I typed the following notes during Hiroki Sayama‘s presentation on “Phase separation and dynamic pattern formation in heterogeneous self-propelled particle systems.” Unfortunately, I couldn’t get a WiFi signal in the room where Sayama gave his talk, so I’m falling short of the gonzo science ideal, posting about the talk after it was given instead of as it occurs.
Sayama is speaking about particle swarm systems, and the phase-separation and dynamic pattern formation behaviors they exhibit. He adds the novel feature of heterogeneity to the particle system. Research on self-propelled particles goes back to Reynolds (1987), Vicsek et al. (1995), Aldana et al. (2003), Chuang et al. (2006), etc. Reynolds was a computer scientist who created a method for simulating bird flocking, which developed into the simulation which created the bats in the otherwise unremarkable Batman Begins. Vicsek and Aldana were physicists.
These systems show collective behaviors such as random clustering, coherent motions and milling. The same system can exhibit all of these behaviors, depending upon the input parameters. Cranking up the noise can induce phase transitions. Almost all of this work focused on homogeneous particle systems, in which all particles share the same kinetic particles. What, then, would happen if two or more types of self-propelled particles were mixed together?
Sayama works in a framework he calls Swarm Chemistry, which is implemented as a Java applet that can be run online.
His particle model is partly based on Reynolds’ famous Boids. It uses simple, semi-autonomous particles moving in a continous 2D open space; each particle has a finite range of perception, within which it can sense the position and velocity of its local neighbors. A salient feature of these particles’ behavior is that conservation laws are not respected: for example, energy can be “pumped in” whenever the program decides that a particle should move faster. The basic rules are as follows:
- If no particles are found within the local perception range, the particles steer randomly.
- Otherwise, steer toward the average position of the local neighbor particles (cohesion), and steer toward their average velocity (alignment). Separation is achieved by steering to avoid collisions, and for a Whimsy factor, steer randomly with a given probability.
- Finally, each particle approximates its speed to its normal speed, to self-regulate.
The three parameters which will be varied are the strengths of the cohesive, aligning and separating forces. (These forces are programmed to fall off as the inverse square.) Varying these constants [tex]c_1[/tex], [tex]c_2[/tex] and [tex]c_3[/tex], two types of particles are randomly created, and each is simulated in isolation as well as in combination. After two hundred time steps, one measures the average linear and angular velocities, the average distance from the center of mass, and the local homogeneity. The last is the most nontrivial: one averages over all particles the probability of finding the same type of particle within the six nearest neighbors. An [tex]H[/tex] near 1.0 implies phase separation; one almost always finds spontaneous phase separation, even though the particles can’t tell which species their neighbors are. Often, this phase separation creates multilayer structures, such as a circle of one species surrounded by a concentric ring of the other.
Mixing two types can also create an emergent motion which is not seen in either species individually. The reasons for this are not yet fully understood.
After Sayama’s talk followed two on measures of information transfer. My notes will require more post-processing to turn them into an intelligible explanation, so I’ll beg off for now with a list of references:
- X. San Liang and Richard Kleeman. “Information Transfer between Dynamical System Components” Physical Review Letters 95, 24 (2005): 244101.
- “A rigorous formalism of information transfer between dynamical system components. I. Discrete mapping” Physica D 227 (2007): 173–82.
- “A rigorous formalism of information transfer between dynamical system components. II. Continuous flow” Physica D 231 (2007): 1–9.