Diagrammatic structure of the general coupled cluster equations

The general formula for the number of diagrammatic terms occurring in the T_n equation within a particular coupled cluster model is derived. Both the antisymmetrized and Goldstone diagrams are considered. In addition to the full coupled cluster equation approximate approaches are discussed, and for each the general formula for the number of terms is given. Analogous expressions are presented for the number of diagrammatic terms contributing to the elements of the transformed Hamiltonian [Hbar] = e^?T He^T .     

On the convex hull of the multiform numerical range

Let A ₁,…,A_m be nxn hermitian matrices. Definine

W(A ₁,…,A_m )={(xA₁x ^?,…xA_mx ^?):x?C ⁿ ,xx ^?=1}. We will show that every point in the convex hull of W(A ₁,…,A_m ) can be represented as a convex combination of not more than k(m,n) points in W(A ₁,…,A_m ) where k(m,n)=min{n,[√m]+δ _n ² _m+1}.     

Elastic properties of spherically anisotropic piezoelectric composites

Effective elastic properties of spherically anisotropic piezoelectric composites, whose spherically anisotropic piezo-electric inclusions are embedded in an infinite non-piezoelectric matrix, are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials under a uniform external strain are derived exactly. Taking into account of the coupling effects of elasticity, permittivity and piezoelectricity, the formula is derived for estimating the effective elastic properties based on the average field theory in the dilute limit. An elastic response mechanism is revealed, in which the effective elastic properties increase as inclusion piezoelectric properties increase and inclusion dielectric properties decrease. Moreover, a piezoelectric response mechanism, of which the effective piezoelectric response vanishes due to the symmetry of spherically anisotropic composite, is also disclosed.     

Spatial extent of the singlet and triplet excitons in luminescent angular-shaped transition-metal diynes and polyynes comprising non-pi-conjugated group 16 main group elements

A novel approach based on conjugation interruption has been developed and is presented for a series of luminescent and thermally stable chalcogen-bridged platinum(II) polyyne polymers trans-[{-Pt(PBu3)2C[triple bond]C(C6H4)E(C6H4)C[triple bond]C-}n] (E = O, S, SO, SO2). Particular attention was focused on the photophysical properties of these Group 10 polymetallaynes and comparison was made to their binuclear model complexes trans-[Pt(Ph)(PEt3)2C[triple bond]C(C6H4)E(C6H4)C[triple bond]CPt(Ph)(PEt3)2] and their closest Group 11 gold(I) and Group 12 mercury(II) neighbours, [MC[triple bond]C(C6H4)E(C6H4)C[triple bond]CM] (M = Au(PPh3), HgMe; E = O, S, SO, SO2). The regiochemical structures of these angular-shaped molecules were studied by NMR spectroscopy and single-crystal X-ray structural analyses. Upon photoexcitation, each one has an intense purple-blue fluorescence emission near 400 nm in dilute fluid solutions at room temperature. Harvesting of the organic triplet emissions harnessed through the strong heavy-atom effects of Group 10-12 transition metals was studied in detail. These metal-containing aryleneethynylenes spaced by chalcogen units were found to have large optical gaps and high-energy triplet states. The influence of metal- and chalcogen-based conjugation interrupters on the intersystem crossing rate and on the spatial extent of the lowest singlet and triplet excitons was fully elucidated. We discuss and compare the phosphorescence spectra of these transition-metal diynes and polyynes in terms of the nature of the metal centre, conjugated chain length and Group 16 spacer unit. Our work here indicates that high-energy triplet states in these materials intrinsically give rise to very efficient phosphorescence with fast radiative decays and one could readily observe room-temperature phosphorescence for the platinum polyynes.     

Transmission characteristics of a Fabry-Perot etalon-microtoroid resonator coupled system

The transmission spectra of a Fabry-Perot etalon coupled to a microtoroid resonator are studied theoretically and experimentally. The resonance line shapes depend strongly on the resonance wavelength detuning and coupling strength between the two resonators. A wide variety of line shapes, ranging from a single to triple peaks, symmetric to asymmetric Fano-like peaks, and notches were predicted and observed experimentally. The capability to modify the spectral line shapes by tuning the coupling between or losses of two resonators may find applications in optical filtering, switching, sensing, and dispersion engineering.     

In situ chemical analysis of modern organic tattooing inks and pigments by micro‐Raman spectroscopy

The chemical composition of tattooing pigments has varied greatly over time according to available technologies and materials. Beginning with naturally derived plant and animal extracts, to coloured inorganic oxides and salts, through to the modern industrial organic pigments favoured in today's tattooing studios. The demand for tattooing is steadily growing as it gains cultural popularity and acceptance in today's society, but ironically, increasing numbers of individuals are seeking laser removal of their tattoos for a variety of reasons. Organic pigments are favoured for tattooing because of their high tinting strength, light fastness, enzymatic resistance, dispersion and relatively inexpensive production costs. Adverse reactions have been reported for some organic inks, as well as potential complications, during laser removal procedures stemming from the unintentional creation of toxic by‐products. Currently, regulatory bodies such as the US Food and Drug Administration have not approved any coloured inks to be injected into the skin, and tattoo ink manufacturers often do not disclose the ingredients in their products to maintain proprietary knowledge of their creations. A methodology was established using micro‐Raman spectroscopy on an animal model to correctly identify the constituents of a selection of modern, organic tattoo inks in situ or post procedure, within the skin. This may serve as a preliminary tool prior to engaging in Q‐switched laser removals to assess the risks of producing potentially hazardous compounds. Likewise, the pigments responsible for causing adverse reactions in some patients may be quickly identified to hasten any corresponding treatment. Copyright © 2008 John Wiley & Sons, Ltd.     

Nonequilibrium phase transition in the sedimentation of reproducing particles

We study numerically and analytically the dynamics of a sedimenting suspension of active, reproducing particles, such as growing bacteria in a gravitational field. In steady state we find a nonequilibrium phase transition between a "sedimentation" regime, analogous to the sedimentation equilibrium of passive colloids, and a "uniform" regime, in which the particle density is constant in all but the top and bottom of the sample. We discuss the importance of fluctuations in particle density in locating the phase-transition point, and report the kinetics of sedimentation at early times.     

Conventional optical microscopy of colloidal suspensions

Optical microscopy can resolve detail at the larger end of the colloidal length scale, and to image suspensions at an individual particle level of resolution would allow the investigation of local behaviour in a way denied to the established scattering techniques. However, to achieve high-contrast single-particle resolution in dense suspensions that are thick enough to show behaviour the same as would be expected in the bulk is not a trivial exercise. We build on established advanced techniques of the conventional (i.e. non-confocal) light microscopy of phase objects to develop a suitable experimental protocol. Furthermore, we demonstrate the effectiveness of this protocol by means of an 'atlas' of the hard-sphere crystalline solid (where random stacking results in many complex facets), which should serve as a compendium for future study.     

Off-diagonal submatrices of a Hermitian matrix

A necessary and sufficient condition is given to a complex matrix to be an off-diagonal block of an Hermitian matrix with prescribed eigenvalues (in terms of the eigenvalues of and singular values of ). The proof depends on some recent breakthroughs in the study of spectral inequalities on the sum of Hermitian matrices by Klyachko and Fulton. Some interesting geometrical properties of the set of all such matrices are derived from the main result. These results improve earlier ones that only give partial information for the set .

     

Neutral Calabi-Yau Structures on Kodaira Manifolds

We construct neutral Calabi-Yau metrics and hypersymplectic structures on some Kodaira manifolds. Our structures are symmetric with respect to the central tori.Partially supported by The European Contract HPRN-CT-2000-00101, MURST and GNSAGA (Indam) of ItalyPartially supported by The European Contract HPRN-CT-2000-00101Partially supported by NSF