arXiv subjects

Bulbul Chakraborty

Publications and source records attributed to Bulbul Chakraborty.

At least 37 records · Page 2Linked to original sources

arXiv2021

$K$-core analysis of shear-thickening suspensions

Shear thickening of suspensions is studied by discrete-particle simulation, accounting for hydrodynamic, repulsive, and contact forces. The contact forces, including friction, are activated when the imposed shear stress $σ$ is able to overcome the repulsive force. The simulation method captures strong continuous and discontinuous shear thickening (CST and DST) in the range of solid volume fraction $0.54 \le ϕ\le 0.56$ studied here. This work presents characteristics of the contact force network developed in the suspension under shear. The number of frictional contacts per particle $Z$ is shown to have a one-to-one relationship with the suspension stress, and the conditions for simple percolation of frictional contacts are found to deviate strongly from those of a random network model. The stress is shown to have important correlations with topological invariant metrics of the contact network known as $k$-cores; the $k$-cores are maximal subgraphs (`clusters') in which all member particles have $k$ or more frictional contacts to other members of the same subgraph. Only $k\le 3$ is found in this work at solid volume fractions $ϕ\le 0.56$. Distinct relationships between the suspension rheology and the $k$-cores are found. One is that the stress susceptibility, defined as $\partial σ/\partial \dotγ$ where $\dotγ$ is the shear rate, is found to peak at the condition of onset of the $3$-core, regardless of whether the system exhibits CST or DST. A second is that the stress per particle within cores of different $k$ increases sharply with increase of $k$ at the onset of DST; in CST, the difference is mild.

cond-mat.soft↗

arXiv2020

Emergent Elasticity in Amorphous Solids

The mechanical response of naturally abundant amorphous solids such as gels, jammed grains, and biological tissues are not described by the conventional paradigm of broken symmetry that defines crystalline elasticity. In contrast, the response of such athermal solids are governed by local conditions of mechanical equilibrium, i.e., force and torque balance of its constituents. Here we show that these constraints have the mathematical structure of a generalized electromagnetism, where the electrostatic limit successfully captures the anisotropic elasticity of amorphous solids. The emergence of elasticity from local mechanical constraints offers a new paradigm for systems with no broken symmetry, analogous to emergent gauge theories of quantum spin liquids. Specifically, our $U(1)$ rank-2 symmetric tensor gauge theory of elasticity translates to the electromagnetism of fractonic phases of matter with the stress mapped to electric displacement and forces to vector charges. We corroborate our theoretical results with numerical simulations of soft frictionless disks in both two and three dimensions, and experiments on frictional disks in two dimensions. We also present experimental evidence indicating that force chains in granular media are sub-dimensional excitations of amorphous elasticity similar to fractons.

cond-mat.dis-nn↗

arXiv2020

Athermal fluctuations in disordered crystals

We analyze the fluctuations in particle positions and inter-particle forces in disordered jammed crystals in the limit of weak disorder. We demonstrate that such athermal systems are fundamentally different from their thermal counterparts, characterized by constrained fluctuations of forces perpendicular to the lattice directions. We develop a disorder perturbation expansion in polydispersity about the crystalline state, which we use to derive exact results to linear order. We show that constrained fluctuations result as a consequence of local force balance conditions, and are characterized by non-Gaussian distributions which we derive exactly. We analytically predict several properties of such systems, including the scaling of the average coordination with polydispersity and packing fraction, which we verify with numerical simulations using soft disks with one-sided harmonic interactions.

cond-mat.soft↗

arXiv2020

Arrested States in Persistent Active Matter: Gelation without Attraction

We explore phase separation and kinetic arrest in a model active colloidal system consisting of self-propelled, hard-core particles with nonconvex shapes. The passive limit of the model, namely cross-shaped particles on a square lattice, exhibits a first-order transition from a fluid phase to a solid phase with increasing density. Quenches into the two-phase coexistence region exhibit an aging regime. The nonconvex shape of the particles eases jamming in the passive system and leads to strong inhibition of rotations of the active particles. Using numerical simulations and analytical modeling, we quantify the nonequilibrium phase behavior as a function of density and activity. If we view activity as the analog of attraction strength, the phase diagram exhibits strong similarities to that of attractive colloids, exhibiting both aging, glassy states and gel-like arrested states. The two types of dynamically arrested states, glasses and gels, are distinguished by the appearance of density heterogenities in the latter. In the infinitely persistent limit, we show that a coarse-grained model based on the asymmetric exclusion process quantitatively predicts the density profiles of the gel states. The predictions remain qualitatively valid for finite rotation rates. Using these results, we classify the activity-driven phases and identify the boundaries separating them.

cond-mat.soft↗

arXiv2020

Timescale divergence at the shear jamming transition

We find that in simulations of quasi-statically sheared frictional disks, the shear jamming transition can be characterized by an abrupt jump in the number of force bearing contacts between particles. This mechanical coordination number increases discontinuously from $Z = 0$ to $Z \gtrsim d +1$ at a critical shear value $γ_c$, as opposed to a smooth increase in the number of geometric contacts. This is accompanied by a diverging timescale $τ^*$ that characterizes the time required by the system to attain force balance when subjected to a perturbation. As the global shear $γ$ approaches the critical value $γ_c$ from below, one observes the divergence of the time taken to relax to a state where all the inter-particle contacts have uniformly zero force. Above $γ_{c}$, the system settles into a state characterized by finite forces between particles, with the timescale also increasing as $γ\to γ_{c}^{+}$. By using two different protocols to generate force balanced configurations, we show that this timescale divergence is a robust feature that accompanies the shear jamming transition.

cond-mat.soft↗

arXiv2020

Is friction essential for dilatancy and shear jamming in granular matter?

Granular packings display the remarkable phenomenon of dilatancy [1], wherein their volume increases upon shear deformation. Conventional wisdom and previous results suggest that dilatancy, as also the related phenomenon of shear-induced jamming, requires frictional interactions [2, 3]. Here, we investigate the occurrence of dilatancy and shear jamming in frictionless packings. We show that the existence of isotropic jamming densities ϕj above the minimal density, the J-point density ϕJ [4, 5], leads both to the emergence of shear-induced jamming and dilatancy. Packings at ϕJ form a significant threshold state into which systems evolve in the limit of vanishing pressure under constant pressure shear, irrespective of the initial jamming density ϕj. While packings for different ϕj display equivalent scaling properties under compression [6], they exhibit striking differences in rheological behaviour under shear. The yield stress under constant volume shear increases discontinuously with density when ϕj > ϕJ, contrary to the continuous behavior in generic packings that jam at ϕJ [4, 7].

cond-mat.stat-mech↗

arXiv2019

Shear jamming and fragility in dense suspensions

The phenomenon of shear-induced jamming is a factor in the complex rheological behavior of dense suspensions. Such shear-jammed states are fragile, i.e., they are not stable against applied stresses that are incompatible with the stress imposed to create them. This peculiar flow-history dependence of the stress response is due to flow-induced microstructures. To examine jammed states realized under constant shear stress, we perform dynamic simulations of non-Brownian particles with frictional contact forces and hydrodynamic lubrication forces. We find clear signatures that distinguish these fragile states from the more conventional isotropic jammed states.

cond-mat.soft↗

arXiv2019

Stress Fluctuations in Transient Active Networks

Inspired by experiments on dynamic extensile gels of biofilaments and motors, we propose a model of a network of linear springs with a kinetics consisting of growth at a prescribed rate, death after a lifetime drawn from a distribution, and birth at a randomly chosen node. The model captures features such as the build-up of self-stress, that are not easily incorporated into hydrodynamic theories. We study the model numerically and show that our observations can largely be understood through a stochastic effective-medium model. The resulting dynamically extending force-dipole network displays many features of yielded plastic solids, and offers a way to incorporate strongly non-affine effects into theories of active solids. A rather distinctive form for the stress distribution, and a Herschel-Bulkley dependence of stress on activity, are our major predictions.

cond-mat.soft↗

arXiv2018

Motion of active tracer in a lattice gas with cross-shaped particles

We analyze the dynamics of an active tracer particle embedded in a thermal lattice gas. All particles are subject to exclusion up to third nearest neighbors on the square lattice, which leads to slow dynamics at high densities. For the case with no rotational diffusion of the tracer, we derive an analytical expression for the resulting drift velocity v of the tracer in terms of non-equilibrium density correlations involving the tracer particle and its neighbors, which we verify using numerical simulations. We show that the properties of the passive system alone do not adequately describe even this simple system of a single non-rotating active tracer. For large activity and low density, we develop an approximation for v. For the case where the tracer undergoes rotational diffusion independent of its neighbors, we relate its diffusion coefficient to the thermal diffusion coefficient and v. Finally we study dynamics where the rotation of the tracer is limited by the presence of neighboring particles. We find that the effect of this rotational locking may be quantitatively described in terms of a reduction of the rotation rate.

cond-mat.soft↗

arXiv2018

Comment on "Field Theory for Amorphous Solids" by Eric DeGiuli

In a recent pair of papers, Eric DeGiuli has developed a field theory of glasses and granular materials based on the Edwards ensemble, extending our earlier theoretical framework. In this comment, we address a misconception regarding the relation between equiprobability of microstates and a flat measure in a field theory, which appears in the DeGiuli papers, and has often plagued discussions surrounding the Edwards ensemble. We point out that modeling this measure is the challenge addressed in both our earlier work and the recent DeGiuli work. Contrary to what is stated in the the DeGiuli papers, we did not assume a flat measure in our earlier work.

cond-mat.soft↗

arXiv2018

Microscopic origin of frictional rheology in dense suspensions: correlations in force space

We develop a statistical framework for the rheology of dense, non-Brownian suspensions, based on correlations in a space representing forces, which is dual to position space. Working with the ensemble of steady state configurations obtained from simulations of suspensions in two dimensions, we find that the anisotropy of the pair correlation function in force space changes with confining shear stress ($σ_{xy}$) and packing fraction ($ϕ$). Using these microscopic correlations, we build a statistical theory for the macroscopic friction coefficient: the anisotropy of the stress tensor, $μ= σ_{xy}/P$. We find that $μ$ decreases (i) as $ϕ$ is increased and (ii) as $σ_{xy}$ is increased. Using a new constitutive relation between $μ$ and viscosity for dense suspensions that generalizes the rate-independent one, we show that our theory predicts a Discontinuous Shear Thickening (DST) flow diagram that is in good agreement with numerical simulations, and the qualitative features of $μ$ that lead to the generic flow diagram of a DST fluid observed in experiments.

cond-mat.soft↗

arXiv2018

Numerical test of the Edwards conjecture shows that all packings are equally probable at jamming

In the late 1980s, Sam Edwards proposed a possible statistical-mechanical framework to describe the properties of disordered granular materials. A key assumption underlying the theory was that all jammed packings are equally likely. In the intervening years it has never been possible to test this bold hypothesis directly. Here we present simulations that provide direct evidence that at the unjamming point, all packings of soft repulsive particles are equally likely, even though generically, jammed packings are not. Typically, jammed granular systems are observed precisely at the unjamming point since grains are not very compressible. Our results therefore support Edwards' original conjecture. We also present evidence that at unjamming the configurational entropy of the system is maximal.

cond-mat.soft↗

arXiv2017

Ergodicity breaking dynamics of arch collapse

Gravity driven flows such as in hoppers and silos are susceptible to clogging due to the formation of arches at the exit whose failure is the key to re-initiation of flow. In vibrated hoppers, clog durations exhibit a broad distribution, which poses a challenge for devising efficient unclogging protocols. Using numerical simulations, we demonstrate that the dynamics of arch shapes preceding failure can be modeled as a continuous time random walk (CTRW) with a broad distribution of waiting times, which breaks ergodicity. Treating arch failure as a first passage process of this random walk, we argue that the distribution of unclogging times is determined by this waiting time distribution. We hypothesize that this is a generic feature of unclogging, and that specific characteristics, such as hopper geometry, and mechanical properties of the grains modify the waiting time distribution.

cond-mat.soft↗

arXiv2017

Stress Response of Granular Systems

We develop a framework for stress response in two dimensional granular media, with and without friction, that respects vector force balance at the microscopic level. We introduce local gauge degrees of freedom that determine the response of contact forces between constituent grains on a given, disordered, contact network, to external perturbations. By mapping this response to the spectral properties of the graph Laplacian corresponding to the underlying contact network, we show that this naturally leads to spatial localization of forces. We present numerical evidence for localization using exact diagonalization studies of network Laplacians of soft disk packings. Finally, we discuss the role of other constraints, such as torque balance, in determining the stability of a granular packing to external perturbations.

cond-mat.dis-nn↗

arXiv2017

Gaps between avalanches in 1D Random Field Ising Models

We analyze the statistics of gaps ($ΔH$) between successive avalanches in one dimensional random field Ising models (RFIMs) in an external field $H$ at zero temperature. In the first part of the paper we study the nearest-neighbour ferromagnetic RFIM. We map the sequence of avalanches in this system to a non-homogeneous Poisson process with an $H$-dependent rate $ρ(H)$. We use this to analytically compute the distribution of gaps $P(ΔH)$ between avalanches as the field is increased monotonically from $-\infty$ to $+\infty$. We show that $P(ΔH)$ tends to a constant $\mathcal{C}(R)$ as $ΔH \to 0^+$, which displays a non-trivial behaviour with the strength of disorder $R$. We verify our predictions with numerical simulations. In the second part of the paper, motivated by avalanche gap distributions in driven disordered amorphous solids, we study a long-range antiferromagnetic RFIM. This model displays a gapped behaviour $P(ΔH) = 0$ up to a system size dependent offset value $ΔH_{\text{off}}$, and $P(ΔH) \sim (ΔH - ΔH_{\text{off}})^θ$ as $ΔH \to H_{\text{off}}^+$. We perform numerical simulations on this model and determine $θ\approx 0.95(5)$. We also discuss mechanisms which would lead to a non-zero exponent $θ$ for general spin models with quenched random fields.

cond-mat.dis-nn↗

arXiv2017

Shear-induced rigidity of frictional particles: Analysis of emergent order in stress space

Solids are distinguished from fluids by their ability to resist shear. In traditional solids, the resistance to shear is associated with the emergence of broken translational symmetry as exhibited by a non-uniform density pattern, which results from either minimizing the energy cost or maximizing the entropy or both. In this work, we focus on a class of systems, where this paradigm is challenged. We show that shear-driven jamming in dry granular materials is a collective process controlled solely by the constraints of mechanical equilibrium. We argue that these constraints lead to a broken translational symmetry in a dual space that encodes the statistics of contact forces and the topology of the contact network. The shear-jamming transition is marked by the appearance of this broken symmetry. We extend our earlier work, by comparing and contrasting real space measures of rheology with those obtained from the dual space. We investigate the structure and behavior of the dual space as the system evolves through the rigidity transition in two different shear protocols. We analyze the robustness of the shear-jamming scenario with respect to protocol and packing fraction, and demonstrate that it is possible to define a protocol-independent order parameter in this dual space, which signals the onset of rigidity.

cond-mat.soft↗

arXiv2017

Scaling Theory for the Frictionless Unjamming Transition

We develop a scaling theory of the unjamming transition of soft frictionless disks in two dimensions by defining local areas, which can be uniquely assigned to each contact. These serve to define local order parameters, whose distribution exhibits divergences as the unjamming transition is approached. We derive scaling forms for these divergences from a mean-field approach that treats the local areas as non interacting entities, and demonstrate that these results agree remarkably well with numerical simulations. We find that the asymptotic behaviour of the scaling functions arises from the geometrical structure of the packing while the overall scaling with the compression energy depends on the force law. We use the scaling forms of the distributions to determine the scaling of the total grain area $A_G$, and the total number of contacts $N_C$.

cond-mat.dis-nn↗

arXiv2017

Disordered Contact Networks in Jammed Packings of Frictionless Disks

We analyse properties of contact networks formed in packings of soft frictionless disks near the unjamming transition. We construct polygonal tilings and triangulations of the contact network that partitions space into convex regions which are either covered or uncovered. This allows us to characterize the local spatial structure of the packing near the transition using well-defined geometric objects. We construct bounds on the number of polygons and triangulation vectors that appear in such packings. We study these networks using simulations of bidispersed disks interacting via a one-sided linear spring potential. We find that several underlying geometric distributions are reproducible and display self averaging properties. We find that the total covered area is a reliable real space parameter that can serve as a substitute for the packing fraction. We find that the unjamming transition occurs at a fraction of covered area $A_G^{*} = 0.446(1)$. We determine scaling exponents of the excess covered area as the energy of the system approaches zero $E_G \to 0^+$, and the coordination number $\langle z_g \rangle$ approaches its isostatic value $ΔZ = \langle z_g \rangle - \langle z_g \rangle_{\rm iso} \to 0^{+}$. We find $ΔA_G \sim Δ{E_G}^{0.28(1)}$ and $ΔA_G \sim ΔZ^{1.00(1)}$, representing new structural critical exponents. We use the distribution functions of local areas to study the underlying geometric disorder in the packings. We find that a finite fraction of order $Ψ_O^* = 0.369(1)$ persists as the transition is approached.

cond-mat.dis-nn↗