相关实验视频
Updated: May 31, 2026

10:33
Research and Development of High-performance Explosives
Published on: February 20, 2016
爆炸物透是连续的
1Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford OX1 3LB, UK. riordan@maths.ox.ac.uk
概括
爆炸性透,一个快速的网络增长现象,以前被认为发生在Achlioptas过程中. 然而,这项研究表明,这些过程实际上表现出连续的相位过渡,而不是不连续的.
科学领域:
- 网络科学 网络科学
- 统计物理 统计物理
- 复杂的系统复杂的系统.
背景情况:
- 爆炸性透描述了在不断发展的网络中快速出现的宏观组件.
- 阿克利奥普塔斯的过程是研究网络增长动态的关键模型.
- 以前的模拟表明,Achlioptas过程中存在不连续的相变.
研究的目的:
- 严格分析Achlioptas过程的相位过渡行为.
- 为了确定Achlioptas过程是否表现出真正的爆炸性透.
- 为了澄清网络增长模型中发生不连续阶段转换的条件.
主要方法:
- 理论分析阿克利奥普塔斯的过程.
- 网络演变的数学建模.
- 与相关网络增长模型的比较.
主要成果:
- 所有Achlioptas过程都表现出连续的相位过渡.
- 爆炸性透的现象在标准Achlioptas过程中并不存在.
- 与大小依赖的节点采样相关的模型可以显示不连续的过渡.
结论:
- 标准Achlioptas工艺没有显示爆炸性透.
- 这些网络模型中的相位过渡是连续的.
- 不连续的转换需要进行超越标准Achlioptas过程的修改,例如增加样本大小.
相关概念视频
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 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:
The mass flow rate is expressed as:
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 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...
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 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...
The electric charge can also be subjected to an analogical...

