Transport through a network of capillaries from ultrametric diffusion equation with quadratic nonlinearity

This paper is about a novel mathematical framework to model transport (of, e.g., fluid or gas) through networks of capillaries. This framework takes into account the tree structure of the networks of capillaries. (Roughly speaking, we use the tree-like system of coordinates.) As is well known, tree-geometry can be topologically described as the geometry of an ultrametric space, i.e., a metric space in which the metric satisfies the strong triangle inequality: in each triangle, the third side is less than or equal to the maximum of two other sides. Thus transport (e.g., of oil or emulsion of oil and water in porous media, or blood and air in biological organisms) through networks of capillaries can be mathematically modelled as ultrametric diffusion. Such modelling was performed in a series of recently published papers of the authors. However, the process of transport through capillaries can be only approximately described by the linear diffusion, because the concentration of, e.g., oil droplets, in a capillary can essentially modify the dynamics. Therefore nonlinear dynamical equations provide a more adequate model of transport in a network of capillaries. We consider a nonlinear ultrametric diffusion equation with quadratic nonlinearity - to model transport in such a network. Here, as in the linear case, we apply the theory of ultrametric wavelets. The paper also contains a simple introduction to theory of ultrametric spaces and analysis on them.     

Synchronization in networks with random interactions: theory and applications

Synchronization is an emergent property in networks of interacting dynamical elements. Here we review some recent results on synchronization in randomly coupled networks. Asymptotical behavior of random matrices is summarized and its impact on the synchronization of network dynamics is presented. Robert May's results on the stability of equilibrium points in linear dynamics are first extended to systems with time delayed coupling and then nonlinear systems where the synchronized dynamics can be periodic or chaotic. Finally, applications of our results to neuroscience, in particular, networks of Hodgkin-Huxley neurons, are included.     

Nanoscale thermal transport: Theoretical method and application

With the size reduction of nanoscale electronic devices, the heat generated by the unit area in integrated circuits will be increasing exponentially, and consequently the thermal management in these devices is a very important issue. In addition, the heat generated by the electronic devices mostly diffuses to the air in the form of waste heat, which makes the thermoelectric energy conversion also an important issue for nowadays. In recent years, the thermal transport properties in nanoscale systems have attracted increasing attention in both experiments and theoretical calculations. In this review, we will discuss various theoretical simulation methods for investigating thermal transport properties and take a glance at several interesting thermal transport phenomena in nanoscale systems. Our emphasizes will lie on the advantage and limitation of calculational method, and the application of nanoscale thermal transport and thermoelectric property.     

Synchronization in complex networks with a modular structure

Networks with a community (or modular) structure arise in social and biological sciences. In such a network individuals tend to form local communities, each having dense internal connections. The linkage among the communities is, however, much more sparse. The dynamics on modular networks, for instance synchronization, may be of great social or biological interest. (Here by synchronization we mean some synchronous behavior among the nodes in the network, not, for example, partially synchronous behavior in the network or the synchronizability of the network with some external dynamics.) By using a recent theoretical framework, the master-stability approach originally introduced by Pecora and Carroll in the context of synchronization in coupled nonlinear oscillators, we address synchronization in complex modular networks. We use a prototype model and develop scaling relations for the network synchronizability with respect to variations of some key network structural parameters. Our results indicate that random, long-range links among distant modules is the key to synchronization. As an application we suggest a viable strategy to achieve synchronous behavior in social networks.     

Temporal networks

A great variety of systems in nature, society and technology–from the web of sexual contacts to the Internet, from the nervous system to power grids–can be modeled as graphs of vertices coupled by edges. The network structure, describing how the graph is wired, helps us understand, predict and optimize the behavior of dynamical systems. In many cases, however, the edges are not continuously active. As an example, in networks of communication via e-mail, text messages, or phone calls, edges represent sequences of instantaneous or practically instantaneous contacts. In some cases, edges are active for non-negligible periods of time: e.g., the proximity patterns of inpatients at hospitals can be represented by a graph where an edge between two individuals is on throughout the time they are at the same ward. Like network topology, the temporal structure of edge activations can affect dynamics of systems interacting through the network, from disease contagion on the network of patients to information diffusion over an e-mail network. In this review, we present the emergent field of temporal networks, and discuss methods for analyzing topological and temporal structure and models for elucidating their relation to the behavior of dynamical systems. In the light of traditional network theory, one can see this framework as moving the information of when things happen from the dynamical system on the network, to the network itself. Since fundamental properties, such as the transitivity of edges, do not necessarily hold in temporal networks, many of these methods need to be quite different from those for static networks. The study of temporal networks is very interdisciplinary in nature. Reflecting this, even the object of study has many names—temporal graphs, evolving graphs, time-varying graphs, time-aggregated graphs, time-stamped graphs, dynamic networks, dynamic graphs, dynamical graphs, and so on. This review covers different fields where temporal graphs are considered, but does not attempt to unify related terminology—rather, we want to make papers readable across disciplines.     

Generalized synchronization of coupled chaotic systems

In this paper we briefly report some recent developments on generalized synchronization. We discuss different methods of detecting generalized synchronization. We first consider two unidirectionally coupled systems and then two mutually coupled systems. We then extend the study to a network of coupled systems. In the study of generalized synchronization of coupled nonidentical systems we discuss the Master Stability Function (MSF) formalism for coupled nearly identical systems. Later we use this MSF to construct synchronized optimized networks. In the optimized networks the nodes which have parameter value at one extreme are chosen as hubs and the pair of nodes with larger difference in parameter are chosen to create links.     

复杂网络上的部分同步化:奇异态、遥同步与集团同步

近年来,复杂网络上耦合振子的部分同步化引起了人们极大的关注,其潜在或背后的原因是部分同步化斑图在大脑网络中广泛存在,并很可能与大脑的认知或记忆等功能有密切的联系.本文对这些进展进行简单的总结与归纳,并按照学者们研究的不同侧重点,将其分成三方面来进行介绍,即奇异态、遥同步与集团同步化.着重强调这三种情形各自出现的条件、常用的研究模型、检测的方法以及侧重解释的生物现象等方面.并对它们三者之间的相互关系及今后的研究方向做一些简单的探讨.     

A Collaboration Network Model with Multiple Evolving Factors

To describe the empirical data of collaboration networks,several evolving mechanisms have been proposed,which usually introduce different dynamics factors controlling the network growth.These models can reasonably reproduce the empirical degree distributions for a number of well-studied real-world collaboration networks.On the basis of the previous studies,in this work we propose a collaboration network model in which the network growth is simultaneously controlled by three factors,including partial preferential attachment,partial random attachment and network growth speed.By using a rate equation method,we obtain an analytical formula for the act degree distribution.We discuss the dependence of the act degree distribution on these different dynamics factors.By fitting to the empirical data of two typical collaboration networks,we can extract the respective contributions of these dynamics factors to the evolution of each networks.     

A survey on UAV placement optimization for UAV-assisted communication in 5G and beyond networks

With the increase in capacity demands and the requirement of ubiquitous coverage in the fifth generation and beyond wireless communications networks, unmanned aerial vehicles (UAVs) have acquired a great attention owing to their outstanding characteristics over traditional base stations and relays. UAVs can be deployed faster and with much lower expenditure than ground base stations. In addition, UAVs can enhance the network performance thanks to their strong line-of-sight link conditions with their associated users and their dynamic nature that adapts to varying network conditions. Optimization of the UAV 3D locations in a UAV-assisted wireless communication network was considered in a large body of research as it is a critical design issue that greatly affects communication performance. Although the topic of UAV placement optimization was considered in few surveys, these surveys reviewed only a small part of the growing literature. In addition, the surveys were brief and did not discuss many important design issues such as the objectives of the optimization problem, the adopted solution techniques, the air-to-ground channel models, the transmission media for access and backhaul links, the limited energy nature of the UAV on-board batteries, co-channel interference and spectrum sharing, the interference management, etc. Motivated by the importance of the topic of UAV placement optimization as well as the need for a detailed review of its recent literature, we survey 100 of the recent research papers and provide in-depth discussion to fill the gaps found in the previous survey papers. The considered research papers are summarized and categorized to highlight the differences in the deployment scenario and system model, the optimization objectives and parameters, the proposed solution techniques, and the decision-making strategies and many other points. We also point to some of the existing challenges and potential research directions that have been considered in the surveyed literature and that requires to be considered     

Detecting community structure in networks

There has been considerable recent interest in algorithms for finding communities in networks--groups of vertices within which connections are dense, but between which connections are sparser. Here we review the progress that has been made towards this end. We begin by describing some traditional methods of community detection, such as spectral bisection, the Kernighan-Lin algorithm and hierarchical clustering based on similarity measures. None of these methods, however, is ideal for the types of real-world network data with which current research is concerned, such as Internet and web data and biological and social networks. We describe a number of more recent algorithms that appear to work well with these data, including algorithms based on edge betweenness scores, on counts of short loops in networks and on voltage differences in resistor networks.Received: 10 November 2003, Published online: 14 May 2004PACS: 89.75.Hc Networks and genealogical trees - 87.23.Ge Dynamics of social systems - 89.20.Hh World Wide Web, Internet - 05.10.-a Computational methods in statistical physics and nonlinear dynamics