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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 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.

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.

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

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.

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