arXiv subjects

Peter Olsson

Publications and source records attributed to Peter Olsson.

At least 19 recordsLinked to original sources

arXiv2024

Considerations on the relaxation time in shear-driven jamming

We study the jamming transition in a model of elastic particles under shear at zero temperature, with a focus on the relaxation time $τ_1$. This relaxation time is from two-step simulations where the first step is the ordinary shearing simulation and the second step is the relaxation of the energy after stopping the shearing. $τ_1$ is determined from the final exponential decay of the energy. Such relaxations are done with many different starting configuration generated by a long shearing simulation in which the shear varible $γ$ slowly increases. We study the correlations of both $τ_1$, determined from the decay, and the pressure, $p_1$, from the starting configurations as a function of the difference in $γ$. We find that the correlations of $p_1$ are more long lived than the ones of $τ_1$ and find that the reason for this is that the individual $τ_1$ is controlled both by $p_1$ of the starting configuration and a random contribution which depends on the relaxation path length -- the average distance moved by the particles during the relaxation. We further conclude that it is $\gammatau$, determined from the correlations of $τ_1$, which is the relevant one when the aim is to generate data that may be used for determining the critical exponent that characterizes the jamming transition.

cond-mat.soft↗

arXiv2023

Slow and fast particles in shear-driven jamming: critical behavior and finite size scaling

We do shear-driven simulations of a simple model of non-Brownian particles in two dimensions. By examining the velocity distribution at different densities and shear rates we find strong evidence for the existence of two different processes, respectively dominated by the slower and the faster particles -- the slow process and the fast process. The leading divergence in the shear viscosity is governed by the fast process. An examination of height and position of the low-velocity peak in the distribution demonstrates that it is the slow process that is responsible for the correction-to-scaling term in the critical scaling analysis. We further find that the long range velocity correlations are primarily due to the slow process which implies that the diverging viscosity and the diverging correlation length are only indirectly related.

cond-mat.soft↗

arXiv2023

Slow and fast particles in shear-driven jamming: critical behavior

We do extensive simulations of a simple model of shear-driven jamming in two dimensions to analyze the velocity distribution at different densities $ϕ$ around the jamming density $ϕ_J$ and at different low shear strain rates, $\dotγ$. We then find that the velocity distribution is made up of two parts which are related to two different physical processes which we call the slow process and the fast process as they are dominated by the slower and the faster particles, respectively. Earlier scaling analyses have shown that the shear viscosity $η$, which diverges as the jamming density is approached from below, consists of two different terms and we present strong evidence that these terms are related to the two different processes: the leading divergence is due to the fast process whereas the correction-to-scaling term is due to the slow process. The analysis of the slow process is possible thanks to the observation that the velocity distribution for different $\dotγ$ and $ϕ$ at and around the shear-driven jamming transition, has a peak at low velocities and that the distribution has a constant shape up to and slightly above this peak. We then find that it is possible to express the contribution to the shear viscosity due to the slow process in terms of height and position of the peak in the velocity distribution and find that this contribution matches the correction-to-scaling term, determined through a standard critical scaling analysis. A further observation is that the collective particle motion is dominated by the slow process. In contrast to the usual picture in critical phenomena with a direct link between the diverging correlation length and a diverging order parameter, we find that correlations and shear viscosity decouple since they are controlled by different sets of particles and that shear-driven jamming is thus an unusual kind of critical phenomenon.

cond-mat.soft↗

arXiv2021

Relaxation times, rheology, and finite size effects

We carry out overdamped simulations in a simple model of jamming - a collection of bi-disperse soft core frictionless disks in two dimensions - with the aim to explore the finite size dependence of different quantities, both the relaxation time obtained from the relaxation of the energy and the pressure-equivalent of the shear viscosity. The motivation for the paper is the observation [Nishikawa et al., J. Stat. Phys, 182, 37 (2021)] that there are finite size effects in the relaxation time, $τ$, that give problems in the determination of the critical divergence, and the claim that this is due to a finite size dependence, $τ\sim\ln N$, which makes $τ$ an ill-defined quantity. Beside analyses to determine the relaxation time for the whole system we determine particle relaxation times which allow us to determine both histograms of particle relaxation times and the average particle relaxation times - two quantities that are very useful for the analyses. The starting configurations for the relaxation simulations are of two different kinds: completely random or taken from steady shearing simulations, and we find that the difference between these two cases are bigger than previously noted and that the observed problems in the determination of the critical divergence obtained when starting from random configurations are not present when instead starting the relaxations from shearing configurations. We also argue that the the effect that causes the $\ln N$-dependence is not as problematic as asserted. When it comes to the finite size dependence of the pressure-equivalent of the shear viscosity we find that our data don't give support for the claimed strong finite size dependence, but also that it is at odds with what one would normally expect for a system with a diverging correlation length, and that this calls for a novel understanding of the phenomenon of shear-driven jamming.

cond-mat.soft↗

arXiv2020

Dynamic length scales in athermal, shear-driven, jamming of frictionless disks in two dimensions

We carry our numerical simulations of athermally sheared, bidisperse, frictionless disks in two dimensions. From an appropriately defined velocity correlation function, we determine that there are two diverging length scales, $ξ$ and $\ell$, as the jamming transition is approached. We analyze our results using a critical scaling ansatz for the correlation function, and argue that the more divergent length $\ell$ is a consequence of a dangerous irrelevant scaling variable, and that it is $ξ$ which is the correlation length that determines the divergence of the system viscosity as jamming is approached from below in the liquid phase. We find that $ξ\sim (ϕ_J-ϕ)^{-ν}$ diverges with the critical exponent $ν=1$. We provide evidence that $ξ$ measures the length scale of fluctuations in the rotation of the particle velocity field, while $\ell$ measures the length scale of fluctuations in the divergence of the velocity field.

cond-mat.soft↗

arXiv2020

Translational and rotational velocities in shear-driven jamming of ellipsoidal particles

We study shear-driven jamming of ellipsoidal particles at zero temperature with a focus on the microscopic dynamics. We find that a change from spherical particles to ellipsoids with aspect ratio $α=1.02$ gives dramatic changes of the microscopic dynamics with much lower translational velocities and a new role for the rotations. Whereas the velocity difference at contacts---and thereby the dissipation---in collections of spheres is dominated by the translational velocities and reduced by the rotations, the same quantity is in collections of ellipsoids instead totally dominated by the rotational velocities. By also examining the effect of different aspect ratios we find that the examined quantities show either a peak or a change in slope at $α\approx1.2$, thus giving evidence for a crossover between different regions of low and high aspect ratio.

cond-mat.soft↗

arXiv2019

Orientational Ordering in Athermally Sheared, Aspherical, Frictionless Particles

We numerically simulate the uniform athermal shearing of bidisperse, frictionless, two dimensional spherocylinders and three dimensional prolate ellipsoids. We focus on the orientational ordering of particles as an asphericity parameter $α\to 0$ and particles approach spherical. We find that the nematic order parameter $S_2$ is non-monotonic in the packing fraction $ϕ$, and that as $α\to 0$ $S_{2}$ stays finite at jamming and above. The approach to spherical particles thus appears to be singular. We also find that sheared particles continue to rotate above jamming, and that particle contacts preferentially lie along the narrowest width of the particles, even as $α\to 0$.

cond-mat.soft↗

arXiv2018

Dimensionality and viscosity exponent in shear-driven jamming

Collections of bidisperse frictionless particles at zero temperature in three dimensions are simulated with a shear-driven dynamics with the aim to compare with behavior in two dimensions. Contrary to the prevailing picture, and in contrast to results from isotropic jamming from compression or quench, we find that the critical exponents in three dimensions are different from those in two dimensions and conclude that shear-driven jamming in two and three dimensions belong to different universality classes.

cond-mat.soft↗

arXiv2017

Shear banding, discontinuous shear thickening, and rheological phase transitions in athermally sheared frictionless disks

We report on numerical simulations of simple models of athermal, bidisperse, soft-core, massive disks in two dimensions, as a function of packing fraction $ϕ$, inelasticity of collisions as measured by a parameter $Q$, and applied uniform shear strain rate $\dotγ$. Our particles have contact interactions consisting of normally directed elastic repulsion and viscous dissipation, as well as tangentially directed viscous dissipation, but no inter-particle Coulombic friction. Mapping the phase diagram in the $(ϕ,Q)$ plane for small $\dotγ$, we find a sharp first-order rheological phase transition from a region with Bagnoldian rheology to a region with Newtonian rheology, and show that the system is always Newtonian at jamming. We consider the rotational motion of particles and demonstrate the crucial importance that the coupling between rotational and translational degrees of freedom has on the phase structure at small $Q$ (strongly inelastic collisions). At small $Q$ we show that, upon increasing $\dotγ$, the sharp Bagnoldian-to-Newtonian transition becomes a coexistence region of finite width in the $(ϕ,\dotγ)$ plane, with coexisting Bagnoldian and Newtonian shear bands. Crossing this coexistence region by increasing $\dotγ$ at fixed $ϕ$, we find that discontinuous shear thickening can result if $\dotγ$ is varied too rapidly for the system to relax to the shear-banded steady state corresponding to the instantaneous value of $\dotγ$.

cond-mat.soft↗

arXiv2017

Effect of Collisional Elasticity on the Bagnold Rheology of Sheared Frictionless Two Dimensional Disks

We carry out constant volume simulations of steady-state, shear driven flow in a simple model of athermal, bidisperse, soft-core, frictionless disks in two dimensions, using a dissipation law that gives rise to Bagnoldian rheology. Focusing on the small strain rate limit, we map out the rheological behavior as a function of particle packing fraction $ϕ$ and a parameter $Q$ that measures the elasticity of binary particle collisions. We find a $Q^*(ϕ)$ that marks the clear crossover from a region characteristic of strongly inelastic collisions, $Q Q^*$, and give evidence that $Q^*(ϕ)$ diverges as $ϕ\toϕ_J$, the shear driven jamming transition. We thus conclude that the jamming transition at any value of $Q$ behaves the same as the strongly inelastic case, provide one is sufficiently close to $ϕ_J$. We further characterize the differing nature of collisions in the strongly inelastic vs weakly inelastic regions, and recast our results into the constituent equation form commonly used in discussions of hard granular matter.

cond-mat.soft↗

arXiv2016

Critical Scaling of Bagnold Rheology at the Jamming Transition of Frictionless Two Dimensional Disks

We carry out constant volume simulations of steady-state, shear driven, rheology in a simple model of bidisperse, soft-core, frictionless disks in two dimensions, using a dissipation law that gives rise to Bagnoldian rheology. We carry out a detailed critical scaling analysis of our resulting data for pressure $p$ and shear stress $σ$, in order to determine the critical exponent $β$ that describes the algebraic divergence of the Bagnold transport coefficients, as the jamming transition is approached from below. We show that it is necessary, for the strain rates considered in this work, to consider the leading correction-to-scaling term in order to achieve a self-consistent analysis of our data. Our resulting value $β\approx 5.0\pm 0.4$ is clearly larger than the theoretical prediction by Otsuki and Hayakawa, and is consistent with earlier numerical results by Peyneau and Roux, and recent theoretical predictions by DeGiuli et al. We have also considered the macroscopic friction $μ\equiv σ/p$ and similarly find results consistent with Peyneau and Roux, and with DeGiuli et al. Our results confirm that the shear driven jamming transition in Bagnoldian systems is well described by a critical scaling theory (as was found previously for Newtonian systems), and we relate this scaling theory to the phenomenological constituent laws for dilatancy and friction.

cond-mat.soft↗

arXiv2016

Dissipation and velocity distribution at the shear-driven jamming transition

We investigate energy dissipation and the distribution of particle velocities at the jamming transition for overdamped shear-driven frictionless disks in two dimensions at zero temperature. We find that the dissipation is caused by the fastest particles and that the fraction of particles responsible for the dissipation decreases towards zero as jamming is approached. These particles belong to an algebraic tail of the velocity distribution that approaches $\sim v^{-3}$ as jamming is approached. We further find that different measures of the velocity diverge differently, which means that concepts like "typical velocity" may no longer be used---a finding that should have implications for analytical approaches to shear-driven jamming.

cond-mat.soft↗

arXiv2015

Search for Hyperuniformity in Mechanically Stable Packings of Frictionless Disks Above Jamming

We numerically simulate mechanically stable packings of soft-core, frictionless, bidisperse disks in two dimensions, above the jamming packing fraction phi_J. For configurations with a fixed isotropic global stress tensor, we investigate the fluctuations of the local packing fraction phi(r) to test whether such configurations display the hyperuniformity that has been claimed to exist exactly at phi_J. For our configurations, generated by a rapid quench protocol, we find that hyperuniformity persists only out to a finite length scale, and that this length scale appears to remain finite as the system stress decreases towards zero, i.e. towards the jamming transition. Our result suggests that the presence of hyperuniformity at jamming may be sensitive to the specific protocol used to construct the jammed configurations.

cond-mat.dis-nn↗

arXiv2015

Relaxation Times and Rheology in Dense Athermal Suspensions

We study the jamming transition in a model of elastic particles under shear at zero temperature. The key quantity is the relaxation time $τ$ which is obtained by stopping the shearing and letting energy and pressure decay to zero. At many different densities and initial shear rates we do several such relaxations to determine the average $τ$. We establish that $τ$ diverges with the same exponent as the viscosity and determine another exponent from the relation between $τ$ and the coordination number. Though most of the simulations are done for the model with dissipation due to the motion of particles relative to an affinely shearing substrate (the RD$_0$ model), we also examine the CD$_0$ model, where the dissipation is instead due to velocity differences of disks in contact, and confirm that the above-mentioned exponent is the same for these two models. We also consider finite size effects on both $τ$ and the coordination number.

cond-mat.soft↗

arXiv2014

Universality of Jamming Criticality in Overdamped Shear-Driven Frictionless Disks

We investigate the criticality of the jamming transition for overdamped shear-driven frictionless disks in two dimensions for two different models of energy dissipation: (i) Durian's bubble model with dissipation proportional to the velocity difference of particles in contact, and (ii) Durian's "mean-field" approximation to (i), with dissipation due to the velocity difference between the particle and the average uniform shear flow velocity. By considering velocity correlations, finite-size behavior of pressure, and the pressure analog of viscosity, we argue that these two models share the same critical behavior.

cond-mat.soft↗

arXiv2014

Dissipation and Rheology of Sheared Soft-Core Frictionless Disks

We use numerical simulations to investigate the effect of different dissipative models on the shearing rheology of massive soft-core frictionless disks in two dimensions. We show that the presence of Newtonian (overdamped) vs Bagnoldian (inertial) rheology is related to the formation of large connected clusters of disks, and that sharp transitions may exist between the two as system parameters vary. In the limit of strongly inelastic collisions, we find that rheological curves collapse to a well-defined limit when plotted against an appropriate dimensionless strain rate.

cond-mat.soft↗

arXiv2014

Correlations of plasticity in sheared glasses

In a recent paper [S. Mandal et al., Phys. Rev. E 88, 022129 (2013)] the nature of spatial correlations of plasticity in hard sphere glasses was addressed both via computer simulations and in experiments. It was found that the experimentally obtained correlations obey a power law whereas the correlations from simulations are better fitted by an exponential decay. We here provide direct evidence--- via simulations of a hard sphere glass in 2D---that this discrepancy is a consequence of the finite system size in the 3D simulations. By extending the study to a 2D soft disk model at zero temperature, the robustness of the power-law decay in sheared amorphous solids is underlined. Deviations from a power law occur when either reducing the packing fraction towards the supercooled regime in the case of hard spheres or changing the dissipation mechanism from contact dissipation to a mean-field type drag for the case of soft disks.

cond-mat.soft↗

arXiv2013

Pressure Distribution and Critical Exponent in Statically Jammed and Shear-Driven Frictionless Disks

We numerically study the distributions of global pressure that are found in ensembles of statically jammed and quasistatically sheared systems of bidisperse, frictionless, disks at fixed packing fraction $ϕ$ in two dimensions. We use these distributions to address the question of how pressure increases as $ϕ$ increases above the jamming point $ϕ_J$, $p\sim |ϕ- ϕ_J|^y$. For statically jammed ensembles, our results are consistent with the exponent $y$ being simply related to the power law of the interparticle soft-core interaction. For sheared systems, however, the value of $y$ is consistent with a non-trivial value, as found previously in rheological simulations.

cond-mat.dis-nn↗