论文标题
非线性光束模型中的纠结动力学
Kink Dynamics in a Nonlinear Beam Model
论文作者
论文摘要
在本文中,我们研究了带有第四个衍生项的非线性束方程的单个扭结和扭结碰撞。我们在数值上探讨了单个扭结的某些关键特征,无论是在其驻波还是行驶波形形式中。重点是研究扭结 - 安提金克碰撞的研究,探索了单弹药(和分离)和无限弹跳(互相扭结和抗恒定陷阱)窗户的临界速度。事实证明,相关的现象学与相应的非线性klein-gordon(即$ ϕ^4 $)模型的现象学大不相同。我们的计算表明,对于较小的初始速度,扭结和安提京克几乎在没有碰撞的情况下反射。对于速度的中间间隔,两个波相互捕获,而对于很大的速度,它们之间发生了单一的无弹性碰撞。最后,我们简要介绍了使用集体坐标方法(CC)方法及其对相关现象学的预测。当CC方法中使用一个自由度时,结果与初始速度值较小的数值非常匹配。但是,对于更大的初始速度价值,可以推断出,需要自由的自由度才能包括在内,以捕获碰撞现象学。
In this paper, we study the single kink and the kink-antikink collisions of a nonlinear beam equation bearing a fourth-derivative term. We numerically explore some of the key characteristics of the single kink both in its standing wave and in its traveling wave form. A point of emphasis is the study of kink-antikink collisions, exploring the critical velocity for single-bounce (and separation) and infinite-bounce (where the kink and antikink trap each other) windows. The relevant phenomenology turns out to be dramatically different than that of the corresponding nonlinear Klein-Gordon (i.e., $ϕ^4$) model. Our computations show that for small initial velocities, the kink and antikink reflect nearly elastically without colliding. For an intermediate interval of velocities, the two waves trap each other, while for large speeds a single inelastic collision between them takes place. Lastly, we briefly touch upon the use of collective coordinates (CC) method and their predictions of the relevant phenomenology. When one degree of freedom is used in the CC approach, the results match well the numerical ones for small values of initial velocity. However, for bigger values of initial velocity, it is inferred that more degrees of freedom need to be self-consistently included in order to capture the collision phenomenology.