自推进粒子算法

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Self-propelled particles (SPP), also referred to as self-driven particles, are terms used by physicists to describe autonomous agents, which convert energy from the environment into directed or persistent motion. Natural systems which have inspired the study and design of these particles include walking, swimming or flying animals. Other biological systems include bacteria, cells, algae and other micro-organisms. Generally, self-propelled particles often refer to artificial systems such as robots or specifically designed particles such as swimming Janus colloids, nanomotors and walking grains. In the case of directed propulsion, which is driven by a chemical gradient, this is referred to as chemotaxis, observed in biological systems, e.g. bacteria quorum sensing and ant pheromone detection, and in synthetic systems, e.g. bimetallic nanorods and enzyme molecule chemotaxis.

Self-propelled particles (SPP), also referred to as self-driven particles, are terms used by physicists to describe autonomous agents, which convert energy from the environment into directed or persistent motion. Natural systems which have inspired the study and design of these particles include walking, swimming or flying animals. Other biological systems include bacteria, cells, algae and other micro-organisms. Generally, self-propelled particles often refer to artificial systems such as robots or specifically designed particles such as swimming Janus colloids, nanomotors and walking grains. In the case of directed propulsion, which is driven by a chemical gradient, this is referred to as chemotaxis, observed in biological systems, e.g. bacteria quorum sensing and ant pheromone detection, and in synthetic systems, e.g. bimetallic nanorods and enzyme molecule chemotaxis.

自推进粒子(SPP)Self-propelled particles ,也被称为自驱动粒子,是物理学家用来描述自治体的术语,它将环境中的能量转化为定向运动或持续运动。激发这些粒子研究和设计灵感的自然系统包括行走、游泳或飞行的动物。其他生物系统包括细菌、细胞、藻类和其他微生物。一般来说, 自推进粒子(SPP) 通常指的是人工系统,如机器人或专门设计的粒子,如游动的 金纳斯Janus胶体、纳米马达和行走颗粒 。在由化学梯度驱动的定向推进的情况下,这被称为 趋化性 Chemotaxis,可以在生物系统中观察到,例如细菌群体感应和蚂蚁信息素检测,以及在合成系统中观察到,例如双金属纳米棒和酶分子趋化性。



Overview概述

Self-propelled particles interact with each other, which can lead to the emergence of collective behaviours. These collective behaviours mimic the self-organization observed with the flocking of birds, the swarming of bugs, the formation of sheep herds, etc.

自推进粒子(SPP) 之间相互作用,会导致集体行为的出现。这些集体行为模仿了鸟类结群、虫子结群、羊群形成等过程中观察到的自组织现象。


To understand the ubiquity of such phenomena, physicists have developed a number of self-propelled particles models. These models predict that self-propelled particles share certain properties at the group level, regardless of the type of animals (or artificial particles) in the swarm.[1] It has become a challenge in theoretical physics to find minimal statistical models that capture these behaviours.[2][3][4]

To understand the ubiquity of such phenomena, physicists have developed a number of self-propelled particles models. These models predict that self-propelled particles share certain properties at the group level, regardless of the type of animals (or artificial particles) in the swarm.

为了理解这种现象的普遍性,物理学家们开发了许多自推进粒子模型。这些模型预测,无论群体中的动物(或人工粒子)类型如何, 自推进粒子(SPP) 在群体水平上都具有某些特性。

Examples 样例

Biological systems 生物系统

Most animals can be seen as SPP: they find energy in their food and exhibit various locomotion strategies, from flying to crawling. The most prominent examples of collective behaviours in these systems are fish schools, birds flocks, sheep herds, human crowds. At a smaller scale, cells and bacteria can also be treated as SPP. These biological systems can propel themselves based on the presence of chemoattractants. At even smaller scale, molecular motors transform ATP energy into directional motion. Recent work has shown that enzyme molecules will also propel themselves.[5] Further, it has been shown that they will preferentially move towards a region of higher substrate concentration,[6] a phenomenon that has been developed into a purification technique to isolate live enzymes.[7] Additionally, microparticles can become self-propelled when they are functionalized with enzymes. The catalytic reactions of the enzymes direct the particles based on corresponding substrate gradients.[8]

Most animals can be seen as SPP: they find energy in their food and exhibit various locomotion strategies, from flying to crawling. The most prominent examples of collective behaviours in these systems are fish schools, birds flocks, sheep herds, human crowds. At a smaller scale, cells and bacteria can also be treated as SPP. These biological systems can propel themselves based on the presence of chemoattractants. At even smaller scale, molecular motors transform ATP energy into directional motion. Recent work has shown that enzyme molecules will also propel themselves. Further, it has been shown that they will preferentially move towards a region of higher substrate concentration, a phenomenon that has been developed into a purification technique to isolate live enzymes. Additionally, microparticles can become self-propelled when they are functionalized with enzymes. The catalytic reactions of the enzymes direct the particles based on corresponding substrate gradients.

大多数动物可以被视为 自推进粒子(SPP) :它们在食物中寻找能量,并表现出从飞行到爬行等各种各样的运动策略。在这些系统中,集体行为最突出的例子是鱼群、鸟群、羊群和人群。在较小的范围内,细胞和细菌也可以被视为SPP。这些生物系统可以基于化学引诱剂的存在而自我推进。在更小的尺度上,分子马达将ATP能量转化为定向运动。最近的研究表明,酶分子也会推动自己。此外,已经证明它们将优先向更高底物浓度的区域移动,这一现象已发展成为分离活酶的纯化技术。此外,当微粒被酶功能化时,可以自我推进。酶的催化反应根据相应的底物梯度引导粒子。


Artificial systems 人造系统

thumb | SPP的一个例子:金铂纳米棒由于自身电泳力在过氧化氢中经历自我推进。| 400x400px

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There is a distinction between wet and dry systems. In the first case the particles "swim" in a surrounding fluid; in the second case the particles "walk" on a substrate.

干湿系统是有区别的。在第一种情况下,粒子在周围的流体中“游动”;在第二种情况下,粒子在基质上“行走”。

Active colloidal particles, dubbed nanomotors, are the prototypical example of wet SPP. Janus particles are colloidal particles with two different sides, having different physical or chemical properties. This symmetry breaking allows, by properly tuning the environment (typically the surrounding solution), for the motion of the Janus particle. For instance, the two sides of the Janus particle can induce a local gradient of, temperature, electric field, or concentration of chemical species. This induces motion of the Janus particle along the gradient through, respectively, thermophoresis, electrophoresis or diffusiophoresis. Because the Janus particles consume energy from their environment (catalysis of chemical reactions, light absorption, etc.), the resulting motion constitutes an irreversible process and the particles are out of equilibrium.

Active colloidal particles, dubbed nanomotors, are the prototypical example of wet SPP. Janus particles are colloidal particles with two different sides, having different physical or chemical properties. This symmetry breaking allows, by properly tuning the environment (typically the surrounding solution), for the motion of the Janus particle. For instance, the two sides of the Janus particle can induce a local gradient of, temperature, electric field, or concentration of chemical species. This induces motion of the Janus particle along the gradient through, respectively, thermophoresis, electrophoresis or diffusiophoresis. Because the Janus particles consume energy from their environment (catalysis of chemical reactions, light absorption, etc.), the resulting motion constitutes an irreversible process and the particles are out of equilibrium.

被称为 纳米马达 的活性胶体颗粒是湿SPP的典型例子。 Janus粒子 是具有两个不同侧面的胶体颗粒,具有不同的物理或化学性质。通过适当调整环境(通常是周围的解决方案),这种对称性破坏允许Janus粒子的运动。例如,Janus粒子的两侧可以引起局部温度、电场或化学物质浓度的梯度。这分别通过热泳、电泳或扩散电泳诱导Janus粒子沿梯度运动。由于Janus粒子消耗来自其环境的能量(化学反应的催化作用、光吸收等),因此产生的运动构成不可逆过程,粒子失去平衡。

  • The first example of an artificial SPP on the nano or micron scale was a gold-platinum bimetallic nanorod developed by Sen and Mallouk.[9] In a solution of hydrogen peroxide, this "nanomotor" would exhibit a catalytic oxidation-reduction reaction, thereby inducing a fluid flow along the surface through self-diffusiophoresis. A similar system used a copper-platinum rod in a bromine solution.[10]
  • 第一个纳米或微米级人工SPP的例子是由 Sen和Mallouk开发的金-铂双金属纳米棒。[11] 在过氧化氢溶液中,这种“纳米马达”将表现出催化氧化还原反应,从而通过自扩散电泳诱导流体沿表面流动。类似的系统在溴溶液中使用铜铂棒。[12]
  • Another Janus SPP was developed by coating half of a polystyrene bead with platinum. These were used to direct the motion of catalytic motors when they were close to a solid surface. These systems were able to move the active colloids using geometric constraints.[13]
  • 另一种Janus SPP是在聚苯乙烯珠的一半上涂上铂制成的。当催化马达接近固体表面时,它们被用来引导其运动。这些系统能够利用几何约束移动活性胶体。[14]
  • Another example of a Janus SPP is an organometallic motor using a gold-silica microsphere.[15] Grubb's catalyst was tethered to the silica half of the particle and in solution of monomer would drive a catalytic polymerization. The resulting concentration gradient across the surface would propel the motor in solution.
  • Janus SPP的另一个例子是使用金硅微球的有机金属马达。[16]格拉布斯催化剂Grub催化剂被拴在颗粒的一半二氧化硅上,单体在溶液中的存在会促进催化聚合。由此产生的表面浓度梯度将电机推动在溶液中。
  • Another example of an artificial SPP are platinum spinner microparticles that have controllable rotations based on their shape and symmetry.[17]
  • 人造SPP的另一个例子是铂自旋微粒,其具有基于其形状和对称性的可控旋转。[18]
  • Several other examples are described in the nanomotor-specific page.
  • 纳米马达<维基>特定页面中描述了其他几个示例。


Walking grains are a typical realization of dry SPP: The grains are milli-metric disks sitting on a vertically vibrating plate, which serves as the source of energy and momentum. The disks have two different contacts ("feet") with the plate, a hard needle-like foot in the front and a large soft rubber foot in the back. When shaken, the disks move in a preferential direction defined by the polar (head-tail) symmetry of the contacts. This together with the vibrational noise result in a persistent random walk.[19]

Walking grains are a typical realization of dry SPP: The grains are milli-metric disks sitting on a vertically vibrating plate, which serves as the source of energy and momentum. The disks have two different contacts ("feet") with the plate, a hard needle-like foot in the front and a large soft rubber foot in the back. When shaken, the disks move in a preferential direction defined by the polar (head-tail) symmetry of the contacts. This together with the vibrational noise result in a persistent random walk.

行走的谷粒是干SPP的典型实现:谷粒是位于垂直振动板上的毫米圆盘,作为能量和动量的来源。磁盘有两个不同的接触(“脚”)与板,一个硬针一样的脚在前面和一个大软橡胶脚在后面。摇动时,圆盘沿由触点极性(头尾)对称性定义的优先方向移动。这与振动噪声一起导致持续的随机游走。


Typical collective behaviour典型的集体行为

Typical collective motion generally includes the formation of self-assembled structures, such as clusters and organized assemblies.

Typical collective motion generally includes the formation of self-assembled structures, such as clusters and organized assemblies.

典型的集体运动一般包括自组装结构的形成,如集群和有组织的集会。


The prominent and most spectacular emergent large scale behaviour observed in assemblies of SPP is directed collective motion. In that case all particles move in the same direction. On top of that, spatial structures can emerge such as bands, vortices, asters, moving clusters.

在SPP集合中观察到的突出和最壮观的突发大规模行为是定向的集体运动。在这种情况下,所有粒子都朝着同一方向运动。最重要的是,空间结构可以出现,如带,漩涡,星群,移动团簇。

The prominent and most spectacular emergent large scale behaviour observed in assemblies of SPP is directed collective motion. In that case all particles move in the same direction. On top of that, spatial structures can emerge such as bands, vortices, asters, moving clusters.

在 SPP 的集合体中观察到的最突出和最壮观的大规模行为是定向集体运动。在这种情况下,所有的粒子都朝同一个方向运动。最重要的是,空间结构可以出现,如带状,涡旋,紫苑,移动星团。


Another class of large scale behaviour, which does not imply directed motion is either the spontaneous formation of clusters or the separation in a gas-like and a liquid-like phase, an unexpected phenomenon when the SPP have purely repulsive interaction. This phase separation has been called Motility Induced Phase Separation (MIPS).

Another class of large scale behaviour, which does not imply directed motion is either the spontaneous formation of clusters or the separation in a gas-like and a liquid-like phase, an unexpected phenomenon when the SPP have purely repulsive interaction. This phase separation has been called Motility Induced Phase Separation (MIPS).

另一类并不意味着定向运动的大尺度行为,要么是团簇的自发形成,要么是类气体和类液体相的分离,这是 SPP 纯粹排斥作用时一个意想不到的现象。这种相分离被称为运动诱导相分离Motility Induced Phase Separation(MIPS)

Examples of modelling 建模示例

The modeling of SPP was introduced in 1995 by Tamás Vicsek et al.[20] as a special case of the Boids model introduced in 1986 by Reynolds.[21] In that case the SPP are point particles, which move with a constant speed. and adopt (at each time increment) the average direction of motion of the other particles in their local neighborhood up to some added noise.[22][23]{{External media

The modeling of SPP was introduced in 1995 by Tamás Vicsek et al. as a special case of the Boids model introduced in 1986 by Reynolds. In that case the SPP are point particles, which move with a constant speed. and adopt (at each time increment) the average direction of motion of the other particles in their local neighborhood up to some added noise.{{External media

SPP的建模由Tamás Vicsek等人于1995年引入,作为雷诺兹Reynolds于1986年引入的博伊德Boids模型的特例。在这种情况下,SPP是以恒定速度移动的点粒子。并采用(在每一时间增量)其他粒子在其局部邻域的平均运动方向以及一些附加的噪声。模板:外部媒体

|video1=SPP model interactive simulation
– needs Java}}

| video1 = [ http://phet.colorado.edu/sims/self-driven-particle-model/self-driven-particle-model_en.jar /SPP 模型交互模拟] < br/>-needs Java }

Simulations demonstrate that a suitable "nearest neighbour rule" eventually results in all the particles swarming together, or moving in the same direction. This emerges, even though there is no centralised coordination, and even though the neighbours for each particle constantly change over time (see the interactive simulation in the box on the right).[20]

Simulations demonstrate that a suitable "nearest neighbour rule" eventually results in all the particles swarming together, or moving in the same direction. This emerges, even though there is no centralised coordination, and even though the neighbours for each particle constantly change over time (see the interactive simulation in the box on the right). This can be the prelude to the development of the vast flying adult locust swarms which devastate vegetation on a continental scale.

模拟结果表明,一个合适的“最近邻规则”最终会导致所有粒子聚集在一起,或朝着同一方向移动。即使没有集中的协调,即使每个粒子的邻域随时间不断变化(请参见右侧框中的交互式模拟),也会出现这种情况。这可能是巨大的飞蝗成虫群发展的前奏,这些蝗群摧毁了整个大陆的植被。[20]

One of the key predictions of the SPP model is that as the population density of a group increases, an abrupt transition occurs from individuals moving in relatively disordered and independent ways within the group to the group moving as a highly aligned whole. Thus, in the case of young desert locusts, a trigger point should occur which turns disorganised and dispersed locusts into a coordinated marching army. When the critical population density is reached, the insects should start marching together in a stable way and in the same direction.

SPP模型的一个关键预测是,随着种群密度的增加,个体在群体内以相对无序和独立的方式移动,到群体作为一个高度一致的整体移动,会发生突变。因此,对于年轻的沙漠蝗虫来说,应该有一个触发点,把散乱的蝗虫变成一支协调一致的队伍。当达到临界种群密度时,昆虫应开始以稳定的方式向同一方向行进。

Since then a number of models have been proposed, ranging from the simples so called Active Brownian Particle to highly elaborated and specialized models aiming at describing specific systems and situations. Among the important ingredients in these models, one can list

从那时起,许多模型被提出,从简单的所谓的活动布朗粒子到高度精细化和专门化的模型,旨在描述特定的系统和情况。在这些模型的重要组成部分中,可以列出

  • Self-propulsion: in the absence of interaction, the SPP speed converges to a prescribed constant value
  • 自推进:在没有相互作用的情况下,SPP速度收敛到规定的恒定值
  • Body interactions: the particles can be considered as points (no body interaction) like in the Vicsek model. Alternatively one can include an interaction potential, either attractive or repulsive. This potential can be isotropic or not to describe spherical or elongated particles.
  • 体相互作用:粒子可以被认为是点(没有体相互作用),就像在维切克模型。或者可以包括相互作用势,吸引或排斥。这种势可以是各向同性的,也可以不描述球形或细长粒子。

In 2006, a group of researchers examined how this model held up in the laboratory. Locusts were placed in a circular arena, and their movements were tracked with computer software. At low densities, below 18 locusts per square metre, the locusts mill about in a disordered way. At intermediate densities, they start falling into line and marching together, punctuated by abrupt but coordinated changes in direction. However, when densities reached a critical value at about 74 locusts/m2, the locusts ceased making rapid and spontaneous changes in direction, and instead marched steadily in the same direction for the full eight hours of the experiment (see video on the left). This confirmed the behaviour predicted by the SPP models.

2006年,一组研究人员研究了这个模型在实验室中的表现。蝗虫被放在一个圆形的竞技场里,并用计算机软件跟踪它们的行动。在低密度,低于每平方米18只蝗虫,蝗虫以一种无序的方式四处游动。在中等密度时,它们开始排成一行,并排行进,不时有方向上的突然但协调的变化。然而,当密度达到一个临界值,约为74只蝗虫/m2时,蝗虫停止了方向上的快速自发变化,而是在整个8小时的实验中稳定地向同一方向行进(见左边的视频)。这证实了SPP模型预测的行为。


  • Body orientation: for those particles with a body-fixed axis, one can include additional degrees of freedom to describe the orientation of the body. The coupling of this body axis with the velocity is an additional option.
  • 体定向:对于那些具有固定体轴的粒子,可以包含额外的自由度来描述体的定向。这个体轴与速度的耦合是一个附加选项。
  • Aligning interaction rules: in the spirit of the Vicsek model, neighboring particles align their velocities. Another possibility is that they align their orientations.
  • 排列相互作用规则:根据维切克模型的精神,相邻粒子排列它们的速度。另一种可能是他们调整方向。

In the field, according to the Food and Agriculture Organization of the United Nations, the average density of marching bands is 50 locusts/m2 (50 million locusts/km2), with a typical range from 20 to 120 locusts/m2.

在野外,根据联合国粮农组织统计,蝗虫群的平均密度为50只/m < sup > 2 (5000万只/km < sup > 2 ) ,典型蝗虫数量为20ー120只/m < sup > 2 。

One can also include effective influences of the surrounding; for instance the nominal velocity of the SPP can be set to depend on the local density, in order to take into account crowding effects.

还可以包括周围环境的有效影响;例如,SPP的标称速度可以设置为取决于局部密度,以便考虑拥挤效应。


In 2010, Bhattacharya and Vicsek used an SPP model to analyse what is happening here. As a paradigm, they considered how flying birds arrive at a collective decision to make a sudden and synchronised change to land. The birds, such as the starlings in the image on the right, have no decision-making leader, yet the flock know exactly how to land in a unified way. The need for the group to land overrides deviating intentions by individual birds. The particle model found that the collective shift to landing depends on perturbations that apply to the individual birds, such as where the birds are in the flock. It is behaviour that can be compared with the way that sand avalanches, if it is piled up, before the point at which symmetric and carefully placed grains would avalanche, because the fluctuations become increasingly non-linear.

2010年,Bhattacharya和Vicsek使用SPP模型来分析这里发生的事情。作为一个范例,他们考虑了飞鸟是如何做出集体决定,做出突然而同步的改变而降落的。这些鸟,如右图中的椋鸟,没有决策的领导者,但它们知道如何以统一的方式降落。群体降落的需要压倒了个别鸟类的偏离意图。粒子模型发现,集体迁移到着陆取决于对个别鸟类的扰动,例如鸟类在群中的位置。这种行为可以与沙子崩塌的方式相比较,(也即)如果沙子堆积起来,在对称和小心放置的颗粒崩塌之前,因为波动而变得越来越非线性。


Some applications to real systems实际系统的一些应用

"Our main motivation was to better understand something which is puzzling and out there in nature, especially in cases involving the stopping or starting of a collective behavioural pattern in a group of people or animals ... We propose a simple model for a system whose members have the tendency to follow the others both in space and in their state of mind concerning a decision about stopping an activity. This is a very general model, which can be applied to similar situations."

“我们的主要动机是更好地理解自然界中令人困惑的东西,特别是在涉及停止或开始一群人或动物的集体行为模式的情况下... ... 我们提出了一个简单的系统模型,其成员在决定停止一项活动时,在空间和精神状态上都倾向于跟随其他人。这是一个非常通用的模型,可以应用于类似的情况。”

模板:External media


Marching locusts行军蝗虫

Young desert locusts are solitary and wingless nymphs. If food is short they can gather together and start occupying neighbouring areas, recruiting more locusts. Eventually they can become a marching army extending over many kilometres.[24] This can be the prelude to the development of the vast flying adult locust swarms which devastate vegetation on a continental scale.[25]

年轻的沙漠蝗虫是孤独和无翼的若虫。如果食物短缺,他们可以聚集在一起,开始占领邻近地区,招募更多的蝗虫。最终他们可以成为一支绵延数公里的行军巨大的飞蝗成虫群在大陆范围内破坏植被的发展前奏。[25]

One of the key predictions of the SPP model is that as the population density of a group increases, an abrupt transition occurs from individuals moving in relatively disordered and independent ways within the group to the group moving as a highly aligned whole.[26] Thus, in the case of young desert locusts, a trigger point should occur which turns disorganised and dispersed locusts into a coordinated marching army. When the critical population density is reached, the insects should start marching together in a stable way and in the same direction.

SPP模型的一个关键预测是,随着群体的种群密度增加,个体在群体内以相对无序和独立的方式移动,突然转变为群体作为高度一致的整体移动。[26] 因此,对于年轻的沙漠蝗虫来说,应该有一个触发点,把散乱的蝗虫变成一支协调一致的队伍。当达到临界种群密度时,昆虫应开始以稳定的方式向同一方向行进。

In 2006, a group of researchers examined how this model held up in the laboratory. Locusts were placed in a circular arena, and their movements were tracked with computer software. At low densities, below 18 locusts per square metre, the locusts mill about in a disordered way. At intermediate densities, they start falling into line and marching together, punctuated by abrupt but coordinated changes in direction. However, when densities reached a critical value at about 74 locusts/m2, the locusts ceased making rapid and spontaneous changes in direction, and instead marched steadily in the same direction for the full eight hours of the experiment (see video on the left). This confirmed the behaviour predicted by the SPP models.[1]

2006年,一组研究人员研究了这个模型在实验室中的表现。蝗虫被放在一个圆形的竞技场里,并用计算机软件跟踪它们的行动。在低密度,低于每平方米18只蝗虫,蝗虫以一种无序的方式四处游动。在中等密度时,它们开始排成一行,并排行进,不时有方向上的突然但协调的变化。然而,当密度达到一个临界值,约为74只蝗虫/m时,蝗虫停止了方向上的快速自发变化,而是在整个8小时的实验中稳定地向同一方向行进(见左边的视频)。这证实了SPP模型预测的行为。[1]

In the field, according to the Food and Agriculture Organization of the United Nations, the average density of marching bands is 50 locusts/m2 (50 million locusts/km2), with a typical range from 20 to 120 locusts/m2.[25]:29 The research findings discussed above demonstrate the dynamic instability that is present at the lower locust densities typical in the field, where marching groups randomly switch direction without any external perturbation. Understanding this phenomenon, together with the switch to fully coordinated marching at higher densities, is essential if the swarming of desert locusts is to be controlled.[1]

在野外,根据联合国粮食及农业组织,行军带的平均密度为50蝗虫/m2(5000万蝗虫/km2),典型范围为20至120蝗虫/m2[25]:29 上面讨论的研究结果表明,在野外典型的蝗虫密度较低时,行军群体在没有任何外部扰动的情况下随机切换方向,存在动态不稳定性。如果要控制沙漠蝗虫的蜂拥,了解这一现象以及在更高密度下转向完全协调的行军是必不可少的。[1]

Bird landings鸟类登陆

文件:The flock of starlings acting as a swarm. - geograph.org.uk - 124593.jpg
Flocks of birds can abruptly change their direction in unison, and then, just as suddenly, make a unanimous group decision to land[27]

拇指|右|成群的鸟可以突然一致地改变方向,然后,就像突然一样,集体一致决定降落[28]

Swarming animals, such as ants, bees, fish and birds, are often observed suddenly switching from one state to another. For example, birds abruptly switch from a flying state to a landing state. Or fish switch from schooling in one direction to schooling in another direction. Such state switches can occur with astonishing speed and synchronicity, as though all the members in the group made a unanimous decision at the same moment. Phenomena like these have long puzzled researchers.[29]

成群的动物,如蚂蚁、蜜蜂、鱼和鸟,经常被观察到突然从一种状态切换到另一种状态。例如,鸟类突然从飞行状态切换到着陆状态。或者鱼从一个方向的学校转向另一个方向的学校。这样的状态转换可以以惊人的速度和同步性发生,就好像团队中的所有成员在同一时刻做出了一致的决定。像这样的现象一直困扰着研究人员。[29]

In 2010, Bhattacharya and Vicsek used an SPP model to analyse what is happening here. As a paradigm, they considered how flying birds arrive at a collective decision to make a sudden and synchronised change to land. The birds, such as the starlings in the image on the right, have no decision-making leader, yet the flock know exactly how to land in a unified way. The need for the group to land overrides deviating intentions by individual birds. The particle model found that the collective shift to landing depends on perturbations that apply to the individual birds, such as where the birds are in the flock.[27] It is behaviour that can be compared with the way that sand avalanches, if it is piled up, before the point at which symmetric and carefully placed grains would avalanche, because the fluctuations become increasingly non-linear.[30]

2010年,Bhattacharya和Vicsek使用SPP模型来分析这里发生的事情。作为一个范例,他们考虑了飞鸟是如何做出集体决定,做出突然而同步的改变降落的。这些鸟,如右图中的椋鸟,没有决策的领导者,但它们知道如何以统一的方式降落。群体降落的需要压倒了个别鸟类的偏离意图。粒子模型发现,集体迁移到着陆取决于对个别鸟类的扰动,例如鸟类在群中的位置。[27]这种行为可以与沙子崩塌的方式相比较,例如沙子堆积起来,在对称和小心放置的颗粒崩塌之前,因为波动变得越来越非线性。[31]


"Our main motivation was to better understand something which is puzzling and out there in nature, especially in cases involving the stopping or starting of a collective behavioural pattern in a group of people or animals ... We propose a simple model for a system whose members have the tendency to follow the others both in space and in their state of mind concerning a decision about stopping an activity. This is a very general model, which can be applied to similar situations."[27] The model could also be applied to a swarm of unmanned drones, to initiating a desired motion in a crowd of people, or to interpreting group patterns when stock market shares are bought or sold.[32]

“我们的主要动机是更好地理解一些令人费解的自然现象,特别是在涉及停止或启动一群人或动物的集体行为模式的情况下。。。对于一个系统,我们提出了一个简单的模型,该系统的成员在空间和精神状态上都倾向于跟随其他成员,以决定是否停止某项活动。这是一个非常通用的模型,可以应用于类似的情况。”[27] 该模型还可以应用于一群无人无人机,在人群中发起所需的运动,或解释股票买卖时的群体模式。[32]

Other examples其他示例

SPP models have been applied in many other areas, such as schooling fish,[33] robotic swarms,[34] molecular motors,[35] the development of human stampedes[36] and the evolution of human trails in urban green spaces.[37] SPP in Stokes flow, such as Janus particles, are often modeled by the squirmer model.[38]

SPP模型已应用于许多其他领域,如鱼群[39] 机器人群s,[40] 分子马达s,[41] [[踩踏]人类踩踏事件]]的发展[42] 以及人类在城市绿地中的演化。[43] Stokes流中的SPP,如Janus粒子,通常用squirmer模型来模拟。[38]

See also请参阅

References参考文献

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Further references进一步参考

Category:Behavior

分类: 行为

Category:Complex systems theory

范畴: 复杂系统理论

Category:Ethology

分类: 行为学

Category:Scientific modeling

类别: 科学建模

Category:Multi-agent systems

类别: 多代理系统

Category:Zoology

分类: 动物学


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