arXiv subjects

Gareth P. Alexander

Publications and source records attributed to Gareth P. Alexander.

45 records · Page 3Linked to original sources

arXiv2013

Nematics, Knots and Non-orientable Surfaces

Knots and knotted fields enrich physical phenomena ranging from DNA and molecular chemistry to the vortices of fluid flows and textures of ordered media. Liquid crystals provide an ideal setting for exploring such topological phenomena through control of their characteristic defects. The use of colloids in generating defects and knotted configurations in liquid crystals has been demonstrated for spherical and toroidal particles and shows promise for the development of novel photonic devices. Extending this existing work, we describe the full topological implications of colloids representing non-orientable surfaces and use it to construct torus knots and links of type ($p$,2) around multiply-twisted Möbius strips.

cond-mat.soft↗

arXiv2012

Threading the Needle: Generating Textures in Nematics

The Hopf fibration is an example of a texture: a topologically stable, smooth, global configuration of a field. Here we demonstrate the controlled sculpting of the Hopf fibration in nematic liquid crystals through the control of point defects. We demonstrate how these are related to torons by use of a topological visualization technique derived from the Pontryagin-Thom construction.

cond-mat.soft↗

arXiv2012

Conformal Smectics and their Many Metrics

We establish that equally-spaced smectic configurations enjoy an infinite-dimensional conformal symmetry and show that there is a natural map between them and null hypersurfaces in maximally-symmetric spacetimes. By choosing the appropriate conformal factor it is possible to restore additional symmetries of focal structures only found before for smectics on flat substrates.

cond-mat.soft↗

arXiv2011

Developed Smectics: When Exact Solutions Agree

In the limit where the bending modulus vanishes, we construct layer configurations with arbitrary dislocation textures by exploiting a connection between uniformly-spaced layers in two dimensions and developable surfaces in three dimensions. We then show how these focal textures can be used to construct layer configurations with finite bending modulus.

cond-mat.soft↗

arXiv2011

Self-Diffusiophoresis in the Advection Dominated Regime

In both biological and artificial systems, concentration gradients can serve as a convenient mechanism for manipulating particles and generating motility. Particles that interact with a solute will move along its gradient; if they themselves generate the gradient, this mechanism provides a means of self-propulsion. We consider a version of this type of motility appropriate to certain biological systems where polymeric filaments provide the concentration gradient. As the filament diffusion is small, this corresponds to a regime of large Péclet number where the motion is dominated by the effects of fluid advection. The nature of such concentration-gradient-driven motion in the advective regime differs in certain fundamental respects from the same process at low Péclet number. In particular, we show that out of four broad scenarios of steady state motion at low Péclet number, only two remain viable in the strongly advecting limit.

cond-mat.soft↗

arXiv2011

Disclination Loops, Hedgehogs, and All That

The homotopy theory of topological defects is a powerful tool for organizing and unifying many ideas across a broad range of physical systems. Recently, experimental progress has been made in controlling and measuring colloidal inclusions in liquid crystalline phases. The topological structure of these systems is quite rich but, at the same time, subtle. Motivated by experiment and the power of topological reasoning, we review and expound upon the classification of defects in uniaxial nematic liquid crystals. Particular attention is paid to the ambiguities that arise in these systems, which have no counterpart in the much-storied XY model or the Heisenberg ferromagnet.

cond-mat.soft↗

arXiv2010

The Power of Poincaré: Elucidating the Hidden Symmetries in Focal Conic Domains

Focal conic domains are typically the "smoking gun" by which smectic liquid crystalline phases are identified. The geometry of the equally-spaced smectic layers is highly generic but, at the same time, difficult to work with. In this Letter we develop an approach to the study of focal sets in smectics which exploits a hidden Poincaré symmetry revealed only by viewing the smectic layers as projections from one-higher dimension. We use this perspective to shed light upon several classic focal conic textures, including the concentric cyclides of Dupin, polygonal textures and tilt-grain boundaries.

cond-mat.soft↗

arXiv2009

Helical Nanofilaments and the High Chirality Limit of Smectics-A

Liquid crystalline systems exhibiting both macroscopic chirality and smectic order experience frustration resulting in mesophases possessing complex three-dimensional order. In the twist-grain-boundary phase, defect lattices mediate the propagation of twist throughout the system. We propose a new chiral smectic structure composed of a lattice of chiral bundles as a model of the helical nanofilament (B4) phase of bent core smectics.

cond-mat.soft↗

arXiv2009

Smectics: Symmetry Breaking, Singularities, and Surfaces

The homotopy theory of topological defects in ordered media fails to completely characterize systems with broken translational symmetry. We argue that the problem can be understood in terms of the lack of rotational Goldstone modes in such systems and provide an alternate approach that correctly accounts for the interaction between translations and rotations. Dislocations are associated, as usual, with branch points in a phase field, while disclinations arise as critical points and singularities in the phase field. We introduce a three-dimensional model for two-dimensional smectics that clarifies the topology of disclinations and geometrically captures known results without the need for compatibility conditions. Our work suggests natural generalizations of the two-dimensional smectic theory to higher dimensions and to crystals.

cond-mat.soft↗