Hierarchies of Critical Points of a Landau-de Gennes Free Energy on Three-Dimensional Cuboids

We investigate critical points of a Landau-de Gennes (LdG) free energy in three-dimensional (3D) cuboids, that model nematic equilibria. We develop a hybrid saddle dynamics-based algorithm to efficiently compute solution landscapes of these 3D systems. Our main results concern (a) the construction of 3D LdG critical points from a database of 2D LdG critical points and (b) studies of the effects of cross-section size and cuboid height on solution landscapes. In doing so, we discover multiple-layer 3D LdG critical points constructed by stacking 3D critical points on top of each other, novel pathways between distinct energy minima mediated by 3D LdG critical points and novel metastable escaped solutions, all of which can be tuned for tailor-made static and dynamic properties of confined nematic liquid crystal systems in 3D.Comment: 28 pages,10 figure

Structuring Stress for Active Materials Control

Active materials are capable of converting free energy into mechanical work to produce autonomous motion, and exhibit striking collective dynamics that biology relies on for essential functions. Controlling those dynamics and transport in synthetic systems has been particularly challenging. Here, we introduce the concept of spatially structured activity as a means to control and manipulate transport in active nematic liquid crystals consisting of actin filaments and light-sensitive myosin motors. Simulations and experiments are used to demonstrate that topological defects can be generated at will, and then constrained to move along specified trajectories, by inducing local stresses in an otherwise passive material. These results provide a foundation for design of autonomous and reconfigurable microfluidic systems where transport is controlled by modulating activity with light

Geometry and mechanics of microdomains in growing bacterial colonies

Bacterial colonies are abundant on living and nonliving surfaces and are known to mediate a broad range of processes in ecology, medicine, and industry. Although extensively researched, from single cells to demographic scales, a comprehensive biomechanical picture, highlighting the cell-to-colony dynamics, is still lacking. Here, using molecular dynamics simulations and continuous modeling, we investigate the geometrical and mechanical properties of a bacterial colony growing on a substrate with a free boundary and demonstrate that such an expanding colony self-organizes into a "mosaic" of microdomains consisting of highly aligned cells. The emergence of microdomains is mediated by two competing forces: the steric forces between neighboring cells, which favor cell alignment, and the extensile stresses due to cell growth that tend to reduce the local orientational order and thereby distort the system. This interplay results in an exponential distribution of the domain areas and sets a characteristic length scale proportional to the square root of the ratio between the system orientational stiffness and the magnitude of the extensile active stress. Our theoretical predictions are finally compared with experiments with freely growing E. coli microcolonies, finding quantitative agreement.Comment: 10 pages, 7 figure

A Reduced Landau-de Gennes Study for Nematic Equilibria in Three-Dimensional Prisms

We model nematic liquid crystal configurations inside three-dimensional prisms, with a polygonal cross-section and Dirichlet boundary conditions on all prism surfaces. We work in a reduced Landau-de Gennes framework, and the Dirichlet conditions on the top and bottom surfaces are special in the sense, that they are critical points of the reduced Landau-de Gennes energy on the polygonal cross-section. The choice of the boundary conditions allows us to make a direct correspondence between the three-dimensional Landau-de Gennes critical points and pathways on the two-dimensional Landau-de Gennes solution landscape on the polygonal cross-section. We explore this concept by means of asymptotic analysis and numerical examples, with emphasis on a cuboid and a hexagonal prism, focusing on three-dimensional multistability tailored by two-dimensional solution landscapes

Change in Stripes for Cholesteric Shells via Anchoring in Moderation

Chirality, ubiquitous in complex biological systems, can be controlled and quantified in synthetic materials such as cholesteric liquid crystal (CLC) systems. In this work, we study spherical shells of CLC under weak anchoring conditions. We induce anchoring transitions at the inner and outer boundaries using two independent methods: by changing the surfactant concentration or by raising the temperature close to the clearing point. The shell confinement leads to new states and associated surface structures: a state where large stripes on the shell can be filled with smaller, perpendicular substripes, and a focal conic domain (FCD) state, where thin stripes wrap into at least two, topologically required, double spirals. Focusing on the latter state, we use a Landau–de Gennes model of the CLC to simulate its detailed configurations as a function of anchoring strength. By abruptly changing the topological constraints on the shell, we are able to study the interconversion between director defects and pitch defects, a phenomenon usually restricted by the complexity of the cholesteric phase. This work extends the knowledge of cholesteric patterns, structures that not only have potential for use as intricate, self-assembly blueprints but are also pervasive in biological systems