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.
In the shearing simulations the configurations are always generated from one
another and it is then interesting to examine how quickly various properties change with
this shearing and thus what the correlations look like. The original motivation for this
study was to get knowledge that helps to make the simulations more efficient, but it
turned out that the study also led to other interesting findings.
[slow-fast-lett] Peter Olsson
Slow and fast particles in shear-driven
jamming: critical behavior and finite size scaling arXiv:2209.13361
Here,
and in the longer paper next below, I describe a new analysis which I
consider to be a true breakthrough in this field. It has long been known that scaling
analyses of the shear viscosity need two different terms. It is here
shown that these two terms are related to two different processes - the fast process and
the slow process - respectively dominated by the faster and the slower particles. The fast
process is behind the leading divergence in the viscosity whereas the slow process is
responsible for the diverging correlation length. This understanding
also turns out to be the key to a successful finite size scaling analysis. The study
focuses on the velocity distribution which was also examined in an
earlier work.
Peter Olsson
Relaxation times, rheology, and finite size effects for non-Brownian
disks in two dimensions Phys. Rev. E
105, 034902 (2022), pdf
This is my response to a direct attack [Y. Nishikawa, A. Ikeda, and
L. Berthier, J. Stat. Phys. 182, 37 (2021)] on the methods I have been using to determine
the critical behavior. I think it is fair to say that I sorted things out in great detail
and showed that the criticism was groundless.
Yann-Edwin Keta, Peter Olsson
Translational and rotational velocities in shear-driven jamming of ellipsoidal particles Phys. Rev. E
102, 052905 (2020), pdf
This is a study in three dimensions of a collection of ellipsoidal particles
and the differences in the dynamics due to the asphericity. (Unlike most of our
simulations we here use a model where the dissipation of energy is due to velocity
differences at contacts.) It is found that already the aspect ratio α=1.02 (where
α=1 for spheres) leads to a dramatically different dynamics, especially so for
small shear strain rates γ̇. We argue that this finding is most likely an effect of
the quartic modes that are present in collections of non-spherical particles. We also find
evidence for a crossover to a large aspect ratio region, with a somewhat different
behavior, for α≥1.2.
A determination of the dynamical length scales in shear-driven jamming. A big
surprise is that there actually are two length scales, respectively related to the
rotation and the divergence of the velocity field.
This is a study of two different systems:
frictionless, two-dimensional spherocylinders and three-dimensional ellipsoids. The main
finding is that the nematic order parameter in both these systems remains finite at
jamming and above even as α→0. (Here α is the asphericity
parameter which is α=0 for spherical particles.)
The main message of this letter is that the viscosity exponent is different
in three dimensions than in two dimensions. This analysis has received quite some
criticism but we believe that a better understanding is needed to resolve that
discussion. A new understanding of shear-driven jamming is
proposed here.
The study relies on two different methods: (1) A scaling analysis of
pressure and (2) studies of the relaxation dynamics which gives values of the
relaxation time τ versus the contact number deficiency, δz≡zc-z.
Daniel Vagberg, Peter Olsson, S. Teitel
Shear banding, discontinuous shear thickening, and rheological phase transitions in athermally sheared frictionless disk Phys. Rev. E
95, 052903 (2017), pdf
Daniel Vagberg, Peter Olsson, S. Teitel
Effect of collisional elasticity on the Bagnold rheology of sheared frictionless two-dimensional disks Phys. Rev. E
95, 012902 (2017), pdf
Daniel Vagberg, Peter Olsson, S. Teitel
Critical Scaling of Bagnold Rheology at the Jamming Transition of Frictionless Two Dimensional Disks Phys. Rev. E
93, 052902 (2016), pdf
This is a study of the velocity distribution at the jamming density
φJ. The velocity in question is the non-affine velocity which is the particle
velocity relative to a uniform shearing field.
Two results: (1) As jamming is approached, i.e. as the shear strain rate goes to zero at
φ=φJ, the dissipation - and thereby the shear stress - is dominated by a small
fraction of very fast particles. (2) Because of the wide distribution of velocities it
turns out that <v> and <v2> behave differently such that
<v>2≠<v2>. This is possible only because there is no limiting
distribution as γ̇→0.
Yegang Wu, Peter Olsson, S. Teitel
Search for Hyperuniformity in Mechanically Stable Packings of Frictionless Disks Above Jamming Phys. Rev. E
92, 052206 (2015), pdf.
This paper
pioneered the use of two-step simulations where one starts from a configuration obtained
in shearing simulations, stops the shearing and lets the systems relax to almost zero
energy. From each such relaxation one then determines the relaxation time τ1 and the
contact number deficiency, δz1≡zc-z1, which is obtained from the final
configuration. Since this is a way to reach the hard disk limit (non-overlaping particles)
it becomes very straightforward to analyze the results from such simulations.
Fathollah Varnik, Suvendu Mandal, Vijaykumar Chikkadi, Dmitry Denisov, Peter Olsson, Daniel Vågberg, Dierk Raabe, and Peter Schall
Correlations of plasticity in sheared glasses Phys. Rev. E
89, 040301(R) (2014), pdf
Daniel Vågberg, Yegang Wu, Peter Olsson, and S. Teitel
Pressure Distribution and Critical Exponent in Statically Jammed and Shear-Driven Frictionless Disks Phys. Rev. E
89, 022201 (2014), pdf
Peter Olsson and S. Teitel
Athermal Jamming vs Thermalized Glassiness in Sheared Frictionless Particles Phys. Rev. E
88, 010301 (2013), pdf
Daniel Vågberg, Daniel Valdez-Balderas, M. A. Moore, Peter Olsson, S. Teitel
Finite-Size-Scaling at the Jamming Transition: Corrections to Scaling and the Correlation Length Critical Exponent Phys. Rev. E
83, 030303(R) (2011), pdf
Daniel Vågberg, Peter Olsson, and S. Teitel
Glassiness, Rigidity and Jamming of Frictionless Soft Core Disks Phys. Rev. E
83, 031307 (2011), pdf
