Peter Olsson

Associate professor in theoretical physics
e-mail: Peter.Olsson@tp.umu.se
phone: +46 90 786 5046
 

Introduction

I study the jamming transition with computer simulations of idealized mathematical models. The concept of jamming - think traffic jam - is the slowing down of the dynamics as the density increases up to the jamming density, where motion is no longer possible. This transition may be thought of as a liquid to solid transition but it is unusual in the sense that the solid is as disordered as the liquid - an ordinary liquid-to-solid transition is from a disordered liquid to an ordered solid - and it is not easy to see exactly what is going on in the transition.

To study this transition we are doing simulations in two, three, and four dimensions. For the two-dimensional case we are mostly using circular disks of two different sizes. The disks interact when they are in contact with a force that is proportional to the particle overlaps and the motion of a given particle is given by the total force on that particle due to all its contacting particles. The simulations are mostly done with 65 536 particles in long runs where the simulation cell is slowly sheared and a key quantity is the viscosity, which is the resistance against this shearing. As the solid phase is approached the viscosity increases rapidly and the value of the exponent that describes this increase, and its dependence on the dimensionality, is a highly disputed subject.
Shearing of a configuration with N=64 particles for illustration purposes; most of other works are with N=65536 particles. The figure shows configurations for γ=0.0, γ=0.1, and γ=0.2. The simulations are performed with periodic boundary conditions and with particles of two different sizes to avoid crystallization. Note that it is possible to shear indefinitely since a sufficiently rhombic simulation cell may be transformed into a square cell.
In the absense of particle contacts the particles get a homogenous shear velocity vi=yiγ̇x̂. In the presence of particle contacts that give a total force fi the total velocity becomes vi=Cfi + yiγ̇x̂, where the constant is usually taken to be C=1. The force between particles i and j in contact is commonly taken to be proportional to the particle overlaps.

In our (Olsson and Teitel) first work on jamming we showed that the shear strain rate, γ̇, is a relevant variable in the renormalisation group sense, which means that the shear-driven jamming transition is perfectly sharp only in the limit γ̇→0. This also implies a critical scaling assumption that has been used in several works. It was however soon realized that one also needs to use a correction-to-scaling term to fit the data and recent works have shown that the correction term is related to the slower particles, seen as a peak in the velocity distribution.

Recent papers


Umeå University
Department of Physics
Theoretical Physics
Last changed on September 22, 2023