Five-fold symmetry in crystalline quasicrystal lattices

To demonstrate that crystallographic methods can be applied to index and interpret diffraction patterns from well-ordered quasicrystals that display non-crystallographic 5-fold symmetry, we have characterized the properties of a series of periodic two-dimensional lattices built from pentagons, called Fibonacci pentilings, which resemble aperiodic Penrose tilings. The computed diffraction patterns from periodic pentilings with moderate size unit cells show decagonal symmetry and are virtually indistinguishable from that of the infinite aperiodic pentiling. We identify the vertices and centers of the pentagons forming the pentiling with the positions of transition metal atoms projected on the plane perpendicular to the decagonal axis of quasicrystals whose structure is related to crystalline η phase alloys. The characteristic length scale of the pentiling lattices, evident from the Patterson (autocorrelation) function, is ∼τ2 times the pentagon edge length, where τ is the golden ratio. Within this distance there are a finite number of local atomic motifs whose structure can be crystallographically refined against the experimentally measured diffraction data.

Mutations in the rotated abdomen locus affect muscle development and reveal an intrinsic asymmetry in Drosophila.

In bilateral animals, the left and right sides of the body usually present asymmetric structures, the genetic bases of whose generation are still largely unknown [CIBA Foundation (1991) Biological Asymmetry and Handedness, CIBA Foundation Symposium 162 (Wiley, New York), pp. 1-327]. In Drosophila melanogaster, mutations in the rotated abdomen (rt) locus cause a clockwise helical rotation of the body. Even null alleles are viable but exhibit defects in embryonic muscle development, rotation of the whole larval body, and helical staggering of cuticular patterns in abdominal segments of the adult. rotated abdomen is expressed in the embryonic mesoderm and midgut but not in the ectoderm; it encodes a putative integral membrane glycoprotein (homologous to key yeast mannosyltransferases). Mesodermal cells defective in O-glycosylation lead to an impaired larval muscular system. We propose that the staggering of the adult abdominal segments would be a consequence of the relaxation of intrinsic rotational torque of muscle architecture, preventing the colateral alignment of the segmental histoblast cells during their proliferation at metamorphosis.

The rotated hypoblast of the chicken embryo does not initiate an ectopic axis in the epiblast.

In the amniotes, two unique layers of cells, the epiblast and the hypoblast, constitute the embryo at the blastula stage. All the tissues of the adult will derive from the epiblast, whereas hypoblast cells will form extraembryonic yolk sac endoderm. During gastrulation, the endoderm and the mesoderm of the embryo arise from the primitive streak, which is an epiblast structure through which cells enter the interior. Previous investigations by others have led to the conclusion that the avian hypoblast, when rotated with regard to the epiblast, has inductive properties that can change the fate of competent cells in the epiblast to form an ectopic embryonic axis. Thus, it has been suggested that the hypoblast normally induces the epiblast to form a primitive streak at a specific locus. In the work reported here, an attempt was made to reexamine the issue of induction. In contrast to previous reports, it was found that the rotated hypoblast of the chicken embryo does not initiate formation of an ectopic axis in the epiblast. The embryonic axis always initiates and develops according to the basic polarity of the epiblast layer. These results provoke a reinterpretation of the issues of mesoderm induction and primitive streak initiation in the avian embryo.

Long-range effects on optical absorption in quasiperiodic lattices

We consider exciton optical absorption in quasiperiodic lattices, focusing our attention on the Fibonacci case as a typical example. The absorption spectrum is evaluated by solving numerically the equation of motion of the Frenkel-exciton problem on the lattice, in which on-site energies take on two values according to the Fibonacci sequence. We find that the quasiperiodic order causes the occurrence of well-defined characteristic features in the absorption spectra. We also develop an analytical method that relates satellite lines with the Fourier pattern of the lattice. Our predictions can be used to determine experimentally the long-range quasiperiodic order from optical measurements.

Propagation of Dyakonon Wave-Packets at the Boundary of Metallodielectric Lattices

We rigorously analyze the propagation of localized surface waves that takes place at the boundary between a semi-infinite layered metal-dielectric (MD) nanostructure cut normally to the layers and a isotropic medium. It is demonstrated that Dyakonov-like surface waves (also coined dyakonons) with hybrid polarization may propagate in a wide angular range. As a consequence, dyakonon-based wave-packets (DWPs) may feature sub-wavelength beamwidths. Due to the hyperbolic-dispersion regime in plasmonic crystals, supported DWPs are still in the canalization regime. The apparent quadratic beam spreading, however, is driven by dissipation effects in metal.

Thermal conductivity of one-dimensional lattices,

Mode of access: Internet.

The energy transport properties of one dimensional anharmonic lattices.

Vita.

A class of translation lattices.

"CU-2-62-NSF G19022-M."

Ultra-cold fermions in optical lattices

We summarize recent theoretical results for the signatures of strongly correlated ultra-cold fermions in optical lattices. In particular, we focus on collective mode calculations, where a sharp decrease in collective mode frequency is predicted at the onset of the Mott metal-insulator transition; and correlation functions at finite temperature, where we employ a new exact technique that applies the stochastic gauge technique with a Gaussian operator basis.

Automated layout of small lattices using layer diagrams

Good quality concept lattice drawings are required to effectively communicate logical structure in Formal Concept Analysis. Data analysis frameworks such as the Toscana System use manually arranged concept lattices to avoid the problem of automatically producing high quality lattices. This limits Toscana systems to a finite number of concept lattices that have been prepared a priori. To extend the use of formal concept analysis, automated techniques are required that can produce high quality concept lattice drawings on demand. This paper proposes and evaluates an adaption of layer diagrams to improve automated lattice drawing. © Springer-Verlag Berlin Heidelberg 2006.