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首页> 外文期刊>Journal of the Mechanics and Physics of Solids >Propagation of transition front in bi-stable nondegenerate chains: Model dependence and universality
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Propagation of transition front in bi-stable nondegenerate chains: Model dependence and universality

机译：双稳态非简并链中过渡前沿的传播：模型依赖性和普遍性

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摘要

We consider a propagation of transition fronts in one-dimensional chains with bi-stable nondegenerate on-site potential. If one adopts linear coupling in the chain and piecewise linear on-site force, then it is possible to develop well-known exact solutions for the front and accompanying oscillatory tail. Our goal is to explore the sensitivity of these propagating-front solutions to fine details of the dynamical model. We numerically explore the linearly coupled chain with other shapes of the on-site potential with the same basic parameters (height of the potential barrier, energy effect and distance between the potential wells). Differences in the shapes of the on-site potential lead to a moderate modification of the front velocities. However, the front initiation may be substantially delayed due to possible localization of the initial excitation. Inclusion of a cubic nonlinearity in the nearest neighbor interaction drastically modifies the front structure and parameters. The energy concentration in the front zone leads to a dominance of the nonlinear term even if formally it is not too large. In this latter case, it turns out that the dynamics can be efficiently studied in terms of an equivalent model with a single degree of freedom. This estimation leads to an accurate prediction of the front velocity and the parameters of the oscillatory tail. Moreover, it turns out that the exact shape of the on-site potential almost does not affect the front parameters. This finding also conforms to the simplified model, since the latter invokes only the general shape characteristics of the on-site potential.
机译：我们考虑过渡前沿在具有双稳态非退化现场电势的一维链中的传播。如果采用链中的线性耦合和分段线性的现场作用力，则可以为前部和伴随的振动尾部开发众所周知的精确解决方案。我们的目标是探索这些传播前解决方案对动力学模型的精细细节的敏感性。我们用相同的基本参数（势垒的高度，能量效应和势阱之间的距离）以数字形式探索具有其他形状的现场势的线性耦合链。现场电势的形状差异导致前速度的适度变化。然而，由于初始激励的可能定位，前部引发可能会大大延迟。在最近的邻居交互中包含三次非线性会极大地修改前端结构和参数。前部区域的能量集中导致非线性项占主导地位，即使在形式上它不是太大。在后一种情况下，事实证明，可以根据具有单个自由度的等效模型有效地研究动力学。该估计导致前速度和振荡尾部参数的准确预测。而且，事实证明，现场电势的确切形状几乎不影响前端参数。该发现也符合简化模型，因为后者仅调用了现场电势的一般形状特征。

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  • 来源
    《Journal of the Mechanics and Physics of Solids》 |2017年第7期|144-156|共13页
  • 作者

    Shiroky I. B.; Gendelman Oleg V.;

  • 作者单位

    Faculty of Mechanical Engineering, Technion, Haifa, Israel;

    Faculty of Mechanical Engineering, Technion, Haifa, Israel;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
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