Jove
Visualize
お問い合わせ
JoVE
x logofacebook logolinkedin logoyoutube logo
JoVEについて
概要リーダーシップブログJoVEヘルプセンター
著者向け
出版プロセス編集委員会範囲と方針査読よくある質問投稿
図書館員向け
推薦の声購読アクセスリソース図書館諮問委員会よくある質問
研究
JoVE JournalMethods CollectionsJoVE Encyclopedia of Experimentsアーカイブ
教育
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab Manual教員リソースセンター教員サイト
利用規約
プライバシーポリシー
ポリシー

関連する概念動画

Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

1.0K
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 from...
1.0K
Separable Differential Equations01:20

Separable Differential Equations

93
A separable differential equation is a type of first-order differential equation where the derivative dy/dx can be expressed as a product of two functions: one that depends only on x and another that depends only on y. This allows for the rearrangement of the equation so that all terms involving y are on one side, and all terms involving x are on the other. This process, known as the separation of variables, simplifies the process of solving the equation by enabling the integration of both...
93
Introduction to Differential Equations01:20

Introduction to Differential Equations

134
A differential equation is a mathematical expression that establishes a relationship between a function and its derivatives. These equations are fundamental in modeling dynamic systems across various fields of science and engineering. The order of a differential equation is defined by the highest order derivative present in the equation. A first-order differential equation includes only the first derivative, while a second-order differential equation includes up to the second derivative of the...
134
Modeling with Differential Equations01:25

Modeling with Differential Equations

84
Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
84
Linear Differential Equations01:27

Linear Differential Equations

83
The integrating factor method provides a systematic way to solve first-order linear differential equations, especially those that cannot be handled by separation of variables. This method is particularly useful in modeling time-dependent physical systems influenced by both constant inputs and resistive forces. A common example is the motion of a car subjected to a constant engine force while experiencing air resistance proportional to its velocity.In such scenarios, Newton’s second law...
83
Differential Equations: Problem Solving01:21

Differential Equations: Problem Solving

77
When analyzing the motion of falling objects, it is essential to consider not only the force of gravity but also the opposing force of air resistance. A practical example involves releasing a heavy test weight during a safety check on a ship. As the weight falls from rest, gravity accelerates it downward while air resistance exerts an upward force that increases with velocity. This dynamic interplay of forces is well described by differential equations, which provide a mathematical framework...
77

こちらも読む

関連記事

共著者、ジャーナル、引用グラフによってこの研究に関連する記事。

並び替え
Same journal

Computational modeling of immersed non-spherical bodies in viscous flows to study embolus-hemodynamics interactions in large-vessel occlusion stroke.

Engineering with computers·2026
Same journal

IGANets: Isogeometric analysis networks and their applications to linear structural analysis problems.

Engineering with computers·2026
Same journal

Parameterized shape optimization of a bi-leaflet heart valved conduit for pediatric applications.

Engineering with computers·2026
Same journal

A computational framework to predict the spreading of Alzheimer's disease.

Engineering with computers·2026
Same journal

Implicit sub-stepping scheme for critical state soil models.

Engineering with computers·2026
Same journal

Isogeometric suitable coupling methods for partitioned multiphysics simulation with application to fluid-structure interaction.

Engineering with computers·2026
関連記事をすべて見る

関連する実験動画

Updated: Feb 5, 2026

The Participant-Reported Implementation Update and Score PRIUS: A Novel Method for Capturing Implementation-Related Data Over Time
06:05

The Participant-Reported Implementation Update and Score PRIUS: A Novel Method for Capturing Implementation-Related Data Over Time

Published on: February 19, 2021

1.8K

トポロジー最適化のための微分方程式駆動型更新戦略：MATLABコードによる実装

Yang Liu1, Wei Tan1

  • 1School of Engineering and Materials Science, Queen Mary University of London, London, E1 4NS UK.

Engineering with computers
|February 4, 2026
PubMed
まとめ
この要約は機械生成です。

本研究は、トポロジー最適化のための新しい微分方程式駆動型手法を導入する。これは密度ベースのアプローチを強化し、工学応用における性能向上に向けた、より応答性の高い設計プロセスを提供する。

キーワード:
密度法微分方程式MATLABコードトポロジー最適化更新スキーム

さらに関連する動画

Author Spotlight: Enhancing PSC-to-Functional Cell Differentiation Using ML Models Based on Live-Cell Bright-Field Imaging
11:38

Author Spotlight: Enhancing PSC-to-Functional Cell Differentiation Using ML Models Based on Live-Cell Bright-Field Imaging

Published on: October 4, 2024

1.1K
Isolation of High-density Lipoproteins for Non-coding Small RNA Quantification
10:39

Isolation of High-density Lipoproteins for Non-coding Small RNA Quantification

Published on: November 28, 2016

11.8K

関連する実験動画

Last Updated: Feb 5, 2026

The Participant-Reported Implementation Update and Score PRIUS: A Novel Method for Capturing Implementation-Related Data Over Time
06:05

The Participant-Reported Implementation Update and Score PRIUS: A Novel Method for Capturing Implementation-Related Data Over Time

Published on: February 19, 2021

1.8K
Author Spotlight: Enhancing PSC-to-Functional Cell Differentiation Using ML Models Based on Live-Cell Bright-Field Imaging
11:38

Author Spotlight: Enhancing PSC-to-Functional Cell Differentiation Using ML Models Based on Live-Cell Bright-Field Imaging

Published on: October 4, 2024

1.1K
Isolation of High-density Lipoproteins for Non-coding Small RNA Quantification
10:39

Isolation of High-density Lipoproteins for Non-coding Small RNA Quantification

Published on: November 28, 2016

11.8K

科学分野:

  • 工学
  • 計算力学
  • 材料科学

背景:

  • トポロジー最適化は、レベルセット法のような境界駆動型手法を一般的に使用する。
  • 微分方程式は、密度ベースのトポロジー最適化にも適用できる。

研究 の 目的:

  • トポロジー最適化のための微分方程式を用いた新しい設計更新スキームを提示する。
  • 従来の相対増分形式に対する絶対増分形式の利点を探る。

主な方法:

  • 要素密度を進化させるための微分方程式を用いた設計更新スキームの定式化。
  • 微分方程式を、最適性基準（OC）法に類似した絶対増分形式に変換する。
  • 複合材料および単一材料の場合のコンプライアンス最小化のためのMATLABコードの実装と説明。

主要な成果:

  • 絶対増分形式は、より能動的で応答性の高い最適化プロセスを提供する。
  • 提案されたスキームは、密度分布最適化問題を効果的に解決する。
  • 数値例は、コンプライアンス最小化におけるスキームの性能を検証する。

結論:

  • 微分方程式駆動型進化戦略は、密度ベースのトポロジー最適化に効果的に使用できる。
  • 絶対増分形式は、古典的な密度法に代わる有望な選択肢であり、優れた設計につながる可能性がある。
  • 提示された方法は、トポロジー最適化タスクに実行可能な代替手段を提供する。