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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.

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.

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.

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., Comment: 13 pages, 8 figures

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.

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.

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., Comment: RevTeX, 6+5 pages, 4+5 figures, 3+1 tables, version accepted for publication

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.

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 Tc2Tc1->T

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 {\Gamma} =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.

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

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.

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., Comment: 17 pages, 3 figures

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., Comment: 8 pages, 4 figures

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., Comment: 31 pages, 10 figures

While the ground-state problem for the random-field Ising model is polynomial, and can be solved using a number of well-known algorithms for maximum flow or graph cut, the analogue random-field Potts model corresponds to a multi-terminal flow problem that is known to be NP hard. Hence an efficient exact algorithm is very unlikely to exist. As we show here, it is nevertheless possible to use an embedding of binary degrees of freedom into the Potts spins in combination with graph-cut methods to solve the corresponding ground-state problem approximately in polynomial time. We benchmark this heuristic algorithm using a set of quasi-exact ground states found for small systems from long parallel tempering runs. For not too large number $q$ of Potts states, the method based on graph cuts finds the same solutions in a fraction of the time. We employ the new technique to analyze the breakup length of the random-field Potts model in two dimensions., Comment: 10 pages, 11 figures, 1 table

A human pathogen, \textit{Neisseria gonorrhoeae} (NG), moves on surfaces by attaching and retracting polymeric structures called Type IV pili. The \textit{tug-of-war} between the pili results in a two-dimensional stochastic motion called \textit{twitching motility}. In this paper, with the help of real time NG trajectories, we develop coarse-grained models for their description. The \textit{fractal properties} of these trajectories are determined and their influence on \textit{first passage time} and formation of bacterial microcolonies is studied. Our main observations are as follows: (i) NG performs a fast ballistic walk on small time scales and a slow diffusive walk over long time scales with a long crossover region; (ii) There exists a characteristic persistent length $l_p^*$ which yields the fastest growth of bacterial aggregates or biofilms. Our simulations reveal that $l_{p}^{*} \sim L^{0.6}$, where $L\times L$ is the surface on which the bacteria move; (iii) The morphologies have distinct fractal characteristics as a consequence of the ballistic and diffusive motion of the constituting bacteria., Comment: 16 pages, 7 figures, accepted PRE (2017)

Interplanetary dust particles (IDPs) are an important constituent of the earth's stratosphere, interstellar and interplanetary medium, cometary comae and tails, etc. Their physical and optical characteristics are significantly influenced by the morphology of silicate aggregates which form the core in IDPs. In this paper we reinterpret scattering data from laboratory analogs of cosmic silicate aggregates created by Volten et al. \cite{volten2007}, to extract their morphological features. By evaluating the structure factor, we find that the aggregates are mass fractals with a mass fractal dimension $d_{m} \simeq 1.75$. The same fractal dimension also characterizes clusters obtained from {\it diffusion limited aggregation} (DLA). This suggests that the analogs are formed by an irreversible aggregation of stochastically-transported silicate particles, Comment: 11 pages, 7 figures, accepted for publication in JQSRT. JQSRT, 2014

We study hysteresis in a micron-sized bead: a non-magnetic matrix embedded with super- paramagnetic nanoparticles. These hold tremendous promise in therapeutic applications as heat generating machines. The theoretical formulation uses a mean-field theory to account for dipolar interactions between the supermoments. The study enables manipulation of heat dissipation by a compatible selection of commercially available beads and the frequency f and amplitude ho of the applied oscillating field in the labortory. We also introduce the possibility of utilizing return point memory for gradual heating of a local region., Comment: 8 pages, 4 figures

We study the dynamics of a suspension of magnetic nanoparticles. Their relaxation times are strongly size-dependent. The dominant mode of relaxation is also governed by the size of the particles. As a result the dynamics is greatly altered due to polydispersity in the sample. We study the effect of polydispersity on the response functions. These exhibit significant changes as the parameters characterizing polydispersity are varied. We also provide a procedure to extract the particle size distribution in a polydisperse sample using Cole-Cole plots. Further the presence of attractive interactions causes aggregation of particles leading to the formation of clusters. Repulsive interactions along with thermal disorder not only hinder aggregation, but also introduce the possibility of removal of particles or "fragmentation" from clusters. The competing mechanisms of aggregation and fragmentation yield a distribution of cluster sizes in the steady-state. We attempt to understand the formation of clusters and their distributions using a model incorporating the phenomena of aggregation and fragmentation. Scaling forms for quantities of interest have been obtained. Finally we compare our numerical results with experimental data. These comparisons are satisfactory., Comment: 30 pages, 8 figures

We study the ground-state (T = 0) morphologies in the d = 3 random-field Ising model (RFIM) using a computationally efficient graph-cut method. We focus on paramagnetic states which arise for disorder strengths \Delta > \Delta c, where \Delta c is the critical disorder strength at T = 0. These paramagnetic states consist of correlated "domains" of up and down spins which are separated by rough, fractal interfaces. They show novel scattering properties with a cusp singularity in the correlation function at short distances., Comment: 10 pages, 6 figures, Accepted for publication in Europhysics Letters

We present a review of nonequilibrium phase transitions in mass-transport models with kinetic processes like fragmentation, diffusion, aggregation, etc. These models have been used extensively to study a wide range of physical problems. We provide a detailed discussion of the analytical and numerical techniques used to study mass-transport phenomena., Comment: 29 pages, 4 figures

We study mass-transport models with multiple-chipping processes. The rates of these processes are dependent on the chip size and mass of the fragmenting site. In this context, we consider k-chip moves (where k = 1, 2, 3, ....); and combinations of 1-chip, 2-chip and 3-chip moves. The corresponding mean-field (MF) equations are solved to obtain the steady-state probability distributions, P (m) vs. m. We also undertake Monte Carlo (MC) simulations of these models. The MC results are in excellent agreement with the corresponding MF results, demonstrating that MF theory is exact for these models., Comment: 18 pages, 4 figures, To appear in European Physical Journal B