Solution to the Conformable Fractional System with Constant Variation Method

2019 ◽  
pp. 706-711
Author(s):  
Liangsong Li ◽  
Yongfang Qi ◽  
Chongci Tang ◽  
Kecheng Xiao
Keyword(s):  
Variation Method ◽  
Fractional System

Exit-surface wave reconstruction using a focal series

1992 ◽  
Vol 50 (2) ◽  
pp. 988-989
Author(s):  
W.J. de Ruijter ◽  
M.R. McCartney ◽  
David J. Smith ◽  
J.K. Weiss
Keyword(s):  
Surface Wave ◽  
Spherical Aberration ◽  
Data Extraction ◽  
High Sensitivity ◽  
Geometric Distortion ◽  
Variation Method ◽  
Objective Lens ◽  
Immediate Reconstruction ◽  
Exit Surface ◽  
Electron Microscopes

Further advances in resolution enhancement of transmission electron microscopes can be expected from digital processing of image data recorded with slow-scan CCD cameras. Image recording with these new cameras is essential because of their high sensitivity, extreme linearity and negligible geometric distortion. Furthermore, digital image acquisition allows for on-line processing which yields virtually immediate reconstruction results. At present, the most promising techniques for exit-surface wave reconstruction are electron holography and the recently proposed focal variation method. The latter method is based on image processing applied to a series of images recorded at equally spaced defocus.Exit-surface wave reconstruction using the focal variation method as proposed by Van Dyck and Op de Beeck proceeds in two stages. First, the complex image wave is retrieved by data extraction from a parabola situated in three-dimensional Fourier space. Then the objective lens spherical aberration, astigmatism and defocus are corrected by simply dividing the image wave by the wave aberration function calculated with the appropriate objective lens aberration coefficients which yields the exit-surface wave.

TRANSFER TENSOR VARIATION METHOD APPLIED TO RANDOM ISING SYSTEMS

1988 ◽  
Vol 49 (C8) ◽  
pp. C8-1251-C8-1252
Author(s):  
W. Brauneck ◽  
O. Jagodzinski ◽  
D. Wagner
Keyword(s):  
Variation Method ◽  
Ising Systems

Thermodynamics of dilute binary solid solutions using the cluster variation method

2012 ◽  
Vol 103 (10) ◽  
pp. 1188-1200 ◽  
Author(s):  
Bandikatla N. Sarma ◽  
Shreyansh N. Shah ◽  
Manoj Kumar ◽  
Shrikant Lele
Keyword(s):  
Solid Solutions ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Cluster Variation

The description of Al, Si ordering in aluminosilicates using the cluster variation method

1999 ◽  
Vol 84 (3) ◽  
pp. 311-324 ◽  
Author(s):  
Victor L. Vinograd ◽  
Andrew Putnis
Keyword(s):  
Cluster Variation Method ◽  
Variation Method ◽  
Cluster Variation

scholarly journals Differential Transform Method as an Effective Tool for Investigating Fractional Dynamical Systems

2021 ◽  
Vol 11 (15) ◽  
pp. 6955
Author(s):  
Andrzej Rysak ◽  
Magdalena Gregorczyk
Keyword(s):  
Optimal Parameter ◽  
Differential Transform Method ◽  
Bifurcation Diagrams ◽  
Transform Method ◽  
Rossler System ◽  
Differential Transform ◽  
Rössler System ◽  
Fractional System ◽  
Parameter Values

This study investigates the use of the differential transform method (DTM) for integrating the Rössler system of the fractional order. Preliminary studies of the integer-order Rössler system, with reference to other well-established integration methods, made it possible to assess the quality of the method and to determine optimal parameter values that should be used when integrating a system with different dynamic characteristics. Bifurcation diagrams obtained for the Rössler fractional system show that, compared to the RK4 scheme-based integration, the DTM results are more resistant to changes in the fractionality of the system.

Neutron diffraction, inelastic scattering and the structure of amphiphiles and macromolecules in solution

1975 ◽  
Vol 345 (1640) ◽  
pp. 119-144 ◽  
Keyword(s):  
Neutron Diffraction ◽  
Inelastic Scattering ◽  
Cross Sections ◽  
Biological Molecules ◽  
Variation Method ◽  
Contrast Variation ◽  
Structure And Dynamics ◽  
Spin Resonance ◽  
Scattering Lengths ◽  
Scattering Cross Sections

The methods by which neutron diffraction and inelastic scattering may be used to study the structure and dynamics of solutions are reviewed, with particular reference to solutions of amphiphile and biological molecules in water. Neutron methods have particular power because the scattering lengths for protons and deuterons are of opposite sign, and hence there exists the possibility of obtaining variable contrast between the scattering of the aqueous medium and the molecules in it. In addition, the contrast variation method is also applicable to inelastic scattering studies whereby the dynamics of one component of the solution can be preferentially studied due to large and variable differences in the scattering cross sections. Both applications of contrast variation are illustrated with examples of amphiphile-water lamellar mesophases, diffraction from collagen, viruses, and polymer solutions. Inelastic scattering observations and the dynamics of water between the lamellar sheets allow microscopic measurements of the water diffusion along and perpendicular to the layers. The information obtained is complementary to that from nuclear magnetic resonance and electron spin resonance studies of diffusion.

scholarly journals A Fractional Approach to a Computational Eco-Epidemiological Model with Holling Type-II Functional Response

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1159
Author(s):  
B. Günay ◽  
Praveen Agarwal ◽  
Juan L. G. Guirao ◽  
Shaher Momani
Keyword(s):  
Numerical Method ◽  
Decision Makers ◽  
Derivative Operator ◽  
Research Fields ◽  
Fractional System ◽  
Chaotic Nature ◽  
And Control ◽  
The Impact ◽  
Distinguishing Features ◽  
Type Ii Functional Response

Eco-epidemiological can be considered as a significant combination of two research fields of computational biology and epidemiology. These problems mainly take ecological systems into account of the impact of epidemiological factors. In this paper, we examine the chaotic nature of a computational system related to the spread of disease into a specific environment involving a novel differential operator called the Atangana–Baleanu fractional derivative. To approximate the solutions of this fractional system, an efficient numerical method is adopted. The numerical method is an implicit approximate method that can provide very suitable numerical approximations for fractional problems due to symmetry. Symmetry is one of the distinguishing features of this technique compared to other methods in the literature. Through considering different choices of parameters in the model, several meaningful numerical simulations are presented. It is clear that hiring a new derivative operator greatly increases the flexibility of the model in describing the different scenarios in the model. The results of this paper can be very useful help for decision-makers to describe the situation related to the problem, in a more efficient way, and control the epidemic.

scholarly journals A Comparative Analysis of Fractional-Order Gas Dynamics Equations via Analytical Techniques

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1735
Author(s):  
Shuang-Shuang Zhou ◽  
Nehad Ali Shah ◽  
Ioannis Dassios ◽  
S. Saleem ◽  
Kamsing Nonlaopon
Keyword(s):  
Homotopy Perturbation Method ◽  
Graphical Representation ◽  
Analytical Techniques ◽  
Variational Iteration Method ◽  
Computational Techniques ◽  
System Of Nonlinear Equations ◽  
Gas Dynamics Equations ◽  
Homotopy Perturbation ◽  
Fractional System ◽  
Modified Forms

This article introduces two well-known computational techniques for solving the time-fractional system of nonlinear equations of unsteady flow of a polytropic gas. The methods suggested are the modified forms of the variational iteration method and the homotopy perturbation method by the Elzaki transformation. Furthermore, an illustrative scheme is introduced to verify the accuracy of the available techniques. A graphical representation of the exact and derived results is presented to show the reliability of the suggested approaches. It is also shown that the findings of the current methodology are in close harmony with the exact solutions. The comparative solution analysis via graphs also represents the higher reliability and accuracy of the current techniques.

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