Particles in a Periodic Potential

a java simulation by Xiao-Gang Wen

Back to Back to the course .

**The Model**:

Each particle feels four kinds of forces

- Uniform driving force
*F=(Fx,Fy)* - Periodic force
*F=(Va*sin(6.28*x), Va*sin(6.28*y))* - Random force
*F=Vr*Vr0([x],[y])*(sin(6.28*x), sin(6.28*y))*, where*Vr0(i,j)*is a random function ranging from*-0.5*to*+0.5* - Coulomb force
*F=50/(r1-r2)^2*

If one sets the uniform force

**Usage:**

- +N/-N: change the number of particles by 1, and restart the simulation.
- +Fx/-Fx, +Fy/-Fy: change the strength and the direction of the uniform driving force.
- OnOff: turn-on/turn-off the uniform force.
- +Va/-Va: change the strength of the periodic force (which comes from a periodic potential).
- +Vr/-Vr: change the strength of the random force
- restart: restart the simulation.
- +Dt/-Dt: change the size of time step (and the speed of simulation). Reduce Dt when simulation becomes unstable.

- Set
*Fx=Fy=0, Va=8, Vr=0*. Then set N=40.

*You will see that the 40 particles settle into a pretty random pattern.* - Set
*Fx=Fy=4*, and hit "restart".

*Very often, the 40 particles will settle into one of two very regular patterns (symmetry breaking and driven to order) which allow them to flow in x or y direction (although the force is in the x+y direction).* - Increase
*Fx*(or*Fy*) to a large value and reduce it back to 4.

*You can cause a phase transition between the two flow patterns.*

Back to Back to the course .