发表机构
Tokyo University of Science; Tokyo University of Agriculture and Technology（东京科学大学; 东京农工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明线性阻尼弹性系统无需非线性效应即可出现振动Mpemba弛豫反转，机制为模态投影调控，并在双模态子空间解析获得普适交叉时间，给出强效应类比。
AI 中文摘要
我们证明，线性阻尼弹性系统可以在没有任何非线性本构响应或振幅相关阻尼的情况下表现出类似Mpemba的振动弛豫反转。其机制纯粹是模态的。对于一维Kelvin–Voigt弹性介质，第n个振动模态的衰减速率按γ_n∝n^2标度。我们将弛豫用正模态包络能量来表述，从而排除仅由振荡相位引起的交叉。随后构造一个单参数初始状态族，使得增加初始弹性激发同时减少对慢基模的投影。在不变的双模态子空间中，弛豫阶交叉被解析地获得，并且对于该状态族，交叉发生在与所选初始状态对无关的普适无量纲时间。在慢模态缺失的极限情况下，主导弛豫速率发生不连续变化，产生强Mpemba效应的直接振动类比。我们进一步表明，同样的弛豫阶反转也发生在普通机械振动能量中，该能量尽管保留了底层模态的振荡动力学，却单调递减。
英文摘要
We show that a linear damped elastic system can display a Mpemba-like reversal of vibrational relaxation without any nonlinear constitutive response or amplitude-dependent damping. The mechanism is purely modal. For a one-dimensional Kelvin--Voigt elastic medium, the decay rate of the $n$-th vibrational mode scales as $γ_n\propto n^2$. We formulate relaxation in terms of a positive modal envelope energy, thereby excluding crossings caused merely by oscillation phase. A one-parameter family of initial states is then constructed such that increasing the initial elastic excitation simultaneously reduces the projection onto the slow fundamental mode. In the invariant two-mode subspace, the relaxation-order crossing is obtained analytically and, for this family, occurs at a universal dimensionless time independent of the selected pair of initial states. In the limiting case where the slowest mode is absent, the dominant relaxation rate changes discontinuously, yielding a direct vibrational analogue of the strong Mpemba effect. We further show that the same relaxation-order reversal occurs in the ordinary mechanical vibrational energy, which decreases monotonically despite retaining the oscillatory dynamics of the underlying modes.
Comments11 pages, 3 figures
