长波低振幅干扰在无和的单维格子中的能量动力学
Stepan Shcherbinin1,2,3, Julia Baimova4, Anton Krivtsov1,2,3
1Higher School of Theoretical Mechanics and Mathematical Physics, Peter the Great Saint Petersburg Polytechnical University, 195251 Saint Petersburg, Russia.
Materials (Basel, Switzerland)
|November 27, 2025
概括
非线性链中的局部干扰与线性系统类似地传播. 随着时间的推移,能量中心和半径线性增加,这表明阿尔法-费米-帕斯塔-乌拉姆链和相关模型中的恒定速度分散.
科学领域:
- 非线性动力学是一种非线性动力学.
- 凝聚物质物理学 凝聚物质物理学
- 数学物理学的数学物理.
背景情况:
- 在非线性网格中研究波传播对于理解能量传输至关重要.
- 阿尔法-费米-帕斯塔-乌拉姆 (FPU) 链是研究非线性格子动态的规范模型.
- 之前的研究集中在FPU链行为的特定方面,但缺乏扰乱演变的统一框架.
研究的目的:
- 以分析的方式研究alpha-FPU链中的局部干扰的演变.
- 将离散α-FPU链中的干扰动态与其连续近似进行比较 (Boussinesq和Korteweg-de Vries方程).
- 建立对弱非线性系统中能量传输的普遍理解.
主要方法:
- 对局部干扰传播的分析研究.
- 专注于干扰特征:能量中心位置和能量半径.
- 使用能量动力学方法.
- 关于单子分解的Korteweg-de Vries (KdV) 方程的杆性质.
主要成果:
- 阿尔法-FPU链中的局部干扰表现出类似于在大时间尺度上的线性系统的行为.
- 干扰能量中心传播,能量半径随时间线性增加,表明恒定速度分散.
- 在KdV方程中的干扰在有效的介质力下演变,然后分解为单离子和分散尾巴.
- 减少的KdV方程 (缺乏分散或非线性) 显示能量中心的恒定速度传播.
结论:
- 该研究将在和链中观察到的行为概括为弱非线性系统.
- 为理解非线性网格中的能量传输提供了一个统一的框架.
- 这些发现突出了离散和连续非线性模型中干扰演变的相似之处.
相关概念视频
The de Broglie Wavelength
32.9K
In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
32.9K
Damped Oscillations
6.7K
In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...
Although friction and other non-conservative...
6.7K
Atomic Nuclei: Nuclear Relaxation Processes
1.2K
In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis, the precessing magnetic moments are randomly oriented around the z-axis.
1.2K
Types of Damping
7.5K
If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...
7.5K
Standing Waves in a Cavity
1.4K
A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:
1.4K
Trends in Lattice Energy: Ion Size and Charge
26.4K
An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
26.4K


