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関連する概念動画

Properties of Continuous Functions01:29

Properties of Continuous Functions

Continuous functions exhibit smooth, uninterrupted behavior, and combining them through standard operations retains this continuity. If f and g are continuous at a point a, then the functions f+g, f-g, cf (where c is a constant), fg, and fg (provided g(a)a) are also continuous at a. This allows the construction of complex functions from simpler continuous parts without losing smoothness.Polynomials, which are expressions formed by sums of powers of x with constant coefficients, are continuous...
Continuity Equation01:28

Continuity Equation

The continuity equation asserts that the mass flow rate must remain constant for a steady flow of an incompressible fluid within a confined system. This principle applies to systems where fluid passes through varying cross-sectional areas, such as nozzles, syringes, and pipes.
The mass flow rate is expressed as:
Continuity Equation01:20

Continuity Equation

The total amount of current flowing per unit cross-sectional area is called the current density. Hence, the current passing through a cross-sectional area can be written as the surface integral of the current density.
Continuity of a Function01:23

Continuity of a Function

A function is continuous at a point a if three conditions are met: the function is defined at a, the limit of the function as x approaches a exists, and this limit equals the function’s value. Mathematically, this is written asThis definition ensures the graph of the function does not exhibit any breaks, holes, or jumps at that point. Discontinuities occur when any of these conditions fail. A removable discontinuity exists when the two-sided limit exists but the function is either undefined or...
Spontaneity02:21

Spontaneity

A spontaneous process is one that occurs naturally under certain conditions. A nonspontaneous process, on the other hand, will not take place unless it is “driven” by the continual input of energy from an external source. Processes have a natural tendency to occur in one direction under a given set of conditions. Water will naturally flow downhill (spontaneous process), but uphill flow (nonspontaneous process) requires outside intervention such as the use of a pump. Iron exposed to the earth’s...
Continuous Charge Distributions01:17

Continuous Charge Distributions

Imagine a bucket of water. It contains many molecules, of the order of 1026 molecules. Thus, although it contains discrete elements (molecules) at the microscopic level, macroscopically, it can be considered continuous. Small volume elements of water, infinitesimal compared to the bulk of the bucket's volume, still contain many molecules. Under this framework, quantized matter is approximated as continuous for practical purposes.
The electric charge can also be subjected to an analogical...

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Research and Development of High-performance Explosives
10:33

Research and Development of High-performance Explosives

Published on: February 20, 2016

爆発物の浸透は絶え間なく続いている.

Oliver Riordan1, Lutz Warnke

  • 1Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford OX1 3LB, UK. riordan@maths.ox.ac.uk

Science (New York, N.Y.)
|July 19, 2011
PubMed
まとめ
この要約は機械生成です。

急速なネットワーク成長現象である爆発的浸透は,以前はアクリオプタスのプロセスで発生すると考えられていた. しかし,この研究は,これらのプロセスが実際に連続的な相変遷を示しており,不連続的な相変遷ではないことを示しています.

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関連する実験動画

Last Updated: May 31, 2026

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10:33

Research and Development of High-performance Explosives

Published on: February 20, 2016

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08:02

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科学分野:

  • ネットワーク科学 ネットワーク科学
  • 統計物理学 統計物理
  • 複雑なシステム 複雑なシステム

背景:

  • 爆発的な浸透は,進化するネットワークにおけるマクロスコーピック構成要素の急速な出現を記述する.
  • アクリオプタスのプロセスは,ネットワークの成長ダイナミクスを研究するための重要なモデルです.
  • 以前のシミュレーションでは,アクリオプタスのプロセスにおける不連続の相移行が示唆されていた.

研究 の 目的:

  • アクリオプタスのプロセスの相変化行動を厳密に分析する.
  • アクリオプタスのプロセスが真の爆発的浸透を示すかどうかを判断する.
  • ネットワークの成長モデルで不連続のフェーズトランジションが起こる条件を明確にする.

主な方法:

  • アクリオプタスのプロセスの理論的分析.
  • ネットワーク進化の数学モデリング.
  • 関連ネットワーク成長モデルとの比較.

主要な成果:

  • すべてのアクリオプタスのプロセスは,連続した相変化を示します.
  • 爆発性浸透の現象は,標準的なアクリオプタスのプロセスには存在しません.
  • サイズに依存したノードサンプリングを持つ関連モデルでは,不連続の移行が表示されます.

結論:

  • 標準的なアクリオプタスのプロセスは,爆発的な浸透を表示しません.
  • これらのネットワークモデルの相変化は連続しています.
  • 不連続的な移行は,サンプルサイズを増やすなど,標準的なアクリオプタスのプロセスを超えた修正を必要とする.