Our fourth class explored numerical simulation, a common computational tool for solving complex, many-body problems. In its most basic classical form, numerical computation is the process of solving for the position (x) and velocity (v) of every object of mass m in a system with a given force law (F) using Newton’s Laws of Motion, following a two-step iterative process:
Our third class was devoted to exploring random processes through random walks. Many physical processes in nature – diffusion, radiation, conduction, current flow, fluid dynamics – can be modeled as a random process. This is certainly true at the quantum mechanical level, where there is inherent uncertainty in the position-momentum of a particle due to its wave-like nature (modeled as a probability wave function); this is Planck’s Uncertainty Principle. But even in “deterministic” classical mechanics, randomness plays a role in modeling complexity; it is simply too hard to measure the precise state of every particle in a system and all of the forces involved. This is where statistical mechanics and thermodynamics become important.
For the second class, we used a model developed as Washington State University as part of the Energy Project called Energy Theater. The idea is to model a system entirely through its energy units, with those energy units being continued in parts in the system but able to transfer between parts and transform between energy types. This was our first outside session at the base of the UCSD Snake Path.
Our first class was based on the idea that physical quantities and the relationships between them (equations) can be represented in physical movement, as well as in symbolic form. This is based on some of Prof. Burgasser’s work exploring physical communication of physical concepts, which itself is rooted in research showing that we learn when we use our bodies.