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

The cuttlefish Sepia officinalis (Sepiidae, Cephalopoda) constructs cuttlebone from a liquid-crystal precursor

Cuttlebone, the sophisticated buoyancy device of cuttlefish, is made of extensive superposed chambers that have a complex internal arrangement of calcified pillars and organic membranes. It has not been clear how this structure is assembled. We find that the membranes result from a myriad of minor membranes initially filling the whole chamber, made of nanofibres evenly oriented within each membrane and slightly rotated with respect to those of adjacent membranes, producing a helical arrangement. We propose that the organism secretes a chitin-protein complex, which self-organizes layer-by-layer as a cholesteric liquid crystal, whereas the pillars are made by viscous fingering. The liquid crystallization mechanism permits us to homologize the elements of the cuttlebone with those of other coleoids and with the nacreous septa and the shells of nautiloids. These results challenge our view of this ultra-light natural material possessing desirable mechanical, structural and biological properties, suggesting that two self-organizing physical principles suffice to understand its formation.Spanish Ministerio de Ciencia e Innovacion [CGL2010-20748-CO2-01, CGL2013-48247-P, FIS2013-48444-C2-2-P]; Andalusian Consejeria de Innovacion Ciencia y Tecnologia [RNM6433]; (Sepiatech, PROMAR program) of the Portuguese Ministerio da Agricultura e do Mar, Portugal [31.03.05.FEP.002]; Junta de Andalucia [RNM363]; FP7 COST Action of the European Community. [TD0903]info:eu-repo/semantics/publishedVersio

An analysis of the fluctuations of the geomagnetic dipole

The time evolution of the strength of the Earth's virtual axial dipole moment (VADM) is analyzed by relating it to the Fokker-Planck equation, which describes a random walk with VADM-dependent drift and diffusion coefficients. We demonstrate first that our method is able to retrieve the correct shape of the drift and diffusion coefficients from a time series generated by a test model. Analysis of the Sint-2000 data shows that the geomagnetic dipole mode has a linear growth time of 13 to 33 kyr, and that the nonlinear quenching of the growth rate follows a quadratic function of the type [1-(x/x0)^2]. On theoretical grounds, the diffusive motion of the VADM is expected to be driven by multiplicative noise, and the corresponding diffusion coefficient to scale quadratically with dipole strength. However, analysis of the Sint-2000 VADM data reveals a diffusion which depends only very weakly on the dipole strength. This may indicate that the magnetic field quenches the amplitude of the turbulent velocity in the Earth's outer core.Comment: 11 pages, 6 figure

Generalised Cantor sets and the dimension of products

In this paper we consider the relationship between the Assouad and box-counting dimension and how both behave under the operation of taking products. We introduce the notion of ‘equi-homogeneity’ of a set, which requires a uniformity in the cardinality of local covers at all length-scales and at all points, and we show that a large class of homogeneous Moran sets have this property. We prove that the Assouad and box-counting dimensions coincide for sets that have equal upper and lower box-counting dimensions provided that the set ‘attains’ these dimensions (analogous to ‘s-sets’ when considering the Hausdorff dimension), and the set is equi-homogeneous. Using this fact we show that for any α ∈ (0, 1) and any β, γ ∈ (0, 1) such that β + γ ≥ 1 we can construct two generalised Cantor sets C and D such that dimBC = αβ, dimBD = α γ, and dimAC = dimAD = dimA (C × D) = dimB (C × D) = α

Pores in Bilayer Membranes of Amphiphilic Molecules: Coarse-Grained Molecular Dynamics Simulations Compared with Simple Mesoscopic Models

We investigate pores in fluid membranes by molecular dynamics simulations of an amphiphile-solvent mixture, using a molecular coarse-grained model. The amphiphilic membranes self-assemble into a lamellar stack of amphiphilic bilayers separated by solvent layers. We focus on the particular case of tension less membranes, in which pores spontaneously appear because of thermal fluctuations. Their spatial distribution is similar to that of a random set of repulsive hard discs. The size and shape distribution of individual pores can be described satisfactorily by a simple mesoscopic model, which accounts only for a pore independent core energy and a line tension penalty at the pore edges. In particular, the pores are not circular: their shapes are fractal and have the same characteristics as those of two dimensional ring polymers. Finally, we study the size-fluctuation dynamics of the pores, and compare the time evolution of their contour length to a random walk in a linear potential

Morphometry and growth of sea pen species from dense habitats in the Gulf of St. Lawrence, eastern Canada

We examined four species of sea pen (Anthoptilum grandiflorum, Halipteris finmarchica, Pennatula aculeata and Pennatula grandis) collected from the Gulf of St. Lawrence and mouth of the Laurentian Channel, eastern Canada. An exponential length–weight relationship was found for all four species, where growth in weight was progressively greater than growth in length with increasing colony size. Halipteris finmarchica, P. grandis and P. aculeata presented the better allometric fits, explaining over 80% of the variance. In addition, a count of growth increments visible in transverse sections in 86 A. grandiflorum and 80 P. aculeata samples was made. Presumed ages ranged between 5 and 28 years for A. grandiflorum and 2 and 21 years for P. aculeata. Radiocarbon assays were inconclusive and could not be used to confirm these ages; further age validation is required. Radial growth of the rod is slow during the first years, increasing at intermediate sizes of the colony and slowing down again for large colonies. Similar results were obtained from the relationship between colony length and number of growth increments where a logistic model was the best fit to the data. On average Spearman’s rank correlations showed 11% of shared variance between sea pen length or weight and environmental variables. Bottom temperature and salinity, depth and summer primary production were significantly correlated to sea pen size for most species.En prensa1,48

Defects in Chiral Columnar Phases: Tilt Grain Boundaries and Iterated Moire Maps

Biomolecules are often very long with a definite chirality. DNA, xanthan and poly-gamma-benzyl-glutamate (PBLG) can all form columnar crystalline phases. The chirality, however, competes with the tendency for crystalline order. For chiral polymers, there are two sorts of chirality: the first describes the usual cholesteric-like twist of the local director around a pitch axis, while the second favors the rotation of the local bond-orientational order and leads to a braiding of the polymers along an average direction. In the former case chirality can be manifested in a tilt grain boundary phase (TGB) analogous to the Renn-Lubensky phase of smectic-A liquid crystals. In the latter case we are led to a new "moire" state with twisted bond order. In the moire state polymers are simultaneously entangled, crystalline, and aligned, on average, in a common direction. In the moire state polymers are simultaneously entangled, crystalline, and aligned, on average, in a common direction. In this case the polymer trajectories in the plane perpendicular to their average direction are described by iterated moire maps of remarkable complexity, reminiscent of dynamical systems.Comment: plain TeX, (33 pages), 17 figures, some uufiled and included, the remaining available at ftp://ftp.sns.ias.edu/pub/kamien/ or by request to [email protected]

Circularly polarized colour reflection from helicoidal structures in the beetle Plusiotis boucardi

Copyright © 2007 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. This is the published version of an article published in New Journal of Physics Vol. 9, article 99. DOI: 10.1088/1367-2630/9/4/099A detailed optical study of the iridescent outer-shell of the beetle Plusiotis boucardi has revealed a novel microstructure which controls both the polarization and wavelength of reflected light. A previously unreported hexagonal array across the integument of the beetle exhibits highly localized regions of reflection of only red and green left-handed circularly-polarized light. Optical and transmission electron microscopy (TEM) imaging reveals the origin of this effect as an array of 'bowl-shaped' recesses on the elytra that are formed from a dual-pitch helicoidal layer. Reflectivity spectra collected from the beetle are compared to theoretical data produced using a multi-layer optics model for modelling chiral, optically anisotropic media such as cholesteric liquid crystals. Excellent agreement is obtained between data and theory produced using a model that incorporates an upper isotropic layer (of cuticular wax), followed by a short pitch (310 (± 1) nm) overlying a longer pitch (370 (±1) nm) helicoidal layer of optically anisotropic material. These layers are backed by an absorbing underlayer. Synthetic replication of this form of structure may provide a route to the fabrication of tuneable micro-mirrors for optical applications

Pathogenic mosaic variants in congenital hypogonadotropic hypogonadism

PURPOSE Congenital hypogonadotropic hypogonadism (CHH) is a rare disorder resulting in absent puberty and infertility. The genetic architecture is complex with multiple loci involved, variable expressivity, and incomplete penetrance. The majority of cases are sporadic, consistent with a disease affecting fertility. The current study aims to investigate mosaicism as a genetic mechanism for CHH, focusing on de novo rare variants in CHH genes. METHODS We evaluated 60 trios for de novo rare sequencing variants (RSV) in known CHH genes using exome sequencing. Potential mosaicism was suspected among RSVs with altered allelic ratios and confirmed using customized ultradeep sequencing (UDS) in multiple tissues. RESULTS Among the 60 trios, 10 probands harbored de novo pathogenic variants in CHH genes. Custom UDS demonstrated that three of these de novo variants were in fact postzygotic mosaicism-two in FGFR1 (p.Leu630Pro and p.Gly348Arg), and one in CHD7 (p.Arg2428*). Statistically significant variation across multiple tissues (DNA from blood, buccal, hair follicle, urine) confirmed their mosaic nature. CONCLUSIONS We identified a significant number of de novo pathogenic variants in CHH of which a notable number (3/10) exhibited mosaicism. This report of postzygotic mosaicism in CHH patients provides valuable information for accurate genetic counseling

Congenital Hypogonadotropic Hypogonadism Due to GNRH Receptor Mutations in Three Brothers Reveal Sites Affecting Conformation and Coupling

Congenital hypogonadotropic hypogonadism (CHH) is characterized by low gonadotropins and failure to progress normally through puberty. Mutations in the gene encoding the GnRH receptor (GNRHR1) result in CHH when present as compound heterozygous or homozygous inactivating mutations. This study identifies and characterizes the properties of two novel GNRHR1 mutations in a family in which three brothers display normosmic CHH while their sister was unaffected. Molecular analysis in the proband and the affected brothers revealed two novel non-synonymous missense GNRHR1 mutations, present in a compound heterozygous state, whereas their unaffected parents possessed only one inactivating mutation, demonstrating the autosomal recessive transmission in this kindred and excluding X-linked inheritance equivocally suggested by the initial pedigree analysis. The first mutation at c.845 C>G introduces an Arg substitution for the conserved Pro 282 in transmembrane domain (TMD) 6. The Pro282Arg mutant is unable to bind radiolabeled GnRH analogue. As this conserved residue is important in receptor conformation, it is likely that the mutation perturbs the binding pocket and affects trafficking to the cell surface. The second mutation at c.968 A>G introduces a Cys substitution for Tyr 323 in the functionally crucial N/DPxxY motif in TMD 7. The Tyr323Cys mutant has an increased GnRH binding affinity but reduced receptor expression at the plasma membrane and impaired G protein-coupling. Inositol phosphate accumulation assays demonstrated absent and impaired Gαq/11 signal transduction by Pro282Arg and Tyr323Cys mutants, respectively. Pretreatment with the membrane permeant GnRHR antagonist NBI-42902, which rescues cell surface expression of many GNRHR1 mutants, significantly increased the levels of radioligand binding and intracellular signaling of the Tyr323Cys mutant but not Pro282Arg. Immunocytochemistry confirmed that both mutants are present on the cell membrane albeit at low levels. Together these molecular deficiencies of the two novel GNRHR1 mutations lead to the CHH phenotype when present as a compound heterozygote