The work is devoted to the description of unsteady thermal processes in low-dimensional structures. To obtain the relationship between the microscopic and macroscopic descriptions of solids, it is necessary to understand the heat transfer mechanism at the micro-level. At the latter, in contrast to the macro-level, analytical, numerical, and experimental studies demonstrate significant deviations from the Fourier’s law. The paper bases on the ballistic heat transfer model, according to which the heat is carried by the thermal waves. This effect can be applied, for example, to signal transmission and heat removal problems. The influence of non-nearest neighbors on processes in discrete media, as well as processes in polyatomic lattices, is investigated. To describe the evolution of the initial thermal perturbation, the dispersion characteristics and group velocities in one-dimensional crystal are analyzed for (i) a diatomic chain with variable masses or stiffnesses and for (ii) a monatomic chain with regard for interaction with second neighbors. A fundamental solution to the heat distribution problem for the corresponding crystal models is obtained and investigated. The fundamental solution allows to obtain a description of waves traveling from a point source, and can serve as the basis for constructing all other solutions. In both cases, the solution consists of two thermal fronts moving one after another with different speeds and intensities. Quantitative estimates of the intensity of the thermal wave front are given, and the dynamics of changes in the velocities and intensities of the waves depending on the parameters of the problem is analyzed. Thus, a simple method for estimating the wavefronts intensity is proposed and tested on two models. These results can be used to identify and analyze those parts of the wave processes that are of interest in terms of interpretation of the effects observed in the experiments.

该工作致力于描述低维结构中的非稳态热过程。为了获得固体的微观描述和宏观描述之间的关系，有必要在微观层次上了解传热机理。在后者，与宏观水平相反，分析，数值和实验研究表明与傅立叶定律有明显的偏差。本文基于弹道传热模型，据此热量由热波传递。这种效果可以应用于例如信号传输和散热问题。研究了非最近邻居对离散介质中的过程以及多原子晶格中的过程的影响。为了描述初始热扰动的演变，一维晶体的色散特性和基团速度分析了（i）具有可变质量或刚度的双原子链，以及（ii）与第二邻居相互作用的单原子链。获得并研究了相应晶体模型的热分布问题的基本解决方案。基本解决方案允许获得从点源传播的波的描述，并且可以用作构建所有其他解决方案的基础。在这两种情况下，解决方案都包括两个热锋面，它们以不同的速度和强度一个接一个地移动。给出了热波阵面强度的定量估计，并分析了取决于问题参数的波速和强度变化的动力学。从而，提出了一种简单的估计波前强度的方法，并在两个模型上进行了测试。这些结果可用于识别和分析波动过程中在解释实验中观察到的影响方面感兴趣的部分。