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相关概念视频

Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

251
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured...
251
Elastic Curve from the Load Distribution01:16

Elastic Curve from the Load Distribution

169
The structural behavior of beams under distributed loads is critical for engineering analysis, which focuses on predicting how beams bend and react under such conditions. Different types of beams (e.g., cantilever, supported, or overhanging) behave differently under distributed load conditions.
For all beams, the analysis of the beam's reaction to distributed loads begins by understanding the relationship between a beam's load and the resulting shear forces and bending moments.
169
Transfer Function to State Space01:23

Transfer Function to State Space

211
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an...
211
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

75
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
75
Relation between Mathematical Equations and Block Diagrams01:20

Relation between Mathematical Equations and Block Diagrams

181
In a spring-mass-damper system, the second-order differential equation describes the dynamic behavior of the system. When transformed into the Laplace domain under zero initial conditions, this equation can be effectively analyzed and manipulated. The transformation into the Laplace domain converts differential equations into algebraic equations, simplifying the process of isolating the output.
181
Second Order systems II01:18

Second Order systems II

96
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
96

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相关实验视频

Updated: Jun 17, 2025

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

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使用更高阶精简微分方程估计捆绑特异性曲谱分布.

Yuanjing Feng1, Lei Xie1, Jingqiang Wang2

  • 1College of Information Engineering, Zhejiang University of Technology, Hangzhou, China; Zhejiang Provincial Collaborative Innovation Center for High-end Digital Intelligence Diagnosis and Treatment Equipment, Hangzhou, China; Zhejiang Provincial United Key Laboratory of Embedded Systems, Hangzhou, China.

NeuroImage
|August 14, 2024
PubMed
概括
此摘要是机器生成的。

本研究介绍了一种使用捆绑式特征图谱分布 (BTD) 函数的捆绑式特征图谱分布 (BST) 方法. 这种方法通过整合全球信息来提高复杂白质区域重建的准确性.

关键词:
捆绑特定的流程分布图分布.扩散式核磁共振成像 (MRI)高级精简微分方程 高级精简微分方程曲谱学 曲谱学 曲谱学 曲谱学

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Diffusion Imaging in the Rat Cervical Spinal Cord
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Diffusion Imaging in the Rat Cervical Spinal Cord

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Co-analysis of Brain Structure and Function using fMRI and Diffusion-weighted Imaging
17:06

Co-analysis of Brain Structure and Function using fMRI and Diffusion-weighted Imaging

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相关实验视频

Last Updated: Jun 17, 2025

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

8.5K
Diffusion Imaging in the Rat Cervical Spinal Cord
10:46

Diffusion Imaging in the Rat Cervical Spinal Cord

Published on: April 7, 2015

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Co-analysis of Brain Structure and Function using fMRI and Diffusion-weighted Imaging
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Co-analysis of Brain Structure and Function using fMRI and Diffusion-weighted Imaging

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科学领域:

  • 神经成像是一种神经成像.
  • 计算神经科学是一种神经科学.
  • 医学图像分析 医学图像分析

背景情况:

  • 流线曲线图依赖于来自光纤定向分布 (FOD) 功能的本地峰值方向,经常错过全球背景.
  • 这种限制导致不准确,包括错误的轨道和错过的真实连接在白质重建.

研究的目的:

  • 开发一种新的捆绑特异性曲谱 (BST) 方法,将全球信息纳入更准确的纤维重建.
  • 引入一个捆绑特定的轨道图分布 (BTD) 功能,以改善轨道图.

主要方法:

  • 提出了一种BST方法,利用BTD函数重建光纤轨迹,从开始到终点区域.
  • 基于扩散矢量场的高阶简化微分方程开发了一个统一的框架.
  • 通过能量优化,简化了通道图到BTD系数估计,整合了来自通道图束信息的解剖学先验.

主要成果:

  • BST方法准确地重建复杂的纤维几何形状,在模拟和真实数据 (HCP,ISMRM,FiberCup) 上表现优于传统方法.
  • BTD 功能有效地减少了局部误差偏差和积累.
  • 在重建远程,扭转和吹风航道方面表现出卓越的性能.

结论:

  • 提出的捆绑特异性通道图 (BST) 方法与捆绑特异性通道图分布 (BTD) 在白质通道重建方面取得了重大进展.
  • 这种方法提高了准确性,特别是在复杂和具有挑战性的光纤架构中.