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An Introduction to Mechanics01:28

An Introduction to Mechanics

5.9K
Humans have been making ships, shelters, pyramids, weapons, agricultural equipment, and many more items without recording the process or theory behind them for centuries. It would be challenging to document the evolution of mechanics from its origin to the present.
According to records, the history of mechanics starts with Aristotle (384–322 BC). He related mechanics to physical theory, aiming for a universal synthesis.
Newton defined mechanics as the branch of physical science that...
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Reduced Mass Coordinates: Isolated Two-body Problem01:12

Reduced Mass Coordinates: Isolated Two-body Problem

2.2K
In classical mechanics, the two-body problem is one of the fundamental problems describing the motion of two interacting bodies under gravity or any other central force. When considering the motion of two bodies, one of the most important concepts is the reduced mass coordinates, a quantity that allows the two-body problem to be solved like a single-body problem. In these circumstances, it is assumed that a single body with reduced mass revolves around another body fixed in a position with an...
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Mechanical Systems01:22

Mechanical Systems

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Mechanical systems are analogous to to electrical networks where springs and masses play similar roles to inductors and capacitors, respectively. A viscous damper in mechanical systems functions similarly to a resistor in electrical networks, dissipating energy. The forces acting on a mass in such systems include an applied force in the direction of motion, counteracted by forces from the spring, a viscous damper, and the mass's acceleration. This interplay of forces is mathematically...
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Collisions in Multiple Dimensions: Introduction01:05

Collisions in Multiple Dimensions: Introduction

6.4K
It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a...
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Symmetry in Maxwell's Equations01:28

Symmetry in Maxwell's Equations

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Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
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First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

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Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about...
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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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デュアリティと非アベルの力学

Michel Fruchart1,2, Yujie Zhou3, Vincenzo Vitelli4,5

  • 1James Franck Institute, University of Chicago, Chicago, IL, USA. fruchart@uchicago.edu.

Nature
|January 22, 2020
PubMed
まとめ

物理学の二元性は 隠された対称性を明らかにします 自己二重構造は,同位体弾性や退化スペクトルのような新興特性を示し,新しいアプリケーションを可能にします.

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The Mechanics of Poro-Elastic Contractile Actomyosin Networks As a Model System of the Cell Cytoskeleton
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科学分野:

  • 物理学
  • 材料科学
  • 数学について

背景:

  • 双重性は,スケール不変性のようなユニークな性質を示す自己双重システムと,異なった物理システムを結びつける.
  • メタマテリアルには調節可能な特性がありますが,その設計は通常,標準の対称性分析に依存しています.
  • 再構成可能な機械構造は 歪んだカゴメの格子のように 形状の変化時に複雑な振る舞いを表します

研究 の 目的:

  • メタマテリアルデザインのダイナミック・マトリックスにおける対称性の強化を図る.
  • 従来のグループ理論を超えた メタマテリアルの新興特性を探求する
  • 再構成可能なシステムのメカニカルクリティカルポイントと自己二重構造を調査する.

主な方法:

  • 動的行列とハミルトン式における二元性の分析
  • 歪んだカゴメの格子とその崩壊メカニズムの研究.
  • 異なる構成で共有される振動スペクトルと弾性モジュールの観察と理論的説明.
  • 自己二重の臨界点とそれに関連する対称性の調査.

主要な成果:

  • 同じ振動スペクトルと弾性モジュールを導いた 機械的な構成の二元性を特定した.
  • 同位体弾力性と2倍退化スペクトルを持つ自己二重の臨界点を特徴づけている.
  • 自己二重点に隠された対称性を明らかにした クレーマーの定理に類似して スペクトル変異の原因だ
  • ノーマルモードでの非アベルの幾何学的な相を観察し,非通行的な機械的反応をもたらした.

結論:

  • 双重性は,新興特性を持つメタマテリアルを設計するための強力なツールを提供します.
  • 機械システムにおける自己二重の臨界点は,顕著な対称性と同位体弾力性を示す.
  • 新興対称性と非アベルの相は,ホロノミック計算と機械スピントロニクスにおける応用のための新しい道を開く.