The issue, in two parts, is devoted to theoretical, computational and experimental studies of transport phenomena in various complex systems (in porous and composite media; systems with physical and chemical reactions and phase and structural transformations; in biological tissues and materials). Various types of these phenomena (heat and mass transfer; hydrodynamic and rheological effects; electromagnetic field propagation) are considered. Anomalous, relaxation and nonlinear transport, as well as transport induced by the impact of external fields and noise, is the focus of this issue. Modern methods of computational modelling, statistical physics and hydrodynamics, nonlinear dynamics and experimental methods are presented and discussed. Special attention is paid to transport phenomena in biological systems (such as haemodynamics in stenosed and thrombosed blood vessels magneto-induced heat generation and propagation in biological tissues, and anomalous transport in living cells) and to the development of a scientific background for progressive methods in cancer, heart attack and insult therapy (magnetic hyperthermia for cancer therapy, magnetically induced circulation flow in thrombosed blood vessels and non-contact determination of the local rate of blood flow in coronary arteries). The present issue includes works on the phenomenological study of transport processes, the derivation of a macroscopic governing equation on the basis of the analysis of a complicated internal reaction and the microscopic determination of macroscopic characteristics of the studied systems.

This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

该问题分为两部分，致力于各种复杂系统（多孔和复合介质；具有物理和化学反应以及相和结构转变的系统；在生物组织和材料中）中的传输现象的理论、计算和实验研究。考虑了这些现象的各种类型（传热和传质；流体动力学和流变效应；电磁场传播）。异常、弛豫和非线性输运，以及由外场和噪声影响引起的输运是本问题的重点。介绍和讨论了计算建模、统计物理学和流体动力学、非线性动力学和实验方法的现代方法。特别关注生物系统中的传输现象（例如狭窄和血栓形成的血管中的血流动力学、生物组织中磁致热的产生和传播，以及活细胞中的异常传输），并发展了渐进式方法的科学背景。癌症、心脏病发作和侮辱疗法（用于癌症治疗的磁热疗、血栓形成的血管中的磁诱导循环流和冠状动脉局部血流速率的非接触测定）。本期内容包括关于传输过程的现象学研究、基于复杂内部反应分析的宏观控制方程的推导以及所研究系统宏观特征的微观确定。

本文是主题问题“复杂系统中的传输现象（第 1 部分）”的一部分。