Flux Ropes as Singularities of the Vector Potential

A flux rope is a domain of concentration of the magnetic field $\textbf{B}$. Insofar as $\textbf{B}$ outside such a domain is considered as vanishingly small, a flux rope can be described as the core of a singularity of the outer vector potential $\textbf{A}$, whose topological invariant is the magnetic flux through the rope. By 'topological' it is meant that $\oint_C\textbf{A}\cdot\mathrm d\textbf{s}$ measures along any loop $C$ surrounding the flux rope the same constant flux $\Phi$. The electric current intensity is another invariant of the theory, but non-topological. We show that, in this theoretical framework, the linear force-free field (LFFF) Lundquist model and the non-linear (NLFFF) Gold-Hoyle model of a flux rope exhibit stable solutions distributed over quantized strata of increasing energies (an infinite number of strata in the first case, only one stratum in the second case); each stratum is made of a continuous set of stable states. The lowest LFFF stratum and the unique NLFFF stratum come numerically close one to the other, and match with a reasonable accuracy the data collected by spacecrafts travelling across magnetic clouds. The other LFFF strata do not match these data at all. It is not possible at this stage to claim which model fits better the magnetic cloud data. We also analyze in some detail the merging of tubes belonging to the same stratum, with conservation of the magnetic helicity, and the transition of a tube from one stratum to another one, which does not conserve magnetic helicity.Comment: 24 pages, 1 figur

Imperfections in focal conic domains: the role of dislocations

It is usual to think of Focal Conic Domains (FCD) as perfect geometric constructions in which the layers are folded into Dupin cyclides, about an ellipse and a hyperbola that are conjugate. This ideal picture is often far from reality. We have investigated in detail the FCDs in several materials which have a transition from a smectic A (SmA) to a nematic phase. The ellipse and the hyperbola are seldom perfect, and the FCD textures also suffer large transformations (in shape or/and in nature) when approaching the transition to the nematic phase, or appear imperfect on cooling from the nematic phase. We interpret these imperfections as due to the interaction of FCDs with dislocations. We analyze theoretically the general principles subtending the interaction mechanisms between FCDs and finite Burgers vector dislocations, namely the formation of kinks on disclinations, to which dislocations are attached, and we present models relating to some experimental results. Whereas the principles of the interactions are very general, their realizations can differ widely in function of the boundary conditions.Comment: 19 pages, 18 figure

Model of hard spheroplatelets near a hard wall

A system of hard spheroplatelets near an impenetrable wall is studied in the low-density Onsager approximation. Spheroplatelets have optimal shape between rods and plates, and the direct transition from the isotropic to biaxial nematic phase is present. A simple local approximation for the one-particle distribution function is used. Analytical results for the surface tension and the entropy contributions are derived. The density and the order-parameter profiles near the wall are calculated. The preferred orientation of the short molecule axes is perpendicular to the wall. Biaxiality close to the wall can appear only if the phase is biaxial in the bulk.Comment: 11 pages, 9 figures, revised version published in PR

Disclinations, dislocations and continuous defects: a reappraisal

Disclinations, first observed in mesomorphic phases, are relevant to a number of ill-ordered condensed matter media, with continuous symmetries or frustrated order. They also appear in polycrystals at the edges of grain boundaries. They are of limited interest in solid single crystals, where, owing to their large elastic stresses, they mostly appear in close pairs of opposite signs. The relaxation mechanisms associated with a disclination in its creation, motion, change of shape, involve an interplay with continuous or quantized dislocations and/or continuous disclinations. These are attached to the disclinations or are akin to Nye's dislocation densities, well suited here. The notion of 'extended Volterra process' takes these relaxation processes into account and covers different situations where this interplay takes place. These concepts are illustrated by applications in amorphous solids, mesomorphic phases and frustrated media in their curved habit space. The powerful topological theory of line defects only considers defects stable against relaxation processes compatible with the structure considered. It can be seen as a simplified case of the approach considered here, well suited for media of high plasticity or/and complex structures. Topological stability cannot guarantee energetic stability and sometimes cannot distinguish finer details of structure of defects.Comment: 72 pages, 36 figure

Annihilation of edge dislocations in smectic A liquid crystals

This paper presents a theoretical study of the annihilation of edge dislocations in the same smectic plane in a bulk smectic-A phase. We use a time-dependent Landau-Ginzburg approach where the smectic ordering is described by the complex order parameter psi( r--> ,t) =eta e(iphi) . This quantity allows both the degree of layering and the position of the layers to be monitored. We are able to follow both precollision and postcollision regimes, and distinguish different early and late behaviors within these regimes. The early precollision regime is driven by changes in the phi ( r--> ) configuration. The relative velocity of the defects is approximately inversely proportional to the interdefect separation distance. In the late precollision regime the symmetry changes within the cores of defects also become influential. Following the defect collision, in the early postcollision stage, bulk layer order is approached exponentially in time. At very late times, however, there seems to be a long-time power-law tail in the order parameter fluctuation relaxation

Discrete symmetries and 1/3-quantum vortices in condensates of F=2 cold atoms

In this Letter we study discrete symmetries of mean field manifolds of condensates of F=2 cold atoms, and various unconventional quantum vortices. Discrete quaternion symmetries result in two species of spin defects that can only appear in integer vortices while {\em cyclic} symmetries are found to result in a phase shift of $2\pi/3$ (or $4\pi/3$) and therefore 1/3- (or 2/3-) quantum vortices in condensates. We also briefly discuss 1/3-quantum vortices in condensates of trimers.Comment: 4 pages, 2 figures included; published versio

A stochastic derivation of the geodesic rule

We argue that the geodesic rule, for global defects, is a consequence of the randomness of the values of the Goldstone field $\phi$ in each causally connected volume. As these volumes collide and coalescence, $\phi$ evolves by performing a random walk on the vacuum manifold $\mathcal{M}$. We derive a Fokker-Planck equation that describes the continuum limit of this process. Its fundamental solution is the heat kernel on $\mathcal{M}$, whose leading asymptotic behavior establishes the geodesic rule.Comment: 12 pages, No figures. To be published in Int. Jour. Mod. Phys.

Nematic liquid crystal dynamics under applied electric fields

In this paper we investigate the dynamics of liquid crystal textures in a two-dimensional nematic under applied electric fields, using numerical simulations performed using a publicly available LIquid CRystal Algorithm (LICRA) developed by the authors. We consider both positive and negative dielectric anisotropies and two different possibilities for the orientation of the electric field (parallel and perpendicular to the two-dimensional lattice). We determine the effect of an applied electric field pulse on the evolution of the characteristic length scale and other properties of the liquid crystal texture network. In particular, we show that different types of defects are produced after the electric field is switched on, depending on the orientation of the electric field and the sign of the dielectric anisotropy.Comment: 7 pages, 12 figure

Defect kinetics and dynamics of pattern coarsening in a two-dimensional smectic-A system

Two-dimensional simulations of the coarsening process of the isotropic/smectic-A phase transition are presented using a high-order Landau-de Gennes type free energy model. Defect annihilation laws for smectic disclinations, elementary dislocations, and total dislocation content are determined. The computed evolution of the orientational correlation length and disclination density is found to be in agreement with previous experimental observations showing that disclination interactions dominate the coarsening process. The mechanism of smectic disclination movement, limited by the absorption and emission of elementary dislocations, is found to be facilitated by curvature walls connecting interacting disclinations. At intermediate times in the coarsening process, split-core dislocation formation and interactions displaying an effective disclination quadrupole configuration are observed. This work provides the framework for further understanding of the formation and dynamics of the diverse set of curvature defects observed in smectic liquid crystals and other layered material systems

Elasticity-mediated self-organization and colloidal interactions of solid spheres with tangential anchoring in a nematic liquid crystal

Using laser tweezers and fluorescence confocal polarizing microscopy, we study colloidal interactions of solid microspheres in the nematic bulk caused by elastic distortions around the particles with strong tangential surface anchoring. The particles aggregate into chains directed at about 30 degrees to the far field director and, at higher concentrations, form complex kinetically trapped structures. We characterize the distance and angular dependencies of the colloidal interaction forces.Comment: 6 pages, 5 figure