硅酸盐层模型中的非线性波
Nonlinear waves in a model for silicate layers
摘要：
一些层状硅酸盐由正离子组成，被具有相反符号的离子层包围。云母白云母是一种特别有趣的材料，因为存在非线性激发的化石和实验证据，沿着钾层内的阳离子行传输局部能量和电荷。这一证据表明，存在具有不同能量和性质的不同种类的激发。一些作者最近提出了一个一维模型的基础上的物理原理和硅酸盐结构。该模型的主要特点是它有一个硬衬底势和两个不同的排斥项，离子和核之间。在以前的工作与这个模型，它被发现的传播crowdions，即，在具有传输质量和电荷的衬底电势的晶格中的晶格扭结。它们具有单一的比速度和能量，与实验数据一致。在目前的工作中，我们执行一个更彻底的搜索在同一模型中的非线性激发使用伪谱方法，以获得精确的nanopteron的解决方案，这是单扭结的尾巴，crowdions和双crowdions。分析了它们的速度、能量、稳定性和不稳定性及其可能的原因。我们将不同的激发与它们可能来自不同β衰变的反冲以及化石径迹联系起来。我们探讨的物理参数的一些变化的后果，因为它们的值并不完全知道。通过不同的方法，我们也发现了静止和运动呼吸子，即具有内部振动的局部非线性激励。运动呼吸体具有较小的振幅和能量，这也与化石证据相一致。
英文摘要：
Some layered silicates are composed of positive ions, surrounded by layers of ions with opposite sign. Mica muscovite is a particularly interesting material, because there exist fossil and experimental evidence for nonlinear excitations transporting localized energy and charge along the cation rows within the potassium layers. This evidence suggest that there are different kinds of excitations with different energies and properties. Some of the authors proposed recently a one-dimensional model based in physical principles and the silicate structure. The main characteristic of the model is that it has a hard substrate potential and two different repulsion terms, between ions and nuclei. In a previous work with this model, it was found the propagation of crowdions, i.e., lattice kinks in a lattice with substrate potential that transport mass and charge. They have a single specific velocity and energy coherent with the experimental data. In the present work we perform a much more thorough search for nonlinear excitations in the same model using the pseudospectral method to obtain exact nanopteron solutions, which are single kinks with tails, crowdions and bi-crowdions. We analyze their velocities, energies and stability or instability and the possible reasons for the latter. We relate the different excitations with their possible origin from recoils from different beta decays and with the fossil tracks. We explore the consequences of some variation of the physical parameters because their values are not perfectly known. Through a different method, we also have found stationary and moving breathers, that is, localized nonlinear excitations with an internal vibration. Moving breathers have small amplitude and energy, which is also coherent with the fossil evidence.
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