Search results for " symmetry"
showing 10 items of 701 documents
Conformal invariance of the writhe of a knot
2008
We give a new proof of an old theorem by Banchoff and White 1975 that claims that the writhe of a knot is conformally invariant.
Generalized evolutes, vertices and conformal invariants of curves in Rn + 1
1999
Abstract We define the generalized evolute of a curve in ( n + 1)-space and find a duality relation between them. We also prove that the conformal torsion is a function of the speed of the generalized evolute and that the singular points of the generalized evolute (vertices) are conformal invariants.
Conformal curvatures of curves in
2001
Abstract We define a complete set of conformal invariants for pairs of spheres in and obtain from these the expressions of the conformal curvatures of curves in (n + 1)-space in terms of the Euclidean invariants.
Spontaneous symmetry-breaking pathways: time-resolved study of agarose gelation
1996
Abstract Extensive time-resolved studies of self-assembly of agarose gels, performed with the use of a variety of techniques allowed identification of the initial break of symmetry and the actual path leading to self-assembly at concentrations well below the random percolation threshold. The overall process is seen to occur through the following sequence: (i) break of symmetry in the sol, causing the spontaneous generation of mesoscopic polymer-rich and solvent-rich regions; (ii) percolation, or nearly percolation [see (iv) below], of polymer-rich regions through the sample, still in the sol state; (iii) start of polymer cross-linking within polymer-rich regions; (iv) progress of cross-link…
Au-40(SR)(24) Cluster as a Chiral Dimer of 8-Electron Superatoms: Structure and Optical Properties
2012
We predict and analyze density-functional theory (DFT)-based structures for the recently isolated Au(40)(SR)(24) cluster. Combining structural information extracted from ligand-exchange reactions, circular dichroism and transmission electron microscopy leads us to propose two families of low-energy structures that have a chiral Au-S framework on the surface. These families have a common geometrical motif where a nonchiral Au(26) bi-icosahedral cluster core is protected by 6 RS-Au-SR and 4 RS-Au-SR-Au-SR oligomeric units, analogously to the "Divide and Protect" motif of known clusters Au(25)(SR)(18)(-/0), Au(38)(SR)(24) and Au(102)(SR)(44). The strongly prolate shape of the proposed Au(26) c…
Formation, TEM study and 3D reconstruction of the human erythrocyte peroxiredoxin-2 dodecahedral higher-order assembly.
2004
The production of a higher-order assembly of peroxiredoxin-2 (Prx-2) from human erythrocytes has been achieved during specimen preparation on holey carbon support films, in the presence of ammonium molybdate and polyethylene glycol. TEM study suggested that this assembly is a regular dodecahedron, containing 12 Prx-2 decamers (Mr 2.62 MDa, external diameter approximately 20 nm). This interpretation has been supported by production of a approximately 1.6 nm 3D reconstruction from the negative stain TEM data, with automated docking of the available X-ray data of the Prx-2 decamer. Comparison with other known protein dodecahedral and viral icosahedral structures indicates that this arrangement…
On the Structure of Thiolate-Protected Au25
2008
Density functional theory is used to explore the structure of Au25(RS)18. The preferred structure consists of an icosahedral Au13 core protected by 6 RS-Au-RS-Au-RS units. The enhanced stability of the structure as an anion is found to originate from closure of an eight-electron shell for delocalized Au(6s) electrons. The evaluated XRD pattern and optical spectra are in good agreement with experimental data.
Structure of a molluscan hemocyanin didecamer (HtH1 from Haliotis tuberculata) at 12 Å resolution by cryoelectron microscopy
2000
A 12 A resolution three-dimensional density map of the Haliotis tuberculata hemocyanin type 1 (HtH1) didecamer has been obtained by cryoelectron microscopy of unstained molecules and angular reconstitution. The dyad symmetry of the 8 MDa D5 HtH1 didecamer, formed by the pairing of two asymmetric 4 MDa ring-like C5 decamers, is emphasised. The major and minor surface helical grooves of the didecamer are well defined, in agreement with earlier data on molluscan hemocyanins. The location of the obliquely orientated repeating unit, a subunit dimer, within the decamer has been defined. Following interactive extraction of this dimer, several new structural features of the dimer and of the subunit…
Nucleation of quasicrystals by rapid cooling of a binary melt: A molecular-dynamics study.
1995
A binary Lennard-Jones fluid was cooled in an NPT ensemble by molecular-dynamics simulations. Depending on the cooling rate, we find a sharp transition from the melt either into a disordered structure or into a phase of icosahedral long-range order. We also observed a decagonal phase.
Diffusion processes and growth on aluminum cluster surfaces
1997
Diffusion processes of adatoms on icosahedral and Wulff polyhedral aluminum cluster surfaces have been studied by molecular dynamics simulations using the effective medium theory. Activation energies of diffusion mechanisms along {111} and {100} facets and from one facet to another, including different hopping and exchange processes as well as more exotic events, have been calculated. Exchange diffusion of an adatom by a chain mechanism through a {100} facet between two {111} facets and hopping diffusion across the edge between two {111} facets via a pull of another adatom on the neighbour facet are shown to play an important role. Adatoms on {111} facets are mobile already at very low temp…