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

Asymmetric Hydrogenation of 1-alkyl and 1-aryl vinyl benzoates: a broad scope procedure for the highly enantioselective synthesis of 1-substituted ethyl benzoates

The enantioselective hydrogenation of enol esters of formula CH2=C(OBz)R with rhodium catalysts based on phosphine-phosphite ligands (P-OP) has been studied. The reaction has a broad scope and it is suitable for the preparation of products possessing a wide variety of R substituents. For the cases where R is a primary alkyl high catalyst activity (S/C = 500) and enantioselectivities (95-99 % ee) were obtained with a catalyst characterized by an ethane backbone and a PPh2 fragment. In contrast, for R = tBu a catalyst possessing a benzene backbone provided the best results (97 % ee). Derivatives with a cycloalkyl R substituent were particularly difficult substrates for this reaction. A broader catalyst screening was required for these substrates, which identified a catalyst possessing a P(m-xylyl)2 fragment as the most appropriate one, affording enantioselectivities between 90 and 95 % ee. Outstanding enantioselectivities (99 % ee) and high catalyst activity (S/C = 500-1000) were also obtained in the case of substrates bearing a Ph or a fluoroaryl R substituent. In addition, the system is also appropriate for the preparation of other synthetically useful esters as those for R = benzyl, 2-phenylethyl or Nphthalimido alkyl chains. Likewise, the hydrogenation of divinyl dibenzoates proceeded with very high diastero- and enantioselectivity, generating rather low amounts of the meso isomer (3-6 %). On the other hand, substrates with Br- and MeO- substituents at the phenyl benzoate ring, suitable for further functionalization, have also been examined. The results obtained indicate no detrimental effect of these substituents in the hydrogenation. Alternatively, the methodology has been applied to the highly enantioselective synthesis of deuterium isotopomers of 1-octyl benzoate bearing CDH2, CD2H or CD3 fragments. Finally, as a practical advantage of the present system, it has been observed that the high performance of the catalysts is retained in high concentrated solutions or even in the neat substrate, then minimizing both the amount of solvent added and the volume of the reactionJunta de Andalucía 2009/FQM-4832CSIC 201480E03 1Ministerio de Ciencia e Innovación CTQ2010- 14796/BQ

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

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

Elliptic Phases: A Study of the Nonlinear Elasticity of Twist-Grain Boundaries

We develop an explicit and tractable representation of a twist-grain-boundary phase of a smectic A liquid crystal. This allows us to calculate the interaction energy between grain boundaries and the relative contributions from the bending and compression deformations. We discuss the special stability of the 90 degree grain boundaries and discuss the relation of this structure to the Schwarz D surface.Comment: 4 pages, 2 figure

Pre-LGM Northern Hemisphere ice sheet topography

We here reconstruct the paleotopography of Northern Hemisphere ice sheets during the glacial maxima of marine isotope stages (MIS) 5b and 4.We employ a combined approach, blending geologically based reconstruction and numerical modeling, to arrive at probable ice sheet extents and topographies for each of these two time slices. For a physically based 3-D calculation based on geologically derived 2-D constraints, we use the University of Maine Ice Sheet Model (UMISM) to calculate ice sheet thickness and topography. The approach and ice sheet modeling strategy is designed to provide robust data sets of sufficient resolution for atmospheric circulation experiments for these previously elusive time periods. Two tunable parameters, a temperature scaling function applied to a spliced Vostok–GRIP record, and spatial adjustment of the climatic pole position, were employed iteratively to achieve a good fit to geological constraints where such were available. The model credibly reproduces the first-order pattern of size and location of geologically indicated ice sheets during marine isotope stages (MIS) 5b (86.2 kyr model age) and 4 (64 kyr model age). From the interglacial state of two north–south obstacles to atmospheric circulation (Rocky Mountains and Greenland), by MIS 5b the emergence of combined Quebec–central Arctic and Scandinavian–Barents-Kara ice sheets had increased the number of such highland obstacles to four. The number of major ice sheets remained constant through MIS 4, but the merging of the Cordilleran and the proto-Laurentide Ice Sheet produced a single continent-wide North American ice sheet at the LGM

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

Glacial geomorphology of the northern Kivalliq region, Nunavut, Canada, with an emphasis on meltwater drainage systems

This paper presents a glacial geomorphological map of glacial lineations, ribbed terrain, moraines, meltwater channels (subglacial and ice-marginal/proglacial), eskers, glaciofluvial deposits, ice-contact outwash fans and deltas and abandoned shorelines on the bed of the former Laurentide Ice Sheet in northern Canada. Mapping was compiled from satellite imagery and digital elevation data and landforms were digitised directly into a Geographical Information System. The map reveals a complex glacial history characterised by multiple ice-flow events, including fast-flowing ice-streams. Moraines record a series of pauses or re-advances during overall SE retreat towards the Keewatin Ice Divide. The distribution of subglacial meltwater landforms indicates that several distinctive scales and modes of drainage system operated beneath the retreating ice sheet. This includes a large (>100 km) integrated network of meltwater channels, eskers, ice-contact outwash fans and deltas and glaciofluvial deposits that originates at the northern edge of Aberdeen Lake. The map comprises zone 66 of the Canadian National Topographic System, which encompasses an area of 160,000 km2. It is presented at a scale of 1:500,000 and is designed to be printed at A0 size

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

Kramers rate theory of ionization and dissociation of bound states

Calculating the microscopic dissociation rate of a bound state, such as a classical diatomic molecule, has been difficult so far. The problem was that standard theories require an energy barrier over which the bound particle (or state) escapes into the preferred low-energy state. This is not the case when the long-range repulsion responsible for the barrier is either absent or screened (as in Cooper pairs, ionized plasma, or biomolecular complexes). We solve this classical problem by accounting for entropic memory at the microscopic level. The theory predicts dissociation rates for arbitrary potentials and is successfully tested on the example of plasma, where it yields an estimate of ionization in the core of Sun in excellent agreement with experiments. In biology, the new theory accounts for crowding in receptor-ligand kinetics and protein aggregation