This simulation is done using SPH(Smoothed Particle Hydrodynamics), a meshless Lagrangian method. SPH represents fluid as a collection of individual particles and calculates the behavior of these particles based on their interactions with neighboring particles.
Simulating one of the iconic experiments, Young's double slit experiment. Here initial wavefunction of a particle is assumed to be Gaussian with known momentum(practically, its not possible), and the evolution of wavefunction is governed by Schrodinger's equations at each time step using the Crank-Nicolson numerical method.
This is a classic example of order from disorder. The key principle at play here is the law of large numbers. When a large number of random events (in this case, the bouncing of balls) occur, the overall outcome tends to converge towards a predictable pattern or average. Each individual ball's path may be unpredictable, but the collective behavior of many balls follows a consistent statistical distribution(bell curve).
This simple system is a physical analog of the Lorenz Attractor. Equations describing Lorenz Attractor turn out similar to set of equations describing this system.
Assume there is a tap at top of the wheel, water comes out at a constant rate from that tap and there is a hole at bottom of every bucket. So, water inside buckets drains out at a rate depending on amount of water at that time in that bucket.
If we simulate such system and trace the Center of Mass of it then a pattern like butterfly wings emerges.
It depends on the track length and starting position.
A tiny curvature in the boundary is sufficient to make it a chaotic system!
When bodies move in concentric circles with different speeds, then wrt to a body, another body appears traveling back while crossing each other. This motion is Retro(back)grade(step) motion. Such motion was when observed in the Mars, puzzled geocentric believers.
Being such a simple system, it is chaotic in nature!
Balls start at almost same postion but their trajectory rapidly diverges after few bounces.
This is a highly chaotic system. Initial position of rays are separated by order of 10^-8!! Still, after few reflections, they diverge rapidly to follow totally different paths.
This is a spring-pendulum internal resonance system.
The system will continue to switch between up and down motion like spring and to and fro motion like pendulum. It is due to the special frequency relation of 2:1 between spring frequency and pendulum frequency.
Initially, pendulum has an angular displacement from vertical of 0.001rad only.
These two springs start at positions differing at 3rd decimal place. After a while, they diverge rapidly and follow different path.
covid19.mp4This Simulation shows effect of vaccination on infection and death.
This interactive simulation shows all sorts of spin rotation.
Click to kick football.
An elegant way to demonstrate conservation of momentum.
