Saroj Kumar Nandi | Indian Institute of Science (original) (raw)

Papers by Saroj Kumar Nandi

How activity modifies the properties of systems compared to their passive counterparts is an open... more How activity modifies the properties of systems compared to their passive counterparts is an open question. Here, we extend a microscopic theory for the glassy dynamics of passive systems in their dense low-temperature limit, namely the Random First-Order Transition (RFOT) theory, to describe an active self-propelled particle system. We generalize and unify the findings of recent simulations and experiments on such systems and provide a number of testable predictions. Self-propulsion force, f0, and persistence time, τp, characterize the activity of the constituent particles, and they were found in previous works to affect the system dynamics quite differently: f0 inhibits glassiness, reducing the glass transition temperature and fragility of the system, whereas τp promotes glassiness and increases these parameters. Our theory explains these opposite effects of the two activity parameters, as arising due to their respective influence on the kinetic energy of the self-propelled particles that are caged within a dense glass.

Aps Meeting Abstracts, Mar 1, 2011

We extend the mode coupling theory (MCT) of glass transition in bulk fluids to the case of confin... more We extend the mode coupling theory (MCT) of glass transition in bulk fluids to the case of confinement, which enhances the feedback mechanism to drive the system to a glassy state. Confinement enters the theory in terms of an external potential that produces an inhomogeneous density background, which in turn forces the fluid to relax diffusively. Below a certain density, the MCT transition becomes continuous and the critical density of continuous to discontinuous transition depends on the nature of the external potential. If the control parameters are in the proper region of phase space, the fluid shows a three-step relaxation scenario. We also incorporate shear in our theory and thereby show that the fluid, when confined, shows shear thinning at much lower shear rate compared to a bulk fluid.

Journal of Statistical Mechanics: Theory and Experiment, 2013

We present a simple model that can be used to account for the rheological behaviour observed in r... more We present a simple model that can be used to account for the rheological behaviour 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.

The lack of clarity of various mode-coupling theory (MCT) approximations, even in equilibrium,mak... more The lack of clarity of various mode-coupling theory (MCT) approximations, even in equilibrium,makes it hard to understand the relation between various MCT approaches for sheared steady states as well as their regime of validity. Here we try to understand these approximations indirectly by deriving the MCT equations through two different approaches for a colloidal system under shear, first, through a microscopic approach, as suggested by Zaccarelli et al, and second, through fluctuating hydrodynamics, where the approximations used in the derivation are quite clear. The qualitative similarity of our theory with a number of existing theories show that linear response theory might play a role in various approximations employed in deriving those theories and one needs to be careful while applying them for systems arbitrarily far away from equilibrium, such as a granular system or when shear is very strong. As a byproduct of our calculation, we obtain the extension of Yvon-Born-Green (YBG) equation for a sheared system and under the assumption of random-phase approximation, the YBG equation yields the distorted structure factor that was earlier obtained through different approaches.

Motivated by the connection between the dynamical transition predicted by the mean-field theory o... more Motivated by the connection between the dynamical transition predicted by the mean-field theory of glass-forming liquids and the spinodal of an Ising model in a quenched random field (RFIM) beyond mean-field, we revisit the phenomenon of spinodals in the presence of quenched disorder and develop a complete theory for it. By working at zero temperature in the quasi-statically driven RFIM, thermal fluctuations are eliminated and one can give a rigorous content to the notion of spinodal. We show that the spinodal transition is due to the depinning and the subsequent expansion of rare droplets. We work out the critical behavior, which, in any finite dimension, is very different from the mean-field one: the characteristic length diverges exponentially and the thermodynamic quantities display very mild non-analyticities much like in a Griffith phenomenon. On the basis of our results we assess the physical content and the status of the dynamical transition predicted by the mean-field theory of glassy dynamics.

We analyse, using Inhomogenous Mode-Coupling Theory, the critical scaling behaviour of the dynami... more We analyse, using Inhomogenous Mode-Coupling Theory, the critical scaling behaviour of the dynamical susceptibility at a distance ǫ from continuous second-order glass transitions. We find that the dynamical correlation length ξ behaves generically as ǫ −1/3 and that the upper critical dimension is equal to six. More surprisingly, we find activated dynamic scaling, where ξ grows with time as ln 2 t exactly at criticality. All these results suggest a deep analogy between the glassy behaviour of attractive colloids or randomly pinned supercooled liquids and that of the Random Field Ising Model.

We study the growth kinetics of glassy correlations in a structural glass by monitoring the evolu... more We study the growth kinetics of glassy correlations in a structural glass by monitoring the evolution, within mode-coupling theory, of a suitably defined three-point function χC(t, tw) with time t and waiting time tw. From the complete wave vector-dependent equations of motion for domain growth we pass to a schematic limit to obtain a numerically tractable form. We find that the peak value χ P C of χC (t, tw), which can be viewed as a correlation volume, grows as t 0.5 w , and the relaxation time as t 0.8 w , following a quench to a point deep in the glassy state. These results constitute a theoretical explanation of the simulation findings of Parisi [J. Phys. Chem. B 103, 4128 (1999)] and Kob and Barrat [Phys. Rev. Lett. 78, 4581 (1997)] and are also in qualitative agreement with Parsaeian and Castillo [Phys. Rev. E 78, 060105(R) ]. On the other hand, if the quench is to a point on the liquid side, the correlation volume grows to saturation. We present a similar calculation for the growth kinetics in a p-spin spin glass mean-field model where we find a slower growth, χ P C ∼ t 0.13 w . Further, we show that a shear rateγ cuts off the growth of glassy correlations when tw ∼ 1/γ for quench in the glassy regime and tw = min(tr, 1/γ) in the liquid, where tr is the relaxation time of the unsheared liquid. The relaxation time of the steady state fluid in this case is ∝γ −0.8 .

We present a simple model to account for the rheological behavior observed in recent experiments ... more 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 FFF is increased, in a range near the yield threshold. The power fluctuations are found to obey a steady-state fluctuation relation (FR) at small FFF. However, the FR is violated when FFF 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.

Arxiv preprint arXiv:1205.1152, Jan 1, 2012

We construct the equations for the growth kinetics of a structural glass within mode-coupling the... more We construct the equations for the growth kinetics of a structural glass within mode-coupling theory, through a non-stationary variant of the 3-density correlator defined in Phys. Rev. Lett. 97, 195701 (2006). We solve a schematic form of the resulting equations to obtain the coarsening of the 3-point correlator χ3(t, tw) as a function of waiting time tw. For a quench into the glass, we find that χ3 attains a peak value ∼ t 0.5 w at t − tw ∼ t 0.8 w , providing a theoretical basis for the numerical observations of Parisi [J. Phys. Chem. B 103, 4128 (1999)] and Kob and Barrat [Phys. Rev. Lett. 78, 4581 (1997)]. The aging is not "simple": the tw dependence cannot be attributed to an evolving effective temperature.

Arxiv preprint arXiv: …, Jan 1, 2011

We show that a fluid under strong spatially periodic confinement displays a glass transition with... more We show that a fluid under strong spatially periodic confinement displays a glass transition within mode-coupling theory (MCT) at a much lower density than the corresponding bulk system.

Physical Review B, Jan 1, 2006

When fluid is confined between two molecularly smooth surfaces to a few molecular diameters, it s... more When fluid is confined between two molecularly smooth surfaces to a few molecular diameters, it shows a large enhancement of its viscosity. From experiments it seems clear that the fluid is squeezed out layer by layer. A simple solution of the Stokes equation for quasi-two-dimensional confined flow, with the assmption of layer-by-layer flow is found. The results presented here correct those in Phys. Rev. B, 50, 5590 (1994), and show that both the kinematic viscosity of the confined fluid and the coefficient of surface drag can be obtained from the time dependence of the area squeezed out. Fitting our solution to the available experimental data gives the value of viscosity which is ∼7 orders of magnitude higher than that in the bulk.

How activity modifies the properties of systems compared to their passive counterparts is an open... more How activity modifies the properties of systems compared to their passive counterparts is an open question. Here, we extend a microscopic theory for the glassy dynamics of passive systems in their dense low-temperature limit, namely the Random First-Order Transition (RFOT) theory, to describe an active self-propelled particle system. We generalize and unify the findings of recent simulations and experiments on such systems and provide a number of testable predictions. Self-propulsion force, f0, and persistence time, τp, characterize the activity of the constituent particles, and they were found in previous works to affect the system dynamics quite differently: f0 inhibits glassiness, reducing the glass transition temperature and fragility of the system, whereas τp promotes glassiness and increases these parameters. Our theory explains these opposite effects of the two activity parameters, as arising due to their respective influence on the kinetic energy of the self-propelled particles that are caged within a dense glass.

Aps Meeting Abstracts, Mar 1, 2011

We extend the mode coupling theory (MCT) of glass transition in bulk fluids to the case of confin... more We extend the mode coupling theory (MCT) of glass transition in bulk fluids to the case of confinement, which enhances the feedback mechanism to drive the system to a glassy state. Confinement enters the theory in terms of an external potential that produces an inhomogeneous density background, which in turn forces the fluid to relax diffusively. Below a certain density, the MCT transition becomes continuous and the critical density of continuous to discontinuous transition depends on the nature of the external potential. If the control parameters are in the proper region of phase space, the fluid shows a three-step relaxation scenario. We also incorporate shear in our theory and thereby show that the fluid, when confined, shows shear thinning at much lower shear rate compared to a bulk fluid.

Journal of Statistical Mechanics: Theory and Experiment, 2013

We present a simple model that can be used to account for the rheological behaviour observed in r... more We present a simple model that can be used to account for the rheological behaviour 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.

The lack of clarity of various mode-coupling theory (MCT) approximations, even in equilibrium,mak... more The lack of clarity of various mode-coupling theory (MCT) approximations, even in equilibrium,makes it hard to understand the relation between various MCT approaches for sheared steady states as well as their regime of validity. Here we try to understand these approximations indirectly by deriving the MCT equations through two different approaches for a colloidal system under shear, first, through a microscopic approach, as suggested by Zaccarelli et al, and second, through fluctuating hydrodynamics, where the approximations used in the derivation are quite clear. The qualitative similarity of our theory with a number of existing theories show that linear response theory might play a role in various approximations employed in deriving those theories and one needs to be careful while applying them for systems arbitrarily far away from equilibrium, such as a granular system or when shear is very strong. As a byproduct of our calculation, we obtain the extension of Yvon-Born-Green (YBG) equation for a sheared system and under the assumption of random-phase approximation, the YBG equation yields the distorted structure factor that was earlier obtained through different approaches.

Motivated by the connection between the dynamical transition predicted by the mean-field theory o... more Motivated by the connection between the dynamical transition predicted by the mean-field theory of glass-forming liquids and the spinodal of an Ising model in a quenched random field (RFIM) beyond mean-field, we revisit the phenomenon of spinodals in the presence of quenched disorder and develop a complete theory for it. By working at zero temperature in the quasi-statically driven RFIM, thermal fluctuations are eliminated and one can give a rigorous content to the notion of spinodal. We show that the spinodal transition is due to the depinning and the subsequent expansion of rare droplets. We work out the critical behavior, which, in any finite dimension, is very different from the mean-field one: the characteristic length diverges exponentially and the thermodynamic quantities display very mild non-analyticities much like in a Griffith phenomenon. On the basis of our results we assess the physical content and the status of the dynamical transition predicted by the mean-field theory of glassy dynamics.

We analyse, using Inhomogenous Mode-Coupling Theory, the critical scaling behaviour of the dynami... more We analyse, using Inhomogenous Mode-Coupling Theory, the critical scaling behaviour of the dynamical susceptibility at a distance ǫ from continuous second-order glass transitions. We find that the dynamical correlation length ξ behaves generically as ǫ −1/3 and that the upper critical dimension is equal to six. More surprisingly, we find activated dynamic scaling, where ξ grows with time as ln 2 t exactly at criticality. All these results suggest a deep analogy between the glassy behaviour of attractive colloids or randomly pinned supercooled liquids and that of the Random Field Ising Model.

We study the growth kinetics of glassy correlations in a structural glass by monitoring the evolu... more We study the growth kinetics of glassy correlations in a structural glass by monitoring the evolution, within mode-coupling theory, of a suitably defined three-point function χC(t, tw) with time t and waiting time tw. From the complete wave vector-dependent equations of motion for domain growth we pass to a schematic limit to obtain a numerically tractable form. We find that the peak value χ P C of χC (t, tw), which can be viewed as a correlation volume, grows as t 0.5 w , and the relaxation time as t 0.8 w , following a quench to a point deep in the glassy state. These results constitute a theoretical explanation of the simulation findings of Parisi [J. Phys. Chem. B 103, 4128 (1999)] and Kob and Barrat [Phys. Rev. Lett. 78, 4581 (1997)] and are also in qualitative agreement with Parsaeian and Castillo [Phys. Rev. E 78, 060105(R) ]. On the other hand, if the quench is to a point on the liquid side, the correlation volume grows to saturation. We present a similar calculation for the growth kinetics in a p-spin spin glass mean-field model where we find a slower growth, χ P C ∼ t 0.13 w . Further, we show that a shear rateγ cuts off the growth of glassy correlations when tw ∼ 1/γ for quench in the glassy regime and tw = min(tr, 1/γ) in the liquid, where tr is the relaxation time of the unsheared liquid. The relaxation time of the steady state fluid in this case is ∝γ −0.8 .

We present a simple model to account for the rheological behavior observed in recent experiments ... more 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 FFF is increased, in a range near the yield threshold. The power fluctuations are found to obey a steady-state fluctuation relation (FR) at small FFF. However, the FR is violated when FFF 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.

Arxiv preprint arXiv:1205.1152, Jan 1, 2012

We construct the equations for the growth kinetics of a structural glass within mode-coupling the... more We construct the equations for the growth kinetics of a structural glass within mode-coupling theory, through a non-stationary variant of the 3-density correlator defined in Phys. Rev. Lett. 97, 195701 (2006). We solve a schematic form of the resulting equations to obtain the coarsening of the 3-point correlator χ3(t, tw) as a function of waiting time tw. For a quench into the glass, we find that χ3 attains a peak value ∼ t 0.5 w at t − tw ∼ t 0.8 w , providing a theoretical basis for the numerical observations of Parisi [J. Phys. Chem. B 103, 4128 (1999)] and Kob and Barrat [Phys. Rev. Lett. 78, 4581 (1997)]. The aging is not "simple": the tw dependence cannot be attributed to an evolving effective temperature.

Arxiv preprint arXiv: …, Jan 1, 2011

We show that a fluid under strong spatially periodic confinement displays a glass transition with... more We show that a fluid under strong spatially periodic confinement displays a glass transition within mode-coupling theory (MCT) at a much lower density than the corresponding bulk system.

Physical Review B, Jan 1, 2006

When fluid is confined between two molecularly smooth surfaces to a few molecular diameters, it s... more When fluid is confined between two molecularly smooth surfaces to a few molecular diameters, it shows a large enhancement of its viscosity. From experiments it seems clear that the fluid is squeezed out layer by layer. A simple solution of the Stokes equation for quasi-two-dimensional confined flow, with the assmption of layer-by-layer flow is found. The results presented here correct those in Phys. Rev. B, 50, 5590 (1994), and show that both the kinematic viscosity of the confined fluid and the coefficient of surface drag can be obtained from the time dependence of the area squeezed out. Fitting our solution to the available experimental data gives the value of viscosity which is ∼7 orders of magnitude higher than that in the bulk.