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Related Concept Videos

Definition of z-Transform01:26

Definition of z-Transform

994
The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is an essential analytical tool, analogous to the Laplace transform used in continuous-time systems. It plays a crucial role in the analysis of signals and systems, complementing the discrete-time Fourier transform. Both the z-transform and the Laplace transform convert differential or difference equations into algebraic equations, simplifying the process of solving complex problems.
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Difference Equation Solution using z-Transform01:24

Difference Equation Solution using z-Transform

408
The z-transform is a powerful tool for analyzing practical discrete-time systems, often represented by linear difference equations. Solving a higher-order difference equation requires knowledge of the input signal and the initial conditions up to one term less than the order of the equation.
The z-transform facilitates handling delayed signals by shifting the signal in the z-domain, which corresponds to delaying the signal in the time domain, and advancing signals by similarly shifting in the...
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Multimachine Stability01:25

Multimachine Stability

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Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
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Region of Convergence01:17

Region of Convergence

613
The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is a crucial tool in the analysis of discrete-time systems, but its convergence is limited to specific values of the complex variable z. This range of values, known as the Region of Convergence (ROC), is fundamental in determining the behavior and stability of a system or signal. The ROC defines the region in the complex plane where the z-transform converges, which can take various...
613

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Neural network potential for Zr-Rh system by machine learning.

Kun Xie1, Chong Qiao2, Hong Shen1

  • 1Shanghai Ultra-Precision Optical Manufacturing Engineering Center, Department of Optical Science and Engineering, Fudan University, Shanghai, 200433, People's Republic of China.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|November 9, 2021
PubMed
Summary
This summary is machine-generated.

Researchers developed a machine learning potential for Zr-Rh metallic glass, improving molecular dynamics simulations. This allows for larger-scale studies of amorphous structures, crucial for material design and applications.

Keywords:
Zr–Rh metallic glassmachine learningmolecular dynamicsneural network potential

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Area of Science:

  • Materials Science
  • Computational Materials Science
  • Amorphous Alloys

Background:

  • Zirconium-Rhodium (Zr-Rh) metallic glass exhibits excellent mechanical properties, leading to applications in automotive and sports equipment.
  • Understanding the microstructure-property relationship in Zr-Rh metallic glass is crucial but limited by current simulation capabilities.

Purpose of the Study:

  • To develop a machine learning-based deep neural network potential for the Zr-Rh system.
  • To overcome the accuracy-efficiency trade-off in molecular dynamics (MD) simulations for Zr-Rh metallic glass.
  • To enable large-scale simulations for exploring amorphous structures and melt-quenching processes.

Main Methods:

  • Developed a deep neural network potential for Zr-Rh using machine learning.
  • Performed molecular dynamics simulations with the developed potential.
  • Validated results against *ab initio* molecular dynamics simulations.
  • Simulated a large model (5400 atoms) to study melt-quenching effects on Zr77Rh23.

Main Results:

  • The deep neural network potential accurately reproduces structural features compared to *ab initio* MD.
  • Simulations achieved significantly improved spatial and temporal scales.
  • Investigated the influence of simulation size and cooling rate on the melt-quenching process of Zr77Rh23.

Conclusions:

  • The machine learning potential provides an accurate and efficient tool for simulating Zr-Rh metallic glass.
  • This approach facilitates the exploration of complex amorphous structures in Zr77Rh23.
  • The findings are significant for the rational design and practical application of Zr-Rh metallic glass.