scholarly journals Utilizing Microcavities To Suppress Third-Order Cascades in Fifth-Order Raman Spectra

2017 ◽  
Vol 8 (14) ◽  
pp. 3387-3391 ◽  
Author(s):  
Zhedong Zhang ◽  
Kochise Bennett ◽  
Vladimir Chernyak ◽  
Shaul Mukamel
Keyword(s):  
Raman Spectra ◽  
Third Order ◽  
Fifth Order

Fifth-order two-dimensional Raman spectra of CS2 are dominated by third-order cascades

1999 ◽  
Vol 111 (7) ◽  
pp. 3105-3114 ◽  
Author(s):  
David A. Blank ◽  
Laura J. Kaufman ◽  
Graham R. Fleming
Keyword(s):  
Raman Spectra ◽  
Two Dimensional ◽  
Third Order ◽  
Fifth Order

scholarly journals Design and Analysis of a Repetitive Current Controller for a Single-Phase Bridgeless SEPIC PFC Converter

Energies ◽  
2018 ◽  
Vol 12 (1) ◽  
pp. 131 ◽  
Author(s):  
Jinwoo Kim ◽  
Sanghun Han ◽  
Wontae Cho ◽  
Younghoon Cho ◽  
Hyunsoo Koh
Keyword(s):  
Controller Design ◽  
Harmonic Distortion ◽  
Input Current ◽  
Order Model ◽  
Third Order ◽  
Current Controller ◽  
The Stability ◽  
Small Signal Modeling ◽  
Fifth Order ◽  
Repetitive Controller

This paper studies a repetitive controller design scheme for a bridgeless single-ended primary inductor converter (SEPIC) power factor correction (PFC) converter to mitigate input current distortions. A small signal modeling of the converter is performed by a fifth-order model. Since the fifth-order model is complex to be applied in designing a current controller, the model is approximated to a third-order model. Using the third-order model, the repetitive controller is designed to reduce the input current distortion. Then, the stability of the repetitive controller is verified with an error transfer function. The proposed controller performance is validated by simulation, and the experiment results show that the input current total harmonic distortion (THD) is improved by applying the proposed controller for an 800 W bridgeless SEPIC PFC converter prototype.

scholarly journals On a Reduced Cost Higher Order Traub-Steffensen-Like Method for Nonlinear Systems

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 891 ◽  
Author(s):  
Janak Raj Sharma ◽  
Deepak Kumar ◽  
Lorentz Jäntschi
Keyword(s):  
Order Of Convergence ◽  
Higher Order ◽  
New Method ◽  
Systems Of Nonlinear Equations ◽  
Third Order ◽  
Type Method ◽  
Cpu Time ◽  
Chebyshev’S Method ◽  
Derivative Free ◽  
Fifth Order

We propose a derivative-free iterative method with fifth order of convergence for solving systems of nonlinear equations. The scheme is composed of three steps, of which the first two steps are that of third order Traub-Steffensen-type method and the last is derivative-free modification of Chebyshev’s method. Computational efficiency is examined and comparison between the efficiencies of presented technique with existing techniques is performed. It is proved that, in general, the new method is more efficient. Numerical problems, including those resulting from practical problems viz. integral equations and boundary value problems, are considered to compare the performance of the proposed method with existing methods. Calculation of computational order of convergence shows that the order of convergence of the new method is preserved in all the numerical examples, which is not so in the case of some of the existing higher order methods. Moreover, the numerical results, including the CPU-time consumed in the execution of program, confirm the accurate and efficient behavior of the new technique.

High-order finite difference WENO schemes with positivity-preserving limiter for correlated random walk with density-dependent turning rates

2015 ◽  
Vol 25 (08) ◽  
pp. 1553-1588 ◽  
Author(s):  
Yan Jiang ◽  
Chi-Wang Shu ◽  
Mengping Zhang
Keyword(s):  
Random Walk ◽  
Finite Difference ◽  
Temporal Integration ◽  
Time Discretization ◽  
High Order ◽  
Correlated Random Walk ◽  
Third Order ◽  
Positivity Preserving ◽  
Fifth Order ◽  
High Order Finite Difference

In this paper, we discuss high-order finite difference weighted essentially non-oscillatory schemes, coupled with total variation diminishing (TVD) Runge–Kutta (RK) temporal integration, for solving the semilinear hyperbolic system of a correlated random walk model describing movement of animals and cells in biology. Since the solutions to this system are non-negative, we discuss a positivity-preserving limiter without compromising accuracy. Analysis is performed to justify the maintenance of third-order spatial/temporal accuracy when the limiters are applied to a third-order finite difference scheme and third-order TVD-RK time discretization for solving this model. Numerical results are also provided to demonstrate these methods up to fifth-order accuracy.

scholarly journals Achieving Seventh-Order Amplitude Accuracy in Leapfrog Integrations

2013 ◽  
Vol 141 (9) ◽  
pp. 3037-3051 ◽  
Author(s):  
Paul D. Williams
Keyword(s):  
Nonlinear System ◽  
Third Order ◽  
First Order ◽  
Time Stepping ◽  
The Third ◽  
Numerical Integrations ◽  
Seventh Order ◽  
Ocean Models ◽  
Stability And Accuracy ◽  
Fifth Order

Abstract The leapfrog time-stepping scheme makes no amplitude errors when integrating linear oscillations. Unfortunately, the Robert–Asselin filter, which is used to damp the computational mode, introduces first-order amplitude errors. The Robert–Asselin–Williams (RAW) filter, which was recently proposed as an improvement, eliminates the first-order amplitude errors and yields third-order amplitude accuracy. However, it has not previously been shown how to further improve the accuracy by eliminating the third- and higher-order amplitude errors. Here, it is shown that leapfrogging over a suitably weighted blend of the filtered and unfiltered tendencies eliminates the third-order amplitude errors and yields fifth-order amplitude accuracy. It is further shown that the use of a more discriminating (1, −4, 6, −4, 1) filter instead of a (1, −2, 1) filter eliminates the fifth-order amplitude errors and yields seventh-order amplitude accuracy. Other related schemes are obtained by varying the values of the filter parameters, and it is found that several combinations offer an appealing compromise of stability and accuracy. The proposed new schemes are tested in numerical integrations of a simple nonlinear system. They appear to be attractive alternatives to the filtered leapfrog schemes currently used in many atmosphere and ocean models.

Suppression of shock-induced separation in fluids having large bulk viscosities

2014 ◽  
Vol 756 ◽  
Author(s):  
F. Bahmani ◽  
M. S. Cramer
Keyword(s):  
Boundary Layer ◽  
Bulk Viscosity ◽  
Shear Viscosity ◽  
Classical Problem ◽  
Two Dimensional ◽  
Perfect Gas ◽  
Third Order ◽  
Large Bulk ◽  
Boundary Layer Interaction ◽  
Fifth Order

AbstractWe examine the effect of large bulk viscosity on the classical problem of two-dimensional shock–boundary-layer interaction. The flow is taken to be steady and supersonic over a flat adiabatic plate. The boundary layer is taken to be laminar and the fluid is modelled as a perfect gas with a bulk viscosity that is large compared with its shear viscosity. The flow details are computed using a fifth-order weighted essentially non-oscillatory finite difference scheme and a third-order Runge–Kutta scheme for the spatial and temporal discretizations. The primary result of interest is the suppression of separation when the ratio of bulk to shear viscosity is sufficiently large.

The geometrical aberrations of general electron optical systems II. The primary (third order) aberrations of orthogonal systems, and the secondary (fifth order) aberrations of round systems

1965 ◽  
Vol 257 (1086) ◽  
pp. 523-552 ◽  
Keyword(s):  
Second Order ◽  
Order Perturbation ◽  
Optical Systems ◽  
Characteristic Functions ◽  
Electron Optics ◽  
Third Order ◽  
Variation Of Parameters ◽  
General Kind ◽  
Fifth Order ◽  
Orthogonal Systems

The theory of characteristic functions, developed by Sturrock for electron optics, is used to calculate the primary aberrations of rectilinear orthogonal systems of the most general kind. In the second part, the secondary aberrations of round systems are calculated with the aid of Sturrock’s second-order perturbation characteristic functions. A proof of the equivalence of the aberration formulae obtained by Melkich, using the variation of parameters method, and those obtained below is offered in an appendix.

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