A new analysis for Klein-Gordon model with local fractional derivative

Abstract This work adopts Yang's local fractional derivative to define the fractional Klein-Gordon equation in a fractal space or microgravity space. The variational principle of local fractional Klein-Gordon equation is successfully established via fractional semi-inverse transform method and the classical He's variational iteration method (HVIM) is used to obtain its approximate analytical solution

Periodic solution of the (2 + 1)-dimensional nonlinear electrical transmission line equation via variational method

Abstract The soliton solutions of the (2 + 1)-dimensional nonlinear electrical transmission line equation are discussed by Md. Abdul Kayum, et al. (Results in Physics, Volume18, 2020, 103269). In this paper, we obtain its periodic solution by the variational method, which is expected to shed a light on the study of the solitary wave theory

Study on the nonlinear vibration of embedded carbon nanotube via the Hamiltonian-based method:

This article mainly studies the vibration of the carbon nanotubes embedded in elastic medium. A new novel method called the Hamiltonian-based method is applied to determine the frequency property of the nonlinear vibration. Finally, the effectiveness and reliability of the proposed method is verified through the numerical results. The obtained results in this work are expected to be helpful for the study of the nonlinear vibration

A ℘-order R-L high-pass filter modeled by local fractional derivative

Abstract As an important electronic device, filter is applied to all kinds of electronic products. In this paper, a new ℘ -order R-L High-pass filter (HPF) modeled by the local fractional derivative (LFD) is proposed for the first time. With the help of the local fractional Laplace transform (LFLT), we obtain the non-differentiable(ND) transfer function, and present the expressions of ND amplitude-frequency characteristic (AFC) and ND phase-frequency characteristics (PFC). The corresponding parameters and properties of the ℘ -order R-L HPF are also studied. What's interesting is that the ℘ -order R-L HPF becomesthe ordinary one in the exceptional case at ℘ = 1. The obtained results in this paper reveal the sufficiency of the local fractional derivative for analyzing the circuit systems in fractal space

On joint analysing XMM-NuSTAR spectra of active galactic nuclei

A recently released XMM-Newton technical note has revealed a significant calibration issue between NuSTAR and XMM-Newton EPIC, and provided an empirical correction to EPIC effective area. To quantify the bias caused by the calibration issue to joint analysis of XMM-NuSTAR spectra and verify the effectiveness of the correction, in this work we perform joint-fitting of NuSTAR and EPIC-pn spectra for a large sample of 104 observation pairs of 44 X-ray bright AGN. The spectra were extracted after requiring perfect simultaneity between XMM-Newton and NuSTAR exposures (merging GTIs from two missions) to avoid bias due to rapid spectral variability of AGN. Before the correction, the EPIC-pn spectra are systematically harder than corresponding NuSTAR spectra by $\Delta \Gamma \sim 0.1$, subsequently yielding significantly underestimated cutoff energy $E_{\rm cut}$ and the strength of reflection component R when performing joint-fitting. We confirm the correction is highly effective and can commendably erase the discrepancy in best-fit $\Gamma$, $E_{\rm cut}$ and R, and thus we urge the community to apply the correction when joint-fitting XMM-NuSTAR spectra. Besides, we show that as merging GTIs from two missions would cause severe loss of NuSTAR net exposure time, in many cases joint-fitting yields no advantage compared with utilizing NuSTAR data alone. We finally present a technical note on filtering periods of high background flares for XMM-Newton EPIC-pn exposures in the Small Window mode.Comment: 14 pages, 8 figures, submitted. Comments are very welcome

Optimization of a 3-D high-power LED lamp: Orthogonal experiment method and experimental verification

The temperature distribution in a 3-D high-power light emitting diode lamp is affect by multiple factors, the orthogonal experiment method is adopted to elucidate three main factors, an experiment is designed to verify the main finding, which is useful for an optimal design of the light emitting diode lamp

Periodic waves travelling along an unsmooth boundary via the fractal variational theory

Abstract The solitary waves of the fractal Korteweg-de Vries (KdV) equation travelling along an unsmooth boundary is studied by Ji-Huan He, et al (Results in Physics, 2021, 104104 [1] ). In this letter, we obtain its periodic waves travelling along an unsmooth boundary via the fractal variational theory, which is expected to open the new perspectives on the study of the fractal travelling wave theory

A new fractal viscoelastic element: Promise and applications to Maxwell-rheological model

This paper proposes a fractal viscoelastic element via He?s fractal derivative, its properties are analyzed in details by the two-scale transform for the first time. The element is used to establish a fractal Maxwell-rheological model, which unifies the fractal creep equation and relaxation equation, and includes the classic elastic model and the classical Maxwell-rheological model as two special cases. This paper sheds a bright light on viscoelasticity, and the model can find wide applications in rock mechanics, plastic mechanics, and non-continuum mechanics