拓扑结构(topological structure )

经常涉及到的拓扑结构一般有 总线型拓扑，星型拓扑，环型拓扑，树型拓扑，总线拓扑等等。

拓扑结构

拓扑结构是指网络中各个站点相互连接的形式，在局域网中明确一点讲就是文件服务器、工作站和电缆等的连接形式。现在最主要的拓扑结构有总线型拓扑、星型拓扑、环型拓扑以及它们的混合型。顾名思义，总线型其实就是将文件服务器和工作站都连在称为总线的一条公共电缆上，且总线两端必须有终结器；星型拓扑则是以一台设备作为中央连接点，各工作站都与它直接相连形成星型；而环型拓扑就是将所有站点彼此串行连接，像链子一样构成一个环形回路；把这三种最基本的拓扑结构混合起来运用自然就是混合型了。

 计算机网络的最主要的拓扑结构有总线型拓扑、星型拓扑、环型拓扑以及它们的混合型。

计算机网络的拓扑结构是把网络中的计算机和通信设备抽象为一个点，把传输介质抽象为一条线，由点和线组成的几何图形就是计算机网络的拓扑结构。

网络的拓扑结构：分为逻辑拓扑和物理拓扑结构这里讲物理拓扑结构。

总线型拓扑：是一种基于多点连接的拓扑结构，所有的设备连接在共同的传输介质上。总线拓扑结构使用一条所有PC都可访问的公共通道，每台PC只要连一条线缆即可但是它的缺点是所有的PC不得不共享线缆，优点是不会因为一条线路发生故障而使整个网络瘫痪。 

 环行拓扑：把每台PC连接起来，数据沿着环依次通过每台PC直接到达目的地，在环行结构中每台PC都与另两台PC相连每台PC的接口适配器必须接收数据再传往另一台一台出错，整个网络会崩溃因为两台PC之间都有电缆，所以能获得好的性能。

树型拓扑结构：把整个电缆连接成树型，树枝分层每个分至点都有一台计算机，数据依次往下传优点是布局灵活但是故障检测较为复杂，PC环不会影响全局。 

 星型拓扑结构：在中心放一台中心计算机，每个臂的端点放置一台PC，所有的数据包及报文通过中心计算机来通讯，除了中心机外每台PC仅有一条连接，这种结构需要大量的电缆，星型拓扑可以看成一层的树型结构不需要多层PC的访问权争用。星型拓扑结构在网络布线中较为常见。

网络拓扑结构是指抛开网络电缆的物理连接来讨论网络系统的连接形式，是指网络电缆构成的几何形状，它能从逻辑上表示出网络服务器、工作站的网络配置和互相之间的连接。

网络拓扑结构按形状可分为：星型、环型、总线型、树型及总线/星型及网状拓扑结构。

一、星型拓扑结构：
星型布局是以中央结点为中心与各结点连接而组成的，各结点与中央结点通过点与点方式连接，中央结点执行集中式通信控制策略，因此中央结点相当复杂，负担也重。
以星型拓扑结构组网，其中任何两个站点要进行通信都要经过中央结点控制。中央结点主要功能有：
1、为需要通信的设备建立物理连接；
2、为两台设备通信过程中维持这一通路；
3、在完成通信或不成功时，拆除通道。
在文件服务器/工作站(File Servers/Workstation )局域网模式中，中心点为文件服务器，存放共享资源。由于这种拓扑结构，中心点与多台工作站相连，为便于集中连线，目前多采用集线器(HUB)。
星型拓扑结构优点：网络结构简单，便于管理、集中控制，组网容易，网络延迟时间短，误码率低。缺点：网络共享能力较差，通信线路利用率不高，中央节点负担过重，容易成为网络的瓶颈，一旦出现故障则全网瘫痪。

二、环型拓扑结构
环形网中各结点通过环路接口连在一条首尾相连的闭合环形通信线路中，环路上任何结点均可以请求发送信息。请求一旦被批准，便可以向环路发送信息。环形网中的数据可以是单向也可是双向传输。由于环线公用，一个结点发出的信息必须穿越环中所有的环路接口，信息流中目的地址与环上某结点地址相符时，信息被该结点的环路接口所接收，而后信息继续流向下一环路接口，一直流回到发送该信息的环路接口结点为止。
环形网的优点：信息在网络中沿固定方向流动，两个结点间仅有唯一的通路，大大简化了路径选择的控制；某个结点发生故障时，可以自动旁路，可靠性较高。缺点：由于信息是串行穿过多个结点环路接口，当结点过多时，影响传输效率，使网络响应时间变长；由于环路封闭故扩充不方便。

三、总线拓扑结构
用一条称为总线的中央主电缆，将相互之间以线性方式连接的工站连接起来的布局方式，称为总线形拓扑。
在总线结构中，所有网上微机都通过相应的硬件接口直接连在总线上， 任何一个结点的信息都可以沿着总线向两个方向传输扩散，并且能被总线中任何一个结点所接收。由于其信息向四周传播，类似于广播电台，故总线网络也被称为广播式网络。
总线有一定的负载能力，因此，总线长度有一定限制，一条总线也只能连接一定数量的结点。
总线布局的特点：结构简单灵活，非常便于扩充；可靠性高，网络响应速度快；设备量少、价格低、安装使用方便；共享资源能力强，非常便于广播式工作，即一个结点发送所有结点都可接收。
在总线两端连接的器件称为端结器（末端阻抗匹配器、或终止器）。主要与总线进行阻抗匹配，最大限度吸收传送端部的能量，避免信号反射回总线产生不必要的干扰。
总线形网络结构是目前使用最广泛的结构，也是最传统的一种主流网络结构，适合于信息管理系统、办公自动化系统领域的应用。

四、树型拓扑结构
树形结构是总线型结构的扩展，它是在总线网上加上分支形成的，其传输介质可有多条分支，但不形成闭合回路，树形网是一种分层网，其结构可以对称，联系固定，具有一定容错能力，一般一个分支和结点的故障不影响另一分支结点的工作，任何一个结点送出的信息都可以传遍整个传输介质，也是广播式网络。一般树形网上的链路相对具有一定的专用性，无须对原网做任何改动就可以扩充工作站。

五、总线/星型拓扑结构
用一条或多条总线把多组设备连接起来，相连的每组设备呈星型分布。采用这种拓扑结构，用户很容易配置和重新配置网络设备。总线采用同轴电缆，星型配置可采用双绞线。

六、网状拓扑结构
将多个子网或多个局域网连接起来构成网际拓扑结构。在一个子网中，集线器、中继器将多个设备连接起来，而桥接器、路由器及网关则将子网连接起来。根据组网硬件不同，主要有三种网际拓扑：
1、网状网：
在一个大的区域内，用无线电通信连路连接一个大型网络时，网状网是最好的拓扑结构。通过路由器与路由器相连，可让网络选择一条最快的路径传送数据。
2、主干网：
通过桥接器与路由器把不同的子网或LAN连接起来形成单个总线或环型拓扑结构，这种网通常采用光纤做主干线。
3、星状相连网：
利用一些叫做超级集线器的设备将网络连接起来，由于星型结构的特点，网络中任一处的故障都可容易查找并修复。
应该指出，在实际组网中，为了符合不同的要求，拓扑结构不一定是单一的，往往都是几种结构的混用。

综合以上所述，可总结出以下计算机网络拓扑结构：
1、总线拓扑结构是将网络中的所有设备通过相应的硬件接口直接连接到公共总线上，结点之间按广播方式通信，一个结点发出的信息，总线上的其它结点均可“收听”到。 优点：结构简单、布线容易、可靠性较高，易于扩充，是局域网常采用的拓扑结构。缺点：所有的数据都需经过总线传送，总线成为整个网络的瓶颈；出现故障诊断较为困难。最著名的总线拓扑结构是以太网（Ethernet）。

2、星型拓扑结构每个结点都由一条单独的通信线路与中心结点连结。 优点：结构简单、容易实现、便于管理，连接点的故障容易监测和排除。缺点：中心结点是全网络的可靠瓶颈，中心结点出现故障会导致网络的瘫痪。

3、环形拓扑结构各结点通过通信线路组成闭合回路，环中数据只能单向传输。 优点：结构简单，适合使用光纤，传输距离远，传输延迟确定。缺点：环网中的每个结点均成为网络可靠性的瓶颈，任意结点出现故障都会造成网络瘫痪，另外故障诊断也较困难。最著名的环形拓扑结构网络是令牌环网（Token Ring）

4、树型拓扑结构是一种层次结构，结点按层次连结，信息交换主要在上下结点之间进行，相邻结点或同层结点之间一般不进行数据交换。优点：连结简单，维护方便，适用于汇集信息的应用要求。缺点：资源共享能力较低，可靠性不高，任何一个工作站或链路的故障都会影响整个网络的运行。

5、 网状拓扑结构又称作无规则结构，结点之间的联结是任意的，没有规律。优点：系统可靠性高，比较容易扩展，但是结构复杂，每一结点都与多点进行连结，因此必须采用路由算法和流量控制方法。目前广域网基本上采用网状拓扑结构。

6、混合型拓扑结构就是两种或两种以上的拓扑结构同时使用。优点：可以对网络的基本拓扑取长补短。缺点：网络配置挂包那里难度大。

7、蜂窝拓扑结构蜂窝拓扑结构是无线局域网中常用的结构。它以无线传输介质(微波、a卫星、红外线、无线发射台等)点到点和点到多点传输为特征，是一种无线网，适用于城市网、校园网、企业网，更适合于移动通信。在计算机网络中还有其他类型的拓扑结构，如总线型与星型混合、总线型与环型混合连接的网络。在局域网中，使用最多的是星型结构。

8、卫星通信拓扑结构。

随着PWM技术的不断发展和完善，开关电源以其高的性价比得到了广泛的应用。开关电源的电路拓扑结构很多，常用的电路拓扑有推挽、全桥、半桥、单端正激和单端反激等形式。其中， 在半桥电路中，变压器初级在整个周期中都流过电流，磁芯利用充分，且没有偏磁的问题，所使用的功率开关管耐压要求较低，开关管的饱和压降减少到了最小，对输入滤波电容使用电压要求也较低。由于以上诸多原因，半桥式变换器在高频开关电源设计中得到广泛的应用。

开关电源常用的基本拓扑约有14种。
每种拓扑都有其自身的特点和适用场合。一些拓扑适用于离线式(电网供电的)AC/DC变换器。其中有些适合小功率输出(<200W)，有些适合大功率输出；有些适合高压输入(≥220V AC)，有些适合120V AC或者更低输入的场合；有些在高压直流输出(>～200V)或者多组(4～5组以上)输出场合有的优势；有些在相同输出功率下使用器件较少或是在器件数与可靠性之间有较好的折中。较小的输入/输出纹波和噪声也是选择拓扑经常考虑的因素。

一些拓扑更适用于DC/DC变换器。选择时还要看是大功率还是小功率，高压输出还是低压输出，以及是否要求器件尽量少等。另外，有些拓扑自身有缺陷，需要附加复杂且难以定量分析的电路才能工作。

因此，要恰当选择拓扑，熟悉各种不同拓扑的优缺点及适用范围是非常重要的。错误的选择会使电源设计一开始就注定失败。
开关电源常用拓扑：
1、buck开关型调整器拓扑
2、boost开关调整器拓扑
3、反极性开关调整器拓扑
4、推挽拓扑
5、正激变换器拓扑
6、双端正激变换器拓扑
7、交错正激变换器拓扑
8、半桥变换器拓扑
9、全桥变换器拓扑
10、反激变换器
11、电流模式拓扑
12、电流馈电拓扑
13、SCR振谐拓扑
14、CUK变换器拓扑
开关电源各种拓扑集锦先给出六种基本DC/DC变换器拓扑。依次为buck，boost，buck－boost，cuk，zeta，sepic变换器。

1、星形拓扑
星形拓扑是由中央节点和通过点到到通信链路接到中央节点的各个站点组成。
星形拓扑结构具有以下优点：
（1）控制简单。
（2）故障诊断和隔离容易。
（3）方便服务。
星形拓扑结构的缺点：
（1）电缆长度和安装工作量可观。
（2）中央节点的负担较重，形成瓶颈。
（3）各站点的分布处理能力较低。

2、总线拓扑
总线拓扑结构采用一个信道作为传输媒体，所有站点都通过相应的硬件接口直接连到这一公共传输媒体上，该公共传输媒体即称为总线。
总线拓扑结构的优点：
（1）总线结构所需要的电缆数量少。
（2）总线结构简单，又是无源工作，有较高的可靠性。
（3）易于扩充，增加或减少用户比较方便。
总线拓扑的缺点：
（1）总线的传输距离有限，通信范围受到限制。
（2）故障诊断和隔离较困难。
（3）分布式协议不能保证信息的及时传送，不具有实时功能。

3、环形拓扑
环形拓扑网络由站点和连接站的链路组成一个闭合环。
环形拓扑的优点：
（1）电缆长度短。
（2）增加或减少工作站时，仅需简单的连接操作。
（3）可使用光纤。
环形拓扑的缺点：
（1）节点的故障会引起全网故障。
（2）故障检测困难。
（3）环形拓扑结构的媒体访问控制协议都采用令牌传达室递的方式，在负载很轻时，信道利用率相对来说就比较低。

4、树形拓扑
树形拓扑从总线拓扑演变而来，形状像一棵倒置的树，顶端是树根，树根以下带分支，每个分支还可再带子分支。
树形拓扑的优点：
（1）易于扩展。
（2）故障隔离较容易。
树形拓扑的缺点：
各个节点对根的依赖性太大。
http://www.hudong.com/wiki/%E6%8B%93%E6%89%91%E7%BB%93%E6%9E%84

 

What is Topology?

Topology is a field of study that investigates the invariant properties that remain after continuous deformation of a structure. Topology originated as a branch of mathematics and has played an important role in the development of the general theory of relativity and quantum theory, which represent 20th century physics. We believe that the concept of topology can be helpful in understanding phenomena in modern materials science, complex system science, networks of life, economics, and information science from a broader perspective. This program aims to explore complex phenomena in various scientific fields (multi-degree-of-freedom, non-equilibrium, non-linear, hierarchical structure) from a topological perspective. Our studies will be based on the results of original research performed by our members, e.g., the discoveries of (a) Möbius crystals, (b) slime mold (myxomycete) network intelligence, and (c) a new order of topological defects, and verification of fractons. Our ultimate goal is to create an innovative field, topological science and technology, which will pursue the discovery of new natural phenomena and laws as well as the development of new technologies.

A. Topological materials

B. Topology in relation to critical phenomena

C. Topology in the life sciences

D. Novel topology-related technologies

We aim to create novel materials with novel general spatial topologies and to discover new phenomena woven by geometric phases. To date, we have created topological materials that show macroscopic quantum order (charge density wave: CDW), such as the NbSe3 ring, and Möbius and figure eight crystals. Utilizing mathematical surface theory, we will develop a new field of topological crystallography and crystal growth, and elucidate the relationships between macroscopic quantum order and topology in view of their CDW properties. We also try to comprehend the relationships between symmetry and topology in view of the physical properties of quasicrystals with fivefold symmetry. In relation to general spatial topology, we will also create copper-oxide high-temperature superconductors and rings of heavy electron materials, and carry out electron wave interference tests on these topological materials.

NbSe3 ring, and Möbius and figure eight crystals
Tanda et al., Nature 417 (2002) 397.

In this project, we also aim to elucidate general system properties from the properties of topological defects found in superconductors, liquid crystals, and various other materials. We have observed a new topological defect order in the copper-oxide high-temperature superconductor La2-xSrxCuO4 magnetic flux line (typical topological defect) lattice, and found that its characteristics correspond to the spatial symmetry of high-temperature superconducting order parameters. This is a good example demonstrating that local typological defects introduced into the system are closely related to the general properties of that system. We will investigate high-temperature superconductivity from the viewpoint of topological defects. We will also study the topology of superconducting order parameters and quantum transport phenomena, another interesting subject of study from a topological perspective.

We will also try to develop topological devices in cooperation with the Novel topology-related technologies project.

A magnetic flux line square lattice observed in the La2-xSrxCuO4 neutron diffraction test
- corresponding to d-wave symmetric superconducting order -
Gilardi et al., PRL 88 (2002) 217003 (collaborative research with Swiss PSI)

 

Various systems in nature have their own characteristic lengths that describe their sizes. In general, the number of lengths characterizing a system depends on the type of system. However, sometimes the number of such characteristic lengths can be zero, i.e., systems lack the characteristic lengths. This type of system is called a "critical system". Critical systems are known to exist at the critical point of thermal or quantum phase transitions. It is also known that a system can spontaneously shift to a critical state in many of non-equilibrium and nonlinear processes in various physical, biological, and social phenomena. Many such critical systems can be observed in nature, as in surface irregularities of ground, living tissue, and the universe. Metric geometry for critical structures is known as fractal geometry, and has long been studied. However, there have been few cases in which critical structures were studied from the topological perspective. This project tries to understand and elucidate properties of critical systems and mechanisms of self-organization of systems developing into critical states, from the viewpoint of network topology. We will also establish methods for quantitative analyses of topological structures observed in a variety of interesting systems obtained in the "Topological Materials Project" and the "Novel Topology-Related Technologies Project". In practice, we have several avenues of investigation:

A mode pattern of fractons, which are localized vibrational excitations on a critical percolation network.

 

This project aims to analyze the topological structures of various networks found in biological systems, and to elucidate the relationships with biological phenomena.

One major theme is the elucidation of the relationships between tissue anomalies and topology. For instance, it is known that the topology of networks produced by tissue anomalies, as represented by cancer tissue, is different from the networks of normal tissues. As a method to characterize these networks, we will carry out analysis using their topological properties. In cooperation with the Novel topology-related technologies project, we will develop technology to visualize the tissue and extract its topological structure. The establishment of this technology may enable us to identify and diagnose cancer tissues without surgical operations.

Another theme of the life science topology studies is to elucidate the spatial topological recognition mechanism of the slime mold (myxomycete) network. Slime mold can freely change its shape, and is known to change its shape by recognizing the topology of its environment. As shown in the figures, when two feeders (AG) were provided to the slime mold plasmodia (marked yellow in Figure a), which was widely spread throughout the maze (approximately 4 cm square), the slime mold shrank its body in approximately 4 hours (as shown in Figure b), to the shortest route (as shown in Figure c), and gathered at the two feeders. This body shape enables the most efficient nutrient absorption possible. Therefore, the slime mold successfully solved the given maze, and obtained the nutrients. This project probes the topological mechanism of the ability to derive the shortest route, which can be considered a type of intelligence of the slime mold.

There are many other phenomena that suggest relationships between the statistical physical properties of various life system networks and their topologies. For instance, it is known that neural networks and the spin glass system have a complementary relationship, and it is possible that topological properties have some effect on memory efficiency. In addition, the network topology of life system interactions will have a substantial effect on the collective motion of those systems. We will explore the basis of life system topology underlying such relationships.

Optical and acoustic measurement can be used to extract a wide variety of physical properties in a non-contact and non-destructive way, by controlling wavelength, intensity, phase, direction of polarization, bandwidth, pulse width, or other parameters. This project will develop new measurement, analysis and processing technologies using light and sound; these technologies will become the basic tools for our studies in Topological Science and Technology. Take an example from the medical field: it is known that the topology of the networks produced by cancer or other tissue anomalies is different from that of normal tissue. To extract this network topology, we will develop technology to visualize tissue, making the most of the advantageous features of optical and acoustic measurement. By combining this technology with the network topology invariant analysis method of the Topology in Relation to Critical Phenomena and the Topology in the Life Sciences projects, we aim to develop non-contact and non-invasive quantitative diagnostic methods. By visualizing not only the static topology of the network, but also its time variation and in-vivo material flow, this should lead to new techniques in tissue anomaly identification and diagnosis. We will also develop other practical technologies based on the combination of topology and optical technologies: Topological Quantum Information, involving the combination of quantum information with the concepts of topology, is a project concerned with the solution of complex quantum superposition and interference problems involving photons. For example, an optical quantum gate to control the Berry phase will be constructed, a topological variable used to solve such problems.

Basic technologies for these projects have already been developed by our group members. For example, the technology for the real-time visualization of surface acoustic waves excited on a (planar) solid surface using laser pulses of femtosecond (10-15 second) duration has been developed. This technology will be extended to allow the real time visualization and analysis of the propagation of surface acoustic waves on spherical, ring-like, or other curved surfaces. The aim in this case is to ascertain how differences in topology affect the propagation of surface acoustic waves.

Visualization of surface waves excited on a (planar) solid surface.

 

http://www.topo.hokudai.ac.jp/en/sousei/b4.html