arXiv subjects

Gautam I. Menon

Publications and source records attributed to Gautam I. Menon.

At least 19 recordsLinked to original sources

arXiv2026

Forces at the scale of the cell

The importance of molecular-scale forces in sculpting biological form and function has been acknowledged for more than a century. Accounting for forces in biology is a problem that lies at the intersection of soft condensed matter physics, statistical mechanics, and experimental methods, all adapted to a cellular context. This review surveys how forces arise within the cell. We provide a summary of the relevant background in cell biophysics, of soft-matter systems in and out of thermodynamic equilibrium, and of various force measurement methods. These ideas are then deployed to describe how forces are generated, transmitted, and sensed in specific cell-scale processes. We emphasize active matter descriptions, methodological tools that provide ways of incorporating non-equilibrium effects in a systematic manner into conceptual as well as quantitative descriptions. Our examples include polymerization forces, the motion of molecular motors, the properties of the actomyosin cortex, the mechanics of cell division, and shape changes in tissues. We suggest that a deeper understanding of cell function will necessarily require integrating the action of cell-scale physical forces with the assimilation and processing of information.

cond-mat.soft↗

arXiv2022

Phototactic cyanobacteria as an active matter system

Flocks of birds, schools of fish, mixtures of motors and cytoskeletal filaments, swimming bacteria and driven granular media are systems of interacting motile units that exhibit collective behaviour. These can all be described as active matter systems, since each individual unit takes energy from an internal energy depot and transduces it into work performed on the environment. We review a model for cyanobacterial phototaxis, emphasising the differences from other models for collective behaviour in active matter systems. The interactions between individual cells during phototaxis are dominated by mechanical forces mediated by their physical attachments through type IV pili (T4P) and through the production of "slime", a complex mixture of non-diffusible polysaccharides deposited by cells that acts to decrease friction locally. The slime, in particular, adds a component to the interaction that is local in space but non-local in time, perhaps most comparable to the pheromones laid down in ant trails. Our results suggest that the time-delayed component of the interactions between bacteria qualify their description as a novel active system, which we refer to as "damp" active matter.

q-bio.CB↗

arXiv2019

Confined crowded polymers near attractive surfaces

We present results from molecular dynamics simulations of a spherically confined neutral polymer in the presence of crowding agents, studying polymer shapes and conformations as a function of the confining potential, solvent quality and the density of crowders. The conformations of the polymer under good solvent conditions are largely independent of crowder density, even when the polymer is strongly confined. However, for poor solvents and attractive walls, the polymer shows a transition between an adsorbed extended state to a globular conformation on the surface as a function of crowder particle density. This state differs from both the desorbed globular conformation in the absence of any wall interactions and the adsorbed globular conformation at low values of the attractive wall interactions. We revisit the earlier understanding of the adsorption of confined polymers on curved, attractive surfaces in the light of these results.

cond-mat.soft↗

arXiv2019

Orientational correlations in fluids with quenched disorder

Snapshots of colloidal particles moving on disordered two-dimensional substrates can be used to extract equal-time many-body correlations in their positions. To understand the systematics of these correlations, we perform Monte Carlo simulations of a two-dimensional model fluid placed in a quenched disordered background. We use configurations generated from these simulations to compute translational and orientational two-point correlations at equal time, concentrating on correlations in local orientational order as a function of density and disorder strength. We calculate both the disorder averaged version of conventional two-point correlation functions for orientational order, as well as the disorder averaged version of a novel correlation function of time-averaged disorder-induced inhomogeneities in local orientation analogous to the Edwards-Anderson correlation function in spin systems. We demonstrate that these correlations can exhibit interesting non-monotonic behavior in proximity to the underlying fluid-solid transition and suggest that this prediction should be experimentally accessible.

cond-mat.soft↗

arXiv2017

Vortex core order and field-driven phase coexistence in the attractive Hubbard model

Superconductivity occurs in the proximity of other competing orders in a wide variety of materials. Such competing phases may reveal themselves when superconductivity is locally suppressed by a magnetic field in the core of a vortex. We explore the competition between superconductivity and charge density wave order in the attractive Hubbard model on a square lattice. Using Bogoliubov-deGennes mean field theory, we study how vortex structures form and evolve as the magnetic flux is tuned. Each vortex seeds a CDW region whose size is determined by the energy cost of the competing phase. The vortices form a lattice whose lattice parameter shrinks with increasing flux. Eventually, their charge-ordered vortex cores overlap, leading to a field-driven coexistence phase exhibiting both macroscopic charge order and superconductivity -- a `supersolid'. Ultimately, superconductivity disappears via a first-order phase transition into a purely charge ordered state. We construct a phase diagram containing these multiple ordered states, using $t'$, the next-nearest neighbour hopping, to tune the competition between phases.

cond-mat.str-el↗

arXiv2011

Suppression of the Melting Line in a Weakly Disordered Flux-line System

An analytic formula describing the suppression of the equilibrium melting line by quenched point pinning disorder is compared to data from ac susceptibility and magnetization measurements in the mixed phase of the layered dichalcogenide low T_c superconductor 2H-NbSe_2. This material exhibits a sharp peak effect in the critical current close to the upper critical field H_c2(T). Arguing that the disorder-suppressed melting line in this system is to be identified with the locus of peak positions of the critical current as magnetic field and temperature are varied, we demonstrate that this formula provides a remarkably accurate fit to the experimental data over three orders of magnitude in magnetic field.

cond-mat.supr-con↗

arXiv2011

Thermodynamic behaviour of two-dimensional vesicles revisited

We study pressurised self-avoiding ring polymers in two dimensions using Monte Carlo simulations, scaling arguments and Flory-type theories, through models which generalise the model of Leibler, Singh and Fisher [Phys. Rev. Lett. Vol. 59, 1989 (1987)]. We demonstrate the existence of a thermodynamic phase transition at a non-zero scaled pressure $\tilde{p}$, where $\tilde{p} = Np/4π$, with the number of monomers $N \rightarrow \infty$ and the pressure $p \rightarrow 0$, keeping $\tilde{p}$ constant, in a class of such models. This transition is driven by bond energetics and can be either continuous or discontinuous. It can be interpreted as a shape transition in which the ring polymer takes the shape, above the critical pressure, of a regular N-gon whose sides scale smoothly with pressure, while staying unfaceted below this critical pressure. In the general case, we argue that the transition is replaced by a sharp crossover. The area, however, scales with $N^2$ for all positive $p$ in all such models, consistent with earlier scaling theories.

cond-mat.stat-mech↗

arXiv2010

Epidemiological dynamics of the 2009 Influenza A(H1N1)v outbreak in India

We analyze the time-series data for the onset of A(H1N1)v influenza pandemic in India during the period June 1- September 30, 2009. Using a variety of statistical fitting procedures, we obtain a robust estimate of the exponential growth rate $\langle λ\rangle \simeq 0.15$. This corresponds to a basic reproductive number $R_0 \simeq 1.45$ for influenza A(H1N1)v in India, a value which lies towards the lower end of the range of values reported for different countries affected by the pandemic.

q-bio.PE↗

arXiv2010

A Coupled Map Lattice Model for Rheological Chaos in Sheared Nematic Liquid Crystals

A variety of complex fluids under shear exhibit complex spatio-temporal behaviour, including what is now termed rheological chaos, at moderate values of the shear rate. Such chaos associated with rheological response occurs in regimes where the Reynolds number is very small. It must thus arise as a consequence of the coupling of the flow to internal structural variables describing the local state of the fluid. We propose a coupled map lattice (CML) model for such complex spatio-temporal behaviour in a passively sheared nematic liquid crystal, using local maps constructed so as to accurately describe the spatially homogeneous case. Such local maps are coupled diffusively to nearest and next nearest neighbours to mimic the effects of spatial gradients in the underlying equations of motion. We investigate the dynamical steady states obtained as parameters in the map and the strength of the spatial coupling are varied, studying local temporal properties at a single site as well as spatio-temporal features of the extended system. Our methods reproduce the full range of spatio-temporal behaviour seen in earlier one-dimensional studies based on partial differential equations. We report results for both the one and two-dimensional cases, showing that spatial coupling favours uniform or periodically time-varying states, as intuitively expected. We demonstrate and characterize regimes of spatio-temporal intermittency out of which chaos develops. Our work suggests that such simplified lattice representations of the spatio-temporal dynamics of complex fluids under shear may provide useful insights as well as fast and numerically tractable alternatives to continuum representations.

cond-mat.soft↗

arXiv2010

Active Matter

The term active matter describes diverse systems, spanning macroscopic (e.g. shoals of fish and flocks of birds) to microscopic scales (e.g. migrating cells, motile bacteria and gels formed through the interaction of nanoscale molecular motors with cytoskeletal filaments within cells). Such systems are often idealizable in terms of collections of individual units, referred to as active particles or self-propelled particles, which take energy from an internal replenishable energy depot or ambient medium and transduce it into useful work performed on the environment, in addition to dissipating a fraction of this energy into heat. These individual units may interact both directly as well as through disturbances propagated via the medium in which they are immersed. Active particles can exhibit remarkable collective behaviour as a consequence of these interactions, including non-equilibrium phase transitions between novel dynamical phases, large fluctuations violating expectations from the central limit theorem and substantial robustness against the disordering effects of thermal fluctuations. In this chapter, following a brief summary of experimental systems which may be classified as examples of active matter, I describe some of the principles which underlie the modeling of such systems.

cond-mat.soft↗

arXiv2010

Fluctuating Nematodynamics using the Stochastic Method of Lines

We construct Langevin equations describing the fluctuations of the tensor order parameter $Q_{αβ}$ in nematic liquid crystals by adding noise terms to time-dependent variational equations that follow from the Ginzburg-Landau-de Gennes free energy. The noise is required to preserve the symmetry and tracelessness of the tensor order parameter and must satisfy a fluctuation-dissipation relation at thermal equilibrium. We construct a noise with these properties in a basis of symmetric traceless matrices and show that the Langevin equations can be solved numerically in this basis using a stochastic version of the method of lines. The numerical method is validated by comparing equilibrium probability distributions, structure factors and dynamic correlations obtained from these numerical solutions with analytic predictions. We demonstrate excellent agreement between numerics and theory. This methodology can be applied to the study of phenomena where fluctuations in both the magnitude and direction of nematic order are important, as for instance in the nematic swarms which produce enhanced opalescence near the isotropic-nematic transition or the problem of nucleation of the nematic from the isotropic phase.

cond-mat.soft↗

arXiv2009

Driven Disordered Polymorphic Solids: Phases and Phase Transitions, Dynamical Coexistence and Peak Effect Anomalies

We study a model for the depinning and driven steady state phases of a solid tuned across a polymorphic phase transition between ground states of triangular and square symmetry. These include pinned states which may have dominantly triangular or square correlations, a plastically flowing liquid-like phase, a moving phase with hexatic correlations, flowing triangular and square states and a dynamic coexistence regime characterized by the complex interconversion of locally square and triangular regions. We locate these phases in a dynamical phase diagram. We demonstrate that the apparent power-law orientational correlations we obtain in our moving hexatic phase arise from circularly averaging an orientational correlation function with qualitatively different behaviour in the longitudinal (drive) and transverse directions. The intermediate coexistence regime exhibits several novel properties, including substantial enhancement in the current noise, an unusual power-law spectrum of current fluctuations and striking metastability effects. This noise arises from the fluctuations of the interface separating locally square and triangular ordered regions. We demonstrate the breakdown of effective ``shaking temperature'' treatments in the coexistence regime by showing that such shaking temperatures are non-monotonic functions of the drive in this regime. Finally we discuss the relevance of these simulations to the anomalous behaviour seen in the peak effect regime of vortex lines in the disordered mixed phase of type-II superconductors. We propose that this anomalous behavior is directly linked to the behavior exhibited in our simulations in the dynamical coexistence regime, thus suggesting a possible solution to the problem of the origin of peak effect anomalies.

cond-mat.supr-con↗

arXiv2009

The Isotropic-Nematic Interface with an Oblique Anchoring Condition

We present numerical and analytic results for uniaxial and biaxial order at the isotropic-nematic interface within Ginzburg-Landau-de Gennes theory. We study the case where an oblique anchoring condition is imposed asymptotically on the nematic side of the interface, reproducing results of previous work when this condition reduces to planar or homoeotropic anchoring. We construct physically motivated and computationally flexible variational profiles for uniaxial and biaxial order, comparing our variational results to numerical results obtained from a minimization of the Ginzburg-Landau-de Gennes free energy. While spatial variations of the scalar uniaxial and biaxial order parameters are confined to the neighbourhood of the interface, nematic elasticity requires that the director orientation interpolate linearly between either planar or homoeotropic anchoring at the location of the interface and the imposed boundary condition at infinity. The selection of planar or homoeotropic anchoring at the interface is governed by the sign of the Ginzburg-Landau-de Gennes elastic coefficient L_2. Our variational calculations are in close agreement with our numerics and agree qualitatively with results from density functional theory and molecular simulations.

cond-mat.soft↗

arXiv2009

Universality Class of the Reversible-Irreversible Transition in Sheared Suspensions

Collections of non-Brownian particles suspended in a viscous fluid and subjected to oscillatory shear at very low Reynolds number have recently been shown to exhibit a remarkable dynamical phase transition separating reversible from irreversible behaviour as the strain amplitude or volume fraction are increased. We present a simple model for this phenomenon, based on which we argue that this transition lies in the universality class of the conserved DP models or, equivalently, the Manna model. This leads to predictions for the scaling behaviour of a large number of experimental observables. Non-Brownian suspensions under oscillatory shear may thus constitute the first experimental realization of an inactive-active phase transition which is not in the universality class of conventional directed percolation.

cond-mat.soft↗

arXiv2009

Biaxiality at the Isotropic-Nematic Interface with Planar Anchoring

We revisit the classic problem of the structure of the isotropic-nematic interface within Ginzburg-Landau-de Gennes theory, refining previous analytic treatments of biaxiality at the interface. We compare our analysis with numerical results obtained through a highly accurate spectral collocation scheme for the solution of the Landau-Ginzburg-de Gennes equations. In comparison to earlier work, we obtain improved agreement with numerics for both the uniaxial and biaxial profiles, accurate asymptotic results for the decay of biaxial order on both nematic and isotropic sides of the interface and accurate fits to data from density functional approaches to this problem.

cond-mat.soft↗

arXiv2008

Numerical Method of Lines for the Relaxational Dynamics of Nematic Liquid Crystals

We propose an efficient numerical scheme, based on the method of lines, for solving the Landau-de Gennes equations describing the relaxational dynamics of nematic liquid crystals. Our method is computationally easy to implement, balancing requirements of efficiency and accuracy. We benchmark our method through the study of the following problems: the isotropic-nematic interface, growth of nematic droplets in the isotropic phase and the kinetics of coarsening following a quench into the nematic phase. Our results, obtained through solutions of the full coarse-grained equations of motion with no approximations, provide a stringent test of the de Gennes ansatz for the isotropic - nematic interface, illustrate the anisotropic character of droplets in the nucleation regime and validate dynamical scaling in the coarsening regime.

cond-mat.soft↗

arXiv2008

Regular and Chaotic States in a Local Map Description of Sheared Nematic Liquid Crystals

We propose and study a local map capable of describing the full variety of dynamical states, ranging from regular to chaotic, obtained when a nematic liquid crystal is subjected to a steady shear flow. The map is formulated in terms of a quaternion parametrization of rotations of the local frame described by the axes of the nematic director, subdirector and the joint normal to these, with two additional scalars describing the strength of ordering. Our model yields kayaking, wagging, tumbling, aligned and coexistence states, in agreement with previous formulations based on coupled ordinary differential equations. Such a map can serve as a building block for the construction of lattice models of the complex spatio-temporal states predicted for sheared nematics.

cond-mat.soft↗

arXiv2007

Asymptotic Behavior of Inflated Lattice Polygons

We study the inflated phase of two dimensional lattice polygons with fixed perimeter $N$ and variable area, associating a weight $\exp[pA - Jb ]$ to a polygon with area $A$ and $b$ bends. For convex and column-convex polygons, we show that $ /A_{max} = 1 - K(J)/\tilde{p}^2 + \mathcal{O}(ρ^{-\tilde{p}})$, where $\tilde{p}=pN \gg 1$, and $ρ<1$. The constant $K(J)$ is found to be the same for both types of polygons. We argue that self-avoiding polygons should exhibit the same asymptotic behavior. For self-avoiding polygons, our predictions are in good agreement with exact enumeration data for J=0 and Monte Carlo simulations for $J \neq 0$. We also study polygons where self-intersections are allowed, verifying numerically that the asymptotic behavior described above continues to hold.

cond-mat.stat-mech↗