What Does Hard-Point Core Interaction Mean in the Ding-a-Ling Model?

[dapias09]

Hi all,

I am studyng the "ding-a-ling" model for the Heat transfer in a 1D chain. Particularly, from this article:
http://polymer.chph.ras.ru/asavin/teplopr/mb97pre.pdf
I need help with the equation (1), I don't know specifically what the "hard-point core" interaction means. I was thinking that is related to infinite barriers of potential but not sure.
Also, I would like to get help with the equation (4), I was thinking that is related to equation (1) meaning that there is a collision whenever this condition is satisfied, and therefore the barrier of potential is infinite but I don't know, it's very weird that the collision is related to the size of lattice.

Really, I would appreciate your help.
Thanks in advance.

 

[eljose79]

Hello,

Thank you for bringing up this interesting topic. The "ding-a-ling" model is a simplified model for studying heat transfer in a 1D chain, where energy is transferred between neighboring particles through collisions. The "hard-point core" interaction refers to the assumption that the particles in the chain are hard spheres, meaning they cannot overlap or pass through each other. This assumption is important in understanding the collisions between particles and how energy is transferred.

In equation (1), the "hard-point core" interaction is represented by the delta function, which describes the instantaneous collision between two particles. This means that when two particles come into contact, they exchange energy instantaneously, without any time delay. The delta function also takes into account the size of the particles, which is why the size of the lattice is related to the collision in equation (4).

I hope this helps clarify the concept of "hard-point core" interaction in the "ding-a-ling" model. If you have any further questions, please don't hesitate to ask. Good luck with your studies!