Escape from the second dimension: A topological distinction between edge and screw dislocations.

Volterra's definition of dislocations in crystals geometrically distinguishes edge and screw defects according to whether the Burgers vector is perpendicular or parallel to the defect. A homotopy-theoretic analysis of dislocations as topological defects fails to differentiate edge and screw. Here we bridge the gap between the geometric and topological descriptions by demonstrating that there is a topological difference between screw and edge defects.

What promotes smectic order: Applying mean-field theory to the ends.

Not every particle that forms a nematic liquid crystal makes a smectic. The particle tip is critical for this behavior. Ellipsoids do not make a smectic, but spherocylinders do.

Expression of Concern: Colossal Density-Driven Resistance Response in the Negative Charge Transfer Insulator MnS_{2} [Phys. Rev. Lett. 127, 016401 (2021)].

This corrects the article DOI: 10.1103/PhysRevLett.127.

Natural Shaping of Acellular Dermal Matrices for Implant-Based Breast Reconstruction via Expansile Kirigami.

To complete a successful and aesthetic breast reconstruction for breast cancer survivors, tissue reinforcing acellular dermal matrices (ADMs) are widely utilized to create slings/pockets to keep breast implants or autologous tissue transfer secured against the chest wall in the desired location. However, ADM sheets are 2D and cannot completely cover the entire implant without wrinkles. Here, guided by finite element modeling, a kirigami strategy is presented to cut the ADM sheets with locally and precisely controlled stretchability, curvature, and elasticity.

Ratchetlike motion of helical bilayers induced by boundary constraints.

We show that application of boundary constraints generates unusual folding behaviors in responsive (swellable) helical bilayer strips. Unlike the smooth folding trajectories typical of free helical bilayers, the boundary-constrained bilayers exhibit intermittent folding behaviors characterized by rapid, steplike movements. We experimentally study bilayer strips as they swell and fold, and we propose a simple model to explain the emergence of ratchetlike behavior.

Twisted loxodromes in spindle-shaped polymer nematics.

We develop an energetic model that captures the twisting behavior of spindle-shaped polymer microparticles with nematic ordering, which display remarkably different twisting behavior to ordinary nematics confined to spindles. We have previously developed a geometric model of the twisting, based on experimental observations, in which we showed that the twist pattern follows loxodrome spirals [Ansell, et al., Phys.

Geodesic fibrations for packing diabolic domains.

We describe a theory of packing hyperboloid "diabolic" domains in bend-free textures of liquid crystals. The domains sew together continuously, providing a menagerie of bend-free textures akin to the packing of focal conic domains in smectic liquid crystals. We show how distinct domains may be related to each other by Lorentz transformations and that this process may lower the elastic energy of the system.

Gnomonious projections for bend-free textures: thoughts on the splay-twist phase.

The Hopf fibration has inspired any number of geometric structures in physical systems, in particular, in chiral liquid crystalline materials. Because the Hopf fibration lives on the three sphere, , some method of projection or distortion must be employed to realize textures in flat space. Here, we explore the geodesic-preserving gnomonic projection of the Hopf fibration, and show that this could be the basis for a new liquid crystalline texture with only splay and twist.

Threading the Spindle: A Geometric Study of Chiral Liquid Crystal Polymer Microparticles.

Polymeric particles are strong candidates for designing artificial materials capable of emulating the complex twisting-based functionality observed in biological systems. In this Letter, we provide the first detailed investigation of the swelling behavior of bipolar polymer liquid crystalline microparticles. Deswelling from the spherical bipolar configuration causes the microparticles to contract anisotropically and twist in the process, resulting in a twisted spindle-shaped structure.

Mechanisms to splay-bend nematic phases.

While twist-bend nematic phases have been extensively studied, the experimental observation of two dimensional, oscillating splay-bend phases is recent. We consider two theoretical models that have been used to explain the formation of twist-bend phases-flexoelectricity and bond orientational order-as mechanisms to induce splay-bend phases. Flexoelectricity is a viable mechanism, and splay and bend flexoelectric couplings can lead to splay-bend phases with different modulations.

Shaping nanoparticle fingerprints at the interface of cholesteric droplets.

The ordering of nanoparticles into predetermined configurations is of importance to the design of advanced technologies. Here, we balance the interfacial energy of nanoparticles against the elastic energy of cholesteric liquid crystals to dynamically shape nanoparticle assemblies at a fluid interface. By adjusting the concentration of surfactant that plays the dual role of tuning the degree of nanoparticle hydrophobicity and altering the molecular anchoring of liquid crystals, we pattern nanoparticles at the interface of cholesteric liquid crystal emulsions.

Edges impose planar alignment in nematic monolayers by directing cell elongation and enhancing migration.

Boundaries play an important role in the emergence of nematic order in classical liquid crystal systems; we explore their importance in adhesive cells that form active nematics. In particular, we study how cells are affected by an edge, which in our experiments is a boundary between adhesive and non-adhesive domains on a planar surface. We find that such edges induce elongation and direct the migration of isolated fibroblasts.

Aspects of nucleation on curved and flat surfaces.

We investigate the energetics of droplets sourced by the thermal fluctuations in a system undergoing a first-order transition. In particular, we confine our studies to two dimensions with explicit calculations in the plane and on the sphere. Using an isoperimetric inequality from the differential geometry literature and a theorem on the inequality's saturation, we show how geometry informs the critical droplet size and shape.

Universal inverse design of surfaces with thin nematic elastomer sheets.

Programmable shape-shifting materials can take different physical forms to achieve multifunctionality in a dynamic and controllable manner. Although morphing a shape from 2D to 3D via programmed inhomogeneous local deformations has been demonstrated in various ways, the inverse problem-finding how to program a sheet in order for it to take an arbitrary desired 3D shape-is much harder yet critical to realize specific functions. Here, we address this inverse problem in thin liquid crystal elastomer (LCE) sheets, where the shape is preprogrammed by precise and local control of the molecular orientation of the liquid crystal monomers.

Gaussian Curvature Directs Stress Fiber Orientation and Cell Migration.

We show that substrates with nonzero Gaussian curvature influence the organization of stress fibers and direct the migration of cells. To study the role of Gaussian curvature, we developed a sphere-with-skirt surface in which a positive Gaussian curvature spherical cap is seamlessly surrounded by a negative Gaussian curvature draping skirt, both with principal radii similar to cell-length scales. We find significant reconfiguration of two subpopulations of stress fibers when fibroblasts are exposed to these curvatures.

Colloidal transport within nematic liquid crystals with arrays of obstacles.

We have investigated the gravity-driven transport of spherical colloids suspended in the nematic liquid crystal 4-cyano-4'-pentylbiphenyl (5CB) within microfluidic arrays of cylindrical obstacles arranged in a square lattice. Homeotropic anchoring at the surfaces of the obstacles created periodic director-field patterns that strongly influenced the motion of the colloids, whose surfaces had planar anchoring. When the gravitational force was oriented parallel to a principal axis of the lattice, the particles moved along channels between columns of obstacles and displayed pronounced modulations in their velocity.

Curvature and Rho activation differentially control the alignment of cells and stress fibers.

In vivo, cells respond to a host of physical cues ranging from substrate stiffness to the organization of micro- and nanoscale fibrous networks. We show that macroscale substrates with radii of curvature from tens to hundreds of micrometers influence cell alignment. In a model system of fibroblasts, isolated cells aligned strongly in the axial direction on cylinders with radii similar to the cell length and more weakly on cylinders of much larger radius.

The smectic order of wrinkles.

A thin elastic sheet lying on a soft substrate develops wrinkled patterns when subject to an external forcing or as a result of geometric incompatibility. Thin sheet elasticity and substrate response equip such wrinkles with a global preferred wrinkle spacing length and with resistance to wrinkle curvature. These features are responsible for the liquid crystalline smectic-like behaviour of such systems at intermediate length scales.