Excited state interactions between the chiral Au 38 L 24 cluster and covalently attached porphyrin

A protected S-acetylthio porphyrin was synthesized and attached to the Au38(2-phenylethanethiolate)24 cluster in a ligand exchange reaction. Chiral high performance liquid chromatography of the functionalized cluster yielded enantiomeric pairs of clusters probably differing in the binding site of the porphyrin. As proven by circular dichroism, the chirality was maintained. Exciton coupling between the cluster and the chromophore is observed. Zinc can be incorporated into the porphyrin attached to the cluster, as evidenced by absorption and fluorescence spectroscopy, however, the reaction is slow. Quenching of the chromophore fluorescence is observed, which can be explained by energy transfer from the porphyrin to the cluster. Transient absorption spectra of Au38(2-phenylethanethiolate)24 and the functionalized cluster probe the bleach of the gold cluster due to ground state absorption and the characteristic excited state absorption signals. Zinc incorporation does not have a pronounced effect on the photophysical behaviour. Decay times are typical for the molecular behaviour of small monolayer protected gold clusters.

Microscopic study of vorticities in relativistic chiral fermions

It is usually believed that unlike the external magnetic field which one can set directly, vorticity is a property of the flow of particles, which is indirectly controlled by external fields and initial conditions. Using the curved-space technics it is shown that the influence of the vorticity on the relativistic chiral fermions can indeed be controlled directly.

On the CFT operator spectrum at large global charge

We calculate the anomalous dimensions of operators with large global charge J in certain strongly coupled conformal field theories in three dimensions, such as the O(2) model and the supersymmetric fixed point with a single chiral superfield and a W = Φ3 superpotential. Working in a 1/J expansion, we find that the large-J sector of both examples is controlled by a conformally invariant effective Lagrangian for a Goldstone boson of the global symmetry. For both these theories, we find that the lowest state with charge J is always a scalar operator whose dimension ΔJ satisfies the sum rule J2ΔJ−(J22+J4+316)ΔJ−1−(J22+J4+316)ΔJ+1=0.04067 up to corrections that vanish at large J . The spectrum of low-lying excited states is also calculable explcitly: for example, the second-lowest primary operator has spin two and dimension ΔJ+3√. In the supersymmetric case, the dimensions of all half-integer-spin operators lie above the dimensions of the integer-spin operators by a gap of order J+12. The propagation speeds of the Goldstone waves and heavy fermions are 12√ and ±12 times the speed of light, respectively. These values, including the negative one, are necessary for the consistent realization of the superconformal symmetry at large J.

Nasolabial symmetry and esthetics in cleft lip and palate: analysis of 3D facial images

OBJECTIVES To determine the relationship between nasolabial symmetry and esthetics in subjects with orofacial clefts. MATERIAL AND METHODS Eighty-four subjects (mean age 10 years, standard deviation 1.5) with various types of nonsyndromic clefts were included: 11 had unilateral cleft lip (UCL); 30 had unilateral cleft lip and alveolus (UCLA); and 43 had unilateral cleft lip, alveolus, and palate (UCLAP). A 3D stereophotogrammetric image of the face was taken for each subject. Symmetry and esthetics were evaluated on cropped 3D facial images. The degree of asymmetry of the nasolabial area was calculated based on all 3D data points using a surface registration algorithm. Esthetic ratings of various elements of nasal morphology were performed by eight lay raters on a 100 mm visual analog scale. Statistical analysis included ANOVA tests and regression models. RESULTS Nasolabial asymmetry increased with growing severity of the cleft (p = 0.029). Overall, nasolabial appearance was affected by nasolabial asymmetry; subjects with more nasolabial asymmetry were judged as having a less esthetically pleasing nasolabial area (p < 0.001). However, the relationship between nasolabial symmetry and esthetics was relatively weak in subjects with UCLAP, in whom only vermilion border esthetics was associated with asymmetry. CONCLUSIONS Nasolabial symmetry assessed with 3D facial imaging can be used as an objective measure of treatment outcome in subjects with less severe cleft deformity. In subjects with more severe cleft types, other factors may play a decisive role. CLINICAL SIGNIFICANCE Assessment of nasolabial symmetry is a useful measure of treatment success in less severe cleft types.

Heisenberg symmetry and hypermultiplet manifolds

We study the emergence of Heisenberg (Bianchi II) algebra in hyper-Kähler and quaternionic spaces. This is motivated by the rôle these spaces with this symmetry play in N = 2 hypermultiplet scalar manifolds. We show how to construct related pairs of hyper-Kähler and quaternionic spaces under general symmetry assumptions, the former being a zooming-in limit of the latter at vanishing scalar curvature. We further apply this method for the two hyper-Kähler spaces with Heisenberg algebra, which is reduced to U (1) × U (1) at the quaternionic level. We also show that no quaternionic spaces exist with a strict Heisenberg symmetry – as opposed to Heisenberg U (1). We finally discuss the realization of the latter by gauging appropriate Sp(2, 4) generators in N = 2 conformal supergravity.

Finite volume effects in chiral perturbation theory with twisted boundary conditions

We study the effects of a finite cubic volume with twisted boundary conditions on pseudoscalar mesons. We apply Chiral Perturbation Theory in the p-regime and introduce the twist by means of a constant vector field. The corrections of masses, decay constants, pseudoscalar coupling constants and form factors are calculated at next-to-leading order. We detail the derivations and compare with results available in the literature. In some case there is disagreement due to a different treatment of new extra terms generated from the breaking of the cubic invariance. We advocate to treat such terms as renormalization terms of the twisting angles and reabsorb them in the on-shell conditions. We confirm that the corrections of masses, decay constants, pseudoscalar coupling constants are related by means of chiral Ward identities. Furthermore, we show that the matrix elements of the scalar (resp. vector) form factor satisfies the Feynman–Hellman Theorem (resp. the Ward–Takahashi identity). To show the Ward–Takahashi identity we construct an effective field theory for charged pions which is invariant under electromagnetic gauge transformations and which reproduces the results obtained with Chiral Perturbation Theory at a vanishing momentum transfer. This generalizes considerations previously published for periodic boundary conditions to twisted boundary conditions. Another method to estimate the corrections in finite volume are asymptotic formulae. Asymptotic formulae were introduced by Lüscher and relate the corrections of a given physical quantity to an integral of a specific amplitude, evaluated in infinite volume. Here, we revise the original derivation of Lüscher and generalize it to finite volume with twisted boundary conditions. In some cases, the derivation involves complications due to extra terms generated from the breaking of the cubic invariance. We isolate such terms and treat them as renormalization terms just as done before. In that way, we derive asymptotic formulae for masses, decay constants, pseudoscalar coupling constants and scalar form factors. At the same time, we derive also asymptotic formulae for renormalization terms. We apply all these formulae in combination with Chiral Perturbation Theory and estimate the corrections beyond next-to-leading order. We show that asymptotic formulae for masses, decay constants, pseudoscalar coupling constants are related by means of chiral Ward identities. A similar relation connects in an independent way asymptotic formulae for renormalization terms. We check these relations for charged pions through a direct calculation. To conclude, a numerical analysis quantifies the importance of finite volume corrections at next-to-leading order and beyond. We perform a generic Analysis and illustrate two possible applications to real simulations.

The Effects of Density, Spatial Pattern, and Competitive Symmetry on Size Variation in Simulated Plant Populations

Patterns of size inequality in crowded plant populations are often taken to be indicative of the degree of size asymmetry of competition, but recent research suggests that some of the patterns attributed to size‐asymmetric competition could be due to spatial structure. To investigate the theoretical relationships between plant density, spatial pattern, and competitive size asymmetry in determining size variation in crowded plant populations, we developed a spatially explicit, individual‐based plant competition model based on overlapping zones of influence. The zone of influence of each plant is modeled as a circle, growing in two dimensions, and is allometrically related to plant biomass. The area of the circle represents resources potentially available to the plant, and plants compete for resources in areas in which they overlap. The size asymmetry of competition is reflected in the rules for dividing up the overlapping areas. Theoretical plant populations were grown in random and in perfectly uniform spatial patterns at four densities under size‐asymmetric and size‐symmetric competition. Both spatial pattern and size asymmetry contributed to size variation, but their relative importance varied greatly over density and over time. Early in stand development, spatial pattern was more important than the symmetry of competition in determining the degree of size variation within the population, but after plants grew and competition intensified, the size asymmetry of competition became a much more important source of size variation. Size variability was slightly higher at higher densities when competition was symmetric and plants were distributed nonuniformly in space. In a uniform spatial pattern, size variation increased with density only when competition was size asymmetric. Our results suggest that when competition is size asymmetric and intense, it will be more important in generating size variation than is local variation in density. Our results and the available data are consistent with the hypothesis that high levels of size inequality commonly observed within crowded plant populations are largely due to size‐asymmetric competition, not to variation in local density.

Chiral, Three-Dimensional Supramolecular Compounds: Homo- and Bimetallic Oxalate- and 1,2-Dithiooxalate-Bridged Networks. A Structural and Photophysical Study.

In analogy to the [M(II)(bpy)(3)](2+) cations, where M(II) is a divalent transition-metal and bpy is 2,2'-bipyridine, the tris-chelated [M(III)(bpy)(3)](3+) cations, where M(III) is Cr(III) or Co(III), induce the crystallization of chiral, anionic three-dimensional (3D) coordination polymers of oxalate-bridged (&mgr;-ox) metal complexes with stoichiometries [M(II)(2)(ox)(3)](n)()(2)(n)()(-) or [M(I)M(III)(ox)(3)](n)()(2)(n)()(-). The tripositive charge is partially compensated by inclusion of additional complex anions like ClO(4)(-), BF(4)(-), or PF(6)(-) which are encapsulated in cubic shaped cavities formed by the bipyridine ligands of the cations. Thus, an elaborate structure of cationic and anionic species within a polymeric anionic network is realized. The compounds isolated and structurally characterized include [Cr(III)(bpy)(3)][ClO(4)] [NaCr(III)(ox)(3)] (1), [Cr(III)(bpy)(3)][ClO(4)][Mn(II)(2)(ox)(3)] (2), [Cr(III)(bpy)(3)][BF(4)] [Mn(II)(2)(ox)(3)] (3), [Co(III)(bpy)(3)][PF(6)][NaCr(III)(ox)(3)] (4). Crystal data: 1, cubic, P2(1)3, a = 15.523(4) Å, Z = 4; 2, cubic, P4(1)32, a = 15.564(3) Å, Z = 4; 3, cubic, P4(1)32, a = 15.553(3) Å, Z = 4; 4, cubic, P2(1)3, a = 15.515(3) Å, Z = 4. Furthermore, it seemed likely that 1,2-dithiooxalate (dto) could act as an alternative to the oxalate bridging ligand, and as a result the compound [Ni(II)(phen)(3)][NaCo(III)(dto)(3)].C(3)H(6)O (5) has successfully been isolated and structurally characterized. Crystal data: 5, orthorhombic, P2(1)2(1)2(1), a = 16.238(4) Å, b = 16.225(4) Å, c = 18.371(5) Å, Z = 4. In addition, the photophysical properties of compound 1 have been investigated in detail. In single crystal absorption spectra of [Cr(III)(bpy)(3)][ClO(4)][NaCr(III)(ox)(3)] (1), the spin-flip transitions of both the [Cr(bpy)(3)](3+) and the [Cr(ox)(3)](3)(-) chromophores are observed and can be clearly distinguished. Irradiating into the spin-allowed (4)A(2) --> (4)T(2) absorption band of [Cr(ox)(3)](3)(-) results in intense luminescence from the (2)E state of [Cr(bpy)(3)](3+) as a result of rapid energy transfer processes.