Home » AT force field is fully open! How to avoid being hit by others in a crowded station passage? —— 2021 Ig Nobel Prize in Physics-PanSci

AT force field is fully open! How to avoid being hit by others in a crowded station passage? —— 2021 Ig Nobel Prize in Physics-PanSci

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No, but the Langevin formula is the protagonist today.

In the past two years, the whole world has been caused by COVID-19 (particularly severe infectious pneumonia, new crown pneumonia, Wuhan pneumonia). In addition to vaccines, “masks, hand washing, and social distancing” can be called “three artifacts of physical epidemic prevention.” We just passed the second Mid-Autumn Festival holiday under the epidemic situation. Seeing the crowds of people in major transportation hubs, we can’t help but worry. How can we maintain social distance when we are crowded into such a virtue?

The recently awarded “31st First” Ig Nobel Prize in Physics in 2021 is also related to “social distancing”: How can everyone avoid each other in a crowded passage to avoid collisions and pass through?

Before the epidemic, everyone’s experience of encountering such situations in their lives should be very frequent. Anyway, they just follow the flow of people. Some people squeeze past and flash each other (and then lie inwardly…sometimes), and go through an uncomfortable one. After the process, it usually passes smoothly.

But is there a way to understand this kind of process that seems simple in life in terms of physics?

The mainstream of physics is “reductionism”: I hope to use the simplest theory to explain various phenomena. For example, in classical physics, a Newton’s second law “F = ma” is used to explain how objects move, and Maxwell’s four equations are used to explain all phenomena of electricity, magnetism, and light. The ultimate goal of physicists is to find a “The Theory of everything” that can understand the past, present and future of the entire universe with an equation. The so-called “everything”, of course, includes “human behavior”!

But scholars in other fields don’t take this set! For example, “human social behavior” involves fields such as neuroscience, psychology, and sociology.Every field is very complicated, how can it be studied with the reductionism of physics?

The physicist doesn’t care about this, just do it first!A research team composed of Eindhoven University of Science and Technology in the Netherlands, California State University Long Beach and the University of Vergata in Italy discussed the “pedestrian dynamics in congested station passages.” Among them, the member of California State University is Professor Chung-min Lee, a female scientist from Taiwan.

The game console becomes an efficient attitude sensor!

The researchers installed the four Microsoft TV game X-BOX, an image capturing peripheral device “Kinect” used to capture the player’s body gestures and movements, above the passage of the Eindhoven train station to record the dynamics of the crowd passing through the passage. One end of this passage is the city center, and the other end is the bus terminal.

Figure 1: (a) The channel plan of Eindhoven station and the configuration of Kinect sensor (K). (b) In the real photo, four Kinect sensors can be seen on the white beam above.

Using these four pedestrian images captured by Kinect, combined with image recognition and tracing algorithms, each pedestrian entering the screen can be calibrated at the same time, and its trajectory can be tracked all the way until it leaves the screen.From October 2014 to March 2015, the whole system continuously recorded for six months, and got a total of about 5 million pedestrian trajectories.

The data is too complicated?Don’t worry, physicists are best at “reduction”

These records are truly complex human behaviors: some are going straight ahead, some are swaying from side to side, some are turning halfway for some reason, and some are really colliding with others… how do physicists play their “reductionist” qualities, Simplify these complex behaviors into mathematical forms that can be analyzed?

The method adopted by the research team is to use this as long as six months,The accumulated videos of millions of pedestrians coming and going are transformed into a “graph” composed of a set of “nodes” and the edges between nodes.

Each node in the figure represents a pedestrian and related information when passing through the passage, such as the direction of travel and the length of the track. If two pedestrians (nodes) appear in the same screen at the same time, the two nodes are connected by a line. The information of this line includes which two nodes it connects, the maximum and minimum distance between the two nodes, At the same time the time on the screen and so on.

Figure 2: The image is transformed into a graph. Each node (represented by a circle with a number) is a pedestrian. If two pedestrians are in the camera at the same time, there will be a line. (a) Schematic diagram of the original image transferred from the image. This image can be divided into four sub-images. (b) Remove the connection between the two nodes that are too far apart and are unlikely to affect each other even though there are simultaneous entry into the mirror (indicated by the dashed line) to simplify the graph even further. (c) A subgraph with “only one line connecting two nodes”. (d) The direction of travel is the same, there is no need to consider collision avoidance, so the connection is removed. (e) The last remaining “two-node subgraph”. Figures/References 1

Suppose a situation is as follows (please show your patience and look at Figure 2(a)): the first pedestrian was captured by the camera at dawn, then the second pedestrian came in behind ①, ① left the screen, ③ and ④ walk in from both sides. After ② and ③ leave the screen, a train enters the station. ⑤⑥⑦ enters the screen one by one, and then everyone leaves. The only gap in the middle is ⑧ passing alone, and then another train comes in. ⑨~⑫ enter the lens together, and the last person who left the lens ⑫ came in immediately before the lens appeared, ⑫ after leaving, ⑭⑮ entered, and then ⑬⑭⑮ came out of the lens one after another, and then ⑯ passed alone.

Looks a bit annoying, right?

But when converted to the notation shown in Figure 2(a), is it clear at a glance? This is the power of “reduction”. Even so, there will be more than 5 million nodes on the graph accumulated over six months, and the number of connections between nodes may be tens of millions, which is still very complicated. However, we can split this large graph into several “subgraphs”: each subgraph contains nodes that can be connected to each other into a piece, and there is no connection between different subgraphs.

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Taking Figure 2(a) as an example, it can be divided into four subgraphs: 1. Node ①~⑦; 2. Node ⑧; 3. Node ⑨~⑮; 4. Node ⑯. Only the nodes inside the subgraph may interact with each other.

However, even if the entire super-large graph with millions of nodes is split into many subgraphs with a small number of nodes, it may still be difficult to analyze. For example, “Subgraph 1” in Figure 2(a) contains seven nodes, which needs to be analyzed. How these seven pedestrians interact and how to adjust their routes to each other is still too complicated. Considering the actual situation, it can be further simplified:

Even if two people appear in the screen at the same time, if the distance is very long or the contact time is short, it is almost impossible to affect each other, so remove the connection between the two people, Such as the previous example “⑫ ⑬ came in moments before the camera”, you can remove the connection. As shown in Figure 2(b), after removing this too weak connection (indicated by the dashed line), the graph will be divided into more and smaller subgraphs. Taking Figure 2(b) as an example, it becomes 8 subgraphs, the largest of which has only four nodes.

Next, this paper will only discuss the two simplest subgraphs: those with only one node, such as ⑧, ⑬, and ⑯ in Figure 2(b), and the two nodes ①②, ③④, and ⑭⑮, as shown in Figure 2( c) ~ (e). Among them, ①② is in the same direction, and there is no need to avoid collisions, so this link is also removed, and it becomes a single node subgraph with each order.

In fact, there are a total of 47,122 “single-node subgraphs” and a total of 9089 “dual-node subgraphs”.

A Editor’s Note: In Figure 2 (a), the “number on the node” represents “the order of entering the shot”, and the “connection between nodes” represents “whether two people appear on the same screen at the same time”, a graph composed in this way 2 (a), it is possible to clearly distinguish which sequences are likely to collide.

Then analyze each connection in detail. If the distance is too far or the contact time is too short, collision or dodge behavior is impossible. The connection that meets this condition is set as a “dashed line” to form Figure 2 (b).

Finally, consider in Figure 2 (b), each node with a solid line connection direction, if the two nodes are in the same direction, there will be no collision or dodge behavior, you can eliminate the need for analysis, and get Figure 2 (e) picture.

Although we physicists often boast that physics is very powerful, in fact we can solve the exact answer to the mechanics problem, only “the movement of one particle” and “the movement of two interacting particles”. The motion of particles interacting with each other is no more. There can only be approximate solutions or numerical simulations. That’s why science fiction works like “Three Body” will appear!

Three, four, five…the problem of particles, physicists can’t count it,But when the number of particles is tens of thousands or more, “thermodynamics” comes on the scene. Physics can answer “the average behavior of many particles” and use it to explain phenomena such as heat, temperature, and pressure.

Back to the topic, human behavior is obviously much more complicated than the mass point, so it is quite reasonable to start with the behavioral model of “one person” and “two people interacting with each other”, and use this as a basis to explore the “collective behavior of many people”. Strategy.

The pedestrian trajectory is actually not a straight line, it is zigzag like dust in the water

Start with the simplest “kinetics of a person”. Without the influence of other people, the trajectory of pedestrians will mostly show a small amplitude “jitter” with a frequency of about 1 Hz (once per second). This is easy to understand because of this. It is about the pace of human beings; in addition, a few trajectories will have relatively large shaking, and even turn their heads and walk back. The research team found that this behavioral pattern is similar to “Brownian motion”-when small objects such as pollen and dust are placed in the water, they will be bumped by running water molecules and then run around.

In that case, let’s try the “Langevin equation” that explains Brownian motion (yes, that’s the Langevin who had an affair with the great Marie Curie)!

The so-called Langevin equation is actually very simple.It is to add “fluid resistance” and “random force” to the “intrinsic tendency of motion” of the object.

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What is the “original tendency” of these pedestrians?Because this is a passage connecting the two ends, whether it is to save energy or in a hurry, most people follow the direction of the parallel passage from one end to the other end with the shortest distance, instead of walking diagonally; the second is the majority. People walk at normal speeds, but there are also a considerable proportion of people who are fast walking or jogging because they are in a hurry. Their average speeds are 1.29 and 2.70 meters per second (converted to speeds of 4.64 and 9.72 kilometers per hour). Finally, they are in both directions. Someone is going.The above “movement tendency” can be written as the equation of Newton’s second law of motion.

Then there is the “fluid resistance”. When a pedestrian starts to deviate from the original route, he will receive a resistance proportional to the speed perpendicular to the original direction, to “push” the person back to the original route.

It may be helpful for you to walk on crowded walkways like Taipei Main Station:Two-way pedestrians will form a “laminar flow” structure, and people walking in the same direction will automatically line up to move forward. This is a way of walking with less resistance and less effort.If you deviate from the team you are in, it may friction or even collide with the team next door and make it difficult to pass, so unless there is a strong reason to change the path, otherwise we will naturally return to the original path.

Finally, there is the “random power”. Other pedestrians around us are in situation at any time. Those who stop to take things, the route is suddenly crooked, the ankle is twisted, the one who forgets to turn back… We must look around and listen to all directions. Respond to these conditions at any time to avoid possible collisions and also cause changes in the path.

After writing down the equation of motion, you can simulate it in the computer and compare it with the real behavior of the pedestrian captured by the camera. The result came out,Human behavior may be no better than the dust in the air, the pollen in the water…

Figure 3: The statistical distribution of pedestrian velocity in (a) the direction of pedestrian flow in parallel aisles, (b) the velocity perpendicular to the direction of pedestrian flow, and (c) the degree of deviation from the path. Comparison of actual observation results (red dots) and computer simulation data (black circles). Figures/References 1

Figure 3 shows the movement statistics of those “single nodes” (not affected by others) that are “walking towards the bus stop at the beginning”. The red dots are the real behaviors captured by the camera, and the black circles are simulated by the Langevin equation. result.

Figure 3(a) shows the velocity distribution in the direction of the parallel channel (the original movement tendency). It can be found that the real behavior is quite consistent with the simulation results!Most people go forward at a speed of 1.29 meters per second, and a few people use running, so there is a small peak at a speed exceeding two meters per second, and a very small number of people will go back (the speed is negative). The captured feature is in the vicinity of zero velocity (stop).Because pedestrians occasionally stop on the road for a variety of reasons, but the tiny particles in Brownian motion can only measure the velocity of zero at the moment of turning.

Figure 3(b) is the velocity perpendicular to the direction of travel (fluid resistance), Figure 3(c) is the distance from the original travel route (random force), and both are quite consistent.

The conclusion is: if the density of pedestrians is quite sparse and there is no need to avoid each other, the behavior of pedestrians is basically similar to the Brownian motion of pollen in the water, which can be simulated by the Langevin equation.

The next step is to consider“Two people are close to each other and need to avoid each other, but there is no one else nearby to disrupt the situation.”, Which is the situation shown in Figure 4.

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Figure 4: A schematic diagram of two pedestrians approaching each other avoiding each other. The gray solid lines are their original predetermined paths, and the black solid lines are the actual routes taken, which will be a bit random, but basically in the same direction as the predetermined paths. (i) After discovering that they may collide with each other, start to adjust the path and change to the dashed line. , When (ii) the two are closest, the distance is d at this time, (iii) pass and then move away from each other, and adjust the path to be parallel to the channel, but there is a translation with the original predetermined path . Figures/References 1

The two people who are close to each other in Figure 4, the original predetermined path, that is, the distance between the two solid gray lines is too close. Open the path distance to avoid collision(In reality, there will be two people who are tacitly flashing to the same side, changing sides at the same time, and changing sides at the same time…the hilarious scene that has never been dazzling, but this paper does not discuss it), and then move away from each other.

Since the real path is twisted and twisted, and everyone starts to turn at different times, we once again brought into play the spirit of “reductionism” and simplified Figure 4 to Figure 5.

Figure 5: A simplified schematic diagram of the two AB approaching, avoiding, and staying away from each other. Figures/References 1

We use the Cartesian coordinate system to define the direction of the passage (also the direction of the movement of people) as the X direction, and the vertical X is the Y direction. When everyone moves along the X direction, “will it collide” is from the Y direction Determined by the distance. When two people enter the screen, the distance between the two paths is Δyi, The distance between the two passing by is Δys, The distance of the path after far away is Δye

In terms of the physical model, it is necessary to add the “two-person interaction force” to the “one person’s Langevin model”. This force is divided into two parts:

  1. “Long-range force” of “Long-range force when I saw someone coming from afar, I should be ready to flash”
  2. “Short-range force” of “Knocked down by fast flash”

Both can be written using mathematical functions and added to equations to become “the Langevin model of two people.”

The research team measured the Δy of all the “two-node subgraphs”i,Δys,Δyie; At the same time, the behavior of pedestrians was simulated on the computer with the “Langevin Model of Two People” and the three values ​​were measured, and then e(Δys) Vs. Δyi , Where e(Δys) Corresponds to the same Δyi All of Δys The average value of; and e(Δye) Vs. Δys The relationship diagrams of are shown in Figure 6 (a) and (b).

Once again, real-world pedestrian behavior (red dot) and computer simulation (dotted line) are quite consistent. In addition, this model can even predict the frequency of “collision” very accurately. Is it true that human behavior really follows the wave of Brownian motion? !

Figure 6: (a) The relationship between the average distance between two people passing by and the distance of the starting path. (b) The relationship between the average distance of the path after two people move away from each other and the distance when they pass by. The red dot is human behavior in the real world, the dotted line is the computer simulation result, and the dotted line passing through the origin is the situation where two people walk straight forward without changing direction. Figures/References 1

Everyone has an AT force field with a radius of 1.4 meters

It is worth noting that when Δyi When it is small, the two people approaching each other will start to adjust the direction, pull the distance apart, so that when the two pass by, they will not collide (Δy> 0.6m).Interestingly, this phenomenon changes from Δyi < 1.4m 就開始發生,在 0.6m~1.4m 這個範圍內,即使不改變方向,也不會撞到,但是這個距離已經夠近,讓人感到「個人領域受到侵犯」的威脅,而開始迴避對方,把距離拉開。

In other words, in a crowded passage, the “reassuring social distance” is 1.4 meters (I really want to call it “AT-Field Absolute Field”…), we don’t want to let strangers get close Within this distance. I want to remind you thatThis is the average value of “a lot of people’s behavior,” and not everyone has the same value.

Although it is said that he was awarded the “Immortal Nobel Prize”, the research process was very rigorous and not funny at all.This research also shows that the thoughts and behaviors of individuals are very complicated, and the interactions between people are very complicated. However, on average, the behaviors of a large number of people may present simple patterns, which can be used in the “reductionism” of physics. “Methods to understand “human group behavior.”

Of course, this is still quite preliminary research, and the crowds moving in the station are just a very simple phenomenon in human social behavior, so there is still a long way to go if you want to use the methodology of physics to study social sciences. (And social scientists may also be unhappy).

However, as the Internet of Things is becoming more and more popular today, all kinds of human activities are converted into a large amount of data and accumulated. It can be foreseen that the ways of studying human behavior will become more and more diversified. In the end, will there be a “psychohistory” like Asimov’s sci-fi classic “base series”, which can predict the future destiny of mankind and reverse its direction? Let’s continue to watch-

references

  1. Alessandro Corbetta, Jasper A. Meeusen, Chung-min Lee, Roberto Benzi, and Federico Toschi, Physics-based modeling and data representation of pairwise interactions among pedestrians, Phys. Rev. E 98, 062310 (2018).

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