arXiv subjects

Saroj Kumar Nandi

Publications and source records attributed to Saroj Kumar Nandi.

35 records · Page 2Linked to original sources

arXiv2021

The origin of universal cell shape variability in a confluent epithelial monolayer

Cell shape is fundamental in biology. The average cell shape can influence crucial biological functions, such as cell fate and division orientation. But cell-to-cell shape variability is often regarded as noise. In contrast, recent works reveal that shape variability in diverse epithelial monolayers follows a nearly universal distribution. However, the origin and implications of this universality are unclear. Here, assuming contractility and adhesion are crucial for cell shape, characterized via aspect ratio (AR), we develop a mean-field analytical theory for shape variability. We find that a single parameter, $α$, containing all the system-specific details, describes the probability distribution function (PDF) of AR; this leads to a universal relation between the standard deviation and the average of AR. The PDF for the scaled AR is not strictly but almost universal. The functional form is not related to jamming, contrary to common beliefs, but a consequence of a mathematical property. In addition, we obtain the scaled area distribution, described by the parameter $μ$. We show that $α$ and $μ$ together can distinguish the effects of changing physical conditions, such as maturation, on different system properties. The theory is verified in simulations of two distinct models of epithelial monolayers and agrees well with existing experiments. We demonstrate that in a confluent monolayer, average shape determines both the shape variability and dynamics. Our results imply the cell shape variability is inevitable, where a single parameter describes both statics and dynamics and provides a framework to analyze and compare diverse epithelial systems.

cond-mat.soft↗

arXiv2021

Theory and simulation for equilibrium glassy dynamics in cellular Potts model of confluent biological tissue

Glassy dynamics in a confluent monolayer is indispensable in morphogenesis, wound healing, bronchial asthma, and many others; a detailed theoretical framework for such a system is, therefore, important. Vertex model (VM) simulations have provided crucial insights into the dynamics of such systems, but their nonequilibrium nature makes it difficult for theoretical development. Cellular Potts model (CPM) of confluent monolayer provides an alternative model for such systems with a well-defined equilibrium limit. We combine numerical simulations of CPM and an analytical study based on one of the most successful theories of equilibrium glass, the random first order transition theory, and develop a comprehensive theoretical framework for a confluent glassy system. We find that the glassy dynamics within CPM is qualitatively similar to that in VM. Our study elucidates the crucial role of geometric constraints in bringing about two distinct regimes in the dynamics, as the target perimeter $P_0$ is varied. The unusual sub-Arrhenius relaxation results from the distinctive interaction potential arising from the perimeter constraint in such systems. Fragility of the system decreases with increasing $P_0$ in the low-$P_0$ regime, whereas the dynamics is independent of $P_0$ in the other regime. The rigidity transition, found in VM, is absent within CPM; this difference seems to come from the nonequilibrium nature of the former. We show that CPM captures the basic phenomenology of glassy dynamics in a confluent biological system via comparison of our numerical results with existing experiments on different systems.

cond-mat.soft↗

arXiv2021

The random first-order transition theory of active glass in the high-activity regime

Dense active matter, in the fluid or amorphous-solid form, has generated intense interest as a model for the dynamics inside living cells and multicellular systems. An extension of the random first-order transition theory (RFOT) to include activity was developed, whereby the activity of the individual particles was added to the free energy of the system in the form of the potential energy of an active particle, trapped by a harmonic potential that describes the effective confinement by the surrounding medium. This active-RFOT model was shown to successfully account for the dependence of the structural relaxation time in the active glass, extracted from simulations, as a function of the activity parameters: the magnitude of the active force ($f_0$) and its persistence time ($τ_p$). However, significant deviations were found in the limit of large activity (large $f_0$ and/or $τ_p$). Here we extend the active-RFOT model to high activity using an activity-dependent harmonic confining potential, which we solve self-consistently. The extended model predicts qualitative changes in the high activity regime, which agree with the results of simulations in both three-dimensional and two-dimensional models of active glass.

cond-mat.soft↗

arXiv2020

Size-Stretched Exponential Relaxation in a Model with Arrested States

We study the effect of rapid quench to zero temperature in a model with competing interactions, evolving through conserved spin dynamics. In a certain regime of model parameters, we find that the model belongs to the broader class of kinetically constrained models, however, the dynamics is different from that of a glass. The system shows stretched exponential relaxation with the unusual feature that the relaxation time diverges as a power of the system size. Explicitly, we find that the spatial correlation function decays as $\exp(-2r/\sqrt{L})$ as a function of spatial separation $r$ in a system with $L$ sites in steady state, while the temporal auto-correlation function follows $\exp(-(t/τ_L)^{1/2})$, where $t$ is the time and $τ_L$ proportional to $L$. In the coarsening regime, after time $t_w$, there are two growing length scales, namely $\mathcal{L}(t_w) \sim t_w^{1/2}$ and $\mathcal{R}(t_w) \sim t_w^{1/4}$; the spatial correlation function decays as $\exp(-r/ \mathcal{R}(t_w))$. Interestingly, the stretched exponential form of the auto-correlation function of a single typical sample in steady state differs markedly from that averaged over an ensemble of initial conditions resulting from different quenches; the latter shows a slow power law decay at large times.

cond-mat.soft↗

arXiv2018

Protein gradients in single cells induced by their coupling to "morphogen"-like diffusion

One of the many ways cells transmit information within their volume is through steady spatial gradients of different proteins. However, the mechanism through which proteins without any sources or sinks form such single-cell gradients is not yet fully understood. One of the models for such gradient formation, based on differential diffusion, is limited to proteins with large ratios of their diffusion constants or to specific protein-large molecule interactions. We introduce a novel mechanism for gradient formation via the coupling of the proteins within a single cell with a molecule, that we call a "pronogen", whose action is similar to that of morphogens in multi-cell assemblies, the pronogen is produced with a fixed flux at one side of the cell. This coupling results in an effectively non-linear diffusion degradation model for the pronogen dynamics within the cell, which leads to a steady-state gradient of the protein concentration. We use a stability analysis to show that these gradients are linearly stable with respect to perturbations.

physics.bio-ph↗

arXiv2018

Activity-dependent self-regulation of viscous length scales in biological systems

Cellular cortex, which is a highly viscous thin cytoplasmic layer just below the cell membrane, controls the cell's mechanical properties, which can be characterized by a hydrodynamic length scale $\ell$. Cells actively regulate $\ell$ via the activity of force generating molecules, such as myosin II. Here we develop a general theory for such systems through coarse-grained hydrodynamic approach including activity in the static description of the system providing an experimentally accessible parameter and elucidate the detailed mechanism of how a living system can actively self-regulate its hydrodynamic length scale, controlling the rigidity of the system. Remarkably, we find that $\ell$, as a function of activity, behaves universally and roughly inversely proportional to the activity of the system. Our theory rationalizes a number of experimental findings on diverse systems and comparison of our theory with existing experimental data show good agreement.

physics.bio-ph↗

arXiv2018

Effective temperature of active fluids and sheared granular matter

The dynamics within active fluids, driven by internal activity of the self-propelled particles, is a subject of intense study in non-equilibrium physics. These systems have been explored using simulations, where the motion of a passive tracer particle is followed. Similar studies have been carried out for passive granular matter that is driven by shearing its boundaries. In both types of systems the non-equilibrium motion have been quantified by defining a set of "effective temperatures", using both the tracer particle kinetic energy and the fluctuation-dissipation relation. We demonstrate that these effective temperatures extracted from the many-body simulations fit analytical expressions that are obtained for a single active particle inside a visco-elastic fluid. This result provides testable predictions and suggests a unified description for the dynamics inside active systems.

physics.bio-ph↗

arXiv2018

Viscosity and effective temperature of an active dense system of self-propelled particles

We obtain a nonequilibrium theory for a simple model of a generic class of active dense systems consisting of self-propelled particles with a self-propulsion force, $f_0$, and persistence time, $τ_p$, of their motion. We consider two models of activity and find the system is characterized by an evolving effective temperature $T_{eff}(τ)$, defined through a generalized fluctuation-dissipation theorem. $T_{eff}(τ)$ is equal to the equilibrium temperature at very short time $τ$ and saturates to $T_{eff}=T_{eff}(τ\to\infty)$ at long times; The transition time $t_{trans}$ when $T_{eff}(τ)$ goes to the long-time limit depends on $τ_p$ alone and $t_{trans}\sim τ_p^{0.85}$ for both models. $f_0$ reduces the viscosity with increasing activity, $τ_p$ on the other hand, may increase or decrease viscosity depending on the details of how the activity is included. However, as a function of $T_{eff}$, viscosity shows the same behavior for different models of activity and $η\sim (T_{eff}-T)^{-γ}$ with $γ=1.74$. Our theory gives reasonable agreement when compared with experimental data and is consistent with several experiments on diverse systems.

cond-mat.soft↗

arXiv2017

Activity controls fragility: A Random First Order Transition Theory for an active glass

How does nonequilibrium activity modify the approach to a glass? This is an important question, since many experiments reveal the near-glassy nature of the cell interior, remodelled by activity. However, different simulations of dense assemblies of active particles, parametrised by a self-propulsion force, $f_0$, and persistence time, $τ_p$, appear to make contradictory predictions about the influence of activity on characteristic features of glass, such as fragility. This calls for a broad conceptual framework to understand active glasses; here we extend the Random First-Order Transition (RFOT) theory to a dense assembly of self-propelled particles. We compute the active contribution to the configurational entropy using an effective medium approach - that of a single particle in a caging-potential. This simple active extension of RFOT provides excellent quantitative fits to existing simulation results. We find that whereas $f_0$ always inhibits glassiness, the effect of $τ_p$ is more subtle and depends on the microscopic details of activity. In doing so, the theory automatically resolves the apparent contradiction between the simulation models. The theory also makes several testable predictions, which we verify by both existing and new simulation data, and should be viewed as a step towards a more rigorous analytical treatment of active glass.

cond-mat.soft↗

arXiv2017

Nonequilibrium mode-coupling theory for dense active systems of self-propelled particles

The physics of active systems of self-propelled particles, in the regime of a dense liquid state, is an open puzzle of great current interest, both for statistical physics and because such systems appear in many biological contexts. We develop a nonequilibrium mode-coupling theory (MCT) for such systems, where activity is included as a colored noise with the particles having a self-propulsion foce $f_0$ and persistence time $τ_p$. Using the extended MCT and a generalized fluctuation-dissipation theorem, we calculate the effective temperature $T_{eff}$ of the active fluid. The nonequilibrium nature of the systems is manifested through a time-dependent $T_{eff}$ that approaches a constant in the long-time limit, which depends on the activity parameters $f_0$ and $τ_p$. We find, phenomenologically, that this long-time limit is captured by the potential energy of a single, trapped active particle (STAP). Through a scaling analysis close to the MCT glass transition point, we show that $τ_α$, the $α$-relaxation time, behaves as $τ_α\sim f_0^{-2γ}$, where $γ=1.74$ is the MCT exponent for the passive system. $τ_α$ may increase or decrease as a function of $τ_p$ depending on the type of active force correlations, but the behavior is always governed by the same value of the exponent $γ$. Comparison with numerical solution of the nonequilibrium MCT as well as simulation results give excellent agreement with the scaling analysis.

cond-mat.soft↗

arXiv2016

Spinodals with Disorder: from Avalanches in Random Magnets to Glassy Dynamics

We revisit the phenomenon of spinodals in the presence of quenched disorder and develop a complete theory for it. We focus on the spinodal of an Ising model in a quenched random field (RFIM), which has applications in many areas from materials to social science. 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 latter is due to the depinning and the subsequent expansion of rare droplets. We work out the associated 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 nonanalyticities much like in a Griffith phenomenon. From the recently established connection between the spinodal of the RFIM and glassy dynamics, our results also allow us to conclusively assess the physical content and the status of the dynamical transition predicted by the mean-field theory of glass-forming liquids.

cond-mat.soft↗

arXiv2015

Understanding the approximations of mode-coupling theory for sheared steady states of colloids

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.

cond-mat.soft↗

arXiv2014

Critical dynamical heterogeneities close to continuous second-order glass transitions

We analyse, using Inhomogenous Mode-Coupling Theory, the critical scaling behaviour of the dynamical susceptibility at a distance epsilon from continuous second-order glass transitions. We find that the dynamical correlation length xi behaves generically as epsilon^{-1/3} and that the upper critical dimension is equal to six. More surprisingly, we find activated dynamic scaling, where xi grows with time as [ln(t)]^2 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.

cond-mat.dis-nn↗

arXiv2013

The glass susceptibility: growth kinetics and saturation under shear

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 $χ_C(t,t_w)$ with time $t$ and waiting time $t_w$. 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 $χ_C^P$ of $χ_C(t,t_w)$, which can be viewed as a correlation volume, grows as $t_w^{0.5}$, and the relaxation time as $t_w^{0.8}$, 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 {\bf 103}, 4128 (1999)] and Kob and Barrat [Phys. Rev. Lett. {\bf 78}, 4581 (1997)] and are also in qualitative agreement with Parsaeian and Castillo [Phys. Rev. E {\bf 78}, 060105(R) (2008)]. On the other hand, if the quench is to a point on the {\em 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, $χ_C^P \sim t_w^{0.13}$. Further, we show that a shear rate $\gdot$ cuts off the growth of glassy correlations when $t_w\sim 1/\gdot$ for quench in the glassy regime and $t_w=\min(t_r,1/\gdot)$ in the liquid, where $t_r$ is the relaxation time of the unsheared liquid. The relaxation time of the steady state fluid in this case is $\propto \gdot^{-0.8}$.

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

The mode-coupling glass transition in a fluid confined by a periodic potential

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. We use fluctuating hydrodynamics, with confinement imposed through a periodic potential whose wavelength plays an important role in our treatment. To make the calculation tractable we implement a detailed calculation in one dimension. Although we do not expect simple 1d fluids to show a glass transition, our results are indicative of the behaviour expected in higher dimensions. In a certain region of parameter space we observe a three-step relaxation reported recently in computer simulations [S.H. Krishnan, PhD thesis, Indian Institute of Science (2005); Kim et al., Eur. Phys. J-ST 189, 135-139 (2010)] and a glass-glass transition. We compare our results to those of Krakoviack, PRE 75, 031503 (2007) and Lang et al., PRL 105, 125701 (2010).

cond-mat.soft↗

arXiv2006

Comment on "Layering transition in confined molecular thin films: Nucleation and growth"

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.

cond-mat.soft↗