arXiv subjects

S. Teitel

Publications and source records attributed to S. Teitel.

At least 19 recordsLinked to original sources

arXiv2022

Comparison of compression vs shearing near jamming, for a simple model of athermal frictionless disks in suspension

Using a simplified model for a non-Brownian suspension, we numerically study the response of athermal, overdamped, frictionless disks in two dimensions to isotropic and uniaxial compression, as well as to pure {\color{black}and simple} shearing, all at finite constant strain rates $\dot\epsilon$. We show that isotropic and uniaxial compression result in the same jamming packing fraction $\phi_J$, while pure shear and simple shear induced jamming occurs at a slightly higher $\phi_J^*$, consistent with that found previously for simple shearing. A critical scaling analysis of pure shearing gives critical exponents consistent with those previously found for both isotropic compression and simple shearing. Using orientational order parameters for contact bond directions, we compare the anisotropy of the force and contact networks at both lowest nematic order, as well as higher $2n$-fold order.

cond-mat.soft↗

arXiv2021

Universality of stress-anisotropic and stress-isotropic jamming of frictionless spheres in three dimensions: Uniaxial vs isotropic compression

We numerically study a three dimensional system of athermal, overdamped, frictionless spheres, using a simplified model for a non-Brownian suspension. We compute the bulk viscosity under both uniaxial and isotropic compression as a means to address the question of whether stress-anisotropic and stress-isotropic jamming are in the same critical universality class. Carrying out a critical scaling analysis of the system pressure $p$, shear stress $\sigma$, and macroscopic friction $\mu=\sigma/p$, as functions of particle packing fraction $\phi$ and compression rate $\dot\epsilon$, we find good agreement for all critical parameters comparing the isotropic and anisotropic cases. In particular, we determine that the bulk viscosity diverges as $p/\dot\epsilon\sim (\phi_J-\phi)^{-\beta}$, with $\beta=3.36\pm 0.09$, as jamming is approached from below. We further demonstrate that the average contact number per particle $Z$ can also be written in a scaling form as a function of $\phi$ and $\dot\epsilon$. Once again, we find good agreement between the uniaxial and isotropic cases. We compare our results to prior simulations and theoretical predictions.

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

Depletion Forces in Athermally Sheared Mixtures of Frictionless Disks and Rods in Two Dimensions

We carry out numerical simulations to study the behavior of an athermal mixture of frictionless circular disks and elongated rods in two dimensions, under three different types of global linear deformation at a finite strain rate: (i) simple shearing, (ii) pure shearing, and (iii) isotropic compression. We find that the fluctuations induced by such deformations lead to depletion forces that cause rods to group in parallel oriented clusters for the cases of simple and pure shear, but not for isotropic compression. For simple shearing, we find that as the fraction of rods increases, this clustering increases, leading to an increase in the average rate of rotation of the rods, and a decrease in the magnitude of their nematic ordering.

cond-mat.soft↗

arXiv2020

Critical Scaling of Compression-Driven Jamming of Athermal Frictionless Spheres in Suspension

We study numerically a system of athermal, overdamped, frictionless spheres, as in a non-Brownian suspension, in two and three dimensions. Compressing the system isotropically at a fixed rate $\dot\epsilon$, we investigate the critical behavior at the jamming transition. The finite compression rate introduces a control timescale, which allows one to probe the critical timescale associated with jamming. As was found previously for steady-state shear-driven jamming, we find for compression-driven jamming that pressure obeys a critical scaling relation as a function of packing fraction $\phi$ and compression rate $\dot\epsilon$, and that the bulk viscosity $p/\dot\epsilon$ diverges upon jamming. A scaling analysis determines the critical exponents associated with the compression-driven jamming transition. Our results suggest that stress-isotropic, compression-driven, jamming may be in the same universality class as stress-anisotropic, shear-driven, jamming.

cond-mat.soft↗

arXiv2020

Shear-Driven Flow of Athermal, Frictionless, Spherocylinder Suspensions in Two Dimensions: Spatial Structure and Correlations

We use numerical simulations to study the flow of athermal, frictionless, soft-core two dimensional spherocylinders driven by a uniform steady-state simple shear applied at a fixed volume and a fixed finite strain rate $\dotγ$. Energy dissipation is via a viscous drag with respect to a uniformly sheared host fluid, giving a simple model for flow in a non-Brownian suspension with Newtonian rheology. We study the resulting spatial structure of the sheared system, and compute correlation functions of the velocity, the particle density, the nematic order parameter, and the particle angular velocity. Correlations of density, nematic order, and angular velocity are shown to be short ranged both below and above jamming. We compare a system of size-bidisperse particles with a system of size-monodisperse particles, and argue how differences in spatial order as the packing increases leads to differences in the global nematic order parameter. We consider the effect of shearing on initially well ordered configurations, and show that in many cases the shearing acts to destroy the order, leading to the same steady-state ensemble as found when starting from random initial configurations.

cond-mat.soft↗

arXiv2020

Shear-Driven Flow of Athermal, Frictionless, Spherocylinder Suspensions in Two Dimensions: Particle Rotations and Orientational Ordering

We use numerical simulations to study the flow of a bidisperse mixture of athermal, frictionless, soft-core two dimensional spherocylinders driven by a uniform steady-state simple shear applied at a fixed volume and a fixed finite strain rate $\dotγ$. Energy dissipation is via a viscous drag with respect to a uniformly sheared host fluid, giving a simple model for flow in a non-Brownian suspension with Newtonian rheology. Considering a range of packing fractions $ϕ$ and particle asphericities $α$ at small $\dotγ$, we study the angular rotation $\dotθ_i$ and the nematic orientational ordering $\mathbf{S}_2$ of the particles induced by the shear flow, finding a non-monotonic behavior as the packing $ϕ$ is varied. We interpret this non-monotonic behavior as a crossover from a small $ϕ$ region where single-particle-like behavior occurs, to a large $ϕ$ region where the geometry of the dense packing dominates, the reduced free volume inhibits motion, and a random Poisson-like process for particle rotations results. We also argue that the finite nematic ordering $\mathbf{S}_2$ is a consequence of the shearing serving as an ordering field, rather than a result of long-ranged cooperative behavior among the particles. We arrive at these conclusions by consideration of (i) the distribution of waiting times for a particle to rotate by $π$, (ii) the behavior of the system under pure, as compared to simple, shearing, (iii) the relaxation of the nematic order parameter $\mathbf{S}_2$ when perturbed away from the steady state, and (iv) by construction a numerical mean-field model for the rotational motion of a particle. Our results also help to explain the singular behavior observed when taking the $α\to 0$ limit approaching circular disks.

cond-mat.soft↗

arXiv2019

Shear-Driven Flow of Athermal, Frictionless, Spherocylinder Suspensions in Two Dimensions: Stress, Jamming, and Contacts

We use numerical simulations to study the flow of a bidisperse mixture of athermal, frictionless, soft-core two dimensional spherocylinders driven in uniform steady state shear. Energy dissipation is via a viscous drag with respect to a uniformly sheared host fluid, giving a model for a non-Brownian suspension with a Newtonian rheology. We study pressure $p$ and deviatoric shear stress $σ$ as a function of packing fraction $ϕ$, strain rate $\dotγ$, and a parameter $α$ that measures the asphericity of the particles. We consider the anisotropy of the stress tensor, the macroscopic friction $μ=σ/p$, and the divergence of the transport coefficient $η_p=p/\dotγ$ as $ϕ$ is increased to the jamming $ϕ_J$. From an analysis of Herschel-Bulkley rheology above jamming, we estimate $ϕ_J$ as a function of $α$ and show that the variation of $ϕ_J$ with $α$ is the main cause for differences in rheology as $α$ is varied. However a detailed scaling analysis of the divergence of $η_p$ for our most elongated particles suggests that the jamming transition of spherocylinders may be in a different universality class than that of circular disks. We compute the number of contacts per particle $Z$ in the system and show that at jamming $Z_J$ is a non-monotonic function of $α$ that is always smaller than the isostatic value. We measure the probability distribution of contacts per unit surface length $\mathcal{P}(\vartheta)$ at polar angle $\vartheta$ with respect to the spherocylinder spine, and find that as $α\to 0$ this distribution seems to diverge at $\vartheta=π/2$, giving a finite limiting probability for contacts on the vanishingly small flat sides of the spherocylinder. Finally we consider the variation of the average contact force as a function of location on the particle surface.

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↗

arXiv2019

Athermal shearing of frictionless cross-shaped particles of varying aspect ratio

We use numerical simulations to study the shear-driven steady-state flow of athermal, frictionless, overdamped, two dimensional cross-shaped particles of varying aspect ratios, and make comparison with the behavior of rod-shaped and staple-shaped particles. We find that the extent of non-convexity of the particle shape plays an important role in determining both the value of the jamming packing fraction as well as the rotational motion and orientational ordering of the particles.

cond-mat.soft↗

arXiv2018

Compression Driven Jamming of Athermal Frictionless Spherocylinders in Two Dimensions

We simulate numerically the compression driven jamming of athermal, frictionless, soft-core spherocylinders in two dimensions, for a range of particle aspect ratios $α$. We find the critical packing fraction $ϕ_J(α)$ for the jamming transition, and the average number of contacts per particle $z_J(α)$ at jamming. We find that both are nonmonotonic, with a peak at $α\approx 1$. We find that configurations at the compression driven jamming point are always hypostatic for all $α$, with $z_J<z_\mathrm{iso}=2d_f=6$ the isostatic value. We show that, for moderately elongated spherocylinders, there is no orientational ordering upon athermal compression through jamming. We analyze in detail the eigenmodes of the dynamical matrix close to the jamming point for a few different values of the aspect ratio, from nearly circular to moderately elongated. We find that there are low frequency bands containing $N(z_\mathrm{iso}-z_J)/2$ modes, such that the frequency of these modes vanish as $ϕ\toϕ_J$. We consider the extended vs localized nature of these low frequency modes, and the extent to which they involve translational or rotational motion, and find many low frequency sliding modes where particles can move with little rotation. We highlight the importance of treating side-to-side contacts, along flat sides of the spherocylinder, properly for the correct determination of $z_J$. We note the singular nature of taking the $α\to 0$ limit. We discuss the similarities and differences with previous work on jammed ellipses and ellipsoids, to illustrate the effects that different particle shape have on configurations at jamming.

cond-mat.dis-nn↗

arXiv2017

Anomalous Stress Fluctuations in Athermal Two Dimensional Amorphous Solids

We numerically study the local stress distribution within athermal, isotropically stressed, mechanically stable, packings of bidisperse frictionless disks above the jamming transition in two dimensions. Considering the Fourier transform of the local stress, we find evidence for algebraically increasing fluctuations in both isotropic and anisotropic components of the stress tensor at small wavenumbers, contrary to recent theoretical predictions. Such increasing fluctuations imply a lack of self-averaging of the stress on large length scales. The crossover to these increasing fluctuations defines a length scale $\ell_0$, however it appears that $\ell_0$ does not vary much with packing fraction $ϕ$, nor does $\ell_0$ seem to be diverging as $ϕ$ approaches the jamming $ϕ_J$. We also find similar large length scale fluctuations of stress in the inherent states of a quenched Lennard-Jones liquid, leading us to speculate that such fluctuations may be a general property of amorphous solids in two dimensions.

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↗

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

Maximum Entropy and the Stress Distribution in Soft Disk Packings Above Jamming

We show that the maximum entropy hypothesis can successfully explain the distribution of stresses on compact clusters of particles within disordered mechanically stable packings of soft, isotropically stressed, frictionless disks above the jamming transition. We show that, in our two dimensional case, it becomes necessary to consider not only the stress but also the Maxwell-Cremona force-tile area, as a constraining variable that determines the stress distribution. The importance of the force-tile area had been suggested by earlier computations on an idealized force-network ensemble.

cond-mat.soft↗

arXiv2015

Compression- and Shear-Driven Jamming of U-Shaped Particles in Two Dimensions

We carry out numerical simulations of soft, U-shaped, frictionless particles in $d=2$ dimensions in order to explore the effects of complex particle shape on the jamming transition. We consider both cases of uniform compression-driven and shear-driven jamming as packing fraction $ϕ$ and compression or shear rate is varied. Upon slow compression, jamming is found to occur when the isostatic condition is satisfied. Under driven steady state shearing, jamming occurs at a higher packing fraction $ϕ_J$ than observed in compression. A growing relaxation time and translational correlation length is found as $ϕ$ increases towards $ϕ_J$. We consider the orientational ordering and rotation of particles induced by the shear flow. Both nematic and tetratic ordering are found, but these decrease as $ϕ$ increases to $ϕ_J$. At the jamming transition, the nematic ordering further decreases, while the tetratic ordering increases, but the orientational correlation lengths remain small throughout. The average angular velocity of the particles is found to increase as $ϕ$ increases, saturating to a plateau just below $ϕ_J$, but then increasing again as $ϕ$ increases above $ϕ_J$.

cond-mat.soft↗