Facile preparation of macroscopic soft colloidal crystals with fiber symmetry

A facile, efficient way to fabricate macroscopic soft colloidal crystals with fiber symmetry by drying a latex dispersion in a tube is presented. A transparent, stable colloidal crystal was obtained from a 25 wt % latex dispersion by complete water evaporation for 4 days. The centimeter-long sample was investigated by means of synchrotron small-angle X-ray diffraction (SAXD). Analysis of a large number of distinct Bragg peaks reveals that uniaxially oriented colloidal crystals with face-centered cubic lattice structure were formed.

The site symmetry of Eu3+ in ZnS : Eu nanoparticle

Nanosized ZnS doped with different concentrations of Eu3+ were prepared and analyzed by x-ray diffraction technique. The experimental results show that ZnS belongs to the cubic structure. From the photoluminescence (PL) emission spectra, it can be seen that the ratio of the emission intensity of Eu3+ 616 nm to that at 590 nm increases as the increasing of Eu3+. This phenomenon reveals that the site symmetry of Eu3+ reduces as the increasing of Eu3+.

Computer perception of topological symmetry by all-paths algorithm

During the development of our ESESOC system (Expert System for the Elucidation of the Structures of Organic Compounds), computer perception of topological symmetry is essential in searching for the canonical description of a molecular structure, removing the irredundant connections in the structure generation process, and specifying the number of peaks in C-13- and H-1-NMR spectra in the structure evaluation process. In the present paper, a new path identifier is introduced and an algorithm for detection of topological symmetry from a connection table is developed by the all-paths method. (C) 1999 Elsevier Science B.V. All rights reserved.

Study on computer perception of topological symmetry

A new algorithm for computer perception of topological symmetry is proposed. A node library containing various kinds of nodes is built, and the index number of the library is used as initial atom class identifier (CI) to discriminate the different types of non-hydrogen atoms. The path index (PI) and ringindex (RI) are calculated from the CI, and the global topological enviroment is defined as the sum of PIs and RIs. The topological symmetry can be detected by the iterative calculation of the global topological enviroment.

STRUCTURE AND SITE-SYMMETRY INVESTIGATION ON THE HEXAGONAL KCAY(PO4)(2)

A new double phosphate, KCaY(PO4)(2), isostructural with hexagonal LaPO4, is reported. It crystallizes in the hexagonal system with a = 0.6903 nm and c = 0.6331 nm. Its vibrational spectra, IR and Raman spectra showed that the site symmetry of the PO4 anion slightly deviated from D-2 toward C-2.

ALGORITHM FOR COMPUTER PERCEPTION OF TOPOLOGICAL SYMMETRY

For the exhaustive and irredundant generation of candidate structures in ESESOC (Expert System for the Elucidation of the Structures of Organic Compounds), a new algorithm for computer perception of topological equivalence classes of the nodes (non-hydrog

Curved Inertia Frames: Visual Attention and Perceptual Organization Using Convexity and Symmetry

In this paper we present an approach to perceptual organization and attention based on Curved Inertia Frames (C.I.F.), a novel definition of "curved axis of inertia'' tolerant to noisy and spurious data. The definition is useful because it can find frames that correspond to large, smooth, convex, symmetric and central parts. It is novel because it is global and can detect curved axes. We discuss briefly the relation to human perception, the recognition of non-rigid objects, shape description, and extensions to finding "features", inside/outside relations, and long- smooth ridges in arbitrary surfaces.

Symmetry-breaking and chaos in electron transport in semiconductor superlattices

We study the motion of electrons in a single miniband of a semiconductor superlattice driven by THz electric field polarized along the growth direction. We work in the semiclassical balance-equation model, including different elastic and inelastic scattering rates, and incorporating the self-consistent electric field generated by electron motion. We explore regions of complex dynamics, which can include chaotic behaviour and symmetry-breaking. We estimate the magnitudes of dc current and dc voltage that spontaneously appear in regions of broken-symmetry for parameters characteristic of modern semiconductor superlattices. This work complements PRL 80(1998)2669 [ cond-mat/9709026 ].

Axial symmetry and transverse trace-free tensors in numerical relativity

Transverse trace-free (TT) tensors play an important role in the initial conditions of numerical relativity, containing two of the component freedoms. Expressing a TT tensor entirely, by the choice of two scalar potentials, is not a trivial task however. Assuming the added condition of axial symmetry, expressions are given in both spherical and cylindrical coordinates, for TT tensors in flat space. A coordinate relation is then calculated between the scalar potentials of each coordinate system. This is extended to a non-flat space, though only one potential is found. The remaining equations are reduced to form a second order partial differential equation in two of the tensor components. With the axially symmetric flat space tensors, the choice of potentials giving Bowen-York conformal curvatures, are derived. A restriction is found for the potentials which ensure an axially symmetric TT tensor, which is regular at the origin, and conditions on the potentials, which give an axially symmetric TT tensor with a spherically symmetric scalar product, are also derived. A comparison is made of the extrinsic curvatures of the exact Kerr solution and numerical Bowen-York solution for axially symmetric black hole space-times. The Brill wave, believed to act as the difference between the Kerr and Bowen-York space-times, is also studied, with an approximate numerical solution found for a mass-factor, under different amplitudes of the metric.

Comparison of the NMR enantiodifferentiation of a chiral ruthenium(II) complex of C2 symmetry using the TRISPHAT anion and a lanthanide shift reagent

The tris[tetrachlorobenzenediolato]phosphate(v) anion (TRISPHAT) is known to be an efficient NMR chiral shift agent for various chiral cationic species. Here we compare the efficiency of TRISPHAT and of a chiral lanthanide shift reagent for the determination of the enantiomeric purity of the chiral building block [Ru(phen)[2]PY[2]][2][+] which possesses C[2] symmetry. We also discuss our results in terms of the geometry of interaction between the Ru(II) complex and the TRISPHAT anion.

Cyclic Pursuit: Symmetry, Reduction and Nonlinear Dynamics

In this dissertation, we explore the use of pursuit interactions as a building block for collective behavior, primarily in the context of constant bearing (CB) cyclic pursuit. Pursuit phenomena are observed throughout the natural environment and also play an important role in technological contexts, such as missile-aircraft encounters and interactions between unmanned vehicles. While pursuit is typically regarded as adversarial, we demonstrate that pursuit interactions within a cyclic pursuit framework give rise to seemingly coordinated group maneuvers. We model a system of agents (e.g. birds, vehicles) as particles tracing out curves in the plane, and illustrate reduction to the shape space of relative positions and velocities. Introducing the CB pursuit strategy and associated pursuit law, we consider the case for which agent i pursues agent i+1 (modulo n) with the CB pursuit law. After deriving closed-loop cyclic pursuit dynamics, we demonstrate asymptotic convergence to an invariant submanifold (corresponding to each agent attaining the CB pursuit strategy), and proceed by analysis of the reduced dynamics restricted to the submanifold. For the general setting, we derive existence conditions for relative equilibria (circling and rectilinear) as well as for system trajectories which preserve the shape of the collective (up to similarity), which we refer to as pure shape equilibria. For two illustrative low-dimensional cases, we provide a more comprehensive analysis, deriving explicit trajectory solutions for the two-particle "mutual pursuit" case, and detailing the stability properties of three-particle relative equilibria and pure shape equilibria. For the three-particle case, we show that a particular choice of CB pursuit parameters gives rise to remarkable almost-periodic trajectories in the physical space. We also extend our study to consider CB pursuit in three dimensions, deriving a feedback law for executing the CB pursuit strategy, and providing a detailed analysis of the two-particle mutual pursuit case. We complete the work by considering evasive strategies to counter the motion camouflage (MC) pursuit law. After demonstrating that a stochastically steering evader is unable to thwart the MC pursuit strategy, we propose a (deterministic) feedback law for the evader and demonstrate the existence of circling equilibria for the closed-loop pursuer-evader dynamics.

Sufficient Conditions for the Existence of Bound States in a Potential without Spherical Symmetry

We give in this paper several suffieient conditions for the existence of negative energy bound states in a purely attractive potential without spherical symmetry. These conditions generalize the condition obtained recently by K. Chadan and A. Martin (C. R. Acad. Sci. Paris290 (1980), 151), and can ensure the existence of n bound states. For the spherically symmetric case, one gets simple formulae which are also new.

[Book review] Symmetry - A Unifying Concept, István Hargittai and Magdolna Hargittai

Tony Mann provides a review of the book: István Hargittai and Magdolna Hargittai, Symmetry - A Unifying Concept, 1994, Ten Speed Press, 222pp. ISBN: 089815-590-8. £14.99

[Reviews] Finding moonshine: a mathematician's journey through symmetry

Review of 'Finding Moonshine: A Mathematician’s Journey Through Symmetry' by Marcus du Sautoy, published by Fourth Estate, 2008 (ISBN 0-007-214618).