[MUSIC] Hi and welcome to our class, Simulation and Modeling of Natural Processes. This weeks class will be about the simulation of particles and other point-like objects. The systems we are going to simulate can be very small, like the molecules which we simulate at nanoscale. Or it can be a very big system, like the stars which we simulate inside the galaxy. The common properties of the system we are going to talk about is some more cases we simulate equations of classical Newtonian mechanics. The difficulty does not come from the physical matter itself, but from the fact that we will have a lot, a big amount of objects which are going to interact. It will be a challenge on the side of the numerical simulation to treat this big system. We're going to talk about different systems, the difference of which consist in the type of potential describing the physics of the interaction between the objects at hand. We're going to talk about numerics, about the algorithmic complexity of the numerical resolution of the systems. And about some possible workarounds and simplifications which makes it possible to simulate these systems. The first module will provide you with an overview over the different systems, particles and other point like objects, we are going to consider. For the first system we will show you this simulation of two galaxies, which collide. The physics of the simulation you are seeing here, is actually extremely simple. We just have a large amount of stars which are modeled as points. A single point which interacts with each other with the laws of gravity. This type of system is known as the n-body problem, where n is the number of stars which interact with each other. In this example, a very simple interaction, the interaction of gravity between a large amount of points leads to a complex interaction, an interaction of collision between two galaxies. What you have observed here is actually going to be the fate of our galaxy. Which is going to collide very soon in only 2 billion years with the Andromeda galaxy. Of course, during such a collision, there is no actual collision between stars, because there is a huge empty space between stars. All that's happening in such a collision is that the stars changed their orbit. Which means that even if you manage to still be alive in 2 billion years, which is highly unlikely, nobody will be hurt by this collision between our galaxy and the Andromeda galaxy. You have seen the first interesting property in this example of the systems you are going to treat. Which is that we treat a large amount of objects as single points, which means we describe the state of these points by their single position, and possibly speed, and maybe some simple additional property. And they interact with each other due to a force which is given by the law at hand, in this case, the law of gravity. In all cases, these forces are Newtonian. This is also true in the second example I'm showing you here, which is the interaction of molecules with each other in a gas. Here we zoom into a gas at nano scale. Again, the gas molecules are modeled as single point like particles. Represented by their instantaneous position and by velocity. As opposed to stars, the molecules don't see each other all the time, because they interact with each other only at a very short range. Most of the time as a consequence of youth and very slow which we are going to see shortly. The molecules just travel along straight directories through empty space. And they interact with each other only when collision between molecules occur. During collision, they change their direction, and potentially their momentum, and continue to travel through empty space on straight path. The third example I would like to show you, is a little bit more complex one, which we have seen before in the lecture about method. Here, the particles, forcing objects we are modeling, are the red blood cells in a section of a human artery. In this section, you have several billion red blood cells. This is a huge amount which makes it impossible to model red blood cells with all their properties. In reality, red blood cells have a complex tree. They are formable. They interact with each other through chemical, biological, and physical processes. But here, we model them, a single point like object which are embedded in the flow, which is the bloodstream. And which interact with each other as a consequence of simple laws. In particular, here, we modeled blood clotting. Which is the aggregation of red blood cells along the wall of the artery. Particle and other point-like object appear in the most unexpected situations and are crucial ingredient to computational science. This is the end of our first module, the overview of a particle and point-like object. Stay tuned for the next module. [MUSIC]
