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Updated: Sep 16, 2025

Microparticle Manipulation by Standing Surface Acoustic Waves with Dual-frequency Excitations
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Microparticle Manipulation by Standing Surface Acoustic Waves with Dual-frequency Excitations

Published on: August 21, 2018

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计算波形的动力学:对分叉,混乱和灵敏度分析的研究

Nur Hasan Mahmud Shahen1,2, Md Al Amin3,4, Foyjonnesa1,2

  • 1Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh.

PloS one
|July 9, 2025
PubMed
概括

这项研究利用萨达尔-分方程方案提取了用于分数级波方程的各种移动波形. 它在浅水波浪模型中揭示了复杂的动态,包括混乱的行为.

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BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
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Plotting and Calibrating the Root Locus01:19

Plotting and Calibrating the Root Locus

Root loci often diverge as system poles shift from the real axis to the complex plane. Key points in this transition are the breakaway and break-in points, indicating where the root locus leaves and reenters the real axis. The branches of the root locus form an angle of 180/n degrees with the real axis, where n is the number of branches at a breakaway or break-in point.
The maximum gain occurs at the breakaway points between open-loop poles on the real axis, while the minimum gain is...
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Bode Plots Construction01:24

Bode Plots Construction

The Bode plot is an essential tool in control system analysis, mapping the frequency response of a system through a magnitude plot and a phase plot, both against a logarithmic frequency axis. To construct a Bode plot, consider the transfer function H(ω):
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Root-Locus Method01:19

Root-Locus Method

A cruise control system in a car is designed to maintain a specified speed automatically by adjusting the gas pedal. The system continuously measures the vehicle's speed and makes fine adjustments to the pedal to achieve this goal. The root locus method is particularly useful for understanding how the cruise control system's behavior changes under varying conditions, such as when the car goes uphill, downhill, or faces strong wind resistance.
This system can be represented by a block...
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Convergence of Fourier Series01:21

Convergence of Fourier Series

The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
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SFG Algebra01:16

SFG Algebra

In Signal Flow Graph (SFG) algebra, the value a node represents is determined by the sum of all signals entering that node. This summed value is then transmitted through every branch leaving the node, making the SFG a powerful tool for visualizing and analyzing control systems.
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