Sol–Gel Encapsulation of Molecules to Generate Functional Optical Materials: A Molecular Programming Approach

The extraordinary opportunities offered by integrating solution chemistry of molecular entities with the solid-state nature of the gel provide the basis for designing a number of novel molecular materials. Herein, we present a strategy based on encapsulation of suitable response active species to impart useful optical properties to sol–gel glasses. The basic concept of this molecular programming approach is based on deliberate incorporation of response-active species in the silica gel framework to elicit specific optical responses. Design of molecular materials for device applications depends on selection of molecules which exhibit well-defined electronic or optical response, and assembly of these molecular components into a geometric structure that retains the rigidity, addressability, and stability necessary for practical applications. The approach is based on using molecules as active species and sol–gel glass as structural matrix in which the molecules are selectively integrated. A designer approach that employs specific molecules for generating optical signals is described. As such the properties of these silica-based glasses can be tuned by varying the composition of encapsulated species. These modified glasses exhibit substantially altered optical properties as compared to pristine silica sol–gels. The optical response of these materials provide initial examples toward designing novel materials whose optical and/or photonic responses can be modulated by structural integration of specific dopant entities.     

The Tersoff potential for phonons in GaAs

We report on the use of the Tersoff empirical potential applied to GaAs. Cohesive and elastic properties, as well as phonon frequencies and Grüneisen parameters at the Γ and X points, are calculated and compared to experimental data. The limitations of the potential and its existing parametrisations are discussed.     

Ergodic Actions of Semisimple Lie Groups on Compact Principal Bundles

Let G = SL(n, ?) (or, more generally, let G be a connected, noncompact, simple Lie group). For any compact Lie group K, it is easy to find a compact manifold M, such that there is a volume-preserving, connection-preserving, ergodic action of G on some smooth, principal K-bundle P over M. Can M can be chosen independent of K? We show that if M = H/Λ is a homogeneous space, and the action of G on M is by translations, then P must also be a homogeneous space H′Λ′. Consequently, there is a strong restriction on the groups K that can arise over this particular M.     

Fermionic Quantization and Configuration Spaces for the Skyrme and Faddeev-Hopf Models

The fundamental group and rational cohomology of the configuration spaces of the Skyrme and Faddeev-Hopf models are computed. Physical space is taken to be a compact oriented 3-manifold, either with or without a marked point representing an end at infinity. For the Skyrme model, the codomain is any Lie group, while for the Faddeev-Hopf model it is S². It is determined when the topology of configuration space permits fermionic and isospinorial quantization of the solitons of the model within generalizations of the frameworks of Finkelstein-Rubinstein and Sorkin. Fermionic quantization of Skyrmions is possible only if the target group contains a symplectic or special unitary factor, while fermionic quantization of Hopfions is always possible. Geometric interpretations of the results are given. The first author was partially supported by NSF grant DMS-0204651 The second author was partially supported by EPSRC grant GR/R66982/01     

The non-orientable genus of some metacyclic groups

We describe non-orientable, octagonal embeddings for certain 4-valent, bipartite Cayley graphs of finite metacyclic groups, and give a class of examples for which this embedding realizes the non-orientable genus of the group. This yields a construction of Cayley graphs for which is arbitrarily large, where and are the orientable genus and the non-orientable genus of the Cayley graph.Work supported in part by the Research Council of Slovenia, Yugoslavia and NSF Contract DMS-8717441.Supported by NSF Contract DMS-8601760.