Jamming! Jamming everywhere!

traffic jam

I wonder, what you think of jamming, when you first see the word without context. Hackers, electronics people probably think of jamming radio signals. Decrease the signal-to-noise ratio and prevent two devices to talk with each other. There are many usages to this word but I will focus on the physics sense of jamming.

In physics jamming is the process of increasing viscosity of granular particles (e.g. coffee beans, sand) with increasing density. When certain granular materials (granular means composed of grains or smaller objects) become denser, they undergo a so called phase transition. Phase transition is a fancy word for changing phase of the material such as from gas to liquid or from solid to liquid. The idea is that if the grains become denser, friction between grains slows them down and prevent the change of neighbors (other grains). If there is no change or slowed down change of neighbors, whole material from outside acts more viscous or solid. You know this probably from a stuck hourglass or squeezed fine sugar, which takes the shape of the spoon. These are examples of jamming. Basically, sugar grains become so packed that they can’t “flow” anymore and stick on the side preserving its shape. Another form of jamming appears with foams. You can imagine each bubble as a particle or grain. When many bubbles are in a tight space together, they get packed and behave like a solid. Theoretically, due to gravity foam on a surface needs to flow down and spread. But, that doesn’t always happen and the foam can build tall vertical structures/shapes.

What gets me excited about this physical phenomenon is the it goes beyond simple physical examples. Actually, scientists use jamming to describe human movement, traffic and even biological tissues.

Let’s start with traffic. Traffic flow attracts mathematicians as many aspects of it and the behavior of traffic as an emergent phenomenon can be modeled and studied with mathematics. I am going to break down last sentence. Traffic flow is in a way very similar to particle physics or fluid dynamics. Each car can be modeled as a particle, which interacts with the surrounding particles. Although, drivers individually can be unpredictable, overall behavior converges on a predictable pattern. This predictability let’s mathematicians apply already well-known formulae of particle physics in order to make predictions about the flow of traffic. Reward of such studies are safer and more optimal traffic regulations.

Modeling traffic for intersections

An interesting similarity of cars with particles is that they both can jam. Literally, we call it “traffic jam” but why is it a jamming phenomenon really? Well, above I mentioned that increasing density increases the viscosity of liquids during jamming. Similarly, when cars come too close to each other, they tend to slow down. This sort of resembles particle friction. Cars don’t really rub against each other but drivers slow down to make sure that never happens. Additionally, when they need to accelerate, they need to wait for the front car to accelerate first, giving a comfortable space in between. If they could accelerate simultaneously, they would avoid jams. This happens in liquids with laminar flow. Molecules move together staying in their “lanes” quickly lowing. Cars can’t do that. Here is a nice explanation to this.

Local jams – snakes

The thing that makes this more like a physical jamming is that after a certain density, probability of jams occurring increases drastically. Because, more cars need to break and start causing small jams, which then fuse into congestion.

Car density and congestion

This is called phase transition. This diagram shows that if you increase the density by keeping temperature (energy or speed of particles, for cars this would mean something like driving speed and maneuver) and load (can be ignored for traffic), you can get jammed grains/traffic. Increasing speed doesn’t necessarily help, as drivers often drive as fast as they can (due to safety or rules). As the video above suggests, by decreasing the number of cars or increasing space, one can avoid this jamming transition.

Phase transition diagram proposed by Liu and Nagel (1998)

This thing about traffic is somewhat intuitive. How about human movement? Do humans jam? Before coming to that let’s appreciate this study, which shows that crowds at a marathon behave like a fluid. Crowds behaving like fluids in general was described much earlier. Or moshers at mosh pits at rock concerts behave similar to gasses. Now to the second question, can a crowd jam? Well… it seems so, especially, when they collide in large densities. This was demonstrated for counter flow in simulations. We also see how dangerous crowd jamming can occur during emergency evacuations. When large number of people rush to emergency exits at the same time, they might collectively block the exit and jam. This knowledge even helps us design better evacuation strategies by putting obstacles on the way. As much as this sounds counter intuitive, this helps the flow of people and avoid interparticle (interhuman) collisions.

Obstacles that direct particle flow to avoid jamming at bottlenecks. Frank & Dorso (2011)

For me maybe most fascinating jamming example are biological tissues/cells. Cells react to their environment, change their physical properties (shape, stiffness, motility etc.). Also they are often in an environment with many other cells. Individual behavior of each cell can emerge as an interesting and functional behavior at the tissue scale (e.g. muscle cells in an heart tissue collectively contracting and synchronizing). There are many of studies on the biophysics of cells. Particularly, tissue fluidity is relevant for development and cancer progression. Of course, when we have grains behaving like fluids, same question comes up, do they jam? It turns out to be, that cells jam too! I think it is worth noting here that cells are way more complex than grains of sand or coffee beans. In terms of interparticle interactions, they might even be more complex than humans. Cells may express a variety of receptors to sense neighboring cells, their types or other surrounding objects. They also react by changing their cytoskeleton (bunch of proteins giving the cells their shape, ability to move and more).

A very simplified view of how cells (pale blue areas) interact with their environment (extracellular matrix e.g. collagen) and other cells via receptors (blue-red pair e.g. integrins, green and brown) and cytoskeleton (red helical filaments e.g. actin filaments).

These environments are often packed densely. Below, you can see images of real tissues by multiphoton imaging (basically an advanced microscopy using infrared (IR) light to penetrate deeper into tissues).

Regular structures (aligned collagen fibers) are imaged with second harmonic generation (SHG) and water-lipid (oil/fat) boundaries are imaged third harmonic generation (THG). Remaining (green) structures are labeled with fluorescent chemicals, which absorb multiple low energy (IR) photons and emit one high energy photon (far red). Weigelin et al. (2016)

These environments don’t provide much comfortable space for cells to move, hence they need to squeeze and crawl. As for the cancer cells, this is a challenge to leave the site of primary tumor and metastasize (spread to other tissues). The same group, who took above picture, described that cancer cells can jam in such dense environments.

Cells are in green and cell nucleus in red. Authors generated either low density (2.5mg/ml) or low temperature polymerized (21°C) collagen to generate large porous collagen mesh. Haeger et al. (2014)

When spheroids of cancer cells are embedded in these meshes, they jam only at tightly porous collagen mesh (middle panel) but not in widely porous collagen or even increased collagen concentration with wide pores. Before this, another study showed that at boundaries between monolayers (a sheet of cells with a thickness of single cells) tissues show a jamming behavior. These findings are particularly important for us to understand how tissues maintain their structures during development but also how cancer cells manage to migrate out of their primary site of tumor and reach other places such as lymphatics and blood vessels. When they spread, are they collective or single cells?

Another more surprising jamming behavior was observed with lung epithelial cells. The idea is that when cells are packed, their shape may cause a transition between jammed and unjammed states. If the tissue is in an unjammed state, single cells can move through the tissue. Otherwise, they are trapped at their location. This was nicely animated by Lucy Reading for Quanta Magazine.

Lucy Reading-Ikkanda for Quanta Magazine

The beautiful thing is that the authors came up with a number (ratio between cell perimeter and square root of cell area), a threshold, at which such transitions occur. Furthermore, the implication of this is even medical.

Here is what authors observed: an epithelial tissue derived from a non-asthmatic patient tends to become jammed and behaves like a solid. When mechanical stress is applied, tissue becomes unjammed but then maturates to jam again. But if they look at tissues derived from asthmatic patients, this jamming is either delayed or completely absent. These states depend heavily on the ratio mentioned above, although the transitions are continuous, meaning cells become progressively slower/faster during transitions. I hope, I could get you excited about jamming. Maybe, one day you will think about this when you are in a traffic jam and feel like, “I have heard about this but it doesn’t help me at this moment”. 🙂