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

North American Environment and Its Linkages to Trade

This article will follow a deductive approach in order to comprehend the intricacies involved in the NAFTA and NAAEC\u27s environmental provisions. It will also contextualize the inseparable relationship between environmental protection and trade which is depicted in these agreements. Part I will review and analyze the NAFTA\u27s environmental provisions, focusing on their relevant mechanisms, nexus to trade, and shortcomings. In Part II, the uniqueness and effectiveness of the formula developed to reconcile trade and the environment in the form of the NAAEC will be introduced. Part III is divided into three categories: the Commission for Environmental Cooperation ( CEC ), Dispute Resolution Mechanisms, and the Submission Process under the NAAEC. Here, each subsection\u27s viability in ensuring that member nations dutifully enforce their environmental laws is examined, as well as each component\u27s efficiency in monitoring the efforts made by the Parties to reach the NAAEC\u27s goals. Part III will consider the mandate and operations of the NAAEC and its relevant elements, the Parties and the CEC, while defining the flaws and virtues of the NAAEC. Finally, Part IV will suggest revisions to particular sections of the NAFTA and NAAEC in light of the North American experience regarding environmental protection and trade since 1994

North American Environment and Its Linkages to Trade

This article will follow a deductive approach in order to comprehend the intricacies involved in the NAFTA and NAAEC\u27s environmental provisions. It will also contextualize the inseparable relationship between environmental protection and trade which is depicted in these agreements. Part I will review and analyze the NAFTA\u27s environmental provisions, focusing on their relevant mechanisms, nexus to trade, and shortcomings. In Part II, the uniqueness and effectiveness of the formula developed to reconcile trade and the environment in the form of the NAAEC will be introduced. Part III is divided into three categories: the Commission for Environmental Cooperation ( CEC ), Dispute Resolution Mechanisms, and the Submission Process under the NAAEC. Here, each subsection\u27s viability in ensuring that member nations dutifully enforce their environmental laws is examined, as well as each component\u27s efficiency in monitoring the efforts made by the Parties to reach the NAAEC\u27s goals. Part III will consider the mandate and operations of the NAAEC and its relevant elements, the Parties and the CEC, while defining the flaws and virtues of the NAAEC. Finally, Part IV will suggest revisions to particular sections of the NAFTA and NAAEC in light of the North American experience regarding environmental protection and trade since 1994

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

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

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

Geodesics around line defects in elastic solids

Topological defects in solids, usually described by complicated boundary conditions in elastic theory, may be described more simply as sources of a gravity- like deformation field in the geometric approach of Katanaev and Volovich. This way, the deformation field is described by non-Euclidean metric that incorporates the boundary imposed by the defects. A possible way of gaining some insight into the motion of particles in a medium with topological defects (e.g., electrons in a dislocated metal) is to look at the geodesics of the medium around the defect. In this work, we find the exact solution for the geodesic equation for elastic medium with a generic line defect, the dispiration, that can either be a screw dislocation or a wedge disclination for particular choices of its parameters.Comment: 10 pages, Latex, 4 figures, accepted for publication in Phys. Lett.

Characteristics of the local distribution of the Y139C resistance gene in Norway rats (Rattus norvegicus

Klemann, N., Esther, A., Endepols, S

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

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.