How to simulate a potential barrier?

[shad0w2000]

Hi,

I am doing simulations on a particle in some potential together with a fluctuating force and friction. To do that, I use the Langevin equation with the fluctuating force being a random number from a normal distribution with a temperature-dependent variance. I use a Verlet-algorithm for the calculation of position, velocity and acceleration (x,v and a) at each timestep.

My problem is how I can implement a high potential barrier - basically a wall. What I tried so far was to change the sign of x and v once it happens that x<0 (I have the barrier at x=0, and a linear potential at x>0).

But this gives unrealistic results, the particle goes way to far away from the barrier at very low temperatures - it looks like the particle in some way gets quite much energy when it hits the wall.

Does anyone have some suggestion on how to implement such a barrier? Or help me explain why my current method fails?

I can mention it probably isn't problems with the Verlet-algorithm itself or something else, since it yields very nice results if I use a harmonic potential.

Let me know if you need more information :)

 

[eljose79]

Hi there,

Thank you for sharing your question and for providing some background information on your simulation. From what I understand, you are trying to simulate a particle in a potential with a fluctuating force and friction, and you are using the Langevin equation with a Verlet-algorithm for the calculation of position, velocity, and acceleration. However, you are having trouble implementing a high potential barrier, as your current method of changing the sign of x and v when x<0 is giving unrealistic results.

One potential reason for this could be that the random number from the normal distribution with temperature-dependent variance is causing the particle to gain too much energy when it hits the wall. This could be due to the fact that the variance is temperature-dependent, meaning that at low temperatures, the particle is more likely to receive a larger force from the fluctuating force, leading to a higher energy. One solution could be to adjust the variance of the fluctuating force to be temperature-independent, so that the particle receives a more consistent force regardless of temperature.

Another potential issue could be with the implementation of the barrier itself. It may be helpful to consider the dynamics of a particle hitting a potential barrier in real life, and try to replicate that in your simulation. For example, when a particle hits a wall, it should experience a sudden change in momentum, rather than just a change in direction. This could be achieved by adding an additional term to your Langevin equation that takes into account the barrier's effect on the particle's momentum.

I hope these suggestions are helpful in addressing your issue with implementing a high potential barrier in your simulation. If you need further assistance, please don't hesitate to provide more information or ask for clarification. Good luck with your research!

 

[astrokreng]

there are several ways you could approach simulating a potential barrier. One possible solution could be to use a potential function that includes a barrier term, such as a step function or a Gaussian potential. This would allow you to explicitly define the location and strength of the barrier and incorporate it into your Langevin equation.

Another approach could be to use a Monte Carlo simulation, where you randomly generate the position and velocity of the particle at each timestep and then use the Langevin equation to update its position and velocity. This method would allow you to easily incorporate a potential barrier by simply adjusting the probability of the particle crossing the barrier at each timestep.

Additionally, it may be helpful to consider the physical properties of the system you are simulating. Are there any other forces or interactions at play that could be affecting the behavior of the particle near the barrier? Are there any other parameters that could be adjusted to better reflect the real-world conditions?

Ultimately, it may be a matter of trial and error and fine-tuning your simulation until you are satisfied with the results. It may also be beneficial to consult with other scientists or experts in the field for their insights and suggestions on simulating a potential barrier.