热传导问题是一个古老而又富有挑战性的课题，很多的科学家都致力于探索在不同的系统中热量的传递、分配、储存和转化。近年来对热传导的热点研究主要集中于低维晶格系统。研究方向主要分为两类：一种是对热力学中基本问题的研究，例如傅里叶定律的成立条件；第二种是对材料特性的研究。本文的重点是第二种情况。在第一章中，我们首先简要介绍一下热传导的概念、研究方法。之后我们介绍了近年来热传导的研究具体状况，并做了详细的综述。在第二章中，我们主要讲述了和本文有关的一些定义,如研究的模型(着重介绍了三种常见的模型)、温度、热流、热浴、声子等。在第三章中，我们主要研究的是非均匀的FK系统。在前人已有的基础上，我们讨论在体系的两端加上同时调制并且有温差的热浴，试图探究其中的二极管效应。从计算的结果可以看出，当热浴的驱动频率较小时，不同的驱动强度对于系统的二极管效应的影响较大；当热浴的驱动强度较大时，系统的二极管效应对于调制频率的变化会更加敏感。通过此研究，可以更加明白系统中的每一个参数对于热流的影响，通过改变这些参数可以实现控制系统中热流的大小进而改变其热二极管的性质，为以后设计材料提供参考。在第四章中，我们主要研究了非均匀的FK晶格的界面效应，系统的两端分别加上三种不同的热浴。从三种不同的情况中，我们得出只要体系中有界面的加入负向热流$J_{-}$就会增大，随着界面厚度的增加，$J_{-}$的大小会逐渐和$J_{+}$的大小相等。我们以后在设计材料时应该考虑到界面对于系统的影响，这是由于当两个物质连接在一起时很有可能会相互渗透，这就相当于中间有了不同厚度的界面。

Heat conduction is a rather old but challenging problem. Understanding how heat is carried, distributed, stored, and converted in various systems has long been the focus of interest. Current research on heat conduction is mainly focused on the transport processes in low-dimensional lattice systems. The current study on this issue includes two categories, one for the fundamental problems, such as the validity of the Fourier law in low dimensions. The other issue is mainly related to applications in materials and rectifications of energy. In this dissertation, we investigate the latter problem by using numerical simulation and theoretical analysis.In Chapter I, we first introduce the history and the significance of the studies on heat conduction. Then we briefly introduce concepts of the normal and anomalous heat conduction.In Chapter II, we give a brief introduction to the concepts associated with this dissertation, such as different lattice models( especially for three important models), the temperature, the heat flux, the heat bath, phonons and so on.In Chapter III, we concentrate on the one-dimensional FK lattices. The ends of the system are in contact with two heat baths, which are modulated simultaneously with thermal bias. Based on our simulation results, the driving amplitude A has significant impact on the diode effect when the driving frequency $\omega$ is small. The diode effect is sensitive to the change of the driving frequency when the driving amplitude $A$ is large. By changing these parameters, we can control the heat transfer in the system. This is very useful for the design of materials.In Chapter IV, we mainly discuss the interface effect in the one-dimensional FK lattices. For three kinds of different heat baths employed at the ends of the system, the results are all the same. When the number of particles in the interface increases, $J_{-}$will increase, and finally equal to $J_{+}$. Since the penetration happens when two kinds of materials are connected, interface effect should be considered in the design of phononics devices.