russell J. Dalton
Keyword(s):  
Political Parties ◽  
Dimensional Space ◽  
New Left ◽  
Party Systems ◽  
European Parliament ◽  
Two Dimensional ◽  
Far Right ◽  
Policy Positions ◽  
Cultural Policies ◽  
Policy Choices

This chapter uses the cleavage positions of Candidates to the European Parliament (CEPs) to as representative of their parties’ political positions. Three surveys of CEPs track the evolution of party supply in European party systems. In 1979 parties were primarily aligned along a Left–Right economic cleavage. Gradually new left and Green parties began to compete in elections and crystallized and represented liberal cultural policies. In recent decades new far-right parties arose to represent culturally conservative positions. The cross-cutting cultural cleavage has also prompted many of the established parties to alter their policy positions. In most multiparty systems, political parties now compete in a fully populated two-dimensional space. This increases the supply of policy choices for the voters. The analyses are based on the Candidates to the European Parliament Studies in 1979, 1994, and 2009.

scholarly journals Three-Dimensional Thematic Map Imaging of the Yacht Port on the Example of the Polish National Sailing Centre Marina in Gdańsk

2021 ◽  
Vol 11 (15) ◽  
pp. 7016
Author(s):  
Pawel S. Dabrowski ◽  
Cezary Specht ◽  
Mariusz Specht ◽  
Artur Makar
Keyword(s):  
Spatial Data ◽  
Convex Surface ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Future Research ◽  
Two Dimensional ◽  
Thematic Maps ◽  
Research Directions ◽  
Future Research Directions ◽  
The Many

The theory of cartographic projections is a tool which can present the convex surface of the Earth on the plane. Of the many types of maps, thematic maps perform an important function due to the wide possibilities of adapting their content to current needs. The limitation of classic maps is their two-dimensional nature. In the era of rapidly growing methods of mass acquisition of spatial data, the use of flat images is often not enough to reveal the level of complexity of certain objects. In this case, it is necessary to use visualization in three-dimensional space. The motivation to conduct the study was the use of cartographic projections methods, spatial transformations, and the possibilities offered by thematic maps to create thematic three-dimensional map imaging (T3DMI). The authors presented a practical verification of the adopted methodology to create a T3DMI visualization of the marina of the National Sailing Centre of the Gdańsk University of Physical Education and Sport (Poland). The profiled characteristics of the object were used to emphasize the key elements of its function. The results confirmed the increase in the interpretative capabilities of the T3DMI method, relative to classic two-dimensional maps. Additionally, the study suggested future research directions of the presented solution.

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