In this work, we first construct Hermite wavelets on the interval [0,1) with it’s product, Operational matrix of integration 2^k M×2^k M is derived, and used it for solving nonlinear Variational problems with reduced it to a system of algebric equations and aid of direct method. Finally, some examples are given to illustrate the efficiency and performance of presented method.
The Caputo definition of fractional derivatives introduces solution to the difficulties appears in the numerical treatment of differential equations due its consistency in differentiating constant functions. In the same time the memory and hereditary behaviors of the time fractional order derivatives (TFODE) still common in all definitions of fractional derivatives. The use of properties of companion matrices appears in reformulating multilevel schemes as generalized two level schemes is employed with the Gerschgorin disc theorems to prove stability condition. Caputo fractional derivatives with finite difference representations is considered. Moreover the effect of using the inverse operator which tr
Nonlinear diffraction pattern can be induced by focusing CW
laser into a thin quartzes cuvette containing nanofluid. The number
of revealed pattern rings indicates to the nonlinear behavior of fluid.
Here, the nonlinear refractive index of each of functionalized single
wall carbon nanotube (F-SWCNTs) suspention and multi wall carbon
nanotube (F-MWCNTs) suspention have been investigated
experimentally .Each of CNTs suspention was at volume fraction of
13×10−5 and 6×10−5. Moreover the laser source at wavelength of
473 nm was used. The results show that SWCNTs suspention
possesses higher nonlinearty than other at the same volume fraction
Background/objectives: To study the motion equation under all perturbations effect for Low Earth Orbit (LEO) satellite. Predicting a satellite’s orbit is an important part of mission exploration. Methodology: Using 4th order Runge–Kutta’s method this equation was integrated numerically. In this study, the accurate perturbed value of orbital elements was calculated by using sub-steps number m during one revolution, also different step numbers nnn during 400 revolutions. The predication algorithm was applied and orbital elements changing were analyzed. The satellite in LEO influences by drag more than other perturbations regardless nnn through semi-major axis and eccentricity reducing. Findings and novelty/improvement: The results demo
... Show MoreThe objective of this study is to investigate the application of advanced oxidation processes (AOPs) in the treatment of wastewater contaminated with furfural. The AOPs investigated is the homogeneous photo-Fenton (UV/H2O2/Fe+2) process. The experiments were conducted by using cylindrical stainless steel batch photo-reactor. The influence of different variables: initial concentration of H2O2 (300-1300mg/L), Fe+2(20-70mg/L), pH(2-7) and initial concentration of furfural (50-300 mg/L) and their relationship with the mineralization efficiency were studied.
Complete mineralization for the system UV/H2O2/Fe+2 was achieved at: initi
... Show MoreThis paper aims to study the second-order geometric nonlinearity effects of P-Delta on the dynamic response of tall reinforced concrete buildings due to a wide range of earthquake ground motion forces, including minor earthquake up to moderate and strong earthquakes. The frequency domain dynamic analysis procedure was used for response assessment. Reinforced concrete building models with different heights up to 50 stories were analyzed. The finite element software ETABS (version 16.0.3) was used to analyze reinforced concrete building models.
The study reveals that the percentage increase in buildings' sway and drift due to P-Delta effects are nearly constant for specific building height irrespective of the seism
... Show MoreIn this work, the switching nonlinear dynamics of a Fabry-Perot etalon are studied. The method used to complete the solution of the differential equations for the nonlinear medium. The Debye relaxation equations solved numerically to predict the behavior of the cavity for modulated input power. The response of the cavity filled with materials of different response time is depicted. For a material with a response time equal to = 50 ns, the cavity switches after about (100 ns). Notice that there is always a finite time delay before the cavity switches. The switch up time is much longer than the cavity build-up time of the corresponding linear cavity which was found to be of the order of a few round-trip ti
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