arXiv subjects

Varsha Banerjee

Publications and source records attributed to Varsha Banerjee.

At least 19 recordsLinked to original sources

arXiv2026

Suppression of Active Super-Diffusion: Impact of String Defects and Canted Multi-Domains

We investigate the transport dynamics of an active Brownian particle (ABP) traversing a complex, non-Newtonian liquid crystal (LC) matrix. Employing the Generalized Lebwohl-Lasher (GLL) model, we systematically vary higher-order orientational interactions to stabilize three distinct host environments: isotropic, uniform nematic, and structurally frustrated canted phases. Modeling the coupled system via off-lattice over-damped Langevin dynamics, the resulting trajectories are characterized by evaluating their step-size distributions (SSDs), mean-square displacements (MSDs), and Hurst exponents. In the uniform nematic phase, the anisotropic matrix elastically channels the ABP, producing a left-skewed exponential SSD and persistent ballistic motion parallel to the director $\hat{\mathbf{n}}$. Similarly, transverse transport obeys a Rayleigh distribution and acquires a prominent $t \ln t$ super-diffusive correction-an explicit signature of the particle coupling to the host's gapless transverse Goldstone modes, as predicted by Toner et al. [Phys. Rev. E {\bf 93}, 062610 (2016)]. Crucially, we reveal that this active super-diffusion is systematically suppressed when the long-range Goldstone fluctuations are disrupted by topological defects. This breakdown manifests both macroscopically within the fractured, multi-domain canted phase due to a structural mass gap, and locally in the unfrustrated nematic phase through scattering by vortex disclination lines. Consequently, while the local SSDs qualitatively mirror the ideal nematic state, the transverse $t \ln t$ scaling vanishes in the presence of these structural constraints. Our findings demonstrate that tuning the background defect architecture of a complex fluid can fundamentally alter the transport universality class of active matter, offering a novel paradigm for controlling microscopic mobility.

cond-mat.soft↗

arXiv2025

Violation of the Fluctuation Dissipation Theorem during Domain Growth in the Long-range Ising Model

The celebrated {\it fluctuation dissipation theorem} (FDT) does not apply to nonequilibrium systems. In this context, Cugliandolo and Kurchan [Phys. Rev. Lett. {\bf 71}, 173 (1993)] introduced a generalized FDT which interprets the nonequilibrium evolution as a composition of {\it time sectors} corresponding to different {\it effective temperatures}. We use this framework to study domain growth in the $d=2$ long-range Ising model (LRIM) with nonconserved kinetics ({\it Glauber spin-flip}) and conserved kinetics ({\it Kawasaki spin-exchange}). We study the dynamical scaling and super-universal (SU) scaling of various two-time quantities, e.g., autocorrelation function, response function, effective temperature, etc. In particular, we investigate how the interaction range and conservation laws affect these characteristic features of domain growth.

cond-mat.stat-mech↗

arXiv2025

Self-assembly of Dipolar Crystals from Magnetic Colloids

We study the self-assembly of magnetic colloids using the Stockmayer (SM) model characterized by short-range Lennard-Jones interactions and long-range dipole-dipole interactions. Using molecular dynamics simulations, we design cooling protocols that yield perfectly assembled single-domain magnetic crystals. We identify cooling rates at which the system transforms from an amorphous glass to a crystal, where magnetic ordering promotes crystalline order. Remarkably, we observe that the latter develops via a spontaneous transition rather than through the traditional nucleation and growth mechanism. For a weakly dipolar fluid ($\mu=1$), this self-assembly results in a face-centered cubic (FCC) colloidal crystal with dipole moments chained along the (111) direction. For fluids with higher dipole moment ($\mu = 2.5$), the crystal structure shifts towards a body-centered orthorhombic (BCO) arrangement due to the compression of chains from strong dipolar attractions. These results provide valuable insights into the mechanisms driving crystallization in magnetic fluids, opening new avenues for understanding the formation of magnetically responsive colloidal magnetic crystals with promising applications.

cond-mat.soft↗

arXiv2024

Two-stage assembly of patchy ellipses: From bent-core particlesto liquid crystal analogs

We investigate the two-dimensional behavior of colloidal patchy ellipsoids specifically designed to follow a two-step assembly process from the monomer state to mesoscopic liquid-crystal phases, via the formation of so-called bent-core units at the intermediate stage. Our model comprises a binary mixture of ellipses interacting via the Gay-Berne potential and decorated by surface patches, with the binary components being mirror-image variants of each other - referred to as left-handed and right-handed ellipses according to the position of their patches. The surface patches are designed so as in the first stage of the assembly the monomers form bent-cores units, i.e. V-shaped dimers with a specific bent angle. The Gay-Berne interactions, which act between the ellipses, drive the dimers to subsequently form the characteristic phase observed in bent-core liquid crystals. We numerically investigate -- by means of both Molecular Dynamics and Monte Carlo simulations -- the described two-step process: we first optimize a target bent-core unit and we then fully characterize its state diagram in temperature and density, defining the regions where the different liquid crystalline phases dominate.

cond-mat.soft↗

arXiv2024

Coarsening in Bent-core Liquid Crystals: Intermediate Splay Bend State en route to the Twist Bend Phase

We use molecular dynamics simulations to study coarsening dynamics in achiral banana-shaped bent-core liquid crystals following a quench from the high concentration polar smectic (SmX) phase to lower concentrations that favor the exotic twist-bend (TB) phase. Our novel result is the identification of an intermediate splay-bend state emerging prior to the eventual TB phase. The latter coarsens via the annihilation of {\it beta lines} which are analogous to string defects in nematic liquid crystals. Our findings are relevant for a large class of chiral systems assembled from achiral entities.

cond-mat.stat-mech↗

arXiv2024

Surface-directed Dynamics in Living Liquid Crystals

We study living liquid crystals (LLCs), which are an amalgam of nematic liquid crystals (LCs) and active matter (AM). These LLCs are placed in contact with surfaces which impose planar/homeotropic boundary conditions on the director field of the LC and the polarization field of the AM. The interplay of LC-AM interactions and the surface-directed conditions yield controlled pattern dynamics in the LLC, which has important technological implications. We discuss two representative examples of this pattern dynamics.

cond-mat.soft↗

arXiv2023

Phase separation of a magnetic fluid: Asymptotic states and non-equilibrium kinetics

We study self-assembly in a colloidal suspension of magnetic particles by performing comprehensive molecular dynamics simulations of the Stockmayer (SM) model which comprises spherical particles decorated by a magnetic moment. The SM potential incorporates dipole-dipole interactions along with the usual Lennard-Jones interaction and exhibits a gas-liquid phase coexistence observed experimentally in magnetic fluids. When this system is quenched from the high-temperature homogeneous phase to the coexistence region, the non-equilibrium evolution to the condensed phase proceeds with the development of spatial as well as magnetic order. We observe density-dependent coarsening mechanisms - a diffusive growth law $\ell(t)\sim t^{1/3}$ in the nucleation regime, and hydrodynamics-driven inertial growth law $\ell(t)\sim t^{2/3}$ in the spinodal regimes. [$\ell(t)$ is the average size of the condensate at time $t$ after the quench.] While the spatial growth is governed by the expected conserved order parameter dynamics, the growth of magnetic order in the spinodal regime exhibits unexpected non-conserved dynamics. The asymptotic morphologies have density-dependent shapes which typically include the isotropic sphere and spherical bubble morphologies in the nucleation region, and the anisotropic cylinder, planar slab, cylindrical bubble morphologies in the spinodal region. The structures are robust and nonvolatile and exhibit characteristic magnetic properties. For example, the oppositely magnetized hemispheres in the spherical morphology impart the characteristics of a {\it Janus particle} to it. The observed structures have versatile applications in catalysis, drug delivery systems, memory devices, and magnetic photonic crystals, to name a few.

cond-mat.soft↗

arXiv2023

Accelerated Inertial Regime in the Spinodal Decomposition of Magnetic Fluids

Furukawa predicted that at late times, the domain growth in binary fluids scales as $\ell(t)\sim t^{2/3}$, and the growth is driven by fluid inertia. The {\it inertial growth regime} has been highly elusive in molecular dynamics (MD) simulations. We perform coarsening studies of the Stockmayer (SM) model comprising of magnetic dipoles that interact via long-range dipolar interactions as well as the usual Lennard-Jones (LJ) potential. This fascinating polar fluid exhibits a gas-liquid phase coexistence, and magnetic order even in the absence of an external field. From comprehensive MD simulations, we observe the inertial scaling [$\ell(t)\sim t^{2/3}$] in the SM fluid for an extended time window. Intriguingly, the fluid inertia is overwhelming from the outset - our simulations do not show the early diffusive regime [$\ell(t)\sim t^{1/3}$] and the intermediate viscous regime [$\ell(t)\sim t$] prevalent in LJ fluids.

cond-mat.stat-mech↗

arXiv2023

Symbiotic Dynamics in Living Liquid Crystals

An amalgamate of nematic liquid crystals and active matter, referred to as living liquid crystals, is a promising self-healing material with futuristic applications for targeted delivery of information and micro-cargo. We provide a phenomenological model to study the symbiotic pattern dynamics in this contemporary system using the Toner-Tu model for active matter (AM), the Landau-de Gennes free energy for liquid crystals (LCs), and an experimentally motivated coupling term that favours co-alignment of the active and nematic components. Our extensive theoretical studies unfold two novel steady states, chimeras and solitons, with sharp regions of distinct orientational order that sweep through the coupled system in synchrony. The induced dynamics in the passive nematic is unprecedented. We show that the symbiotic dynamics of the AM and LC components can be exploited to induce and manipulate order in an otherwise disordered system.

physics.comp-ph↗

arXiv2022

Critical behavior of the three-state random-field Potts model in three dimensions

Enormous advances have been made in the past 20 years in our understanding of the random-field Ising model, and there is now consensus on many aspects of its behavior at least in thermal equilibrium. In contrast, little is known about its generalization to the random-field Potts model which has wide-ranging applications. Here we start filling this gap with an investigation of the three-state random-field Potts model in three dimensions. Building on the success of ground-state calculations for the Ising system, we use a recently developed approximate scheme based on graph-cut methods to study the properties of the zero-temperature random fixed point of the system that determines the zero and non-zero temperature transition behavior. We find compelling evidence for a continuous phase transition. Implementing an extensive finite-size scaling (FSS) analysis, we determine the critical exponents and compare them to those of the random-field Ising model.

cond-mat.stat-mech↗

arXiv2022

Emergence of Biaxiality in Nematic Liquid Crystals with Magnetic Inclusions: Some Theoretical Insights

The biaxial phase in nematic liquid crystals has been elusive for several decades after its prediction in the 1970s. A recent experimental breakthrough was achieved by Liu et al. [PNAS 113, 10479 (2016)] in a liquid crystalline medium with magnetic nanoparticles (MNPs). They exploited the different length scales of dipolar and magneto-nematic interactions to obtain an equilibrium state where the magnetic moments are at an angle to the nematic director. This tilt introduces a second distinguished direction for orientational ordering or biaxiality in the two-component system. Using coarse-grained Ginzburg-Landau free energy models for the nematic and magnetic fields, we provide a theoretical framework which allows for the manipulation of morphologies and quantitative estimates of biaxial order.

cond-mat.soft↗

arXiv2022

Equilibrium phases and domain growth kinetics of calamitic liquid crystals

The anisotropic shape of calamitic LC particles results in distinct energy values when nematogens are placed side-by-side or end-to-end. The energy anisotropy governed by parameter K' has deep consequences on equilibrium & non-equilibrium properties. Using GB model, which shows Nm & low temperature Sm order, we undertake large-scale MC & MD simulations to probe effect of K' on the equilibrium phase diagram & the non-equilibrium domain growth following a quench in the temperature T (coarsening). There are 2 transitions in the model, I->Nm at Tc1 & Nm->Sm at Tc2 Tc1->T<Tc2) that we consider has SmB order with a hexatic arrangement of the LC molecules in the layers. Coarsening in this phase exhibits a striking two-time-scale scenario: first the LC molecules align & develop orientational order, followed by emergence of characteristic layering along with the hexatic bond-orientational-order within layers. Consequently, the growth follows the LAC law L(t)~t^0.5 at early times & then shows a sharp crossover to a slower growth regime at later times. Our observations strongly suggest L(t)~t^0.25 in this regime. Interestingly, the correlation function shows dynamical scaling in both the regimes & the scaling function is universal. The dynamics is also robust with respect to changes in K', but the smecticity is more pronounced at larger values. Further, the early-time dynamics is governed by string defects, while the late-time evolution is dictated by interfacial defects. We believe this scenario is generic to Sm phase even with other kinds of local order within Sm layers.

cond-mat.stat-mech↗

arXiv2021

Dipolar Ising Model: Phases, Growth Laws and Universality

The behavior of many magnetic and dielectric solids, and the more contemporary magnetic super-lattices, is governed by dipolar interactions. They are anisotropic and long-ranged, having varied consequences ranging from ground states with complicated magnetic order to the presence of glassy dynamics characterised by a plethora of relaxation times.These systems are well-captured by the dipolar Ising model (DIM) with nearest-neighbor exchange interactions (J) and long-range dipolar interactions (D). Depending on the relative interaction strength Γ =J/D, there are four phases of distinct magnetic order and symmetry. Using Monte Carlo simulations, we perform deep quenches to study domain growth or coarsening in the d= 3 DIM. This important non-equilibrium phenomenon has not been addressed as dipolar interactions are notoriously difficult to handle theoretically. Our study reveals that, in spite of the anisotropy in interactions and diversity in ground state configurations, we observe universality in the ordering dynamics of all phases.

cond-mat.stat-mech↗

arXiv2020

Ordering Kinetics of Canted and Uniform States in Nematic Liquid Crystals

We undertake a comprehensive Monte Carlo (MC) study of the ordering kinetics in nematic liquid crystals (NLCs) in 3-dimensions $(d=3)$ by performing deep quenches from the isotropic $(T>T_c)$ to the nematic $(T<T_c)$ phase. The inter-molecular potential between the nematogens, represented by continuous $O(3)$ spins with inversion symmetry, is accurately mimicked by the {\it generalised Lebwohl Lasher} (GLL) model. It incorporates second and fourth order Legendre interactions, and their relative interaction strength is $λ$. For $λ<-0.3$, we observe {\it canted} morphologies with a $λ$-dependent angle-of-tilt between the neighbouring rod-like molecules. For $λ\geq-0.3$, the molecules align to yield {\it uniform} states. The coarsening morphologies obey {\it generalized dynamical scaling} in the two regimes, but the scaling function is not robust with respect to $λ$. The structure factor tail in the canted regime follows the {\it Porod law}: $S(k,t)\sim k^{-4}$, implying that the coarsening dynamics is due to the annihilation of interfacial defects. This is unexpected, as the GLL model is characterised by a continuous order parameter. The uniform regime on the other hand, exhibits the expected {\it generalized Porod decay}: $S(k,t)\sim k^{-5}$, characteristic of scattering from {\it string defects}. Finally, the domain growth obeys the {\it Lifshitz-Allen-Cahn law}: $L(t)\sim t^{1/2}$ for all values of $λ$. Our results for the novel {\it canted} regime are relevant for a large class of systems with orientational ordering, e.g. active matter, membranes, LC elastomers, etc. We hope that our work triggers-off stimulating investigations in them.

cond-mat.soft↗

arXiv2020

Domain Growth in Ferronematics: Slaved Coarsening, Emergent Morphologies and Growth Laws

Ferronematics (FNs) are suspensions of magnetic nanoparticles in nematic liquid crystals (NLCs). They have attracted much experimental attention, and are of great interest both scientifically and technologically. There are very few theoretical studies of FNs, even in equilibrium. In this paper, we study the non-equilibrium phenomenon of domain growth after a thermal quench (or coarsening) in this coupled system. Our modeling is based on coupled time-dependent Ginzburg-Landau (TDGL) equations for two order parameters: the LC tensor order parameter ${\bf Q}$, and the magnetization ${\bf M}$. We consider both shallow and deep quenches from a high-temperature disordered phase. The system coarsens by the collision and annihilation of topological defects. We focus on slaved coarsening, where a disordered ${\bf Q}$ (or ${\bf M}$) field is driven to coarsen by an ordered ${\bf M}$ (or ${\bf Q}$) field. We present detailed results for the morphologies and growth laws, which exhibit unusual features purely due to the magneto-nematic coupling. To the best of our knowledge, this is the first study of non-equilibrium phenomena in FNs.

cond-mat.stat-mech↗

arXiv2019

Tailored Morphologies in 2D Ferronematic Wells

We focus on a dilute uniform suspension of magnetic nanoparticles in a nematic-filled micron-sized shallow well with tangent boundary conditions, as a paradigm system with two coupled order parameters. This system exhibits spontaneous magnetization without magnetic fields. We numerically obtain the stable nematic and associated magnetization morphologies, induced purely by the geometry, boundary conditions and the coupling between the magnetic nanoparticles and the host nematic medium. Our most striking observations pertain to domain walls in the magnetization profile whose location can be manipulated by the coupling and material properties, and stable interior and boundary nematic defects, whose location and multiplicity can be tailored by the coupling too. These novel morphologies are not accessible in uncoupled systems and can be used for new multistable systems with singularities and stable interfaces.

cond-mat.soft↗

arXiv2019

Slaved Coarsening in Ferronematics

We focus on understanding the influence of the two-component coupling in ferronematics, a colloidal suspension of magnetic nanoparticles in nematic liquid crystals. Using coarse-grained Landau-de Gennes free energies, we study the ordering dynamics of this complex fluid and present a range of analytical and numerical results. Our main observations are: (i) slaved coarsening for quench temperatures $T$ intermediate to the critical temperatures of the uncoupled components, (ii) slower growth similar to the Lifshitz-Slyozov law ($L \sim t^{1/3}$) for symmetric magneto-nematic coupling, (iii) sub-domain morphologies dominated by interfacial defects for asymmetric coupling strengths. These novel results will serve to guide future experiments on this technologically important system.

cond-mat.stat-mech↗

arXiv2018

Magnetic Nanoparticles in a Nematic Channel: A One-Dimensional Study

We study a ferromagnetic suspension or a suspension of magnetic nanoparticles in an anisotropic nematic medium, in three different one-dimensional variational settings, ordered in terms of increasing complexity. The three models are featured by a nematic energy, a magnetic energy and a magneto-nematic coupling energy and the experimentally observed patterns are modelled as local or global energy minimizers. We numerically observe polydomains with distinct states of magnetization for weak to moderate magneto-nematic coupling in our models. We demonstrate that these polydomains are stabilised by lowering the temperature (as in Mertelj et al., 2013) and that the polydomain structures lose stability as the magneto-nematic coupling increases. Some exact solutions for prototypical situations are also obtained.

cond-mat.soft↗