On a High-Pass Filter Described by Local Fractional Derivative

Numerical Methods Partial

2020

At a microgravity condition, a spaceflight might be subject to a microgravity‐induced vibration. There is no theory so far to study the effect of microgravity on the vibration property. Here we give a fractal vibration model by the two‐scale thermodynamics. The fractal oscillator in the microgravity space is modeled by using the fractal derivative, and its frequency is obtained by He's frequency formula. The variational principle of the fractal model is established by the fractal semi‐inverse method. The example shows that the proposed method is simple, efficient, and accurate. The frequency‐amplitude relationship is elucidated and the effect of the microgravity condition on vibration property is discussed.

Section: Fractal Two‐scale Transform Methodsmentioning

confidence: 99%

Section: Fractal Two-scale Transform Methodsmentioning

confidence: 99%

He's frequency formulation for fractal nonlinear oscillator arising in a microgravity space

Numerical Methods Partial

2020

“…Nonlinear partial differential equations are widely used to model different physical phenomena, 1–7 and its solution method is always the focus of research 8–15 . In this paper, we aim to study a fourth‐order nonlinear generalized Boussinesq water wave equation, which is given as follows 8,16 :

η_{tt} - m η_{xx} - n {(η^{2})}_{xx} + k η_{italicxx x x} = 0,

where m , n , and k are arbitrary constants.…”

Section: Introductionmentioning

confidence: 99%

Solitary and periodic wave solutions of the generalized fourth‐order Boussinesq equation via He's variational methods

Math Methods in App Sciences

2021

Yu‐Lan Ma, et al. (Mathematical Methods in the Applied Sciences, 2019,42(1)) make outstanding contributions for the soliton solutions of the generalized fourth‐order Boussinesq equation, which is used to describe the wave motion in fluid mechanics. But the periodic wave solution is not reported. So in this paper, He's variational methods are employed to find the solitary and periodic wave solutions of the generalized fourth‐order Boussinesq equation. The greatest advantage of the variational method is that it can reduce the order of the research equation, make the equation more simple, and obtain the optimal solution. Finally, the numerical results are shown in the form of a graph to prove the applicability and effectiveness of the method. The results reveal that variational method is simple and straightforward and can avoid the tedious calculation process, which is expected to shed a light to the new research frontiers of solitary wave theory.

“…However, the three-dimensional stacking structure greatly increases the power density in a unit volume, which easily leads to high working temperature, as a result, it will affects the normal operation of the chip, and even leads to the thermal failure. Therefore, the thermal management of the 3-D ICs faces great challenges, and effective cooling methods have become one of the key issues in the development of 3-D ICs [8][9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Thermal management of 3-D integrated circuits with special structures

2021

THERM SCI

Self Cite

Different stacked structures affect greatly the temperature distribution of a three-dimensional integrated circuit(3-D IC), and an optimal structure is much needed to reduce the maximal temperature. This paper suggests a numerical approach to such structures with different heat source distributions. The results show that an optimal stacked structure can reduce the maximum temperature by 8.7?C.