scholarly journals Chebyshev wavelet collocation method for Ginzburg-Landau equation

2019 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 57-65
Author(s):  
Aydin Secer ◽  
Yasemin Bakir
Keyword(s):  
Collocation Method ◽  
Landau Equation ◽  
Linear Equations ◽  
Operational Matrix ◽  
Ginzburg Landau ◽  
Chebyshev Wavelets ◽  
Ginzburg Landau Equation ◽  
Wavelet Collocation Method ◽  
Non Linear ◽  
Chebyshev Wavelet

The main aim of this paper is to investigate the efficient Chebyshev wavelet collocation method for Ginzburg-Landau equation. The basic idea of this method is to have the approximation of Chebyshev wavelet series of a non-linear PDE. We demonstrate how to use the method for the numerical solution of the Ginzburg-Landau equation with initial and boundary conditions. For this purpose, we have obtained operational matrix for Chebyshev wavelets. By applying this technique in Ginzburg-Landau equation, the PDE is converted into an algebraic system of non-linear equations and this system has been solved using MAPLE computer algebra system. We demonstrate the validity and applicability of this technique which has been clarified by using an example. Exact solution is compared with an approximate solution. Moreover, Chebyshev wavelet collocation method is found to be acceptable, efficient, accurate and computational for the non-linear or PDE.

The Study on Surface Critical Magnetic Field of a Layered Magnetic Superconductors

2014 ◽  
Vol 979 ◽  
pp. 224-227 ◽  
Author(s):  
Sumitta Meakniti ◽  
Arpapong Changjan ◽  
Pongkaew Udomsamuthirun
Keyword(s):  
Magnetic Field ◽  
Magnetic Property ◽  
Variational Method ◽  
Critical Field ◽  
Landau Equation ◽  
Critical Magnetic Field ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Non Linear

In this research, we studied the surface critical magnetic field () of a layered magnetic superconductors by Ginzburg-Landau approach. After the 1st Ginzburg-Landau equation was calculated, a surface critical field was solved by variational method analytically. Our formula obtained was depended on the magnetic property of superconductor. We found that Hc3 of antiferromagnetism and paramagnetism superconductors were shown the same behaviour as non-magnetic superconductors. For diamagnetism and ferromagnetism superconductors, the higher and the lower values of critical magnetic field were found, respectively. However, the Hc3 was strongly depended on the non-linear of magnetic field intend of all kind magnetism.

scholarly journals A Chebyshev Wavelet Collocation Method for Some Types of Differential Problems

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 536
Author(s):  
Sharanjeet Dhawan ◽  
José A. Tenreir Machado ◽  
Dariusz W. Brzeziński ◽  
Mohamed S. Osman
Keyword(s):  
Truncation Error ◽  
Operational Matrix ◽  
Chebyshev Wavelets ◽  
Fundamental Properties ◽  
The Past ◽  
Collocation Points ◽  
Wavelet Collocation Method ◽  
Chebyshev Wavelet ◽  
Expansion Coefficients ◽  
Upper Estimate

In the past decade, various types of wavelet-based algorithms were proposed, leading to a key tool in the solution of a number of numerical problems. This work adopts the Chebyshev wavelets for the numerical solution of several models. A Chebyshev operational matrix is developed, for selected collocation points, using the fundamental properties. Moreover, the convergence of the expansion coefficients and an upper estimate for the truncation error are included. The obtained results for several case studies illustrate the accuracy and reliability of the proposed approach.

scholarly journals Bacterial communication and relevance of quantum theory

2017 ◽  
Author(s):  
Sarangam Majumdar ◽  
Sisir Roy
Keyword(s):  
Kinematic Viscosity ◽  
Landau Equation ◽  
Bacterial Species ◽  
Thermal Fluctuations ◽  
Communication Process ◽  
Dinger Equation ◽  
Ginzburg Landau ◽  
Bacterial Communication ◽  
Ginzburg Landau Equation ◽  
Non Linear

The recent findings confirm that bacteria communicate each other through chemical and electrical signals. Bacteria use chemical signaling molecules which are called as quorum sensing molecules(QSMs) or autoinducers. Moreover, the ion channels in bacteria conduct a long-range electrical signaling within biofilm communities through propagated waves of potassium ions and biofilms attracts other bacterial species too. Both communication process are used by bacteria to make their own survival strategies. In this article, we model this bacterial communication mechanism by complex Ginzburg- Landau equation and discuss the formation of patterns depending on kinematic viscosity associated with internal noise. Again, the potassium wave propagation is described by the non-linear Schrödinger equation in a dissipative environment. By adding perturbation to non-linear Schrödinger equation one arrives at Complex Ginzburg-Landau equation. In this paper we emphasize that at the cellular level(bacteria) we use Complex Ginzburg - Landau equation as a perturbed Nonlinear Schrödinger equation to understand the bacterial communication as well as pattern formation in Biofilms for certain range of kinematic viscosity which can be tested in laboratory experiment. Here, the perturbation is due to the existence of non thermal fluctuations associated to the finite size of the bacteria. It sheds new light on the relevance of quantum formalism in understanding the cell to cell communication.

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