arXiv subjects

Bulbul Chakraborty

Publications and source records attributed to Bulbul Chakraborty.

At least 55 records · Page 3Linked to original sources

arXiv2017

Shear-induced organization of forces in dense suspensions: signatures of discontinuous shear thickening

Dense suspensions can exhibit an abrupt change in their viscosity in response to increasing shear rate. The origin of this discontinuous shear thickening (DST) has been ascribed to the transformation of lubricated contacts to frictional, particle-on-particle contacts. Recent research on the flowing and jamming behavior of dense suspensions has explored the intersection of ideas from granular physics and Stokesian fluid dynamics to better understand this transition from lubricated to frictional rheology. DST is reminiscent of classical phase transitions, and a key question is how interactions between the microscopic constituents give rise to a macroscopic transition. In this paper, we extend a formalism that has proven to be successful in understanding shear jamming of dry grains to dense suspensions. Quantitative analysis of the collective evolution of the contact-force network accompanying the DST transition demonstrates clear changes in the distribution of microscopic variables, and leads to the identification of an "order parameter" characterizing DST.

cond-mat.soft↗

arXiv2016

Theory of microphase separation in bidisperse chiral membranes

We present a Ginzburg-Landau theory of micro phase separation in a bidisperse chiral membrane consisting of rods of opposite handendness. This model system undergoes a phase transition from an equilibrium state where the two components are completely phase separated to a microphase separated state composed of domains of a finite size comparable to the twist penetration depth. Characterizing the phenomenology using linear stability analysis and numerical studies, we trace the origin of the discontinuous change in domain size that occurs during this to a competition between the cost of creating an interface and the gain in twist energy for small domains in which the twist penetrates deep into the center of the domain.

cond-mat.soft↗

arXiv2015

Synchronization Patterns in Geometrically Frustrated Turing Rings

Coupled nonlinear oscillators can exhibit a wide variety of patterns. We study the Brusselator as a prototypical autocatalytic reaction diffusion model. Working in the limit of strong nonlinearity provides a clear timescale separation that leads to a canard explosion in a single Brusselator. In this highly nonlinear regime it is numerically found that rings of coupled Brusselators do not follow the predictions from Turning analysis. We find that the behavior can be explained using a piecewise linear approximation.

nlin.PS↗

arXiv2015

Shear induced rigidity in athermal materials: a unified statistical framework

Recent studies of athermal systems such as dry grains and dense, non-Brownian suspensions have shown that shear can lead to solidification through the process of shear jamming in grains and discontinuous shear thickening in suspensions. The similarities observed between these two distinct phenomena suggest that the physical processes leading to shear-induced rigidity in athermal materials are universal. We present a non-equilibrium statistical mechanics model, which exhibits the phenomenology of these shear-driven transitions: shear jamming and discontinuous shear thickening in different regions of the predicted phase diagram. Our analysis identifies the crucial physical processes underlying shear-driven rigidity transitions, and clarifies the distinct roles played by shearing forces and the density of grains.

cond-mat.soft↗

arXiv2014

The Statistical Physics of Athermal Materials

At the core of equilibrium statistical mechanics lies the notion of statistical ensembles: a collection of microstates, each occurring with a given a priori probability that depends only on a few macroscopic parameters such as temperature, pressure, volume, and energy. In this review article, we discuss recent advances in establishing statistical ensembles for athermal materials. The broad class of granular and particulate materials is immune from the effects of thermal fluctuations because the constituents are macroscopic. In addition, interactions between grains are frictional and dissipative, which invalidates the fundamental postulates of equilibrium statistical mechanics. However, granular materials exhibit distributions of microscopic quantities that are reproducible and often depend on only a few macroscopic parameters. We explore the history of statistical ensemble ideas in the context of granular materials, clarify the nature of such ensembles and their foundational principles, highlight advances in testing key ideas, and discuss applications of ensembles to analyze the collective behavior of granular materials.

cond-mat.stat-mech↗

arXiv2013

Origin of Rigidity in Dry Granular Solids

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. In this work, we focus on the emergence of shear-rigidity in a class of solids where this paradigm is challenged. Dry granular materials have no energetically or entropically preferred density modulations. We show that, in contrast to traditional solids, the emergence of shear rigidity in these granular solids is a collective process, which is controlled solely by boundary forces, the constraints of force and torque balance, and the positivity of the contact forces. We develop a theoretical framework based on these constraints, which connects rigidity to broken translational symmetry in the space of forces, not positions of grains. We apply our theory to experimentally generated shear-jammed (SJ) states and show that these states are indeed characterized by a persistent, non-uniform density modulation in force space, which emerges at the shear-jamming transition.

cond-mat.soft↗

arXiv2013

Effects of intrinsic fluctuations in a prototypical chemical oscillator: metastability and switching

Intrinsic or demographic noise has been shown to play an important role in the dynamics of a variety of systems including predator-prey populations, intracellular biochemical reactions, and oscillatory chemical reaction systems, and is known to give rise to oscillations and pattern formation well outside the parameter range predicted by standard mean-field analysis. Initially motivated by an experimental model of cells and tissues where the cells are represented by chemical reagents isolated in emulsion droplets, we study the stochastic Brusselator, a simple activator-inhibitor chemical reaction model. Our work builds on the results of recent studies and looks to understand the role played by intrinsic fluctuations when the timescale of the inhibitor species is fast compared to that of the activator. In this limit, we observe a noise induced switching between small and large amplitude oscillations that persists for large system sizes (N), and deep into the non oscillatory part of the mean-field phase diagram. We obtain a scaling relation for the first passage times between the two oscillating states. From our scaling function, we show that the first passage times have a well defined form in the large N limit. Thus in the limit of small noise and large timescale separation a careful treatment of the noise will lead to a set of non-trivial deterministic equations different from those obtained from the standard mean-field limit.

cond-mat.stat-mech↗

arXiv2013

Fluctuations in Shear-Jammed States: A Statistical Ensemble Approach

Granular matter exists out of thermal equilibrium, i.e. it is athermal. While conventional equilibrium statistical mechanics is not useful for characterizing granular materials, the idea of constructing a statistical ensemble analogous to its equilibrium counterpart to describe static granular matter was proposed by Edwards and Oakshott more than two decades ago. Recent years have seen several implementations of this idea. One of these is the stress ensemble, which is based on properties of the force moment tensor, and applies to frictional and frictionless grains. We demonstrate the full utility of this statistical framework in shear jammed (SJ) experimental states [1,2], a special class of granular solids created by pure shear, which is a strictly non-equilbrium protocol for creating solids. We demonstrate that the stress ensemble provides an excellent quantitative description of fluctuations in experimental SJ states. We show that the stress fluctuations are controlled by a single tensorial quantity: the angoricity of the system, which is a direct analog of the thermodynamic temperature. SJ states exhibit significant correlations in local stresses and are thus inherently different from density-driven, isotropically jammed (IJ) states.

cond-mat.soft↗

arXiv2013

Yielding and large deviations in micellar gels: a model

We present a simple model to account for the rheological behavior observed in recent experiments on micellar gels. The model combines attachment-detachment kinetics with stretching due to shear, and shows well-defined jammed and flowing states. The large deviation function (LDF) for the coarse-grained velocity becomes increasingly non-quadratic as the applied force $F$ is increased, in a range near the yield threshold. The power fluctuations are found to obey a steady-state fluctuation relation (FR) at small $F$. However, the FR is violated when $F$ is near the transition from the flowing to the jammed state although the LDF still exists; the antisymmetric part of the LDF is found to be nonlinear in its argument. Our approach suggests that large fluctuations and motion in a direction opposite to an imposed force are likely to occur in a wider class of systems near yielding.

cond-mat.stat-mech↗

arXiv2012

Signatures of Incipient Jamming in Collisional Hopper Flows

Many disordered systems experience a transition from a fluid-like state to a solid-like state following a sudden arrest in dynamics called jamming. In contrast to jamming in spatially homogeneous systems, jamming in hoppers occurs under extremely inhomogeneous conditions as the gravity-driven flow of grains enclosed by rigid walls converges towards a small opening. In this work, we study velocity fluctuations in a collisional flow near jamming using event-driven simulations. The average flow in a hopper geometry is known to have strong gradients, especially near the walls and the orifice. We find, in addition, a spatially heterogeneous distribution of fluctuations, most striking in the velocity autocorrelation relaxation times. At high flow rates, the flow at the center has lower kinetic temperatures and longer autocorrelation times than at the boundary. Remarkably, however, this trend reverses itself as the flow rate slows, with fluctuations relaxing more slowly at the boundaries though the kinetic temperatures remain high in that region. The slowing down of the dynamics is accompanied by increasing non-Gaussianity in the velocity distributions, which also have large spatial variations.

cond-mat.soft↗

arXiv2012

Rods are less fragile than spheres: Structural relaxation in dense liquids composed of anisotropic particles

We perform extensive molecular dynamics simulations of dense liquids composed of bidisperse dimer- and ellipse-shaped particles in 2D that interact via repulsive contact forces. We measure the structural relaxation times obtained from the long-time decay of the self-part of the intermediate scattering function for the translational and rotational degrees of freedom (DOF) as a function of packing fraction ϕ, temperature T, and aspect ratio α. We are able to collapse the ϕand T-dependent structural relaxation times for disks, and dimers and ellipses over a wide range of α, onto a universal scaling function {\cal F}_{\pm}(|ϕ-ϕ_0|,T,α), which is similar to that employed in previous studies of dense liquids composed of purely repulsive spherical particles in 3D. {\cal F_{\pm}} for both the translational and rotational DOF are characterized by the α-dependent scaling exponents μand δand packing fraction ϕ_0(α) that signals the crossover in the scaling form {\cal F}_{\pm} from hard-particle dynamics to super-Arrhenius behavior for each aspect ratio. We find that the fragility at ϕ_0, m(ϕ_0), decreases monotonically with increasing aspect ratio for both ellipses and dimers. Moreover, the results for the slow dynamics of dense liquids composed of dimer- and ellipse-shaped particles are qualitatively the same, despite the fact that zero-temperature static packings of dimers are isostatic, while static packings of ellipses are hypostatic.

cond-mat.soft↗

arXiv2012

Constraints and vibrations in static packings of ellipsoidal particles

We numerically investigate the mechanical properties of static packings of ellipsoidal particles in 2D and 3D over a range of aspect ratio and compression $Δϕ$. While amorphous packings of spherical particles at jamming onset ($Δϕ=0$) are isostatic and possess the minimum contact number $z_{\rm iso}$ required for them to be collectively jammed, amorphous packings of ellipsoidal particles generally possess fewer contacts than expected for collective jamming ($z < z_{\rm iso}$) from naive counting arguments, which assume that all contacts give rise to linearly independent constraints on interparticle separations. To understand this behavior, we decompose the dynamical matrix $M=H-S$ for static packings of ellipsoidal particles into two important components: the stiffness $H$ and stress $S$ matrices. We find that the stiffness matrix possesses $N(z_{\rm iso} - z)$ eigenmodes ${\hat e}_0$ with zero eigenvalues even at finite compression, where $N$ is the number of particles. In addition, these modes ${\hat e}_0$ are nearly eigenvectors of the dynamical matrix with eigenvalues that scale as $Δϕ$, and thus finite compression stabilizes packings of ellipsoidal particles. At jamming onset, the harmonic response of static packings of ellipsoidal particles vanishes, and the total potential energy scales as $δ^4$ for perturbations by amplitude $δ$ along these `quartic' modes, ${\hat e}_0$. These findings illustrate the significant differences between static packings of spherical and ellipsoidal particles.

cond-mat.soft↗

arXiv2012

Origin of Corrections to Mean-field at the Onset of Unjamming

We present a detailed analysis of the unjamming transition in 2D frictionless disk packings using a static correlation function that has been widely used to study disordered systems. We show that this point-to-set (PTS) correlation function exhibits a dominant length scale that diverges as the unjamming transition is approached through decompression. In addition, we identify deviations from meanfield predictions, and present detailed analysis of the origin of non-meanfield behavior. A mean-field bulk-surface argument is reviewed. Corrections to this argument are identified, which lead to a change in the functional form of the critical PTS boundary size. An entropic description of the origin of the correlations is presented, and simple rigidity assumptions are shown to predict the functional form of the critical PTS boundary size as a function of the pressure.

cond-mat.stat-mech↗

arXiv2011

Prolonging assembly through dissociation:A self assembly paradigm in microtubules

We study a one-dimensional model of microtubule assembly/disassembly in which GTP bound to tubulins within the microtubule undergoes stochastic hydrolysis. In contrast to models that only consider a cap of GTP-bound tubulin, stochastic hydrolysis allows GTP-bound tubulin remnants to exist within the microtubule. We find that these buried GTP remnants enable an alternative mechanism of recovery from shrinkage, and enhances fluctuations of filament lengths. Under conditions for which this alternative mechanism dominates, an increasing depolymerization rate leads to a decrease in dissociation rate and thus a net increase in assembly.

q-bio.BM↗

arXiv2011

Phase and frequency entrainment in locally coupled phase oscillators with repulsive interactions

Recent experiments in one and two-dimensional microfluidic arrays of droplets containing Belousov -Zhabotinsky reactants show a rich variety of spatial patterns [J. Phys. Chem. Lett. 1, 1241-1246 (2010)]. The dominant coupling between these droplets is inhibitory. Motivated by this experimental system, we study repulsively coupled Kuramoto oscillators with nearest neighbor interactions, on a linear chain as well as a ring in one dimension, and on a triangular lattice in two dimensions. In one dimension, we show using linear stability analysis as well as numerical study, that the stable phase patterns depend on the geometry of the lattice. We show that a transition to the ordered state does not exist in the thermodynamic limit. In two dimensions, we show that the geometry of the lattice constrains the phase difference between two neighbouring oscillators to 120 degrees. We report the existence of domains with either clockwise or anti-clockwise helicity, leading to defects in the lattice. We study the time dependence of these domains and show that at large coupling strengths, the domains freeze due to frequency synchronization. Signatures of the above phenomena can be seen in the spatial correlation functions.

nlin.CD↗

arXiv2010

Unjamming of Granular Packings as a Constraint Satisfaction Problem: Evidence for a Growing Static Length Scale in Frictionless Packings

An outstanding question in the physics of soft jammed packings concerns the nature of the correlations that arise near the unjamming transition. In this work, we treat unjamming as a constraint satisfaction problem and demonstrate that a static correlation function, which probes sensitivity to boundary conditions,exhibits a diverging correlation length as the packing is decompressed. This length scale is related to isostaticity, and has been connected earlier to the existence of soft modes in isostatic packings. The form of the correlation function is remarkably similar to one predicted in the mosaic theory of the glass transition, and we relate the nature of the growing correlations to the entropy of packings.

cond-mat.dis-nn↗

arXiv2009

Segregation of Polymers in Confined Spaces

We investigate the motion of two overlapping polymers with self-avoidance confined in a narrow 2d box. A statistical model is constructed using blob free-energy arguments. We find spontaneous segregation under the condition: $L > R_{//}$, and mixing under $L < R_{//}$, where L is the length of the box, and $R_{//}$ the polymer extension in an infinite slit. Segregation time scales are determined by solving a mean first-passage time problem, and by performing Monte Carlo simulations. Predictions of the two methods show good agreement. Our results may elucidate a driving force for chromosomes segregation in bacteria.

physics.bio-ph↗

arXiv2009

Rheology of Granular Materials: Dynamics in a Stress Landscape

We present a framework for analyzing the rheology of dense driven granular materials, based on a recent proposal of a stress-based ensemble. In this ensemble fluctuations in a granular system near jamming are controlled by a temperature-like parameter, the angoricity, which is conjugate to the stress of the system. In this paper, we develop a model for slowly driven granular materials based on the stress ensemble and the idea of a landscape in stress space. The idea of an activated process driven by the angoricity has been shown by Behringer et al (2008) to describe the logarithmic strengthening of granular materials. Just as in the Soft Glassy Rheology (SGR) picture, our model represents the evolution of a small patch of granular material (a mesoscopic region) in a stress-based trap landscape. The angoricity plays the role of the fluctuation temperature in SGR. We determine (a) the constitutive equation, (b) the yield stress, and (c) the distribution of stress dissipated during granular shearing experiments, and compare these predictions to experiments of Hartley & Behringer (2003).

cond-mat.soft↗