scholarly journals Analytic approximations to non-linear third order jerk equations via modified global error minimization method

2021 ◽  
Vol 33 (1) ◽  
pp. 101219
Author(s):  
Gamal M. Ismail ◽  
Hanaa Abu-Zinadah
Keyword(s):  
Global Error ◽  
Error Minimization ◽  
Third Order ◽  
Minimization Method ◽  
Analytic Approximations ◽  
Non Linear

Global Error Minimization method for nonlinear oscillators with highly nonlinearity

2013 ◽  
Vol 7 (4) ◽  
pp. 1557-1561
Author(s):  
Muhammad Aslam Noor ◽  
Waseem Asghar Khan
Keyword(s):  
Nonlinear Oscillators ◽  
Global Error ◽  
Error Minimization ◽  
Minimization Method

scholarly journals Approximate Periodic Solution for the Nonlinear Helmholtz-Duffing Oscillator via Analytical Approaches

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
A. Mirzabeigy ◽  
M. K. Yazdi ◽  
M. H. Nasehi
Keyword(s):  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Duffing Oscillator ◽  
Analytical Techniques ◽  
Second Order ◽  
Global Error ◽  
Error Minimization ◽  
Minimization Method ◽  
Engineering Problems ◽  
Analytical Approaches

The conservative Helmholtz-Duffing oscillator is analyzed by means of three analytical techniques. The max-min, second-order of the Hamiltonian, and the global error minimization approaches are applied to achieve natural frequencies. The obtained results are compared with the homotopy perturbation method and numerical solutions. The results show that second-order of the global error minimization method is very accurate, so it can be widely applicable in engineering problems.

Third-order Non-linear Optical Properties of Tellurium-based Composite Films

2011 ◽  
Vol 26 (3) ◽  
pp. 295-299 ◽  
Author(s):  
Ping GAN ◽  
Min GU ◽  
Qiang LI ◽  
Xiao-Dong XIAN
Keyword(s):  
Optical Properties ◽  
Composite Films ◽  
Third Order ◽  
Non Linear ◽  
Linear Optical Properties ◽  
Linear Optical

scholarly journals Perturbative linearization of super-Yang-Mills theories in general gauges

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Hannes Malcha ◽  
Hermann Nicolai
Keyword(s):  
Large Class ◽  
Fourth Order ◽  
Landau Gauge ◽  
Third Order ◽  
Yang Mills ◽  
Free Theory ◽  
Non Linear ◽  
Functional Measure ◽  
Non Local ◽  
Jacobi Determinant

Abstract Supersymmetric Yang-Mills theories can be characterized by a non-local and non-linear transformation of the bosonic fields (Nicolai map) mapping the interacting functional measure to that of a free theory, such that the Jacobi determinant of the transformation equals the product of the fermionic determinants obtained by integrating out the gauginos and ghosts at least on the gauge hypersurface. While this transformation has been known so far only for the Landau gauge and to third order in the Yang-Mills coupling, we here extend the construction to a large class of (possibly non-linear and non-local) gauges, and exhibit the conditions for all statements to remain valid off the gauge hypersurface. Finally, we present explicit results to second order in the axial gauge and to fourth order in the Landau gauge.

Mitigating the Effects of Non-Linear Distortion Using Polarizers in Microwave Photonic Link

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Sarika Singh ◽  
Sandeep K. Arya ◽  
Shelly Singla
Keyword(s):  
Dynamic Range ◽  
Extinction Ratio ◽  
Polarization Angle ◽  
Third Order ◽  
Microwave Photonic ◽  
Linear Behavior ◽  
Spurious Free Dynamic Range ◽  
Non Linear ◽  
Intermodulation Distortions ◽  
Insertion Losses

AbstractA scheme to suppress nonlinear intermodulation distortion in microwave photonic (MWP) link is proposed by using polarizers to compensate inherent non-linear behavior of dual-electrode Mach-Zehnder modulator (DE-MZM). Insertion losses and extinction ratio have also been considered. Simulation results depict that spurious free dynamic range (SFDR) of proposed link reaches to 130.743 dB.Hz2/3. A suppression of 41 dB in third order intermodulation distortions and an improvement of 15.3 dB is reported when compared with the conventional link. In addition, an electrical spectrum at different polarization angles is extracted and 79^\circ is found to be optimum value of polarization angle.

scholarly journals A Unified Mathematical Formalism for First to Third Order Dielectric Response of Matter: Application to Surface-Specific Two-Colour Vibrational Optical Spectroscopy

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 153 ◽  
Author(s):  
Christophe Humbert ◽  
Thomas Noblet
Keyword(s):  
Dielectric Response ◽  
Structure And Properties ◽  
Linear Optics ◽  
Third Order ◽  
Mathematical Functions ◽  
Sum Frequency ◽  
Non Linear Optics ◽  
Non Linear ◽  
Light Excitation

To take advantage of the singular properties of matter, as well as to characterize it, we need to interact with it. The role of optical spectroscopies is to enable us to demonstrate the existence of physical objects by observing their response to light excitation. The ability of spectroscopy to reveal the structure and properties of matter then relies on mathematical functions called optical (or dielectric) response functions. Technically, these are tensor Green’s functions, and not scalar functions. The complexity of this tensor formalism sometimes leads to confusion within some articles and books. Here, we do clarify this formalism by introducing the physical foundations of linear and non-linear spectroscopies as simple and rigorous as possible. We dwell on both the mathematical and experimental aspects, examining extinction, infrared, Raman and sum-frequency generation spectroscopies. In this review, we thus give a personal presentation with the aim of offering the reader a coherent vision of linear and non-linear optics, and to remove the ambiguities that we have encountered in reference books and articles.

Fast third-order non-linear optical response of novel conjugated silicon-ethynylene polymers and metallocomplexes

2002 ◽  
Author(s):  
O.L. Antipov ◽  
B.A. Bushuk ◽  
G.A. Domrachev ◽  
W.E. Douglas ◽  
L.G. Klapshina ◽  
...  
Keyword(s):  
Optical Response ◽  
Third Order ◽  
Non Linear ◽  
Linear Optical

scholarly journals Linear and Third Order Non-Linear Optical Properties of Urea Salicylic Acid Crystal

2016 ◽  
Vol 28 (4) ◽  
pp. 797-800
Author(s):  
C. Andal ◽  
P. Murugakoothan
Keyword(s):  
Optical Properties ◽  
Salicylic Acid ◽  
Third Order ◽  
Acid Crystal ◽  
Non Linear ◽  
Linear Optical Properties ◽  
Linear Optical

scholarly journals On non-homogeneous canonical third-order linear differential equations

1994 ◽  
Vol 57 (2) ◽  
pp. 138-148 ◽  
Author(s):  
N. Parhi
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Sufficient Conditions ◽  
Linear Differential Equations ◽  
Third Order ◽  
Order Linear ◽  
Non Linear ◽  
Linear Differential ◽  
Non Linear Equations

AbstractIn this paper sufficient conditions have been obtained for non-oscillation of non-homogeneous canonical linear differential equations of third order. Some of these results have been extended to non-linear equations.

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